Trends in major-ion constituents and properties for selected sampling sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years 1980-2010

Sando, Steven K.- sksando@usgs.gov, Vecchia, Aldo V.-, Barnhart, Elliott P.- epbarnhart@usgs.gov, Sando, Roy- · 2014 · Report

The primary purpose of this report is to present information relating to flow-adjusted temporal trends in major-ion constituents and properties for 16

This 2014 document, Trends in major-ion constituents and properties for selected sampling sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years 1980-2010, is preserved in the Mountain Man Mining Library for research and reference. Original source: pubs.usgs.gov.

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds, Montana and Wyoming, Based on Data Collected During Water Years 1980-2010 Prepared in cooperation with the Montana Department of Natural Resources and Conservation, Water Management Bureau Scientific Investigations Report 2013-5179 U.S. Department of the Interior U.S. Geological Survey

Cover photograph.  Looking downstream at Montana Highway 4 bridge on the Tongue River near Birney, Montana, on April 19, 2006. (Photograph by Stacy M. Kinsey, U.S. Geological Survey).

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds, Montana and Wyoming, Based on Data Collected During Water Years 1980-2010 By Steven K. Sando, Aldo V. Vecchia, Elliott P. Barnhart, Thomas R. Sando, Melanie L. Clark, and David L. Lorenz Prepared in cooperation with the Montana Department of Natural Resources and Conservation, Water Management Bureau Scientific Investigations Report 2013-5179 U.S. Department of the Interior U.S. Geological Survey

U.S. Department of the Interior SALLY JEWELL, Secretary U.S. Geological Survey Suzette M. Kimball, Acting Director U.S. Geological Survey, Reston, Virginia: 2014 For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS. For an overview of USGS information products, including maps, imagery, and publications, visit http://www.usgs.gov/pubprod To order this and other USGS information products, visit http://store.usgs.gov Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner. Suggested citation: Sando, S.K., Vecchia, A.V., Barnhart, E.P., Sando, T.R., Clark, M.L., and Lorenz, D.L., 2014, Trends in major-ion constitu­ ents and properties for selected sampling sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years 1980-2010: U.S. Geological Survey Scientific Investigations Report 2013-5179, p. 123, http://dx.doi.org/10.3133/sir20135179/. ISSN 2328-031X (print) ISSN 2328-0328 (online) ISBN 978-1-4113-3759-6

Contents Abstract 1 Introduction 2 Purpose and Scope 3 Previous Investigations 3 Description of Study Area 6 Physiographic, Climatic, and Hydrologic Characteristics 6 Geologic Characteristics 6 Coal-Bed Methane and Other Resource Extraction Activities 6 Data Collection, Analytical Methods, Review, and Quality Control 8 Streamflow Data 8 Water-Quality Data 8 Sampling and Analytical Methods 8 Data Review and Quality Control 9 Water Quality and Streamflow Characteristics for Selected Sampling Sites and Comparison with Water Quality and Volume Characteristics of Coal-Bed Methane Produced Water 10 Water Quality and Streamflow Characteristics for Selected Sampling Sites 10 Tongue River Watershed 13 Powder River Watershed 13 Estimation of Volume, Flow-Rate, and Water Quality of Coal-Bed Methane Produced Water in Selected Sampling-Site Watersheds in the Tongue and Powder River Watersheds 14 Comparison of Water Quality and Streamflow of Selected Sampling Sites with Water-Quality and Volume of Coal-Bed Methane Produced Water 14 Tongue River Watershed 15 Powder River Watershed 18 Trend Analysis Methods 20 Time-Series Model 21 Ordinary Least Squares Regression on Time, Streamflow, and Season 22 Selection of Trend-Analysis Time Periods 22 Streamflow Conditions and Other Factors that Affect Trend Results 22 Streamflow Conditions 23 Factors that Affect Trend Results and Interpretation 23 Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds 32 Tongue River Watershed 39 Trend Results for Selected Sampling Sites on the Main-Stem Tongue River 39 Trend Results for Selected Sampling Sites on Tongue River Tributaries 42 Powder River Watershed 44 Trend Results for Selected Sampling Sites on the Main-Stem Powder River 44 Trend Results for Selected Sampling Sites on the Little Powder River 47 Selected Trend Results in Relation to Results of Previous Studies 48 Summary and Conclusions 52

References Cited 54 Supplement 1.   Summary Tables Relating to Quality-Control, Water-Quality, Streamflow, and Coal-Bed Methane Produced-Water Data 59 Supplement 2.  Summary of the Time-Series Model as Applied in this Study 93 Supplement 3.  Summary of Ordinary Least Squares Regression of Water-Quality Constituents on Time, Streamflow, and Season, as Applied in this Study 95 Supplement 4.  Tables and Figures Presenting Detailed Trend-Analysis Results 97 Figures

1.  Map showing location of selected sampling sites, coal-bed methane wells, and monitoring wells in coal-bed methane seams in the Tongue and Powder River watersheds, Montana and Wyoming 4

2.  Boxplots showing statistical distributions of sodium adsorption ratio, sodium, and alkalinity for selected sites in the Tongue River watershed based on data collected during water years 2001-10 11

3.  Boxplots showing statistical distributions of sodium adsorption ratio, sodium, and alkalinity for selected sites in the Powder River watershed based on data collected during water years 2001-10 12

4.  Graphs showing selected water-quality and flow-rate characteristics for sites in the Tongue River watershed and for coal-bed methane produced water in the watersheds upstream from the sites 16

5.  Graphs showing selected water-quality and flow-rate characteristics for sites in the Powder River watershed and for coal-bed methane produced water in the watersheds upstream from the sites 19

6.  Graphs showing daily mean streamflow and annual streamflow anomaly determined by using the time-series model for sites in the Tongue River watershed, water years 1980-2010 24

7.  Graphs showing daily mean streamflow and annual streamflow anomaly determined by using the time-series mode for sites in the Powder River watershed, water years 1980-2010 25

8.  Graphs showing sodium flow-adjusted concentrations and fitted trends determined by using the time series model, and unadjusted concentrations for sites in the Tongue River watershed, water years 1980-2010 26

9.  Graphs showing estimated alkalinity flow-adjusted concentrations and fitted trends determined by using the time series model, and unadjusted concentrations for sites in the Tongue River watershed, water years 1980-2010 27

10.  Graphs showing sodium flow-adjusted concentrations and fitted trends determined by using the time series model, and unadjusted concentrations for sites in the Powder River watershed, water years 1980-2010 28

11.  Graphs showing estimated alkalinity flow-adjusted concentrations and fitted trends determined by using the time series model, and unadjusted concentrations for sites in the Powder River watershed, water years 1980-2010 29

4.1.  Graphs showing fitted trends determined by using ordinary least squares regression on time, streamflow, and season for selected major-ion constituents and properties for site 1, based on analysis of available data collected during water years 2001-2010 108

4.2.  Graphs showing fitted trends determined by using ordinary least squares recession on time, streamflow, and season for selected major-ion constituents and properties for site 2 109

4.3.  Graphs showing fitted trends determined by using ordinary least squares regression on time, streamflow, and season for selected major-ion constituents and properties for site 3 110

4.4.  Graphs showing fitted trends determined by using ordinary least squares regression on time, streamflow, and season for selected major-ion constituents and properties for site 4 111

4.5.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 5 112

4.6.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 6 113

4.7.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 7 114

4.8.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 8 115

4.9.  Graphs showing fitted trends determined by using ordinary least squares regression on time, streamflow, and season for selected major-ion constituents and properties for site 9 116 4.10.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 10 117 4.11.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 11 118 4.12.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 12 119 4.13.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 13 120 4.14.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 14 121 4.15.  Graphs showing fitted trends determined by using ordinary least squares regression on time, streamflow, and season for selected major-ion constituents and properties for site 15 122 4.16.  Graphs showing fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 16 123

Tables

1.  Information for sites in the Tongue and Powder River watersheds, Montana and Wyoming 5

2.  Summary of trend results determined by using the time-series model for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years 1980-2010 33

3.  Summary of trend results determined by using ordinary least squares regression on time, streamflow, and season for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years 2001-10 35

4.  Summary of trend results determined by using the time-series model for major-ion constituents and properties for sites in the Powder River watershed, Wyoming and Montana, based on analysis of data collected during water years 1980-2010 37

5.  Summary of trend results determined by using ordinary least squares regression on time, streamflow, and season for major-ion constituents and properties for Little Powder River near Broadus, Mont. based on analysis of data collected during water years 2001-10 39

6.  Statistically significant trend results determined by using the time-series model and statistically significant trend results from Clark for trend-analysis period 2 49

7.  Statistically significant trend results determined by using ordinary least squares regression on time, streamflow, and season and statistically significant trend results from Clark 51

1.1.  Summary information relating to quality-control samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years1 1980-2010 59

1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods 60

1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010 74

1.4.  Summary information relating to major-ion constituents and properties in groundwater samples collected from coal-bed methane wells and monitoring wells in coal beds in the watersheds upstream from sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years 2001-10 89

1.5.  Relative differences in mean values of major-ion constituents and properties between stream-water samples and coal-bed methane groundwater samples for sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years 2001-10 92

4.1.  Trend-analysis results determined by using the time-series model for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years 1980-2010 98

4.2.  Trend-analysis results determined by using ordinary least squares regression on time, streamflow, and season for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years 2001-10 101

4.3.  Trend-analysis results determined by using the time-series model for major-ion constituents and properties for sites in the Powder River watershed, Wyoming and Montana, based on analysis of data collected during water years 1980-2010 103

4.4.  Trend-analysis results determined by using ordinary least squares regression on time, streamflow, and season for major-ion constituents and properties for Little Powder River near Broadus, Mont. based on analysis of data collected during water years 2001-10 106

4.5.  Information on percent differences in cation and anion balances for fitted trends and flow-adjusted concentrations for selected sampling sites in the Tongue and Powder River watersheds, Montana and Wyoming 107

Conversion Factors Multiply By To obtain Length inch (in.) centimeter (cm) foot (ft) meter (m) mile (mi) kilometer (km) Area acre hectare (ha) square mile (mi2) square kilometer (km2) Volume gallon (gal) liter (L) cubic foot (ft3) cubic meter (m3) Flow rate acre-foot (acre-ft) 1,233 cubic meter (m3) cubic foot per second (ft3/s) cubic meter per second (m3/s) Mass ounce, avoirdupois (oz) gram (g) Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows: °F=(1.8×°C)+32 Vertical coordinate information is referenced to the "National Geodetic Vertical Datum of 1988 (NGVD 88)." Horizontal coordinate information is referenced to "North American Datum of 1983 (NAD 83)." Altitude, as used in this report, refers to distance above the vertical datum. Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (µS/cm at 25 °C). Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L) or milliequivalents per liter (meq/L). Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009.

Abbreviations acre-ft acre-feet ANC acid neutralizing capacity ANNC annual concentration anomaly (dimensionless) ANNQ annual streamflow anomaly (dimensionless);

concentration, in milligrams per liter CaCO3 calcium carbonate CBM coal-bed methane NED National Elevation Dataset FAC flow-adjusted concentration ft

feet ft3/s

cubic feet per second HFVC high-frequency variability of the concentration (dimensionless). HFVQ high-frequency streamflow variability (dimensionless). log

less than MC

long-term mean of the log-transformed concentration, as the base-10 logarithm

of milligrams per liter µS/cm microsiemens per centimeter at 25 degrees Celsius mg/L milligrams per liter mi

miles mi2

square miles MQ

long-term mean of the log-transformed streamflow, as the base-10 logarithm of

cubic feet per second NGVD National Geodetic Vertical Datum NWQL National Water Quality Laboratory NWIS National Water Information System OLS

ordinary least squares regression of concentration on time, streamflow, and season p-value statistical significance level PRB Powder River structural basin Q

daily mean streamflow, in cubic feet per second QC

quality control RPD relative percent difference SAR sodium adsorption ratio SEASC seasonal concentration anomaly (dimensionless)

SEASQ seasonal streamflow anomaly (dimensionless) SEE

standard error of estimate, in percent TREND concentration trend (dimensionless) TSM time-series model USGS U.S. Geological Survey

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds, Montana and Wyoming, Based on Data Collected During Water Years 1980-2010 By Steven K. Sando, Aldo V. Vecchia, Elliott P. Barnhart, Thomas R. Sando, Melanie L. Clark, and David L. Lorenz Abstract The primary purpose of this report is to present informa­ tion relating to flow-adjusted temporal trends in major-ion constituents and properties for 16 sampling sites in the Tongue and Powder River watersheds based on data collected dur­ ing 1980-2010. In association with this primary purpose, the report presents background information on major-ion charac­ teristics (including specific conductance, calcium, magnesium, potassium, sodium adsorption ratio, sodium, alkalinity, chlo­ ride, fluoride, dissolved sulfate, and dissolved solids) of the sampling sites and coal-bed methane (CBM) produced water (groundwater pumped from coal seams) in the site watersheds, trend analysis methods, streamflow conditions, and factors that affect trend results. The Tongue and Powder River watersheds overlie the Powder River structural basin (PRB) in northeastern Wyoming and southeastern Montana. Limited extraction of coal-bed methane (CBM) from the PRB began in the early 1990's, and increased dramatically during the late 1990's and early 2000's. CBM-extraction activities produce discharges of water with high concentrations of dissolved solids (particularly sodium and bicarbonate ions) relative to most stream water in the Tongue and Powder River watersheds. Water-quality of CBMproduced water is of concern because of potential effects of sodium on agricultural soils and potential effects of bicarbon­ ate on aquatic biota. Two parametric trend-analysis methods were used in this study: the time-series model (TSM) and ordinary least squares regression (OLS) on time, streamflow, and season. The TSM was used to analyze trends for 11 of the 16 study sites. For five sites, data requirements of the TSM were not met and OLS was used to analyze trends. Two primary 10-year trend-analysis periods were selected. Trend-analysis period 1 (water years 1986-95; hereinafter referred to as period 1) was selected to represent variability in major-ion concentrations in the Tongue and Powder River watersheds before potential effects of CBM-extraction activities. Trend analysis period 2 (water years 2001-10; hereinafter referred to as period 2) was selected because it encompassed substantial CBM-extraction activities and therefore might indicate potential effects of CBM-extraction activities on water quality of receiving streams in the Tongue and Powder River watersheds. For sites that did not satisfy data requirements for the TSM, OLS was used to analyze trends for period 2 (if complete data were available) or a 6-year period (2005-10). Flow-rate characteristics of CBM-produced water were estimated to allow general comparisons with streamflow characteristics of the sampling sites. The information on flow-rate characteristics of CBM-produced water in relation to streamflow does not account for effects of disposal, treatment, or other remediation activities on the potential quantitative effects of CBM-produced water on receiving streams. In many places, CBM-produced water is discharged into impound­ ments or channels in upper reaches of tributary watersheds where water infiltrates and does not directly contribute to streamflow. For Tongue River at State line (site 4) mean annual pumping rate of CBM-produced water during water years 2001-10 (hereinafter referred to as mean CBM pump­ ing rate) was 6 percent of the mean of annual median stream­ flows during water years 2001-10 (hereinafter referred to as 2001-10 median streamflow). For main-stem Tongue River sites 5, 7, and 10, mean CBM pumping rate was 8-12 per­ cent of 2001-10 median streamflow. For main-stem Powder River sites (sites 12, 13, and 16), mean CBM pumping rates were 26, 28, and 34 percent of 2001-10 median streamflows, respectively. For main-stem Tongue River sites analyzed by using the TSM and downstream from substantial CBM-extraction activities [Tongue River at State line (site 4), Tongue River at Tongue River Dam (site 5), Tongue River at Birney Day School (site 7), and Tongue River at Miles City (site 10)], generally small significant or nonsignificant decreases in most constituents are indicated for period 1. For period 2 for these sites, the TSM trend results do not allow confident conclusions

2    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds concerning detection of effects of CBM-extraction activities on stream water quality. Detection of significant trends in major-ion constituents and properties for period 2 generally was infrequent, and direction, magnitudes, and significance of fitted trends were not strongly consistent with relative differ­ ences in water quality between stream water and CBM-pro­ duced water. The TSM indicated significant or generally large magnitude increases in median values of sodium adsorption ratio (SAR), sodium, and alkalinity for period 2 for sites 5 and 7, which might indicate potential effects of CBM-extraction activities on stream water. However, other factors, including operations of Tongue River Reservoir, irrigation activities, contributions of saline groundwater, and operations of the Decker coal mine, confound confident determination of causes of detected significant trends for sites 5 and 7. For all mainstem Tongue River sites, trends for period 2 generally are within ranges of those for period 1 before substantial CBMextraction activities. For main-stem Powder River sites analyzed by using the TSM [Powder River at Sussex (site 11), Powder River at Arvada (site 12), Powder River at Moorhead (site 13), and Powder River near Locate (site 16)], significant or generally large magnitude decreases in median values of SAR, sodium, estimated alkalinity, chloride, fluoride, specific conductance, and dissolved solids are indicated for period 1. Patterns in trend results for period 1 for main-stem Powder River sites are consistent with effects of Salt Creek oil-brine reinjection that started in 1990. Trend results for all main-stem Powder River sites downstream from substantial CBM-extraction activities (sites 12, 13, and 16) indicate evidence of potential effects of CBM-extraction activities on stream water quality, although evidence is stronger for sites 12 and 13 than for site 16. Evidence in support of potential CBM effects includes significant increases in median values of SAR, sodium, and estimated alkalinity for period 2 for sites 12, 13, and 16 that are consistent with relative differences between stream water and CBM-produced water. Significant increases in median values of these constituents for period 2 are not indicated for Powder River at Sussex (site 11) upstream from substantial CBM-extraction activities. In interpreting the trend results, it is notable that the fitted trends evaluate changes in median concentrations and also notable that changes in median con­ centrations that might be attributed to CBM-extraction activi­ ties probably are more strongly evident during low to median streamflow conditions than during mean to high streamflow conditions. This observation is relevant in assessing trend results in relation to specific water-quality concerns, including effects of water-quality changes on irrigators and effects on stream biota and ecology. Introduction The Tongue and Powder River watersheds overlie the Powder River structural basin (PRB) in northeastern Wyoming (Wyo.) and southeastern Montana (Mont.). The PRB contains large deposits of energy resources (coal, oil, natural gas) and, since the late 1800's, extraction activities have been extensive. Limited extraction of coal-bed methane (CBM) from the PRB began in the early 1990's, and increased dramatically during the late 1990's and early 2000's (Peck, 1999; Bryner, 2002; Hower and others, 2003). Tongue and Powder River water users have historically been faced with difficulties in obtain­ ing sufficient water of sufficient quality to maintain alfalfa production in support of ranching operations. Although natural watershed characteristics and semiarid climate have histori­ cally limited water supplies to farmers and ranchers, upstream agricultural development (for example, irrigation and water storage projects) from the 1930's to present, has prompted further concerns about reduced water supply and potential water-quality effects. In addition, CBM-extraction activities produce discharges of water with high concentrations of dis­ solved solids (particularly sodium and bicarbonate ions; Quil­ linen, 2011) relative to most stream waters in the Tongue and Powder River watersheds. Water quality of CBM-produced water is of concern because of potential effects on downstream agricultural producers who irrigate soils that can contain large amounts of clay. Surface applications of waters that have high sodium-adsorption ratio (SAR) values can result in cation exchange, with sodium replacing calcium and magnesium in clay particles of soils, thereby inducing soil swelling (Hanson and others, 1999), reducing infiltration rates, and increasing erosion. Another concern with respect to discharge of CBMproduced water to stream channels is effects on aquatic biota. Farag and Harper (2012) reported reduced survival of fathead minnows and pallid sturgeon as a result of exposure to CBMproduced water, with sodium bicarbonate (which contains the two most dominant ions in CBM-produced water) identified as the toxic compound. Bicarbonate has been identified as the primary toxic fraction of sodium bicarbonate (Mount and oth­ ers, 1997). Peterson and others (2011) reported that biological conditions were reduced in the middle reaches of the Powder River and that these reduced conditions potentially could be linked to cumulative effects from CBM-produced water. Several studies have characterized water-quality and analyzed temporal trends in water-quality constituents in the Powder River (Clark and Mason, 2007; Wang and others, 2007; Clark, 2012) and Tongue River (Clark and Mason, 2007; Clark, 2012) watersheds. These studies primarily focused on stream sites in Wyoming, with less emphasis in Montana. Fur­ ther, those analyses generally used nonparametric statistical methods (for example, the seasonal Kendall analysis), which are robust and generally do not require extensive datasets, to test for monotonic trends (single direction through the entire trend period). Parametric trend analysis procedures, which are more rigorous and sometimes require more extensive datasets, present alternative trend-analysis approaches to nonpara­ metric procedures (Vecchia, 2005; Helsel and Hirsch, 2002). This study was done by the U.S. Geological Survey (USGS) in cooperation with the Montana Department of Natural

Introduction    3 Resources and Conservation to test for temporal trends in water quality using two parametric trends analysis methods: a joint time-series model (TSM; Vecchia, 2005) for concen­ tration and streamflow; and ordinary least squares regres­ sion (OLS) of concentration on time, streamflow, and season (Helsel and Hirsch, 2002). Also, this study included sites in Montana and Wyoming in the Tongue and Powder River watersheds. The trend analysis includes an extended period of record (water years 1980-2010) that encompasses conditions before and after substantial CBM-extraction activities. Water year is the 12-month period from October 1 through Septem­ ber 30 and is designated by the year in which it ends. Purpose and Scope The primary purpose of this report is to present informa­ tion relating to flow-adjusted temporal trends in major-ion constituents and properties for 16 sampling sites in the Tongue and Powder River watersheds based on data collected dur­ ing water years 1980-2010. In association with this primary purpose, the report presents background information on water-quality characteristics of the sampling sites and CBMproduced water in the site watersheds, trend analysis methods, streamflow conditions, and factors that affect trend results. This information is presented to assist in evaluating trend results. Trend analyses were structured to specifically aid in identification of water-quality trends that might be attributable to CBM-extraction activities in the Tongue and Powder River watersheds. The trend analyses include sites with periods of record that represent conditions before and after CBM-extrac­ tion activities and also sites located upstream and downstream from substantial CBM-extraction activities. In this report, substantial CBM-extraction activities are defined in terms of amount of water produced in association with CBM extrac­ tion and are considered to be activities that result in greater than about 500 acre-feet per year of produced water. The study period encompasses about 30 years and includes about 15 years before the start of substantial CBM-extraction activities in the watersheds. The intent of this aspect of the study design was to characterize water-quality variability before and after substantial CBM-extraction activities to aid in evaluating the magnitude of trends that might be attributable to CBM-extrac­ tion activities. In many respects, this report complements and shares similar objectives with the study by Clark (2012) that inves­ tigated water-quality trends with a focus on Wyoming sites in the Tongue and Powder River watersheds. However, this report is based on different statistical methods, increases the geographic scope to include more Montana sites, and uses a longer study period for trend analysis. Previous Investigations Research on potential environmental effects of CBMextraction activities in the Tongue and Powder River watersheds has been extensive. However, discussion here of previous investigations is restricted to research specifically related to statistical analysis of flow-adjusted temporal trends in major-ion constituents and properties (Cary, 1991; Wang and others, 2007, Clark and Mason, 2007; and Clark, 2012). Cary (1991) analyzed trends in 8 major-ion constituents and properties at 10 sites in the Powder River watershed for the period 1975-1988 by using the nonparametric seasonal Kendall test (Hirsch and Slack, 1984). Significant increasing trends in SAR were detected at five sites, two of which correspond with sites included in this report [Powder River at Sussex (site 11) and Powder River at Arvada (site 12); fig. 1, table 1]. The study period of Cary (1991) was before substantial CBM-extraction activities in the Tongue and Powder River watersheds. Cary (1991) noted that irrigation return flows and discharge of oilfield production water might increase concentrations of some constituents in the Powder River; however, specific identifica­ tion of probable causes of the observed trends was not provided. In a study of water-quality changes in the Powder River as a result of CBM development, Wang and others (2007) analyzed flow-adjusted trends in 14 different water-quality variables (primarily major-ion constituents and properties) for 4 mainstem Powder River sites using ordinary least squares regression of concentration on time and streamflow and the nonparamet­ ric seasonal Kendall test, based on data through 2002. For the period 1990-2002, no significant trends in specific conduc­ tance or SAR were detected at Powder River at Sussex (site 11; upstream from substantial CBM-extraction activities). For the same period, significant increases in specific conductance and SAR were detected for Powder River at Arvada (site 12) Powder River at Moorhead (site 13), and Powder River near Locate (site 16), which are downstream from substantial CBMextraction activities. Clark and Mason (2007) analyzed flow-adjusted trends in major-ion constituents and properties using the nonparametric seasonal Kendall test at sites in the Tongue and Powder River watersheds (as well as the Cheyenne and Belle Fourche River watersheds; not shown on fig. 1) for water years 1991-2005. Significant increases in SAR were detected at Powder River at Sussex (site 11) and Powder River at Arvada (site 12). Sig­ nificant decreases in calcium and magnesium, and significant increases in sodium were detected at site 12. Clark (2012) analyzed flow-adjusted trends in major-ion constituents and properties for water years 2001-10 for 17 sites generally on the main-stem streams and primary tributaries in the Tongue and Powder River watersheds. No significant trends in SAR were detected for sites in the Tongue River water­ shed. In the Powder River watershed, significant increases in SAR and alkalinity were detected at Powder River at Arvada (site 12). At Powder River at Moorhead (site 13), a significant increase in SAR was not detected but a significant increase in alkalinity was detected.

4    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Bi gh or n Mo un ta in s ROSEBUD CUSTER BIG HORN POWDER RIVER FALLON TREASURE MUSSELLSHELL MUSSELLSHELL YELLOWSTONE CARTER CAMPBELL JOHNSON NATRONA CONVERSE SHERIDAN CROOK WASHAKIE WESTON BIGHORN FREMONT HOT SPRINGS NIOBRARA WYOMING MONTANA Colstrip Miles City Hardin Locate Ashland Weston Birney Broadus Moorhead Arvada Sussex Acme Monarch Decker Gillette Sheridan Buffalo Wright 105° 106° 107° 46° 45° 44° 43° Powder River structural basin MONTANA WYOMING Map area DECKER COAL MINE Salt Creek oil field Powder River structural basin MONTANA WYOMING Map area Powder River structural basin MONTANA WYOMING Map area 40 MILES KILOMETERS Base modified from U.S. Geological Survey Digital Line Graph (DLG), 1:100,000, 1996, U.S. Census Bureau TIGER, 1:100,000, variously dated and Wyoming Geographic Information Science Center (WYGISC), 1:100,000, 1996 and 1997. Albers Equal-Area Conic Projection standard parallels 29 30' and 45 30' central meridian -106, and North American Datum of 1983 (NAD 83) EXPLANATION Watershed Tongue River Powder River Powder River structural basin Trend-analysis sampling site and site number (table 1) Coal-bed methane well in production in 1999 Coal-bed methane well in production in 2010 Coal-bed methane well or coal-seam monitoring well with water-quality data Creek Creek Otte r

Cree k O F allo n

ree k Powde r

R e r Rosebud Bighorn River Little Powder River Pumpkin Creek Tongue River Tongue River Yello w s t o n e

R iver Salt Creek Powder River Hanging Woman Creek Goose Creek Clear Creek Crazy Woman Barber Beaver Willow Creek Creek Burger Draw Prairie Dog Creek Tongue River Reservoir Mizpah Creek Creek Figure 1.  Location of selected sampling sites, coal-bed methane (CBM) wells, and monitoring wells in CBM seams in the Tongue and Powder River watersheds, Montana and Wyoming.

Introduction    5 Table 1.  Information for sites in the Tongue and Powder River watersheds, Montana and Wyoming. [USGS, U.S. Geological Survey; CBM, coal-bed methane; Wyo., Wyoming; OLS, ordinary least squares regression on time, streamflow, and season; Mont., Montana; TSM, time-series model] Site number (fig. 1) USGS site identification number USGS site name Abbreviated site name Drainage area, in square miles General site description Substantial CBM-extraction activities in watershed upstream from site1 Trend analysis method Trend analysis periods, in water years Tongue River watershed Tongue River at Monarch, Wyo. Tongue River at Monarch Tongue River main stem No OLS 2005-10 Goose Creek below Sheridan, Wyo. Goose Creek Tongue River mountain tributary No OLS 2001-10, 2005-10 Prairie Dog Creek near Acme, Wyo. Prairie Dog Creek Tongue River plains tributary Yes OLS 2001-10, 2005-10 Tongue River at State line, near Decker, Mont. Tongue River at State line 1,453 Tongue River main stem Yes TSM 2001-10, 2005-10 Tongue River at Tongue River Dam, near Decker, Mont. Tongue River at Tongue River Dam 1,770 Tongue River main stem Yes TSM 1986-95, 2001-10 Hanging Woman Creek near Birney, Mont. Hanging Woman Creek Tongue River plains tributary Yes TSM 2005-10 Tongue River at Birney Day School, near Birney, Mont. Tongue River at Birney Day School 2,621 Tongue River main stem Yes TSM 1986-95, 2001-10 Otter Creek at Ashland, Mont. Otter Creek Tongue River plains tributary No TSM 1986-95, 2001-10 Pumpkin Creek near Miles City, Mont. Pumpkin Creek Tongue River plains tributary No OLS 2005-10 Tongue River at Miles City, Mont. Tongue River at Miles City 5,379 Tongue River main stem Yes TSM 1986-95, 2001-10 Powder River watershed Powder River at Sussex, Wyo. Powder River at Sussex 3,090 Powder River main stem No TSM 1986-95, 2001-10 Powder River at Arvada, Wyo. Powder River at Arvada 6,050 Powder River main stem Yes TSM 1986-95, 2001-10 Powder River at Moorhead, Mont. Powder River at Moorhead 8,086 Powder River main stem Yes TSM 1986-95, 2001-10 Little Powder River above Dry Creek, near Weston, Wyo. Little Powder River above Dry Creek 1,237 Little Powder River Yes TSM 1986-95, 2001-10 Little Powder River near Broadus, Mont. Little Powder River near Broadus 1,974 Little Powder River Yes OLS 2005-10 Powder River near Locate, Mont. Powder River near Locate 13,068 Powder River main stem Yes TSM 1986-95, 2001-10 1In this report, substantial CBM-extraction activities are defined in terms of amount of water produced in association with CBM extraction and are considered to be activities that result in greater than about 500 acre-feet per year of produced water.

6    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Description of Study Area The study area consists of the Tongue and Powder River watersheds in northeastern Wyoming and southeastern Mon­ tana (fig. 1); the watersheds overlie the PRB and account for 22 and 37 percent of surficial area of the PRB, respectively. Information on physiographic, climatic, hydrologic, and geo­ logic characteristics, and CBM and other resource extraction activities is presented in this section of the report. Physiographic, Climatic, and Hydrologic Characteristics The study area includes parts of the Middle Rocky Moun­ tains and Northwestern Great Plains ecoregions (Omernik, 1987; Woods and others, 2002; Zelt and others, 1999; Clark, 2012). Dominant land cover in the Bighorn Mountains (the primary mountainous region of the study area) is evergreen forest and mixed forest (Homer and others, 2004). Dominant land cover in the plains is shrubland and herbaceous grass­ land. Agricultural land cover is sparse in the study area and the main areas with pasture/hay or cultivated crops are along parts of the Tongue River, Goose Creek, and Prairie Dog Creek in the Tongue River watershed, and along Clear Creek and the Powder River in the Powder River watershed. Large strip mines produce coal in the Tongue River watershed (near Decker, Mont.) and in the Little Powder River watershed (near Gillette, Wyo.). The Tongue River is a large tributary [drainage area of about 5,500 square miles (mi2) near the mouth] to the Yellow­ stone River. Altitudes, determined by analysis of the National Elevation Dataset (NED; 30-meter digital elevation data; Gesch and others, 2002), range from about 2,350-11,700 feet (ft) above NGVD 88. Areally-weighted mean annual precipi­ tation [1980-2010, 30-year normal; PRISM Climate Group (2012)] is about 16.5 in. for the Tongue River watershed (range of 11.6-34.9 in. across the watershed). Streamflow largely is derived from snowmelt from the Bighorn Mountains and rainfall throughout the watershed. Long-term mean annual streamflow near the mouth of the Tongue River is 409 ft3/s based on 68 years of data collection during water years 1939- 2011 for Tongue River at Miles City [site 10; USGS Water Data for Montana (http://waterdata.usgs.gov/mt/nwis)]. Major tributaries include Goose and Prairie Dog Creeks that enter the Tongue River in Wyoming, and Hanging Woman, Otter, and Pumpkin Creeks that enter in Montana. Hydrologic charac­ teristics of the Tongue River are described in more detail by Clark and Mason (2007) and Clark (2012). The Powder River is a large tributary (drainage area of about 13,000 mi2 near the mouth) to the Yellowstone River. Altitudes range from about 2,210-13,200 ft above NGVD 88. Streamflow largely is derived from snowmelt from the Big­ horn Mountains and rainfall throughout the watershed. The long-term mean annual streamflow near the mouth of the Pow­ der River is 570 ft3/s based on data for water years 1939-2011 for Powder River near Locate [site 16; USGS Water Data for Montana (http://waterdata.usgs.gov/mt/nwis)]. Major tributar­ ies include Salt, Crazy Woman, and Clear Creeks that enter the Powder River in Wyoming, and the Little Powder River and Mizpah Creek that enter in Montana. Hydrologic characteris­ tics of the Powder River are described in more detail by Clark and Mason (2007) and Clark (2012). Geologic Characteristics Geology of the Tongue and Powder River watersheds is variable (Clark, 2012). Detailed geology for the State of Wyoming is presented by Love and Christiansen (1985). Gen­ eralized maps for the Tongue and Powder River watersheds (Zelt and others, 1999) and the Powder River structural basin (Rice and others, 2002) describe the geology for the Montana part of the study area. Bedrock of the western edges of the Tongue and Powder River watersheds includes metamorphic gneiss and plutonic igneous rocks from the Precambrian era. Sedimentary rocks of marine origin from the Paleozoic and Mesozoic eras compose the Bighorn Mountains (Love and Christiansen, 1985). The bedrock of the eastern part of the Tongue River watershed and a large part of the central Powder River watershed is underlain by the Wasatch Formation. The Fort Union Formation is exposed in the northern, downstream parts of the Tongue River, Powder River, and Little Powder River watersheds. Coal-Bed Methane and Other Resource Extraction Activities The Powder River structural basin (PRB; fig. 1) in northeastern Wyoming and southeastern Montana is a coalrich foreland basin primarily formed by the rise of the Black Hills uplift on the eastern side and the Hartville uplift to the southeast (Perry and Flores, 1997). The PRB accounted for about 40 percent of the U.S. coal supply in 2009 (U.S. Energy Information Administration, 2010). The main coal-bearing for­ mation is the Tertiary Fort Union Formation (2,300-5,910 ft thick), which is low in sulfur and ash making it desirable for energy production. However, much of the coal is buried too deep to be accessible by conventional coal mining techniques (Luppens and others, 2008). The uppermost Fort Union Formation (the Tongue River Member) contains sandstone, siltstone, shale, some carbonates and conglomerates, and regionally-extensive coal beds (as much as about 250 ft thick) referred to as the Wyodak-Anderson coal zone (Flores, 2004). This coal zone is a regional aquifer within the Fort Union Formation (Daddow, 1986; Lowry and others, 1986; Bartos and Ogle, 2002) and has been a major target of CBM produc­ tion since the 1990s. In general, the basin structure consists of a north-plunging asymmetric syncline. Groundwater along the southeast and western margin of the PRB flows from the Black Hills (not shown on fig. 1) and Bighorn Mountains towards the north and northeast, in a similar direction to the

Introduction    7 Tongue and Powder Rivers flowing towards the Yellowstone River (Bates and others, 2011; Lobmeyer, 1985; Meredith and others, 2012). Estimates of recoverable CBM from the PRB vary, but typically range from about 15-30 trillion cubic feet (Decker, 2001; Schenk and others, 2001). CBM exploration in the PRB began in the 1980's, affected by U.S. energy policy promot­ ing (through tax credits and research funding) increased development of domestic energy sources (Bryner, 2002). The PRB has been estimated to account for about 12 percent of proved CBM reserves in the United States (National Research Council, 2010). Limited CBM extraction in the PRB started in 1993 when extraction technologies and economic factors began to provide favorable conditions for CBM development (Peck, 1999). In the late 1990's and early 2000's, CBM extrac­ tion from the PRB accelerated rapidly and at a rate exceeding any other major coal deposit in the United States (Peck, 1999; Bryner, 2002; Hower and others, 2003). That growth in CBM extraction was affected by low drilling costs for the shallow coal beds, inexpensive disposal of water by direct release at the surface in the initially developed areas of the basin (Whea­ ton and Donato, 2004), and favorable conditions with respect to natural gas prices and U.S. energy policy (Bryner, 2002). CBM development in the PRB increased to a peak of about 17,500 active production wells in 2008 (based on analysis of data obtained from the Montana Board of Oil and Gas Con­ servation [2011] and the Wyoming Oil and Gas Conservation Commission [2011]) and consequently gained attention from regulators, land and resource management agencies, special interest groups, and landowners. Heightened awareness of CBM production led to concerns largely related to water, particularly disposal of large amounts of produced water and potential wasting of high-quality groundwater resources (Keith and others, 2012). Methane found in the generally shallow coal beds of the PRB is adsorbed onto organic matter and held in place by hydrostatic pressure; thus, groundwater in the coal bed must be extracted to produce natural gas. The PRB coal beds have a ratio of produced water to produced gas that is higher than other major CBM-producing coal beds (Rice and Nuc­ cio, 2000). Estimates of mean annual water production per well for CBM extraction in the PRB vary, but generally range from about 15-25 acre-ft per year per well (Rice and Nuc­ cio, 2000; Wheaton and Donato, 2004). In parts of the PRB, groundwater extraction has led to major declines in the water table (as much as about 625 ft; Clarey and others, 2010); however, 10 years of groundwater monitoring by the Montana Bureau of Mines and Geology has indicated that drawdown exceeding 20 ft rarely extends beyond 2 mi from the edge of CBM-extraction activities (Meredith and others, 2012). Typi­ cal methods of disposal of CBM-produced water in the PRB since production began have included discharge to lined and unlined holding ponds, direct discharge to surface-water chan­ nels, use for irrigation, and reinjection to groundwater (Clark, 2012; Wheaton and Donato, 2004; Sowder and others, 2010; National Research Council, 2010; Meredith and others, 2012). Selection of disposal method depends on quality of CBM-pro­ duced water, quality of either groundwaters or surface waters that receive CBM-produced water, and Federal and State regulations that govern produced-water disposal (National Research Council, 2010; Rice and Nuccio, 2000). The most common disposal method in the PRB has been discharge to holding ponds, accounting for about 64 percent of produced water (National Research Council, 2010; Clark, 2012). Hold­ ing ponds are inexpensive, if unlined, and provide disposal of CBM-produced water through infiltration to groundwater and evaporation (Sowder and others, 2010; Healy and oth­ ers, 2008). Potential problems associated with CBM ponds are related to accumulation of trace elements and salts, which could potentially be released into surface water channels (by seepage into alluvium and through dams, and overtopping and failure of dams) and also might degrade underlying ground­ water as CBM-produced water percolates downward beneath holding ponds (Healy and others, 2008, Sowder and others, 2010). Direct discharge of CBM-produced water (treated and untreated) to surface-water channels throughout the PRB accounts for about 20 percent of produced water (National Research Council, 2010; Clark, 2012); in 2009, annual mean direct discharge of CBM-produced water to surface-water channels in the Powder River watershed was estimated to be about 33 ft3/s (Kempema and others, 2011). Based on analysis of permitting data provided by the Wyoming Department of Environmental Quality (Jason Thomas, Wyoming Department of Environmental Quality, written commun., July, 2012), in the Wyoming part of the Tongue River watershed about 18 percent of CBM-production wells are permitted to directly discharge to surface-water channels. In the Montana part of the Tongue River watershed, about 61-65 percent of CBMproduced water in 2009 was treated and discharged to surfacewater channels (National Research Council, 2010). Currently (2013) all CBM-produced water discharge to surface-water channels in Montana must be treated. In addition to large coal and CBM deposits, the PRB also has areas that are rich in petroleum deposits. The Salt Creek oil field in Natrona County (discovered in1889; Wegemann, 1918) is the largest oil field in Wyoming and oil-extraction activities have affected surface-water quality in the Salt Creek and Powder River watersheds (Lindner-Lunsford and others, 1992). During oil production, a mix of petroleum and water that is trapped in petroleum-bearing rocks is pumped to the surface. Produced water is then separated from the oil and disposed of by various means, including direct discharge to surface-water channels and reinjection to subsurface. Pro­ duced water from the Salt Creek oil field (hereinafter referred to as Salt Creek oil brine) typically has high concentrations of total dissolved solids, the major ions sodium and chloride, and some trace elements that either are natural constituents in the water or are added during the production and separation of the water (Lindner-Lunsford and others, 1992). Some of these constituents can be toxic to freshwater biota in receiv­ ing streams (Boelter and others, 1992). Before 1990, Salt Creek oil brine was discharged directly into Salt Creek, which

8    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds flows through the Salt Creek oil field and then for about 35 mi before joining the Powder River. In 1990, deep disposal by reinjection to subsurface of most Salt Creek oil brine was implemented and resulted in a decrease of about 77 percent in direct discharge of brine to Salt Creek (Lindner-Lunsford and others, 1992). Data Collection, Analytical Methods, Review, and Quality Control Initially, most USGS gaging stations with associated water-quality data in the Tongue and Powder River watersheds were screened for inclusion in this study. Selection of sites for trend analysis largely was based on availability of sufficient data, with emphasis on application of the time-series model (TSM). A specific criterion used in site selection included at least 6 years of water-quality data that extended through water year 2010. Sixteen sampling sites were included in this study (table 1; fig. 1). Streamflow Data Daily mean streamflows at sites with continuous stream­ flow gages were determined by applying stage-discharge relations developed from periodic instantaneous streamflow measurements to continuous record of stage according to procedures described by Rantz and others (1982). Instanta­ neous streamflow at time of sampling typically was measured by using a current meter according to procedures described by Rantz and others (1982). However, some instantaneous streamflow measurements at sites with streamflow gages were obtained by recording gage heights and determining stream­ flow using the most current streamflow rating curve. Stream­ flow data are available in the USGS National Water Informa­ tion System [NWIS; USGS Water Data for Montana (http:// waterdata.usgs.gov/mt/nwis)]. Water-Quality Data Water-quality data for 16 sites (table 1; fig. 1) in the Tongue and Powder River watersheds were compiled from NWIS [USGS Water Data for Montana (http://waterdata. usgs.gov/mt/nwis)]. Water-quality constituents and properties discussed in the report are related to major-ion chemistry and include specific conductance, dissolved calcium, dissolved magnesium, dissolved potassium, SAR, dissolved sodium, alkalinity, acid neutralizing capacity (ANC), dissolved chlo­ ride, dissolved fluoride, dissolved sulfate, and dissolved solids (sum of constituents). Sampling and Analytical Methods Field measurements were made and surface-water samples were collected in accordance with methods estab­ lished by USGS (U.S. Geological Survey, 1984; Ward and Harr, 1990; Edwards and Glysson, 1999; and U.S. Geological Survey, variously dated). Samples generally were collected by using depth-integrated samplers and applying the equalwidth-increment method described by Ward and Harr (1990) and Edwards and Glysson (1999). When conditions did not allow use of depth-integrated samples, multiple-vertical grab sampling techniques were used. Samples were processed onsite using standard methods and equipment described by U.S. Geological Survey (1984) and U.S. Geological Survey (variously dated). Subsamples analyzed for major ion concentrations were filtered in the field using a filter with a pore size of 0.45 micrometer, and concentrations are reported as dissolved. Samples were sent to the USGS National Water Quality Laboratory in Lakewood, Colorado., for analysis using standard USGS methods (Fish­ man and Friedman, 1989; Fishman, 1993) for most major ions, and a "Standard Methods" procedure for potassium (American Public Health Association, American Water Works Associa­ tion, and Water Environment Federation, 1998) starting in about water year 2004. Sampling and analytical methods generally remained consistent during the study period for all major ions except alkalinity, which is an important water-quality property with respect to investigating potential effects of CBM-produced water. Alkalinity provides information on dissolved inorganic carbon (predominantly carbonate and bicarbonate ions). In the pH range of 5.5-8.3, bicarbonate is the dominant inorganic carbon species (Hem, 1985). At a pH of 9, bicarbonate still accounts for about 98 percent of inorganic carbon. For sites in the Tongue and Powder River watersheds, pH ranges are such that nearly all dissolved inorganic carbon can be reason­ ably assumed to be bicarbonate. An acid titration procedure is used to measure inorganic carbon in water samples and the result commonly is reported as milligrams per liter as cal­ cium carbonate (or mg/L as CaCO3). A complicating factor in investigating inorganic carbon characteristics for an extensive dataset is that the titration procedure is sometimes performed on filtered samples (and the result reported as alkalinity) and sometimes performed on unfiltered samples (and the result reported as acid neutralizing capacity or ANC). Alkalinity and ANC measurements can differ because of contribution to acid neutralization by suspended sediment in the unfiltered ANC samples. Magnitude of difference between alkalinity and ANC for a given water sample depends on amount and characteris­ tics of suspended sediment in the sample. In many cases, when suspended sediment concentrations are not high, alkalinity and ANC measurements are similar. However, for samples with high suspended sediment concentrations, ANC measurements can be much higher than alkalinity measurements. For water-quality samples collected in the Tongue and Powder River watersheds during water years 1980-97,

Data Collection, Analytical Methods, Review, and Quality Control    9 inorganic carbon measurements predominantly were ANC measurements. Inorganic carbon measurements for water samples collected after water year 1997 predominantly were alkalinity measurements. Because of the importance of dissolved inorganic carbon with respect to evaluating potential effects of CBM-produced water, in the final datasets a single property, referred to as estimated alkalinity, was compiled by merging the ANC and alkalinity data to allow evaluation of trends for the study period. For samples with available alkalinity measurements, estimated alkalinity generally was set to the measured alkalinity. However, if percent difference in cation and anion balance for a sample was outside plus or minus 5 percent, possibly indicating that the alkalinity measurement was problematic, and an ANC measurement was available and resolved the problem, then estimated alkalinity was set to the measured ANC. For water samples with only ANC measurements, estimated alkalinity was set to the measured ANC, given the constraint of an acceptable percent difference in cation and anion balance. Detailed investigations were done to determine potential effects of use of the estimated alkalinity property on trend analysis. There are 551 water samples collected during water years 1980-2010 for the 16 sampling sites (table 1) that have associated alkalinity and ANC measurements. Median relative percent difference (RPD) between alkalinity and ANC for the samples was -3.1 percent. RPD is calculated by using the following equation:

/ 2 Y Rpd Y

RPD is the relative percent difference;

is the alkalinity (milligrams per liter as CaCO3); and

Y is the ANC (milligrams per liter as CaCO3). Although the median RPD is not large, it indicates a positive bias in ANC relative to alkalinity, presumably because of higher ANC values that result from presence of suspended sediment. Further, the 25th percentile RPD was -15 percent and the 75th percentile RPD was -0.00 percent. Although these values are within typical quality control (QC) acceptance criteria for replicate analyses (Taylor, 1987), they confirm positive bias in ANC. However, use of the estimated alkalinity property was determined to be acceptable for meeting study objectives based on several factors. Temporal segregation of setting estimated alkalinity to either alkalinity or ANC measurements was distinct. For water samples collected through water year 1997, ANC measurements accounted for 99 percent of assigned estimated alkalinity values. For water samples collected after water year 1997, alkalinity measurements accounted for 98 percent of assigned estimated alkalinity values. Percent differences in cation and anion balances for the two periods were similar. For water samples collected during water years 1980-97 (when ANC predominantly accounted for assigned estimated alkalinity values), mean percent difference was -0.41 percent, with 98 percent of percent differences being within the range of -7.3 to +7.1 percent. For water samples collected during water years 1998-2010 (when alkalinity predominantly accounted for assigned estimated alkalinity values), mean percent difference was -0.35 percent, with 98 percent of percent differences being within the range of -5.0 to + 5.7 percent. Thus, errors associated with positive bias in ANC relative to alkalinity were not large enough to cause much variability in proportions of major ions. Also, temporal segregation of estimated alkalinity being set to either alkalinity or ANC measurements was considered with respect to a primary objective of identifying water-quality trends that might result from introduction of CBM-produced water into native streams. Trend analysis time periods generally were structured to identify trends during distinct 10-year periods before and after start of CBM-extraction activities in the watersheds upstream from the sites. Start of CBM-extraction activities in most of the watersheds typically ranged from about 1997-99 (Clark, 2012), which closely corresponds to the timing of the change from ANC measurements to alkalinity measurements in water year 1998. Thus, trend results, relative to addressing a primary objective, probably are not strongly affected. However, positive bias because of setting estimated alkalinity predominantly to ANC for water years 1980-1997 is acknowledged. Concentrations of estimated alkalinity for trend periods before start of CBM-extraction activities might be slightly elevated relative to those after start of CBM-extraction activities. Thus, with respect to possible effects of using ANC and alkalinity determinations in the trend analysis, any increasing trends identified in estimated alkalinity after substantial CBMextraction activities might be slightly conservative. In this report, the term estimated alkalinity is used when data are presented that encompass the study period and include ANC and alkalinity determinations. The standard term (alkalinity) is used when data are presented that only encompass the period after 1998 when analyses almost exclusively were done on filtered samples. Data Review and Quality Control Because the study period is relatively long (about 30 years) and includes variability in QC practices and datacollection objectives and personnel, all water-quality data for the study period were reviewed and quality assured as consistently as reasonably possible. Initially, water-quality data were retrieved from NWIS [USGS Water Data for Montana (http://waterdata.usgs.gov/mt/nwis)] for the study sites (table 1, fig. 1). Final water-quality datasets included no more than one record per day. For days with multiple records in NWIS, if only one record had a complete set of the constituents determined for that day, it was selected as the record for that day. If more than one record had a complete set of the constituents determined for that day, the record nearest the center of the day was selected. If there were multiple records for a

10    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds given day and none of the records were complete, the records were merged to create a single record with a complete set of constituents. Intensive review procedures were applied to all waterquality data. Specific conductance data were reviewed by first comparing associated field and laboratory measurements, when available. If field and laboratory measurements had an RPD (eq. 1, with X equal to field measurement and Y equal to lab measurement) within plus or minus 5 percent, the field value was accepted. When associated field and laboratory measurements had an RPD outside the range of plus or minus 5 percent, dissolved solids to specific conductance ratios were examined and compared with samples collected closely in time or at similar seasonal and streamflow conditions. If field specific conductance was missing or rejected, and laboratory specific conductance was determined to be acceptable, labora­ tory specific conductance was included in the final dataset. Major ion concentrations were reviewed by investigating percent differences in cation and anion balances and checked against typical ratios of individual ions to specific conduc­ tance. When percent differences in cation and anion balances were outside the range of plus or minus 5 percent, concentra­ tions of individual ions were checked against typical ratios and clearly problematic ions were removed from the final data­ set. Samples affected by removal of one or more major-ion constituents accounted for less than 1 percent of total samples. In some cases, percent differences in cation and anion bal­ ances were outside the range of plus or minus 5 percent, but clearly problematic ions could not be identified; all ions were included in the final dataset. After reviewing all samples and resolving problematic samples, there were 3,184 samples with sufficient data to calculate cation and anion balances. Mean percent difference in cation and anion balance was -0.37 per­ cent and about 98 percent of the samples were within the range -4.8 to +5.0 percent. Analytical results for water-quality QC samples (includ­ ing field blank and replicate samples) for the study period are difficult to precisely characterize because of several factors, including the following: changes in reporting of QC informa­ tion with time; changes in frequency of QC data collection with time; and changes in electronic storage of and capability of accessing QC data with time. Given these considerations, QC information for the study period is summarized as pre­ cisely as reasonably possible. Available QC samples collected at sites in the Tongue and Powder River watersheds during water years 1980-2010 are summarized in table 1.1 in supple­ ment 1 (at the back of this report). Analytical results for avail­ able QC samples indicate acceptable quality for trend analysis. Water Quality and Streamflow Characteristics for Selected Sampling Sites and Comparison with Water Quality and Volume Characteristics of Coal-Bed Methane Produced Water Statistically summarizing water-quality characteristics of the sites is useful for generally describing water quality in the site watersheds and in providing general information relevant for interpretation of trend results. Comparison between waterquality characteristics of receiving streams and water-quality characteristics of CBM-produced water in the site watersheds provides context for evaluating whether any identified trends might be attributable to CBM-extraction activities. Compari­ son between streamflow characteristics of receiving streams and volume of CBM-produced water in the site watersheds also provides relevant information. Water Quality and Streamflow Characteristics for Selected Sampling Sites Statistical summaries of water-quality data for sites in the Tongue and Powder River watersheds are presented in table 1.2 in supplement 1 (at the back of this report). Data are sum­ marized for two time periods (water years 1986-95, for sites with available data, and water years 2001-10 for all sites), corresponding to trend-analysis time periods (as discussed in the section of this report "Selection of Trend Analysis Time Periods"). Statistical distributions (boxplots) of SAR, sodium, and alkalinity for sites in the Tongue and Powder River water­ sheds are presented in figures 2 and 3, respectively. Statisti­ cal distributions (boxplots) are based on data collected only during water years 2001-10 because all sites had available data for the period. Mean annual streamflow for water years 2001-10 (included in table 1.3) sometimes is referenced to assist in evaluating differences in water-quality characteristics between sites. Brief descriptions of major-ion characteristics of the sites are presented by watershed in the following paragraphs of this section of the report. Mean annual streamflow retrieved from USGS Water Data for Montana (http://waterdata.usgs.gov/mt/ nwis) for sites with continuous streamflow data during water years 2001-10 also is presented. Information is presented for all sites, whether or not there have been substantial CBMextraction activities in their watersheds. Specific information is presented for sodium, SAR, and alkalinity because these constituents are of primary relevance and concern with respect to potential effects of CBM-extraction activities. SAR values were calculated by using analytical results for dissolved cal­ cium, dissolved magnesium, and dissolved sodium obtained for a given sample according to the equation:

Water Quality and Streamflow Characteristics for Selected Sampling Sites  11 [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Number of values EXPLANATION 75th percentile median 25th percentile Data value less than or equal to 1.5 times the interquartile range outside the quartile Interquartile range Data value greater than 1.5 times the interquartile range outside the quartile Site number (table 1, fig. 1) 1,000 1,000 Sodium adsorption ratio, dimensionless Sodium concentration, in milligrams per liter Alkalinity concentration, in milligrams per liter as calcium carbonate Figure 2.  Statistical distributions of sodium adsorption ratio, sodium, and alkalinity for selected sites in the Tongue River watershed based on data collected during water years 2001-10.

12    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Number of values EXPLANATION 75th percentile median 25th percentile Data value less than or equal to 1.5 times the interquartile range outside the quartile Interquartile range Data value greater than 1.5 times the interquartile range outside the quartile Site number (table 1, fig. 1) 1,000 1,500 1,000 Sodium adsorption ratio, dimensionless Sodium concentration, in milligrams per liter Alkalinity concentration, in milligrams per liter as calcium carbonate Figure 3.  Statistical distributions of sodium adsorption ratio, sodium, and alkalinity for selected sites in the Powder River watershed based on data collected during water years 2001-10.

Water Quality and Streamflow Characteristics for Selected Sampling Sites  13 where Na+, Ca2+, and Mg2+ represent concentrations expressed in milliequivalents per liter for sodium, calcium, and magnesium, respectively. Tongue River Watershed Stream water-quality characteristics are variable for main-stem Tongue River sites [Tongue River at Monarch (site 1), Tongue River at State line (site 4), Tongue River at Tongue River Dam (site 5), Tongue River at Birney Day School (site 7), and Tongue River at Miles City (site 10); table 1.2, fig. 2], but all sites (except site 10) are generally low ionic strength (based on total concentrations of major ions in meq/L; figs. 4-5) and mixed calcium-magnesium-bicarbonate type. Water-quality for site 10 is characterized by generally high ionic strength and mixed sodium-magnesium-calciumsulfate-bicarbonate type. There is a general downstream increase in mean specific conductance [385, 609, 586, 598, and 827 microsiemens per centimeter (µS/cm) for sites 1, 4, 5, 7, and 10, respectively; table 1.2]. Sodium and SAR are low; mean SAR is less than 1.0 for all main-stem sites except site 10 (mean SAR of 2.0). Mean alkalinities range from 164 (site 1) to 237 (site 10) mg/L as CaCO3. Water-quality characteristics of the main-stem Tongue River are affected by the water being sourced primarily in the Bighorn Mountains with high precipitation, resistant geologic materials, and steep gradients (Clark, 2012). There is a general downstream increase in sodium, SAR, and sulfate affected by contributions from plains tributaries, which have higher concentrations of these constituents, and irrigation effects (especially downstream from site 5), such that sodium and sulfate are co-dominant ions at site 10 (fig. 4). Variability in major-ion concentrations tends to be smaller for sites 5 and 7 than sites 4 and 10, probably because of storage and mixing effects in Tongue River Reservoir (as discussed in the section of this report "Streamflow Conditions"). Mean annual streamflow during water years 2001-10 for sites 1, 4, 5, 7, and 10 was 216, 343, 333, 332, and 289 ft3/s, respectively (table 1.3). The decrease in mean annual streamflow downstream from site 4 largely is because of irrigation consumptive use and evaporation from Tongue River Reservoir. Stream water-quality characteristics for Tongue River tributary sites are variable among sites. Goose Creek (site 2) has a moderately large watershed predominantly located in the Bighorn Mountains. Water quality is low ionic strength (mean specific conductance of 583 µS/cm) and mixed magnesiumcalcium-bicarbonate type (table 1.2). Mean SAR is 0.56 and mean alkalinity is 209 mg/L as CaCO3. Water quality for plains tributary sites (sites 3, 6, 8, and 9; table 1.2) are moderately high ionic strength with variable type. Prairie Dog Creek (site 3; streamflows are augmented by transbasin diversions for irrigation; Clark, 2012) has a mean specific conductance of

1,450 µS/cm and is mixed magnesium-calcium-sulfate-bicarbonate type. Mean SAR is 1.4 and mean alkalinity is 315 mg/L as CaCO3. Mean annual streamflow during water years 2001-10 for site 3 was 25 ft3/s. Hanging Woman Creek (site 6) and Otter Creek (site 8) have mean specific conductance of 2,510 and 2,880 µS/cm, respectively, and are mixed sodiummagnesium-sulfate-bicarbonate type. Mean SAR values are 5.0 and 6.0 for sites 6 and 8, respectively, and mean alkalinity is 547 mg/L as CaCO3 for both sites. Mean annual streamflow during water years 2001-10 for sites 6 and 8 was 0.83 and 2.6 ft3/s, respectively. Pumpkin Creek (site 9) has a mean specific conductance of 1,500 µS/cm and is sodium-sulfate type. Mean SAR is 8.3 and mean alkalinity is 226 mg/L as CaCO3. Water-quality characteristics of Tongue River plains tributaries are affected by low precipitation, soluble geologic materials, and generally low gradients that produce slow stream velocities and long contact times (Clark, 2012). Powder River Watershed Stream water quality generally is less variable among sites in the Powder River watershed than in the Tongue River watershed. Stream water quality for main-stem Powder River sites [Powder River at Sussex (site 11), Powder River at Arvada (site 12), Powder River at Moorhead (site 13), and Powder River near Locate, (site 16); table 1.2] is moderately high ionic strength and sodium-sulfate type. Mean specific conductance for sites 11, 12, 13, and 16 is 2,660, 2,350, 1,820, and 2,080 µS/cm, respectively. Mean SAR values for sites 11, 12, 13, and 16 are 6.6, 5.8, 4.0, and 5.2, respectively. Mean alkalinities for main-stem Powder River sites are similar, ranging from 208-242 mg/L as CaCO3. These characteristics are affected by main-stem Powder River receiving contributions from both the Bighorn Mountains and plains tributaries. Salt Creek, a plains tributary with oil-extraction activities in its watershed, enters the Powder River upstream from site 11 and strongly affects water-quality of main-stem Powder River sites (Lindner-Lunsford and others, 1992; Clark, 2012). Tributaries that drain the Bighorn Mountains have a dilution effect on water-quality constituents in the Powder River downstream from site 11 (Clark, 2012). Mean annual streamflow during water years 2001-10 for sites 11, 12, 13, and 16 was 163, 192, 327, and 380 ft3/s, respectively. Stream water quality for Little Powder River sites [Little Powder River above Dry Creek (site 14) and Little Powder River near Broadus (site 15); table 1.2] is higher ionic strength than for main-stem Powder River sites and is sodium-sulfate type. Mean specific conductance for sites 14 and 15 are 3,150 and 2,470 µS/cm, respectively. Mean SAR values for sites 14 and 15 are 6.7 and 8.2, respectively. Mean alkalinities for sites 14 and 15 are 342 and 345 mg/L as CaCO3, respectively. Water-quality characteristics of Little Powder River sites are affected by low precipitation, soluble geologic materials, and generally low gradients that produce slow stream velocities and long contact times (Clark, 2012). Mean annual streamflow during water years 2001-10 for site 14 was 17 ft3/s.

14    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Estimation of Volume, Flow-Rate, and Water Quality of Coal-Bed Methane (CBM) Produced Water in Selected Sampling-Site Watersheds in the Tongue and Powder River Watersheds Water-quality, volume, and flow-rate characteristics of CBM-produced water were estimated to allow general com­ parisons with water-quality and streamflow characteristics of receiving streams. The boundary of the watershed upstream from each site was delineated using the Spatial Analyst exten­ sion of ArcGIS 10. The 30-meter NED was filled to prevent misrepresentation of flowlines by lakes or depressions (Pop­ penga and Worstell, 2008). Flow direction and flow accumula­ tion rasters were then derived from the filled NED. The sites were snapped to locations on the nearest flowline defined by the flow accumulation raster. Final watershed boundaries were then delineated individually on the flow direction raster. Location and production information for CBM-produc­ tion wells were retrieved from Wyoming Oil and Gas Con­ servation Commission (2011) and Montana Board of Oil and Gas Conservation (2011), which were presumed to be the most comprehensive and accurate public sources of information concerning construction, location, and gas and water pro­ duced by CBM-production wells in the PRB in Montana and Wyoming. Locations of CBM-production wells were geospa­ tially plotted in conjunction with the delineated watershed boundaries. CBM water-production data were summed by site watershed and by year and converted from units of barrels to acre-feet (acre-ft), but otherwise were accepted as presented in the source databases. The annual volume of produced water in acre-ft also was converted to annual mean pumping rate in ft3/s to facilitate comparisons with streamflow data. Water-quality data and location information for CBM wells and monitoring wells penetrating coal zones in CBM production areas were retrieved and compiled from several sources, including Campbell and others (2008); Frost and others (2002); Montana Bureau of Mines and Geology (2012); Pearson (2002); Quillinan (2011); U.S. Geological Survey (2012); and Wyoming Department of Environmental Qual­ ity (published in Quillinan, 2011). For wells with more than one sample, constituent and property values were averaged to provide a single water-quality record for a given well. Constituent concentrations in water-quality samples collected from CBM wells and monitoring wells in each samplingsite watershed were averaged to develop basin-wide general estimates of quality of CBM-produced water for each site watershed. Summary statistics for well water-quality data are presented in table 1.4 for each sampling-site watershed. The primary objective of compiling and summarizing water-quality data representative of CBM-produced water was to allow large-scale assessment of relative differences in water quality between CBM-produced water and receiving stream water of the sites. As used in this report, relative differences in waterquality between CBM-produced water and receiving stream water refer to differences that exist between the raw solutions independent from effects of biogeochemical processes that might occur between the time when CBM-produced water is pumped from an aquifer and the time that it is actually transmitted to the stream site. Consideration of relative dif­ ferences between CBM-produced water and receiving stream water provides additional context for evaluating trend results; however, the summarization of water-quality data representa­ tive of CBM-produced water was not intended as a substan­ tive detailed quantification of water-quality characteristics of CBM-produced water in the site watersheds. Water-quality characteristics of CBM-produced water from different coal zones can have large variability (Rice and others, 2000; Clarey and Stafford, 2008). However, Quillinan (2011) noted that water-quality characteristics of CBM-produced water were more strongly correlated to geographic location than to coal zone, providing a basis for meeting the primary objective of compiling and summarizing water-quality data representative of CBM-produced water. Description of water-quality of CBM-produced water is restricted to selected major-ion constituents and properties: calcium, magnesium, SAR, sodium, alkalinity, chloride, and sulfate. Potassium and fluoride were not included because data for those constituents typically were absent from datasets for CBM wells and monitoring wells penetrating coal zones in CBM production areas. However, Brinck and others (2008) reported that CBM-produced water in the Powder River watershed had generally high fluoride concentrations (median greater than 1 mg/L); higher than fluoride concentrations for most sampling sites (table 1.2). Comparison of Water Quality and Streamflow of Selected Sampling Sites with Water-Quality and Volume of Coal-Bed Methane (CBM) Produced Water Water-quality and flow-rate characteristics of stream water at the sites and CBM-produced water in site water­ sheds were compared for sites that have had substantial CBM-extraction activities in their watersheds. Ratios of mean values of major-ion constituent and properties in stream-water samples to mean values in CBM-produced water are presented in table 1.5 to provide information on relative differences in constituents between stream water and CBM-produced water. Summary information related to volumes and flow rates of stream water and CBM-produced water is presented in table 1.3. Differences in water-quality and flow-rate characteris­ tics between stream water and CBM-produced water also are presented in figures 4 and 5. On the left-hand side of figures 4 and 5, Stiff plots, which show mean concentrations [in milliequivalents per liter (meq/L)] of selected major ions, provide information on total ionic strength and proportions of major ions. On the right-hand side of figures 4 and 5, line plots showing annual median streamflow and annual mean pumping rate for CBM-produced water provide information

Water Quality and Streamflow Characteristics for Selected Sampling Sites  15 on flow-rate characteristics of CBM-produced water rela­ tive to streamflow. Annual median values for streamflow (as opposed to annual mean values) are presented to maintain consistency with the trend-analysis procedures used for this study. The trend-analysis procedures incorporate logarithm (base 10) transformation and, thus, evaluate changes in con­ centration and streamflow relations in reference to geometric means, which generally are more closely associated with untransformed medians than untransformed means. Annual mean pumping rate for CBM-produced water was estimated by converting total annual volume of CBM-produced water to flow rate assuming constant pumping rate during the year; thus, annual mean pumping rate does not account for effects of retention of CBM-produced water in holding ponds or other remediation activities on potential quantitative effects of CBM-produced water on receiving streams. Direct discharge data for CBM-produced water contributions to receiving streams would provide a more meaningful comparison with streamflow, but direct discharge data are not readily available on temporal and spatial scales relevant to this study. Figures 4 and 5 and tables 1.4 and 1.5 provide informa­ tion on two factors relevant to potential effects of CBM-pro­ duced water on receiving streams: (1) water quality of stream water relative to water quality of CBM-produced water; and (2) streamflow characteristics at the sites relative to flow-rate characteristics of CBM-produced water in site watersheds. However, information provided in figures 4 and 5 and tables 1.4 and 1.5 does not account for effects of disposal, treat­ ment, or other remediation activities on potential qualitative or quantitative effects of CBM-produced water on receiving streams. In many places, CBM-produced water is discharged into impoundments or channels in upper reaches of tributary watersheds where water infiltrates and does not directly con­ tribute to streamflow. CBM-produced water throughout the PRB consistently is sodium-bicarbonate type, but variable in ionic strength (figs. 4 and 5; Van Voast, 2003). In general, ionic strength and sodicity of CBM-produced water in the PRB increase from southeast to northwest (Quillinan, 2011; Rice and others, 2000). This pattern reflects chemical and biological reactions along the flow paths of water in the PRB (Bates and others, 2011; Meredith and others, 2012). Flow of water in the PRB generally is toward the north or northeast, with water entering from the uplifted mountains in Wyoming and flowing toward the Yellowstone River of Montana. As water initially recharges the coal beds it dissolves calcium and magnesium salts present in soil and shallow substrate (Meredith and others, 2012). Fort Union Formation aquifer systems have long flow paths and therefore ample time for cation exchange reactions between groundwater and the prevalent clays. The cation exchange reactions increase sodium concentrations and decrease calcium and magnesium concentrations in groundwater (Daddow, 1986; Lowry and others, 1986; Bartos and Ogle, 2002; Bates and others 2011; Meredith and others, 2012). There are several areas of groundwater recharge along the western margin of the PRB especially near the Wyoming and Montana border (Bates and others, 2011). Complex biogeochemical processes associ­ ated with introduction of the recharge water to the groundwa­ ter system might also affect the low calcium and magnesium concentrations, slight decrease in sodium concentrations, and high SAR values in the area. Tongue River Watershed In the Tongue River watershed, located in the western part of the PRB (fig. 1), water quality of CBM-produced water generally is similar among sites, with low mean calcium and magnesium concentrations (ranging from 5.3-7.9 mg/L and 2.2-4.7 mg/L, respectively; table 1.4), which in combina­ tion with high mean sodium concentrations (ranging from 457-574 mg/L) results in high mean SAR values (ranging from 42-50). CBM-produced water in the Tongue River watershed has mean alkalinity concentrations that range from 986-1,250 mg/L as CaCO3. Sites in the Tongue River watershed with substantial CBM-extraction activities in their watersheds include Prairie Dog Creek (site 3), Tongue River at State line (site 4), Tongue River at Tongue River Dam (site 5), Hanging Woman Creek (site 6), Tongue River at Birney Day School (site 7), and Tongue River at Miles City (site 10). Ionic strength (based on total concentrations of major ions in meq/L) of CBM-pro­ duced water is much different from stream water at main-stem Tongue River sites (sites 4, 5, 7, and 10), but less different from stream water at plains tributary sites (sites 3 and 6). For example, ionic strength in stream water at main-stem sites (sites 4, 5, 7, and 10) is about 28-39 percent of ionic strength for CBM-produced water in the site watersheds (fig. 4). Ionic strength in stream water at plains tributary sites (sites 3 and 6) is about 70 and 120 percent, respectively, of ionic strength for CBM-produced water. For all sites in the Tongue River water­ shed with substantial CBM-extraction, relative differences in individual constituents between stream water and CBM-pro­ duced water (table 1.5) generally are similar: calcium, magne­ sium, and sulfate concentrations are higher, and SAR, sodium, alkalinity and chloride values are lower in stream water than in CBM-produced water. At main-stem Tongue River sites (sites 4, 5, and 7), SAR and sodium, in particular, are much lower in stream water relative to CBM-produced water. Relations between streamflow and pumping rates of CBM-produced water are variable among sites in the Tongue River watershed (fig. 4, table 1.3). For Tongue River at State line (site 4) mean annual pumping rate of CBM-produced water during water years 2001-10 (hereinafter referred to as mean CBM pumping rate) was 6 percent of the mean of annual median streamflows during water years 2001-10 (hereinafter referred to as 2001-10 median streamflow). For main-stem Tongue River sites 5, 7, and 10, mean CBM pump­ ing rate was 8-12 percent of 2001-10 median streamflow. For plains tributaries (sites 3 and 6), mean CBM pumping rates were 35 and about 700 percent of 2001-10 median stream­ flows, respectively.

16    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Mean concentrations of selected major ions (in milliequivalents per liter) Annual median streamflow and annual mean pumping rate of coal-bed methane-produced water [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] EXPLANATION Mean annual median streamflow for water years 2001-10 Annual median streamflow, in cubic feet per second Mean annual pumping rate of coal-bed methane-produced water in the watershed upstream from the site for water years 2001-10 Annual mean pumping rate of coal-bed methane-produced water in the watershed upstream from the site Bicarbonate Chloride Sulfate Calcium Sodium Magnesium Stiff plot for mean concentrations for stream samples (gray plot) Stiff plot for mean estimated concentrations for coal-bed methane-produced water (black plot) Water year 1,000 1,000 1,000 1,000 Concentration, in milliequivalents per liter No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed Tongue River at State line, near Decker, Montana (site 4) Prairie Dog Creek near Acme, Wyoming (site 3) Goose Creek below Sheridan, Wyoming (site 2) Tongue River at Monarch, Wyoming (site 1) No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed Streamflow or pumping rate of coal-based methane-produced water, in cubic feet per second Figure 4.  Selected water-quality and flow-rate characteristics for sites in the Tongue River watershed and for coal-bed methane (CBM) produced water in the watersheds upstream from the sites.

Water Quality and Streamflow Characteristics for Selected Sampling Sites  17 Mean concentrations of selected major ions (in milliequivalents per liter) Annual median streamflow and annual mean pumping rate of coal-bed methane-produced water [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] EXPLANATION Mean annual median streamflow for water years 2001-10 Annual median streamflow, in cubic feet per second Mean annual pumping rate of coal-bed methane-produced water in the watershed upstream from the site for water years 2001-10 Annual mean pumping rate of coal-bed methane-produced water in the watershed upstream from the site Bicarbonate Chloride Sulfate Calcium Sodium Magnesium Stiff plot for mean concentrations for stream samples (gray plot) Stiff plot for mean estimated concentrations for coal-bed methane-produced water (black plot) Water year 1,000 1,000 1,000 1,000 Concentration, in milliequivalents per liter No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed Tongue River at Tongue River Dam, near Decker, Montana (site 5) No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed Streamflow or pumping rate of coal-based methane-produced water, in cubic feet per second Otter Creek at Ashland, Montana (site 8) Tongue River at Birney Day School, near Decker, Montana (site 7) Hanging Woman Creek near Birney, Montana (site 6) Figure 4.  Selected water-quality and flow-rate characteristics for sites in the Tongue River watershed and for coal-bed methane (CBM) produced water in the watersheds upstream from the sites.—Continued

18    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Mean concentrations of selected major ions (in milliequivalents per liter) Annual median streamflow and annual mean pumping rate of coal-bed methane-produced water [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] EXPLANATION Mean annual median streamflow for water years 2001-10 Annual median streamflow, in cubic feet per second Mean annual pumping rate of coal-bed methane-produced water in the watershed upstream from the site for water years 2001-10 Annual mean pumping rate of coal-bed methane-produced water in the watershed upstream from the site Bicarbonate Chloride Sulfate Calcium Sodium Magnesium Stiff plot for mean concentrations for stream samples (gray plot) Stiff plot for mean estimated concentrations for Coal-bed methane-produced water (black plot) Water year 1,000 1,000 Concentration, in milliequivalents per liter Tongue River at Miles City, Montana (site 10) Pumpkin Creek near Miles City, Montana (site 9) No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed Streamflow or pumping rate of coal-based methane-produced water, in cubic feet per second Figure 4.  Selected water-quality and flow-rate characteristics for sites in the Tongue River watershed and for coal-bed methane (CBM) produced water in the watersheds upstream from the sites.—Continued Powder River Watershed In the Powder River watershed, located in the central part of the PRB (fig. 1), water quality of CBM-produced water is variable among sites. Sites in the Powder River watershed with substantial CBM-extraction activities include Powder River at Arvada (site 12), Powder River at Moorhead (site 13), Little Powder River above Dry Creek (site 14), Little Pow­ der River near Broadus (site 15), and Powder River near Locate (site 16). For main-stem Powder River sites (sites 12, 13, and 16), CBM-produced water generally has higher mean calcium and magnesium concentrations (ranging from 26-28 and 16-17 mg/L, respectively) than in the Tongue River watershed. Mean sodium concentrations (ranging from 584-660 mg/L) also are slightly higher in watersheds of main-stem Powder River sites, but less so than calcium and magnesium. Thus, mean SAR values (ranging from 24-27) are much lower than in the Tongue River watershed. CBMproduced water in watersheds of main-stem Powder River sites has mean alkalinity concentrations that range from 1,640-1,900 mg/L as CaCO3. For Little Powder River (sites 14 and 15), CBM-produced water has mean calcium and mag­ nesium concentrations of 32 and 17 mg/L, respectively, mean sodium concentrations of 274 mg/L, mean SAR values of 10, and mean alkalinity concentrations of 790 mg/L as CaCO3. Ionic strength in stream water at main-stem Powder River sites (sites 12, 13, and 16) is about 62-76 percent of ionic strength for CBM-produced water in the site watersheds (fig. 5). Ionic strength in stream water at Little Powder River sites (sites 14 and 15) is about 180 and 240 percent, respec­ tively, of ionic strength for CBM-produced water. In the Little Powder River watershed, CBM-produced water has much lower ionic strength than in watersheds of all Tongue River watershed sites and main-stem Powder River sites. Relative

Water Quality and Streamflow Characteristics for Selected Sampling Sites  19 Little Powder River above Dry Creek, near Weston, Wyoming (site 14) Powder River at Arvada, Wyoming (site 12) Powder River at Moorhead, Montana (site 13) Powder River at Sussex, wyoming (site 11) Mean concentrations of selected major ions (in milliequivalents per liter) Annual median streamflow and annual mean pumping rate of coal-bed methane-produced water 1,000 1,000 1,000 1,000 Concentration, in milliequivalents per liter Streamflow or pumping rate of coal-based methane-produced water, in cubic feet per second Water year [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] EXPLANATION Mean annual median streamflow for water years 2001-10 Annual median streamflow, in cubic feet per second Mean annual pumping rate of coal-bed methane-produced water in the watershed upstream from the site for water years 2001-10 Annual mean pumping rate of coal-bed methane-produced water in the watershed upstream from the site Bicarbonate Chloride Sulfate Calcium Sodium Magnesium Stiff plot for mean concentrations for stream samples (gray plot) Stiff plot for mean estimated concentrations for coal-bed methane-produced water (black plot) No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed No data for coal-bed methane-produced water No substantial coal-bed methane-extraction activities in watershed Figure 5.  Selected water-quality and flow-rate characteristics for sites in the Powder River watershed and for coal-bed methane (CBM) produced water in the watersheds upstream from the sites.

20    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Little Powder River near Broadus, Montana (site 15) Powder River near Locate, Montana (site 16) No streamflow data available 1,000 1,000 Streamflow or pumping rate of coal-based methane-produced water, in cubic feet per second [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] EXPLANATION Mean annual median streamflow for water years 2001-10 Annual median streamflow, in cubic feet per second Mean annual pumping rate of coal-bed methane-produced water in the watershed upstream from the site for water years 2001-10 Annual mean pumping rate of coal-bed methane-produced water in the watershed upstream from the site Bicarbonate Chloride Sulfate Calcium Sodium Magnesium Stiff plot for mean concentrations for stream samples (gray plot) Stiff plot for mean estimated concentrations for Coal-bed methane-produced water (black plot) Water year Concentration, in milliequivalents per liter Mean concentrations of selected major ions (in milliequivalents per liter) Annual median streamflow and annual mean pumping rate of coal-bed methane-produced water Figure 5.  Selected water-quality and flow-rate characteristics for sites in the Powder River watershed and for coal-bed methane (CBM) produced water in the watersheds upstream from the sites. —Continued differences in individual constituents between CBM-produced water and stream water (table 1.5) generally is similar among main-stem Powder River sites (sites 12, 13, and 16): calcium, magnesium, chloride, and sulfate concentrations are higher, and SAR, sodium, and alkalinity values are lower in stream water than in CBM-produced water. Relative differences are similar for Little Powder River sites (sites 14 and 15) com­ pared to the main-stem sites, except sodium concentrations are higher in stream water than in CBM-produced water. Relations between streamflow and pumping rates of CBM-produced water are variable among sites in the Powder River watershed (fig. 5, table 1.3). For main-stem sites (sites 12, 13, and 16), mean CBM pumping rates were 26, 28, and 34 percent of 2001-10 median streamflows, respectively. For site 14 in the Little Powder River watershed mean CBM pumping rate was about 360 percent of 2001-10 median streamflow. Trend Analysis Methods A variety of methods are available for analysis of water-quality trends, including nonparametric and paramet­ ric procedures (Hirsch and Slack, 1984; Helsel and Hirsch, 2002). Nonparametric procedures have been used in previ­ ous studies of water-quality trends in the Tongue and Powder River watersheds (Clark and Mason, 2007), Wang and others (2007), and Clark (2012). Two parametric trend-analysis methods were used in this study: the time-series model (TSM; Vecchia, 2005) and ordinary least squares regression (OLS) on time, streamflow, and season (Helsel and Hirsch, 2002 ). Both of these trend-analysis methods analyze trends in flowadjusted concentrations (FACs); that is, the methods calculate FACs, determine best-fit fitted trends that represent temporal changes in FACs, and determine the statistical significance of the estimated changes. Flow adjustment is necessary because

Trend Analysis Methods     21 concentrations of many water-quality constituents are depen­ dent on streamflow conditions that primarily are affected by climatic variability (interannual and seasonal). The intent of flow-adjustment is to identify and remove streamflow-related variability in concentration and thereby enhance capability to detect trends independent from effects of climatic variability. Flow-adjustment procedures produce FACs that are estimates of constituent concentrations after removing effects of stream­ flow variability. Flow-adjustment procedures vary between the TSM and OLS, which are discussed in more detail in supple­ ments 2 and 3, respectively. In general, the primary differ­ ence between the two approaches is that TSM uses multiple flow-related variables computed from concurrent (same day as the concentration sample) and antecedent (days before the concentration sample) daily streamflow in the flow-adjustment process, whereas OLS [and the nonparametric procedures used by (Clark and Mason, 2007), Wang and others (2007), and Clark (2012)] use only concurrently measured streamflow. Thus, FACs determined by the TSM are analogous to FACs determined by OLS, in that FACs of both methods account for streamflow effects, but TSM FACs provide more detailed accounting by incorporating interannual, seasonal, and shortterm streamflow variability (Vecchia, 2005). Overviews of the TSM and OLS methods are presented in the following sections of this report. Time-Series Model (TSM) A statistical time-series model for streamflow and con­ stituent concentration (Vecchia, 2005) was used in this report to detect water-quality trends. Details on theory and parameter estimation for the model are described in Vecchia (2005) and the model is summarized in supplement 2 (at the back of this report). As applied in this study, the TSM required at least 15 years of continuous streamflow data and at least 10 years of water-quality data with at least 75 total samples and at least 10 samples in each 3-month season. For site and constituent combinations with data that met requirements of the TSM, only the TSM results are presented to simplify and condense presentation of results. Specific information concerning suit­ ability of application of the TSM to the study datasets and procedures for determination of statistical significance and magnitude of trends is presented in supplement 2. Included in supplement 2 are definitions of anomaly terms that are used in the TSM and are important in contribut­ ing to the rigor of the TSM. In analysis of concentration and streamflow relations, the TSM partitions effects of stream­ flow variability into separate components for interannual, seasonal, and short-term (day-to-day) variability, and relative importance of each of these components is quantified. The annual concentration anomaly (ANNC) quantifies interannual variability in concentration that is related to interannual vari­ ability in streamflow [as determined by the annual streamflow anomaly (ANNQ)]. For dissolved constituents, ANNC typi­ cally indicates an inverse relation between concentration and streamflow. That is, annual median concentration will tend to be low [relative to long-term (that is, the period of analysis) median concentration] when annual median streamflow is high (relative to long-term median streamflow) and high when annual median streamflow is low. The seasonal concentration anomaly (SEASC) quantifies seasonal variability in concentra­ tion that is related to seasonal variability in streamflow [as determined by the seasonal streamflow anomaly (SEASQ)]. For dissolved constituents, SEASC typically also indicates an inverse seasonal relation between concentration and stream­ flow. That is, seasonal median concentration will tend to be low (relative to annual median concentration) when sea­ sonal median streamflow is high (relative to annual median streamflow) and high when seasonal median streamflow is low. Although ANNC and SEASC might indicate an inverse relation between concentration and streamflow, the strength of the relations might strongly differ among sites and constitu­ ents. For some site and constituent combinations, constituent concentration might be more sensitive to annual streamflow variability than seasonal streamflow variability and for other combinations, the reverse situation might hold. Short-term variability in concentration, also referred to as high-frequency variability (HFVC), is variability remaining after removing ANNC and SEASC. Similarly, high-frequency variability in streamflow (HFVQ) is variability remaining after removing ANNQ and SEASQ. Relations between HFVC and HFVQ gener­ ally are more complex than relations for ANNC and ANNQ and for SEASC and SEASQ. In accounting for relations between HFVC and HFVQ, the TSM can account for effects of shortterm streamflow variability (for example, hysteresis) and also potential serial correlation. In this study, the TSM was selected as the preferred trend-analysis method to OLS and nonparametric methods used in previous studies [for example, Clark and Mason (2007), Wang and others (2007), and Clark (2012)]. This pref­ erence primarily is because of the large percentage of sites that had continuous streamflow data available (11 of 16 study sites) and the incorporation of continuous streamflow data for the entire study period in the TSM. Detailed analysis of continu­ ous streamflow data provides better definition of concentra­ tion and streamflow relations through time, better handling of temporal variability in sampling frequency, and interpolation of trend patterns to periods when water-quality data are sparse or absent. The TSM accounts for effects of serial correlation, which allows for inclusion of more data in the analysis and greater flexibility in timing of sample collection. Further, the TSM incorporates interannual, seasonal, and short-term infor­ mation in flow-adjustment procedures, and ANNC and SEASC allow quantification of interannual and seasonal components of variability in concentration and streamflow relations. The OLS method used in this study and the nonparametric methods used in previous studies [Clark and Mason (2007), Wang and others (2007), and Clark (2012)] incorporate only concur­ rently measured streamflow and fixed seasonal functions; thus, the concentration and streamflow relation at a given time of sampling is assumed to depend only on streamflow magni­ tude and season with no accounting for streamflow conditions

22    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds before sampling. For example, if two water-quality samples were collected at similar streamflow magnitudes at the same time of year, the flow-adjustment applied to the samples would be identical regardless of differences in streamflow conditions before sampling. If one sample was collected during increas­ ing streamflow (for example on the rising limb of snowmelt runoff) in a dry year and the other sample was collected at a similar streamflow during decreasing streamflow (for example on the receding limb of snowmelt runoff) in a wet year, the same flow-adjustment would be applied to concentrations of both samples; there is no accounting for interannual or shortterm hysteresis factors that affect concentration and stream­ flow relations (Vecchia, 2005; Peterson and others, 1996; Chanat and others, 2002). The TSM, however, analyzes con­ tinuous streamflow data to determine the context of stream­ flow conditions associated with a given time of sampling and account for interannual, seasonal, and short-term streamflow variability in flow-adjustment procedures. Ordinary Least Squares Regression (OLS) on Time, Streamflow, and Season For five sites, data requirements of the TSM were not met. In these cases, OLS on time, streamflow, and season was used to analyze trends. OLS generally is regarded as an acceptable alternative trend-analysis method relative to nonparametric methods, such as the seasonal Kendall tau, when data distributions are approximately normal (Helsel and Hirsch, 2002). OLS for trend analysis was applied following guidelines presented in Helsel and Hirsch (2002) and specific information concerning application of OLS in this study is presented in supplement 3. As applied in this study, OLS required at least 6 sequen­ tial years of water-quality data with six or more samples per year (temporally distributed consistently among years) and associated instantaneous streamflow measurements at times of sample collection. A consistent OLS model was used to pro­ vide general application for the numerous site and constituent combinations with large variability in availability of data, and water-quality and streamflow relations. In general, constituent concentrations were regressed on streamflow, decimal time, and periodic functions to represent seasonal variability in con­ centration and streamflow relations. Specific information con­ cerning suitability of application of OLS to the study datasets, and procedures for determination of the statistical significance and magnitude of trends is presented in supplement 2. Selection of Trend-Analysis Time Periods Appropriate selection of trend analysis time periods is important because trend-analysis results are dependent on how the time periods are structured. Factors considered in selection of trend analysis time periods included the following: timing of known watershed perturbations that might have affected stream water quality; examination of residual plots from TSM and OLS analyses with no trend (that is, no decimal time term in the models); temporal distribution of available data; defini­ tion of time periods of sufficient length to provide reasonably meaningful information on temporal variability; and mainte­ nance of consistent trend-analysis time periods among sites, where possible, to assist in comparison of results. Two primary 10-year trend-analysis periods were selected. Trend-analysis 10-year period 1 (water years 1986-95; hereinafter referred to as period 1) was selected to represent variability in major-ion concentrations in the Tongue and Powder River watersheds before potential effects of CBM-extraction activities. Trend analysis 10-year period 2 (water years 2001-10; hereinafter referred to as period 2) was selected because it encompassed substantial CBM-extraction activities and therefore might indicate potential effects of CBM-extraction activities on water quality of receiving streams in the Tongue and Powder River watersheds. These two 10-year trend analysis periods were used for all sites that satisfied requirements for the data-intensive TSM. The inter­ vening time interval (water years 1996-2000) between period 1 and period 2 was not specified for trend analysis, largely because sufficient data generally were not available. For sites that did not satisfy data requirements for the TSM, OLS was used to analyze trends for period 2 (if complete data were available) or a 6-year period (2005-10) to provide information on water-quality characteristics that might have been affected by CBM-extraction activities. Additional data collection at these sites will increase record length for future analysis of temporal trends. The selected OLS trend-analysis periods correspond to trend-analysis periods of Clark (2012) for sites in Wyoming in the Tongue and Powder River watersheds. Information on trend-analysis methods and time periods for sites in the Tongue and Powder River watersheds are presented in table 1. Streamflow Conditions and Other Factors that Affect Trend Results Several factors affect temporal trends in water quality. Climatic variability (interannual and seasonal) affects concen­ tration and streamflow relations and is indicated in variability in streamflow conditions. Trend methods vary with respect to accounting for streamflow variability. Thus, investigating streamflow conditions during the study period is relevant to interpreting trend results. Other factors also are relevant to understanding trend-analysis procedures and interpreting trend results. The other factors discussed in this section of the report include the following: relations between unadjusted concen­ trations and FACs; differences in data-collection activities and frequency between sites; effects of trend-analysis period definition; how the TSM procedures account for data gaps; and data transformation. The TSM is emphasized in this sec­ tion because it is the method used for most sites in this study and it provides convenient access to relevant intermediate

Streamflow Conditions and Other Factors that Affect Trend Results     23 results to show trend-analysis concepts. Streamflow conditions during the study period also are discussed, primarily based on patterns in the TSM ANNQ for selected stations. Then, example data and trend results are presented for selected sites to provide information on flow-adjustment characteristics, variability in data-collection activities, effects of data gaps, and other factors that affect trend results. Streamflow Conditions In general terms, ANNQ determined by the TSM statisti­ cally describes the temporal deviation of streamflow from long-term median daily streamflow, after smoothing out typi­ cal repetitive seasonal variability and high-frequency variabil­ ity in streamflow (that is, removing SEASQ and HFVQ). ANNQ essentially can be interpreted as the moving geometric mean streamflow (generally equivalent to median streamflow) and provides an estimate of central tendency in streamflow through time. Daily mean streamflow and ANNQ for water years 1980-2010 for selected sites in the Tongue and Powder River watersheds are presented in figures 6, and 7, respectively. Temporal patterns in streamflow conditions during water years 1980-2010 were similar in the Tongue and Powder River watersheds. During period 1, streamflow generally was near the long-term (water years 1980-2010) median with generally small short-term (about 2-3 years) deviation above and below the long-term median (figs. 6 and 7). During water years 1996-2000 (the time interval between period 1 and period 2), streamflow generally was higher than the long-term median. Substantial CBM-extraction activities began during this period, with start dates in the site watersheds generally ranging from about 1997-99 (figs. 4 and 5; and Clark, 2012). During period 2, streamflow initially was below the long-term median (water years 2001-07), but then increased to above the long-term median (water years 2008-10). This pattern gener­ ally is consistent between the Tongue River and Powder River watersheds. Variable streamflow conditions during period 2 coincide with large increases in CBM-extraction activities in the Tongue and Powder River watersheds. Variable streamflow conditions in association with a large increase in CBM-extrac­ tion activities is relevant to flow-adjustment procedures and interpretation of trend results. Effects of Tongue River Dam operations in regulating and decreasing seasonal streamflow variability are apparent in figure 6 by comparison of streamflow at Tongue River at State line (site 4; upstream from the dam) with streamflow at Tongue River at Tongue River Dam (site 5) and Tongue River at Birney Day School (site 7), which are downstream from the dam. General operations of Tongue River Dam include capture of high streamflows during spring snowmelt runoff to fill the reservoir (Kevin Smith, Montana Department of Natural Resources and Conservation, written commun., July 2012). After the reservoir is filled, contract water marketed by the Tongue River Water Users Association is released upon call by the water users. Contract water can be delivered May through September, although contract-water releases typically start in mid-July. Depending on remaining reservoir storage and climatic conditions, fall and winter releases are set in October and typically are not adjusted until late winter or early spring. Storage and subsequent release of water from the dam mixes chemical constituents and moderates streamflow variability downstream from the dam. Regulation effects of Tongue River Dam are relevant to flow-adjustment procedures and interpre­ tation of trend results. Factors that Affect Trend Results and Interpretation To provide examples of factors that affect trend results and interpretation, sodium and estimated alkalinity data are presented in figures 8 and 9 for selected main-stem Tongue River sites and figures 10 and 11 for main-stem Powder River sites. FACs and fitted trends determined by using the TSM, and unadjusted concentrations for selected sites, are presented in the figures. Sodium and estimated alkalinity were selected as example constituents because they typically have large dif­ ferences in concentrations between CBM-produced water and stream water; are constituents of primary concern with respect to potential effects of CBM-produced water on stream water quality; and have different chemical properties with respect to solubility relations, and concentration and streamflow relations that are suitable for showing concepts that generally apply to most other constituents. Main-stem Tongue River sites (sites 4, 5, 7, and 10) and main-stem Powder River sites (sites 11, 12, 13, and 16) were selected for presentation in figures 8-11 to provide examples for showing concepts that generally apply to most other sites. In some cases, issues relating to sites not shown in figures 8-11 that are relevant to interpretation of trend results are discussed. Several factors that potentially affect trend results are illustrated in figures 8-11, including the following: relations between unadjusted concentrations and FACs; differences in data-collection activities and frequency between sites; effects of trend-analysis period definition; and how the TSM procedures account for data gaps. FACs are estimates of constituent concentrations after removing effects of streamflow variability. Thus, FACs typically have less variability than unadjusted concentrations, although the strength of this pattern is variable among sites and also can be variable through time for a given site. For dissolved major-ion constituents, unadjusted concentrations tend to be low during high-streamflow conditions and high during low-streamflow conditions. During high streamflow conditions, dilute atmo­ spheric water (as rainfall or snowmelt) with short contact with soil and rock materials accounts for a large part of streamflow. During low-streamflow conditions, stream water typically con­ tains a larger proportion of groundwater contributions, has had more contact with geological materials, and therefore incorpo­ rated more dissolved constituents. Flow-adjustment procedures account for these characteristics and produce FACs that are repre­ sentative of variability within a consistent streamflow framework.

24    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Daily mean streamflow (three values per month)— Plotting frequency for daily mean streamflow corresponds to the sampling frequency used in the time-series model (supplement 2) Fitted annual streamflow anomaly determined by using the time-series model Median daily mean streamflow for water years 1980-2010 [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] EXPLANATION Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Water year 1,000 10,000 1,000 10,000 1,000 10,000 A. Tongue River at State line, near Decker, Montana (site 4) B. Tongue River at Tongue River Dam, near Decker, Montana (site 5) C. Tongue River at Birney Day School, near Birney, Montana (site 7) Daily mean streamflow or annual streamflow anomaly, in cubic feet per second Figure 6.  Daily mean streamflow (three values per month) and annual streamflow anomaly determined by using the time-series model (TSM) for sites in the Tongue River watershed, water years 1980-2010.

Streamflow Conditions and Other Factors that Affect Trend Results     25 Daily mean streamflow (three values per month)— Plotting frequency for daily mean streamflow corresponds to the sampling frequency used in the time-series model (supplement 2) Fitted annual streamflow anomaly determined by using the time-series model Median daily mean streamflow for water years 1980-2010 [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] EXPLANATION Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Water year 1,000 10,000 1,000 10,000 1,000 10,000 A. Powder River at Arvada, Wyoming (site 12) B. Powder River at Moorhead, Montana (site 13) C. Powder River near Locate, Montana (site 16) Daily mean streamflow or annual streamflow anomaly, in cubic feet per second Figure 7.  Daily mean streamflow (three values per month) and annual streamflow anomaly determined by using the time-series model (TSM) for sites in the Powder River watershed, water years 1980-2010.

26    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds EXPLANATION Fitted trend determined by using the time series model— Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time series model Unadjusted concentration [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Water year B. Tongue River at Tongue River Dam, near Decker, Montana (site 5) D. Tongue River at Miles City, Montana (site 10) Sodium concentration, in milligrams per liter A. Tongue River at State line, near Decker, Montana (site 4) C. Tongue River at Birney Day School, near Birney, Montana (site 7) Figure 8.  Sodium flow-adjusted concentrations and fitted trends determined by using the time series model (TSM), and unadjusted concentrations for sites in the Tongue River watershed, water years 1980-2010.

Streamflow Conditions and Other Factors that Affect Trend Results     27 EXPLANATION Fitted trend determined by using the time series model— Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time series model Unadjusted concentration [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin B. Tongue River at Tongue River Dam, near Decker, Montana (site 5) D. Tongue River at Miles City, Montana (site 10) A. Tongue River at State line, near Decker, Montana (site 4) C. Tongue River at Birney Day School, near Birney, Montana (site 7) Water year *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." Estimated alkalinity concentration, in milligrams per liter as calcium carbonate* Figure 9.  Estimated alkalinity flow-adjusted concentrations and fitted trends determined by using the time series model (TSM), and unadjusted concentrations for sites in the Tongue River watershed, water years 1980-2010.

28    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds C. Powder River at Moorhead, Montana (site 13) B. Powder River at Arvada, Wyoming (site 12) A. Powder River at Sussex, Wyoming (site 11) D. Powder River near Locate, Montana (site 16) EXPLANATION Fitted trend determined by using the time series model— Bold line segments indicate statistical significance at p-value less than Flow-adjusted concentration determined by using the time series model Unadjusted concentration [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Water year 1,000 1,500 1,000 1,500 1,000 1,500 1,000 1,500 Sodium concentration, in milligrams per liter Figure 10.  Sodium flow-adjusted concentrations and fitted trends determined by using the time series model (TSM), and unadjusted concentrations for sites in the Powder River watershed, water years 1980-2010.

Streamflow Conditions and Other Factors that Affect Trend Results     29 C. Powder River at Moorhead, Montana (site 13) B. Powder River at Arvada, Wyoming (site 12) A. Powder River at Sussex, Wyoming (site 11) D. Powder River near Locate, Montana (site 16) Water year Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION Fitted trend determined by using the time series model— Bold line segments indicate statistical significance at p-value less than Flow-adjusted concentration determined by using the time series model Unadjusted concentration [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." Estimated alkalinity concentration, in milligrams per liter as calcium carbonate* Figure 11.  Estimated alkalinity flow-adjusted concentrations and fitted trends determined by using the time series model (TSM), and unadjusted concentrations for sites in the Powder River watershed, water years 1980-2010.

30    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Thus, for typical streams in eastern Montana and Wyoming during low-streamflow conditions, FACs of dissolved majorion constituents will tend to be less variable and lower than unadjusted concentrations. Sodium data for Powder River at Arvada (site 12; fig. 10B; water years 2001-05) provide an example of this pattern. Conversely, during high-streamflow conditions, FACs will tend to be less variable and higher than unadjusted concentrations. Alkalinity data for Powder River at Moorhead (site 13; fig. 11C; water years 2008-10) provide an example of this pattern. During near median streamflow condi­ tions, FACs will tend to be less variable and centered within unadjusted concentrations. Alkalinity data for Tongue River at Tongue River Dam (site 5; fig. 9B; water years 1986-95) provide an example of this pattern. For the period 2008-10 following transition from low-streamflow to high-streamflow conditions, several sites have associated decreases in unad­ justed concentrations. However, the TSM flow-adjustment procedures compensate for the streamflow variability and for some sites (for example, sites 12 and 13; figs. 10 and 11) the FACs and fitted trends indicate consistent increase in concen­ trations within a consistent streamflow framework. These pat­ terns indicate importance of flow-adjusted trend analysis for identifying patterns in constituent concentrations independent from streamflow conditions. Frequency and temporal variability in data-collection activities during the study period affect trend results. Datacollection characteristics were highly variable among sites in the Tongue and Powder River watersheds, as evidenced by the temporal distribution of unadjusted sodium data shown in figs. 8 and 10, respectively. In the Tongue River watershed, datacollection activities and frequency were variable, but all waterquality datasets have large data gaps (fig. 8). Tongue River at Monarch (site 1; not shown in fig. 8) is the only main-stem Tongue River site upstream from substantial CBM-extraction activities, but this site has sparse continuous streamflow data during the study period and the data could not be analyzed by using the TSM. Data density for the tributaries Goose Creek, Prairie Dog Creek, and Pumpkin Creek (sites 2, 3, and 9, respectively; not shown in fig. 8) generally was similar to site 1. Tongue River at State line (site 4; fig. 8A) is important because it is the first main-stem Tongue River site downstream from substantial CBM-extraction activities and located at the Wyoming and Montana border. However, water-quality data collection for site 4 was infrequent before substantial CBM-extraction activities and the water-quality dataset is less suitable for the TSM trend analysis than most other sites to which the TSM was applied. Larger datasets that include good seasonal representation through long time periods increase capability of the TSM to define concentration and streamflow relations and accurately quantify interannual, seasonal, and short-term effects on the relations. Because the site 4 dataset lacks good representation through a long time period, the trend results should be used with caution. Tongue River at Tongue River Dam (site 5; fig. 8B) had frequent water-quality data collection through water year 1995, but a large data gap dur­ ing a critical period (water years 1996-2003). Tongue River at Birney Day School (site 7; fig. 8C) had water-quality data collection similar to site 5, but the data gap was larger, extend­ ing from 1994-2003. Water-quality data collection for the tributaries Hanging Woman Creek and Otter Creek (sites 6 and 8, respectively; not shown in fig. 8) generally was similar to sites 5 and 7, but with minor variability in start and end times of intermediate data gaps. Tongue River at Miles City (site 10; fig. 8D) had water-quality data collection generally similar to site 5. Factors that limit capability to detect trends potentially attributable to CBM-extraction activities for main-stem Tongue River sites include the following: there are no mainstem Tongue River sites upstream from substantial CBMextraction activities that have sufficient data for analysis using the TSM ; and data gaps for sites downstream from substantial CBM-extraction activities generally extend past the start of substantial CBM-extraction activities to a time when CBMextraction activities in the Tongue River watershed were nearly constant. Further, although some main-stem Tongue River sites have datasets that are more suitable for trend analy­ sis than others, datasets for all main-stem Tongue River sites have data gaps or time periods with infrequent sample col­ lection. However, the datasets typically are sufficient to make general observations on how changes in water quality after the start of substantial CBM-extraction activities relate to patterns before the start of substantial CBM-extraction activities. In the Powder River watershed, data-collection activities and frequency were variable; but datasets for main-stem Pow­ der River sites are considered more suitable for trend analysis than datasets for main-stem Tongue River sites. Datasets for main-stem Powder River sites generally were denser and encompassed longer time periods than datasets for main-stem Tongue River sites (figs. 8 and 10). Powder River at Sussex (site 11; fig. 10A) is upstream from substantial CBM-extrac­ tion activities and has sufficient data collection before and after CBM-extraction activities to characterize water-quality patterns during the two periods. Powder River at Arvada (site 12; fig. 10B), the first site main-stem Powder River site downstream from substantial CBM-extraction activities, had water-quality data collection similar to site 11. Powder River at Moorhead (site 13; fig. 10C) and Powder River near Locate (site 16; fig. 10D) had water-quality data collection with vari­ able data gaps (extending from water years 1991-2002 and 1995-98, respectively). Investigation of trend results for sites 13 and 16 (with data gaps) in conjunction with site 12 (with no data gaps) generally allows for evaluation of effects of CBMextraction activities on the main-stem Powder River from near the point of first potential effects to near the mouth of the Powder River. However, the large data gap for site 13 might affect trend results (as discussed in the section of this report "Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds"). Water-quality data collection for the two sites on the Little Powder River (a large plains tributary to the main-stem Pow­ der River) was variable. Little Powder River above Dry Creek (site 14; not shown in fig. 10) is downstream from substantial

Streamflow Conditions and Other Factors that Affect Trend Results     31 CBM-extraction activities and had data collection generally similar to site 12. Little Powder River near Broadus (site 15; not shown in fig. 10) also is downstream from substantial CBM-extraction activities and had data collection restricted to the period water years 2005-10, generally similar to tributary site 2 in the Tongue River watershed. Definition of trend-analysis periods affects trend-analysis results. For the TSM, fitted trends in FACs during a defined trend-analysis period are monotonic trends that are smoothed to produce generally consistent slopes across the middle sec­ tion of the trend-analysis period that become flatter near the ends. The flatter slopes near the ends provide gradual transi­ tion from trend-analysis periods to time intervals with no trend analysis. In some cases, the fitted trends do not precisely follow the patterns in FACs and unresolved trending in FACs is apparent. For example, large and abrupt decreases in sodium and estimated alkalinity FACs at Powder River at Sussex (site 11; the first main-stem Powder River site downstream from Salt Creek) were associated with the period starting in 1990 when Salt Creek oil brine was reinjected to deep disposal (figs. 10A and 11A). Sodium and estimated alkalinity FACs indicate near complete response to the oil-brine reinjection by water year 1992 and then generally stable patterns through the end of period 1 (water year 1995; figs. 10A and 11A). How­ ever, the fitted-trend decrease in sodium and estimated alka­ linity generally was distributed consistently across period 1 (figs 10A and 11A). Thus, there are short-term trend patterns in the FACs that are unresolved in the fitted trends. Although the smoothed fitted trend from the TSM was less abrupt than the apparent change in FACs, the overall change from the start to the end of the period was accurately represented. Better temporal resolution in fitted trends for site 11 (or other sites) might have been attained by defining two or more additional trend-analysis periods within the selected 10-year trendanalysis periods. However, this approach would have required detailed site-by-site trend analysis for potentially inconsistent time periods among the 16 sites in this study. An important consideration in the design of the trend-analysis structure of this study was the capability to make general comparisons among the 16 sites with respect to potential effects of CBMextraction activities on a large-scale basis throughout con­ sistent time periods. Further, the overall fitted trends during the defined trend-analysis periods are consistent with overall patterns in FACs (figs. 8-11). Data gaps present complications for trend analysis. If data gaps are of long duration and include important time intervals, such as intervals during baseline conditions before known watershed perturbations or intervals during which effects of perturbations would be expected to be changing abruptly, the available data might not be sufficient to accurately define trends. During periods of data gaps within defined trendanalysis periods (indicated for several sites in figs. 8-11), the TSM interpolates forward or backward (depending on location of the data gap within the defined trend analysis period) to the start or end of the defined trend-analysis period, or to the next closest FAC, based on fitted model coefficients (Vecchia, 2003). The intervening time interval (water years 1996-2000) between period 1 and period 2 was not specified for trend analysis primarily because of the large number of sites that had no data collection during the interval. Within the interval the TSM applies a straight-line fit between the fitted trend at the end of period 1 and the start of the second trend-analysis period. Thus, changes in patterns of FACs are applied to the fitted trends within the defined trend-analysis periods. General stationarity during the interval between period 1 and period 2 is important in accurate determination of fitted trends. Large trending in FACs during the interval could result in unrepre­ sentative fitted trends. This factor was considered in defining trend-analysis periods used in this study. In the Powder River watershed, Powder River at Sussex (site 11), Powder River at Arvada (site 12), Little Powder River above Dry Creek (site 14), and Powder River near Locate (site 16) had sufficient data during the interval between period 1 and period 2 to conclude that large trending in FACs was absent during the interval (for example, see patterns in sodium and estimated alkalinity FACs; figs. 10A, B, D, 11A, B, D). Conclusions for sites 11, 12, 14, and 16, concerning general stationarity in FACs during the interval, were extrapolated to conclude that large trending in FACs probably was absent during the interval for Powder River at Moorhead (site 13). However, site 13 lacks data dur­ ing a substantial part of period 1, with no data during water years 1991-95 to define concentration and streamflow rela­ tions after Salt Creek oil brine reinjection. This data gap for site 13 might have affected trend results (as discussed in the section of this report "Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Pow­ der River Watersheds"). In the Tongue River watershed, there were no sites with complete datasets during the intervening time interval between period 1 and period 2. Some sites had specific conductance data that generally indicated stationarity during the intervening period. Specific conductance generally provides an accurate indicator of ionic strength, but it might not be an accurate indicator of variability in concentrations of individual major ions if proportions of major ions in stream water change because of natural or anthropogenic causes. Also, most sites in the Tongue River watershed had data gaps during either period 1 or period 2. The issues of stationarity during the interval between period 1 and period 2, and data gaps during the trend-analysis periods are factors contributing to greater uncertainty in fitted trends for sites in the Tongue River watershed than for sites in the Powder River watershed. An important consideration in interpreting trend results relates to the trend-analysis methods incorporating loga­ rithm (base 10) transformation of constituent concentrations. Log-transformation results in datasets that are approximately normally distributed and allows analysis using rigorous para­ metric procedures. However, log-transformation decreases variability in the data relative to the original untransformed units representative of actual environmental variability. The effects of data transformation do not negatively influence a primary purpose of this study in determining water-quality trends and evaluating relative temporal changes in major-ion

32    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds characteristics among sites. In the trend analyses, all data (high and low values) affect changes in flow-adjusted median values. Thus, the fitted trends truly represent unbiased esti­ mates of overall changes in central tendency. The overall changes in central tendency are quantified with respect to geo­ metric mean (generally equivalent to median) concentration in reference to log-transformed streamflow. In general, changes in median concentrations that might be attributed to CBMextraction activities probably are more strongly evident during low-to-median streamflow conditions (when CBM-produced water would be expected to account for a larger proportion of streamflow) than during mean-to-high streamflow condi­ tions. This observation is relevant in assessing trend results in relation to specific water-quality concerns, including effects of water-quality changes on agricultural producers and effects on stream biota and ecology. Trends in median concentrations in reference to log-transformed streamflow provide general infor­ mation on overall temporal changes (in terms of directions and relative magnitudes) in concentrations, but might be difficult to interpret with respect to how those changes translate into specific effects on agricultural producers or stream ecology. Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Trend results are presented in this report for all sites (by watershed), whether or not there have been substantial CBM-extraction activities in their watersheds. Summaries of trend results (tables 2-5) include information on trend direc­ tions, magnitudes, and significance, and estimated fitted trend values at the start and end of trend-analysis periods. Statistical significance of trends was based on a p-value less than 0.01, used by Vecchia (2005) for the TSM analysis. Magnitudes of trends are expressed as total percent change during the speci­ fied trend-analysis period; an approach also used by Vecchia (2005). Detailed trend-analysis results are presented in figures 4.1-4.16 and tables 4.1-4.4. The figures and tables present a large amount of information concerning major ion characteris­ tics in the Tongue and Powder River watersheds. For brevity, discussion in this section generally is limited to observations concerning trend results that might relate to potential effects of CBM-extraction activities in the site watersheds. Investiga­ tion of possible causal factors of trend results for sites or time periods not affected by CBM-extraction activities was beyond the scope of this study. For TSM results, ANNC and SEASC coefficients are discussed to present information on relative influence of interannual and seasonal effects on concentra­ tion and streamflow relations and trend results. The TSM also incorporates short-term effects (HFVC) on concentration and streamflow relations; however, HFVC relations are complex and, for brevity, are not discussed. The patterns in the fitted trends shown in figures 4.1-4.16 (as well as the directions and magnitudes of the trends pre­ sented in tables 2-5 and 4.1-4.4) are considered to provide important information beyond the strict statistical character­ istics of the trend results (in terms of p-values and levels of significance). If CBM-extraction activities are affecting water quality, intuitively there should be increases in some major ions and associated decreases in other major ions, with rela­ tive variability dependent on water-quality characteristics for a given site and CBM-produced water in the site watershed. Data analyzed in this study are complex and variable, with respect to several factors, including concentration and stream­ flow relations and data-collection characteristics. Consider­ ation of patterns in direction and magnitude of fitted trends for various major ions for a given site or among sites might provide relevant information in interpreting trend results, even though results for each major ion might not have been determined to be statistically significant; thus, in some cases nonsignificant trend results are discussed. Visualization of fitted trends in relation to FACs (as shown in figs. 4.1-4.16), on which the fitted trends are based, provides information to evaluate how trend results and determination of significance levels might be affected by variability in data collection. Accurate FACs and fitted trends should be consistent with chemical processes. Consistency of FACs and fitted trends with chemical processes was evaluated by examining per­ cent differences in cation and anion balances, and agreement between magnitudes of fitted trends for specific conductance and dissolved solids. Mean percent differences in cation and anion balances for fitted trends and FACs (table 4.5) were within +/- 3 percent for all sites except Tongue River at State line (site 4) and indicated general consistency with chemical processes. Percent differences in cation and anion balances for the TSM fitted trends and FACs for site 4 indicate posi­ tive bias and the range in percent differences in cation and anion balances of FACs is much larger than for other sites. For example, for the fitted trends, site 4 had a mean percent differ­ ence in cation and anion balances of +5.6 and a range of +3.4 to +7.0 percent (table 4.5). In contrast, the combined mean percent difference in cation and ion balances for the other 10 sites analyzed by using the TSM was -0.05 with a mean range of -1.4 to +1.4. For the FACs, site 4 had a mean percent difference in cation and anion balances of +4.6 and a range of -28 to +15 percent. In contrast, the combined mean percent difference in cation and ion balances for the FACs at the other 10 sites analyzed by using the TSM was -0.18 with a mean range of -5.9 to +8.0. Trend analyses for site 4 probably are affected by marginally sufficient data, which are sparse and poorly distributed during period 1, and might not be of suffi­ cient detail for accurately determining concentration and flow relations by using the TSM. For a given site and trend-period combination, agreement between trend magnitude for specific conductance and dissolved solids was evaluated by determin­ ing whether the RPD (eq. 1, with X equal to trend magnitude for specific conductance and Y equal to trend magnitude for dissolved solids) was within the range of +/- 20 percent, or

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds    33 Table 2.  Summary of trend results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010. [Bold values indicate statistically significant (at p-value 0.01) trend results. Dark gray shading indicates downward fitted trend. Light gray shading indicates upward fitted trend. p-value, statistical significance level; less than; Mont., Montana] Constituent or property Fitted trend value at start of water year 1986 (start of period 1) Fitted trend value at end of water year 1995 (end of period 1) Estimated total percent change for period 1 Fitted trend value at start of water year 2001 (start of period 2) Fitted trend value at end of water year 2010 (end of period 2) Estimated total percent change for period 2 Tongue River main-stem sites Tongue River at State line, near Decker, Mont. (site 4, fig. 1) Specific conductance Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) Tongue River at Tongue River Dam, near Decker, Mont. (site 5, fig. 1) Specific conductance Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) Tongue River at Birney Day School, near Birney, Mont. (site 7, fig. 1) Specific conductance Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents)

34    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 2.  Summary of trend results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010.—Continued [Bold values indicate statistically significant (at p-value 0.01) trend results. Dark gray shading indicates downward fitted trend. Light gray shading indicates upward fitted trend. p-value, statistical significance level; less than; Mont., Montana] Constituent or property Fitted trend value at start of water year 1986 (start of period 1) Fitted trend value at end of water year 1995 (end of period 1) Estimated total percent change for period 1 Fitted trend value at start of water year 2001 (start of period 2) Fitted trend value at end of water year 2010 (end of period 2) Estimated total percent change for period 2 Tongue River at Miles City, Mont. (site 10, fig. 1) Specific conductance Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) Tongue River tributary sites Hanging Woman Creek near Birney, Mont. (site 6, fig. 1) Specific conductance 2,320 2,550 2,550 2,720 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) 1,710 1,790 1,790 2,000 Otter Creek at Ashland, Mont. (site 8, fig. 1) Specific conductance 2,880 2,600 2,600 2,990 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved 1,080 1,230 Solids, dissolved, (sum of constituents) 2,060 1,820 1,820 2,300 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2"Estimated alkalinity" data were developed by selecting either alkalinity or acid neutralizing capacity (ANC), depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods."

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds    35 Table 3.  Summary of trend results determined by using ordinary least squares regression (OLS) on time, streamflow, and season for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 2001-10. [Bold values indicate statistically significant (at p-value 0.01) trend results. Dark gray shading indicates downward fitted trend. Light gray shading indicates upward fitted trend. p-value, statistical significance level; less than; Wyo., Wyoming; Mont., Montana; NR, not reported; SEE, standard error of estimate] Constituent or property Fitted trend value at start of indicatedtrend-analysis period Fitted trend value at end of indicated trend-analysis period Estimated total percent change during indicated trend-analysis period Tongue River at Monarch, Wyo. (site 1, fig. 1) Trend-analysis period water years 2005-10 Specific conductance Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved Alkalinity Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) Goose Creek below Sheridan, Wyo. (site 2, fig. 1) Trend-analysis period water years 2001-10 Specific conductance Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved Alkalinity Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) Trend-analysis period water years 2005-10 Specific conductance Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved Alkalinity Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents)

36    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 3.  Summary of trend results determined by using ordinary least squares regression (OLS) on time, streamflow, and season for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 2001-10.—Continued [Bold values indicate statistically significant (at p-value 0.01) trend results. Dark gray shading indicates downward fitted trend. Light gray shading indicates upward fitted trend. p-value, statistical significance level; less than; Wyo., Wyoming; Mont., Montana; NR, not reported; SEE, standard error of estimate] Constituent or property Fitted trend value at start of indicatedtrend-analysis period Fitted trend value at end of indicated trend-analysis period Estimated total percent change during indicated trend-analysis period Prairie Dog Creek near Acme, Wyo. (site 3, fig. 1) Trend-analysis period water years 2001-10 Specific conductance 1,270 1,480 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved Alkalinity Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) 1,070 Trend-analysis period water years 2005-10 Specific conductance 1,260 1,480 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved Alkalinity Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) 1,070 Pumpkin Creek near Miles City, Mont. (site 9, fig. 1) Trend-analysis period water years 2005-10 Specific conductance 2,100 Calcium, dissolved NR2 NR2 NR2 Magnesium, dissolved NR2 NR2 NR2 Potassium, dissolved Sodium adsorption ratio Sodium, dissolved Alkalinity Chloride, dissolved Fluoride, dissolved Sulfate, dissolved NR2 NR2 NR2 Solids, dissolved, (sum of constituents) 2,010 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Results not reported because of regression standard error of estimate (SEE) greater than 75 percent.

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds    37 Table 4.  Summary of trend results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Powder River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010. [Bold values indicate statistically significant (at p-value 0.01) trend results. Dark gray shading indicates downward fitted trend. Light green shading indicates upward fitted trend. p-value, statistical significance level; less than; Wyo., Wyoming; Mont., Montana] Constituent or property Fitted trend value at start of water year 1986 (start of period 1) Fitted trend value at end of water year 1995 (end of period 1) Estimated total percent change for period 1 Fitted trend value at start of water year 2001 (start of period 2) Fitted trend value at end of water year 2010 (end of period 2) Estimated total percent change for period 2 Powder River main-stem sites Powder River at Sussex, Wyo. (site 11, fig. 1) Specific conductance 3,120 2,160 2,160 2,340 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) 2,020 1,440 1,440 1,550 Powder River at Arvada, Wyo. (site 12, fig. 1) Specific conductance 3,090 2,170 2,170 2,370 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) 2,050 1,500 1,500 1,560 Powder River at Moorhead, Mont. (site 13, fig. 1) Specific conductance 2,120 1,640 1,640 1,710 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) 1,400 1,100 1,100 1,130

38    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 4.  Summary of trend results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Powder River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010.—Continued [Bold values indicate statistically significant (at p-value 0.01) trend results. Dark gray shading indicates downward fitted trend. Light gray shading indicates upward fitted trend. p-value, statistical significance level; less than; Mont., Montana] Constituent or property Fitted trend value at start of water year 1986 (start of period 1) Fitted trend value at end of water year 1995 (end of period 1) Estimated total percent change for period 1 Fitted trend value at start of water year 2001 (start of period 2) Fitted trend value at end of water year 2010 (end of period 2) Estimated total percent change for period 2 Powder River near Locate, Mont. (site 16, fig. 1) Specific conductance 2,310 1,850 1,850 2,070 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) 1,650 1,300 1,300 1,470 Little Powder River site Little Powder River above Dry Creek, near Weston, Wyo. (site 14, fig. 1) Specific conductance 2,540 2,830 2,830 3,050 Calcium, dissolved Magnesium, dissolved Potassium, dissolved Sodium adsorption ratio Sodium, dissolved "Estimated alkalinity"2 Chloride, dissolved Fluoride, dissolved Sulfate, dissolved 1,210 1,220 1,220 1,320 Solids, dissolved, (sum of constituents) 1,960 2,170 2,170 2,390 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2"Estimated alkalinity" data were developed by selecting either alkalinity or acid neutralizing capacity (ANC), depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods."

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds    39 Table 5.  Summary of trend results determined by using ordinary least squares regression (OLS) on time, streamflow, and season for major-ion constituents and properties for Little Powder River near Broadus, Mont. (site 15) based on analysis of data collected during water years1 2001-10. [Bold values indicate statistically significant (at p-value 0.01) trend results. Dark gray shading indicates downward fitted trend. Light gray shading indicates upward fitted trend. p-value, statistical significance level; less than; Mont., Montana; NR, not reported; greater than] Constituent or property Fitted trend value at start of indi­ cated trend-analysis period Fitted trend value at end of indicated trend-analysis period Estimated total percent change during indicated trend-analysis period Little Powder River near Broadus, Mont. (site 15, fig. 1) Trend-analysis period water years 2005-10 Specific conductance 2,300 3,130 Calcium, dissolved Magnesium, dissolved NR2 NR2 NR2 Potassium, dissolved NR2 NR2 NR2 Sodium adsorption ratio Sodium, dissolved Alkalinity Chloride, dissolved Fluoride, dissolved Sulfate, dissolved Solids, dissolved, (sum of constituents) 1,650 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Results not reported because of nonsignificant relation between constituent and streamflow (p-value 0.05). the absolute value of the difference between trend magnitude for specific conductance and dissolved solids was less than 6. These criteria were met for greater than 80 percent of site and trend-period combinations. Site and trend-period combinations not meeting the criteria had nonsignificant trends for either specific conductance, dissolved solids, or both, and in almost all cases, the 95-percent confidence intervals (presented in tables 4.1-4.4) for the trend magnitude for specific conduc­ tance and dissolved solids strongly overlapped. Thus, general agreement between magnitudes of fitted trends for specific conductance and dissolved solids indicated consistency with chemical processes. In the discussion of trend results, qualitative observations on trend magnitudes sometimes are made. Trend magnitudes were considered to be: large, if the deviation from zero was greater than about 40 percent; moderate, if the deviation from zero was within the range of about 25-40 percent; small, if the deviation from zero was within the range of about 15-25 percent; and minor, if the deviation from zero was within the range of about 0-15 percent. In some cases, when trending was within a small range at low concentrations, moderate and large trend magnitudes (on a percentage basis) qualitatively were considered to be minor or small. In all cases, when the terms "significant" or "significantly" are used, it is in refer­ ence to statistical significance (p-value less than 0.01, unless specifically stated otherwise). Tongue River Watershed Trends for Tongue River at State line (site 4), Tongue River at Tongue River Dam (site 5), Hanging Woman Creek (site 6), Tongue River at Birney Day School (site 7), Otter Creek (site 8), and Tongue River at Miles City (site 10) were determined by using the TSM (table 2, table 4.2), and for Tongue River at Monarch (site 1), Goose Creek (site 2), Prairie Dog Creek (site 3), and Pumpkin Creek (site 9) were determined by using OLS (table 3, table 4.3). Trend results are presented and discussed, on a site-by-site basis, for sites on the main-stem Tongue River and then for sites on Tongue River tributaries. Trend Results for Selected Sampling Sites on the Main-Stem Tongue River Trend results for main-stem Tongue River sites are vari­ able among sites. Trend results for Tongue River at Monarch (site 1; determined by using OLS) indicate generally small but significant increases in median values of calcium, magnesium, alkalinity, chloride, sulfate, specific conductance, and dis­ solved solids during water years 2005-10 (table 3, table 4.2, fig. 4.1). There are no substantial CBM-extraction activities in the site watershed. A factor affecting direct comparison of

40    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds trend results for site 1 (determined by using OLS) in rela­ tion to trend results for other main-stem Tongue River sites (determined by using the TSM) is that the TSM incorporates interannual, seasonal, and short-term information in flowadjustment and trend-analysis procedures that is not accounted for in OLS. Trend results for Tongue River at State line (site 4; determined by using the TSM) indicate a small significant decrease in median specific conductance during period 1 and a moderate significant increase in median chloride concentration during period 2 (table 2; table 4.1; fig. 4.4). ANNC and SEASC coefficients for site 4 (table 4.1) are highly significant and of similar magnitude for most constituents, which indicates that interannual and seasonal effects on concentration and streamflow relations were important in the trend analysis, but neither interannual nor seasonal effects was more strongly dominant. The small significant decrease in median specific conductance during period 1 is associated with nonsignificant decreases in other major ions (except fluoride and SAR) at site 4 during period 1 (table 2). However, data collection at site 4 was sparse during period 1, and the trend results should be used with caution. The pattern of decreases in major-ion constituents and properties, whether statistically significant or nonsignificant, during period 1 is weaker than (in terms of magnitude and significance) but generally directionally con­ sistent with other main-stem Tongue River sites (table 2) and is further discussed in a following paragraph of this section of the report. There are substantial CBM-extraction activities in the site 4 watershed, but a moderate significant increase in median chloride concentration during period 2 is difficult to interpret with respect to those activities. Chloride concentra­ tion in stream water is about one-sixth of the concentration in CBM-produced water for site 4 (table 1.5). Chloride can increase in concentration between CBM-produced water discharges and holding ponds and groundwater beneath hold­ ing ponds (Healy and others, 2008; Healy and others, 2011). Thus, geochemical processes relating to interaction of CBMproduced water with soil and rock materials in holding ponds and ephemeral channels in the site 4 watershed might have affected chloride concentrations. However, significant trends are not indicated for any constituent other than chloride during period 2 for site 4, which contributes to difficulty in interpret­ ing chloride trend results; the chloride trend results should be used with caution. Trends at site 4 and capability to detect trends potentially attributable to CBM-extraction activities during period 2 are affected by several factors, including the following: mean CBM pumping rate in the site 4 watershed is small (about 6 percent) relative to 2001-10 median stream­ flow (fig. 4, table 1.3); annual mean CBM pumping rate in the site 4 watershed increased during 2001-02 then decreased during 2003-10 (fig. 4); and water-quality data for site 4 are less suitable for trend analysis than most other sites to which the TSM was applied. Percent differences in cation and anion balances (table 4.5) indicate less chemical consistency in trend results for site 4 than for other sites, which might indicate that concentration and streamflow relations for site 4 were not well defined by the TSM. Largest potential for CBM-extraction activities to affect site 4 water-quality probably was during water years 2000-02 when streamflow conditions were low and CBM-extraction activities were rapidly increasing (fig. 4). Generally high individual unadjusted and flow-adjusted concentrations of sodium and alkalinity during water years 2000-02 (figs. 8, 9, and 4.4) might indicate short-term effects of CBM-extraction activities; however, there is no strong indication of unresolved trending in FACs of any constituent during water years 2000-02 (fig. 4.4). Thus, it is difficult to confidently determine whether or not CBM-extraction activi­ ties have affected water-quality at site 4, but potential effects of CBM-extraction activities are not strongly indicated. Better determination of possible effects of CBM-extraction activities on water-quality at site 4 might be possible with consistent future water-quality monitoring. Trend results for Tongue River at Tongue River Dam (site 5; determined by using the TSM) indicate generally small significant decreases in median concentrations of calcium, magnesium, potassium, sodium, estimated alkalinity, sulfate, and dissolved solids during period 1, and minor to moderate significant increases in median concentrations of sodium, alka­ linity, and dissolved solids during period 2 (table 2; table 4.1; fig. 4.5). ANNC and SEASC coefficients for site 5 (table 4.1) are highly significant for most constituents. For many con­ stituents (including calcium, magnesium, estimated alkalinity, chloride, sulfate, specific conductance, and dissolved solids), SEASC has stronger magnitude than ANNC, which indicates that seasonal effects on concentration and streamflow relations generally were of greater importance than interannual effects in the trend analysis. Significant or nonsignificant decreases in all major ions are indicated for period 1, a pattern generally consistent with other main-stem Tongue River sites. There are substantial CBM-extraction activities in the site 5 watershed. The moderate significant increase in median sodium, and the small significant increase in estimated alkalinity concentra­ tions during period 2 are consistent with relative differences between stream water and CBM-produced water for site 5 (table 1.5), which might indicate effects of CBM-extraction activities on stream water. Mean sodium concentration in stream water is about one-sixteenth of the concentration in CBM-produced water; mean alkalinity concentration in stream water is about one-sixth of the concentration in CBMproduced water for site 5 (table 1.5). However, Tongue River at State line (site 4) accounts for nearly all of the streamflow contributed to site 5 and significant increases in median values of SAR, sodium, and alkalinity were not indicated for site 4. A factor that might affect differences in trend results between sites 4 and 5 is that annual mean CBM pumping rate in the site 4 watershed peaked in 2002 then decreased during 2003-10 (fig. 4, table 1.3). In contrast, annual mean CBM pumping rate in the site 5 watershed increased by about 50 percent (from 15 to 22 ft3/s; table 1.3) during 2003-08 (primarily because of increased CBM-extraction activities in the intervening watershed between sites 4 and 5). However, the mean CBM pumping rate in the site 5 watershed still is small (about

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds    41 8 percent) relative to 2001-10 median streamflow and only slightly higher than for site 4 (fig. 4). Other factors related to the intervening watershed that also might affect trend results include operations of Tongue River Reservoir, irrigation activities, contributions of saline groundwater, and operations of the Decker coal mine. Typical operations of Tongue River Reservoir capture high streamflows during spring snowmelt runoff when native streamflow would be strongly dominant as opposed to the potential contribution of CBM-produced water. The stored water is then released during summer and fall low-streamflow periods when contributions of CBM-produced water might account for a larger proportion of streamflow. Intuitively, storage and mixing of dilute spring runoff water with more concentrated water during low-streamflow periods would lessen potential effects of CBM-extraction activities during low-streamflow periods in summer and fall. Irriga­ tion activities and groundwater contributions might increase concentrations of most major ions (National Research Coun­ cil, 1989; Cary, 1991). Permitted wastewater discharges from the Decker coal mine that are contributed to the Tongue River upstream from the reservoir and directly to the reservoir also might affect major-ion relations and trend results. Better determination of water-quality effects of factors related to the intervening watershed between sites 4 and 5 might be pos­ sible with more detailed and consistent future water-quality monitoring. Thus, although significant increases in median values of sodium and estimated alkalinity during period 2 are consistent with relative differences between CBM-produced water and stream water, other factors confound confident determination of causes of the observed trends for site 5. FACs and fitted trends for period 2 for site 5 generally are within ranges of those for period 1 before substantial CBM-extraction activities (fig. 4.5). Trend results for Tongue River at Birney Day School (site 7; determined by using the TSM) indicate small to mod­ erate significant decreases in median concentrations of mag­ nesium, potassium, estimated alkalinity, sulfate, and dissolved solids during period 1, and small significant increases in median concentrations of magnesium, alkalinity, and dissolved solids during period 2 (table 2; table 4.1; fig. 4.7). ANNC and SEASC coefficients for site 5 (table 4.1) are highly signifi­ cant for most constituents. For many constituents (including calcium, magnesium, estimated alkalinity, chloride, sulfate, specific conductance, and dissolved solids), SEASC has stronger magnitude than ANNC, which indicates that seasonal effects on concentration and streamflow relations generally were of greater importance than interannual effects in the trend analysis. Significant or nonsignificant decreases in all major ions are indicated for period 1, a pattern generally consistent with other main-stem Tongue River sites. There are substantial CBM-extraction activities in the site 7 watershed; mean CBM pumping rate was about 9 percent of 2001-10 median stream­ flow (table 1.3). The significant increase in median estimated alkalinity concentration during period 2 is consistent with relative differences between stream water and CBM-produced water for site 7 (table 1.5), which might provide indication of effects of CBM-extraction activities on stream water. Mean alkalinity concentration in stream water is one-sixth of the concentration in CBM-produced water relative to stream water at site 7 (table 1.5). Although not detected as significant for site 7, magnitude of increasing trend for median sodium concentration (50 percent, 95-percent confidence interval 27-77 percent) for site 7 generally was similar to a significant increasing trend for median sodium concentration (36 percent, 95-percent confidence interval 24-50 percent) for Tongue River at Tongue River Dam (site 5; table 4.1). Site 5 accounts for nearly all of the streamflow contributed to site 7, which accounts for similarities in trend results between sites 5 and 7. Further, the site 5 and 7 watersheds have similar amounts of CBM-extraction activities. Differences in trend results between sites 5 and 7 include a small significant increase in median magnesium concentration during period 2 for site 7, which was not detected for site 5. FACs and fitted trends for period 2 for site 7 generally are within ranges of those for period 1 before substantial CBM-extraction activities. Trend results for Tongue River at Miles City (site 10; determined by using the TSM) indicate small significant decreases in median concentrations of magnesium, chloride, sulfate, and dissolved solids during period 1, and a small significant increase in median chloride concentration dur­ ing period 2 (table 2; table 4.1; fig. 4.10). ANNC and SEASC coefficients for site 5 (table 4.1) are highly significant for most constituents. SEASC had stronger magnitude than ANNC for all constituents except fluoride, which indicates that seasonal effects on concentration and streamflow relations gener­ ally were of greater importance than interannual effects in the trend analysis. Significant or nonsignificant decreases in all major ions are indicated for period 1, a pattern generally consistent with other main-stem Tongue River sites. There are substantial CBM-extraction activities in the site 10 watershed, but the significant increase in median chloride concentration during period 2 is difficult to interpret with respect to those activities. Chloride concentration in stream water is about one-fifth of the concentration in CBM-produced water for site 10 (table 1.5). Chloride can increase in concentration between CBM-produced water discharges and holding ponds and groundwater beneath holding ponds (Healy and others, 2008; Healy and others, 2011). Thus, geochemical processes relating to interaction of CBM-produced water with soil and rock materials in holding ponds and ephemeral channels in the site 10 watershed might have affected chloride concentra­ tions. However, significant trends are not indicated for any constituent other than chloride during period 2 for site 10, which contributes to difficulty in interpreting chloride trend results; the chloride trend results should be used with caution. Site 10 is a long distance (about 142 river miles) downstream from Tongue River at Birney Day School (site 7) and also from locations of CBM-extraction activities in the Tongue River watershed. Site 7 accounts for nearly all of the stream­ flow contributed to site 10, but intervening irrigation activities and streamflow contributions from plains tributaries might strongly affect differences in water quality between sites 7 and

42    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds 10. Mean annual streamflow decreases by about 10 percent between sites 7 and 10, largely because of irrigation consump­ tive use. FACs and fitted trends for period 2 for site 10 gener­ ally are within ranges of those for period 1 before substantial CBM-extraction activities (fig. 4.10). A pattern of decreases, whether statistically significant or nonsignificant, in major-ion concentrations during period 1 generally was consistent among main-stem Tongue River sites (table 2), but potential causes of the pattern were unknown. Because of the unusual circumstance, this issue was inves­ tigated as thoroughly as possible given available data. Data for Tongue River at Tongue River Dam (site 5), which had the most complete representation of any main-stem site for period 1, were investigated to determine whether the TSM flow-adjustment and trend-analysis procedures provided accurate results for main-stem sites during period 1. Waterquality data collected during water years 1986-88 (near the start of period 1) and during water years 1993-95 (near the end of period 1) at generally similar streamflows (within the interquartile range for site 5 continuous-record daily mean streamflows) were compiled and statistically summarized (table 1.6). The Wilcoxon rank-sum test was used to determine whether median major ion concentrations were statistically higher (p-value less than 0.05; alpha level commonly used for the test) during water years 1986-88 than during wateryears 1993-95 in samples collected at similar streamflow conditions. Statistical summaries and results of the Wilcoxon rank-sum test (table 1.6) indicated the following: the median concurrently-measured streamflow (258 ft3/s) for 15 samples collected during water years 1986-88 was slightly higher than but not statistically different from the median stream­ flow (197 ft3/s) for 17 samples collected during water years 1993-95; median concentrations of all major ions were higher in samples collected during water years 1986-88 than in samples collected during water years 1993-95; and differ­ ences in median values between the two periods were statisti­ cally significant for specific conductance, magnesium, SAR, sodium, fluoride, and sulfate. These results were judged to generally confirm that the TSM flow-adjustment and trendanalysis procedures provided accurate results for main-stem sites during period 1. For main-stem Tongue River sites analyzed by using the TSM and downstream from substantial CBM-extraction activities [Tongue River at State line (site 4), Tongue River at Tongue River Dam (site 5), Tongue River at Birney Day School (site 7), and Tongue River at Miles City (site 10)], significant or nonsignificant decreases in most constituents are indicated for period 1. For period 2 for these sites, the TSM trend results do not allow confident conclusions concerning detection of effects of CBM-extraction activities on stream water quality. Detection of significant trends in major-ion con­ stituents and properties for period 2 generally was infrequent, and direction, significance, and magnitudes of fitted trends were not strongly consistent with relative differences between stream water and CBM-produced water. The TSM indicated significant or large magnitude increases in median values of SAR, sodium, and alkalinity for period 2 for sites 5 and 7, which are consistent with relative differences between stream water and CBM-produced water and might indicate potential CBM effects. However, other factors, including operations of Tongue River Reservoir, irrigation activities, contribu­ tions of saline groundwater, and operations of the Decker coal mine, confound confident determination of causes of detected significant trends for sites 5 and 7. For all main-stem Tongue River sites, FACs and fitted trends for period 2 generally are within ranges of those for period 1 before substantial CBMextraction activities. Trend Results for Selected Sampling Sites on Tongue River Tributaries Trend results for Tongue River tributary sites are variable among sites. Trend results for Goose Creek (site 2; determined by using OLS) do not indicate any significant trends during water years 2001-10 or during water years 2005-10 (table 3; table 4.2; fig. 4.2). There are no substantial CBM-extraction activities in the site 2 watershed. Trend results for Prairie Dog Creek (site 3; determined by using OLS) indicate generally small to large significant increases in median values of magnesium, SAR, sodium, alka­ linity, chloride, sulfate, specific conductance, and dissolved solids during water years 2001-10 and similar magnitude sig­ nificant increases in SAR, sodium, chloride, sulfate, specific conductance, and dissolved solids during water years 2005-10 (table 3, table 4.3, fig. 4.3). There are substantial CBM-extrac­ tion activities in the site 3 watershed; CBM pumping rate was about 35 percent of 2001-10 median streamflow (table 1.3). Significant increases in median values of SAR, sodium, alkalinity, and chloride are consistent with relative differences between stream water and CBM-produced water for site 3; these constituents are much lower in stream water relative to CBM-produced water for site 3 (table 1.5). However, signifi­ cant increases in median concentrations of magnesium and especially sulfate are not consistent with relative differences between CBM-produced water and stream water. Magnesium and sulfate are about 40 and 73 times, respectively, higher in stream water relative to CBM-produced water for site 3 (table 1.5). Magnesium and sulfate can increase in concentra­ tion between CBM-produced water discharges and holding ponds, groundwater beneath holding ponds, and ephemeral channels (Healy and others, 2008; Healy and others, 2011; Patz and others, 2004). Thus, geochemical processes relat­ ing to interaction of CBM-produced water with soil and rock materials in holding ponds and ephemeral channels in the site 3 watershed might have affected magnesium and sulfate concentrations. Trend results for Hanging Woman Creek (site 6; deter­ mined by using the TSM) indicate a small significant increase in median potassium concentration during period 1, and a small significant increase in median estimated alkalinity concentration during period 2 (table 2; table 4.1; fig. 4.6).

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds    43 ANNC and SEASC coefficients for site 6 (table 4.1) are highly significant for most constituents. ANNC had stronger magni­ tude than SEASC for most constituents, which indicates that interannual effects on concentration and streamflow relations generally were of greater importance than seasonal effects in the trend analysis. Further, ANNC and SEASC coefficients are positive for most major-ion constituents and properties, which indicates that constituent concentrations tended to be higher during higher streamflow conditions. The pattern of generally positive ANNC and SEASC coefficients is unusual among sites in the Tongue and Powder River watersheds to which the TSM was applied. Sites exhibiting the pattern in all cases are char­ acterized by ephemerality. Accumulation of salts in ephemeral channels and stream banks during zero-streamflow periods and subsequent dissolution and mobilization of salts dur­ ing wetter periods might contribute to the pattern. Site 6 had periods of zero streamflow in about 68 percent of years with continuous streamflow records during water years 1980-2010. There are substantial CBM-extraction activities in the site 6 watershed; mean annual volume of CBM-produced water was about 700 percent of median annual streamflow volume during period 2 (table 1.3). The significant increase in estimated alka­ linity concentration during period 2 for site 6 is consistent with relative differences between stream water and CBM-produced water, but the significant increase in estimated alkalinity is difficult to interpret with respect to CBM-extraction activities. Relative differences between stream water and CBM-produced water for site 6 generally are smaller than most other sites and stream water for site 6 has slightly higher ionic strength than CBM-produced water (fig. 4). Significant changes during period 2 for site 6 were not indicated for any constituent other than "estimated alkalinity." FACs and fitted trends for period 2 for site 6 generally are within ranges of those for period 1 before substantial CBM-extraction activities. Trend results for Otter Creek (site 8; determined by using the TSM) indicate generally small significant decreases in median values of sulfate, specific conductance, and dissolved solids during period 1, and small to moderate significant increases in median values of estimated alkalinity, sulfate, specific conductance, and dissolved solids during period 2 (table 2; table 4.1; fig. 4.8). ANNC and SEASC coefficients for site 8 (table 4.1) generally are nonsignificant or of small mag­ nitude, indicating that interannual and seasonal effects did not strongly affect concentration and streamflow relations. How­ ever, as for Hanging Woman Creek (site 6), ANNC and SEASC coefficients are positive for most major-ion constituents and properties for site 8, which also exhibits ephemerality. Site 8 had periods of zero streamflow in about 43 percent of years with continuous streamflow records during water years 1980-2010. There are no substantial CBM-extraction activi­ ties in the site 8 watershed. Thus, the observed significant trends in periods 1 and 2 illustrate large temporal variability in water quality in plains streams in Montana and Wyoming that are affected by complex interactions between surface water, groundwater, and geologic materials in a semiarid environment (Lambing and Cleasby, 2006; Clark, 2012; Clark and Mason, 2007). Trend results for Pumpkin Creek (site 9; determined by using OLS) indicate large significant increases in median values of potassium, sodium, alkalinity, chloride, specific conductance, and dissolved solids during water years 2005-10 (table 3; table 4.2; fig. 4.9). There are no substantial CBMextraction activities in the site 9 watershed. Site 9 is strongly ephemeral and had periods of zero-streamflow in 100 percent of years with continuous streamflow records during water years 1980-2010. Trend results for site 9 were not deter­ mined by using the TSM and thus there was no accounting for interannual effects on concentration and streamflow rela­ tions. Unusual interannual effects (as evidenced by generally positive ANNC coefficients determined by using the TSM) indicated for the ephemeral tributaries Hanging Woman Creek (site 6) and, to a lesser extent, Otter Creek (site 8) might also affect concentration and streamflow relations at the highly ephemeral site 9. Streamflow conditions generally were lower near the start of water years 2005-10 and higher near the end of water years 2005-10. If interannual effects on concentra­ tion and streamflow relations for site 9 are indeed positive, not accounting for the effects for this site in particular might have strongly affected trend results. However, available data for site 9 were not sufficient for TSM analysis, and given the short period of analysis and limitations of the OLS procedure, trend results for site 9 should be used with caution. Trend results for Tongue River tributary sites down­ stream from substantial CBM-extraction activities [Prairie Dog Creek (site 3) and Hanging Woman Creek (site 6)] are variable among sites. Significant increases in median values of SAR, sodium, alkalinity, and chloride during period 2 (deter­ mined by using OLS) are consistent with relative differences between stream water and CBM-produced water for site 3. Significant increases in median concentrations of magne­ sium and sulfate during period 2 for site 3 might have been affected by geochemical processes relating to interaction of CBM-produced water with soil and rock materials in holding ponds and ephemeral channels in the site 3 watershed. Thus, CBM-extraction activities might have affected the observed significant increases in some major-ion constituents and prop­ erties for site 3. The significant increase in estimated alkalin­ ity concentration during period 2 is consistent with relative differences between stream water and CBM-produced water for site 6, but the significant increase in estimated alkalinity is difficult to interpret with respect to CBM-extraction activities. Relative differences between stream water and CBM-produced water for site 6 generally are smaller than most other sites and stream water for site 6 has slightly higher ionic strength than CBM-produced water (fig. 4). Significant changes during period 2 for site 6 were not indicated for any constituent other than "estimated alkalinity." FACs and fitted trends for period 2 for site 6 generally are within ranges of those for period 1 before substantial CBM-extraction activities.

44    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Powder River Watershed Water-quality trends for Powder River at Sussex (site 11), Powder River at Arvada (site 12), Powder River at Moorhead (site 13), Little Powder River above Dry Creek (site 14), and Powder River near Locate (site 16) were determined by using the TSM (table 4.4), and for Little Powder River near Broadus (site 15) were determined by using OLS (table 4.5). Trend results are presented and discussed, on a site-by-site basis, for sites on the main-stem Powder River and then for sites on the Little Powder River. Trend Results for Selected Sampling Sites on the Main-Stem Powder River Trend results for main-stem Powder River sites are vari­ able among sites. Trend results for Powder River at Sussex (site 11; determined by using the TSM) indicate generally moderate to large significant decreases in median values of potassium, SAR, estimated alkalinity, chloride, fluoride, and dissolved solids during period 1, and small to large significant increases in median concentrations of potassium, chloride, and fluoride during period 2 (table 4; table 4.3; fig. 4.11). ANNC and SEASC coefficients for site 11 (table 4.3) are highly sig­ nificant for most constituents. For most constituents (and espe­ cially potassium, SAR, sodium, chloride, and fluoride), ANNC has stronger magnitude than SEASC, which indicates that interannual effects on concentration and streamflow relations generally were of greater importance than seasonal effects in the trend analysis. Although there are no substantial CBMextraction activities in the site watershed, discussion of causes of significant fitted trends for site 11 is relevant to understand­ ing trend patterns at main-stem Powder River sites that are downstream from site 11 that have substantial CBM-extraction activities in their watersheds. Site 11 is the first main-stem Powder River site downstream from the Salt Creek oil field. Reinjection of oil brine began in 1990 (Lindner-Lunsford and others, 1992) and affects changes in major ions during period 1. Salt Creek oil brine is strongly sodium chloride type; how­ ever, alkalinity concentrations also are much higher relative to Powder River water (Cary, 1991; Boelter and others, 1992). Before the oil-brine reinjection, unadjusted and flow-adjusted concentrations of some major ions (including sodium, chlo­ ride, and alkalinity) were high and highly variable (figs. 10A, 11A, 4.11). After oil-brine reinjection, sodium, chloride, and alkalinity concentrations decreased sharply at site 11 with near complete response by water year 1992. Calcium FACs increased because dilution of stream water by calcium-poor oil brine ceased (fig. 4.11). The significant decreases in sodium and estimated alkalinity associated with the oil-brine reinjec­ tion (figs. 10A, 11A; 4.11) were accompanied by decreases in variability of unadjusted and flow-adjusted concentrations (fig. 11A) during water years 1992-2000. For sodium, vari­ ability in unadjusted concentrations increased during water years 2001-07 (fig. 10A), in association with low-streamflow conditions prevalent in the Powder River watershed (fig. 7). However, the TSM results indicate that when streamflow variability is accounted for, median sodium concentration represented by the fitted trend (fig. 4.11) and variability of sodium FACs generally were similar, indicating general stationarity in sodium concentrations, during the time period following oil-brine reinjection (water years 1992-2010). For estimated alkalinity, the fitted trend as well as unadjusted and flow-adjusted concentrations indicate general stationarity during the time period following oil-brine reinjection. Dif­ ferences in patterns of unadjusted concentrations between sodium and estimated alkalinity during water years 2001-07 probably relate to differences in chemical properties. Sodium is conservative and tends to remain in solution within a large range of water-quality and ionic-strength conditions (Hem, 1985). Alkalinity is much less conservative and can precipitate from solution (primarily as calcium and magnesium carbonate minerals; Hem, 1985) in high ionic strength conditions typi­ cally associated with low-streamflow conditions. Thus, during water-years 2001-07, high estimated alkalinity concentrations might have been limited by mineral precipitation in pres­ ence of relatively higher calcium concentrations (in relation to water-quality conditions before the Salt Creek oil-brine reinjection). Differences between determinations of estimated alkalinity for period 1 (when ANC predominantly accounted for the assigned estimated alkalinity values) and period 2 (when alkalinity predominantly accounted for the assigned estimated alkalinity values) probably did not affect patterns in estimated alkalinity before and after oil-brine reinjection. Largest differences between patterns in estimated alkalinity before and after oil-brine reinjection are associated with higher concentrations, generally from about the median concentration to the annual maximum concentrations. Estimated alkalinity concentrations for site 11 are inversely related to streamflow (as evidenced by negative ANNC and SEASC coefficients; table 4.3) and will tend to be high when streamflow is low. However, suspended sediment concentrations, which account for differences between ANC and alkalinity measurements, generally tend to be low when streamflow is low and thus probably did not strongly affect high estimated alkalinity con­ centrations. The significant increases in median concentrations of potassium, chloride, and fluoride (with trend magnitudes of 28, 44, and 20 percent, respectively) for site 11 during period 2 are unrelated to CBM-extraction activities and investigation of possible causal factors was beyond the scope of this study. Patterns in trend results for site 11 (upstream from substantial CBM-extraction activities) are relevant for comparison with main-stem Powder River sites downstream from site 11 and also downstream from substantial CBM-extraction activities. For period 1, trend results for Powder River at Arvada (site 12; determined by using the TSM) indicate a small significant increase in median calcium concentration, and moderate to large significant decreases in median values of SAR, sodium, estimated alkalinity, chloride, fluoride, specific conductance, and dissolved solids (table 4; table 4.3; fig. 4.12). For period 2, trend results indicate generally large significant

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds    45 increases in median values of potassium, SAR, sodium, esti­ mated alkalinity, chloride, and fluoride, and small significant decreases in median concentrations of calcium, magnesium, and sulfate (table 4; table 4.3; fig. 4.12). ANNC and SEASC coefficients for site 12 (table 4.3) are highly significant for most constituents. For most constituents (especially potassium, SAR, sodium, estimated alkalinity, chloride, and fluoride), ANNC has stronger magnitude than SEASC, which indicates that interannual effects on concentration and streamflow relations generally were of greater importance than seasonal effects in the trend analysis. Patterns in trend results for site 12 for period 1 are consistent with those of Powder River at Sussex (site 11) and also indicate effects of the Salt Creek oilbrine reinjection. There are substantial CBM-extraction activi­ ties in the site 12 watershed; mean CBM pumping rate was 26 percent of 2001-10 median streamflow (table 1.3). Sig­ nificant trends (increases and decreases) in median values of calcium, magnesium, SAR, sodium, estimated alkalinity, and sulfate are consistent with relative differences between stream water and CBM-produced water for site 12 (table 1.5). Similar significant trends in these constituents during period 2 are not indicated for site 11, which is upstream from CBM-extraction activities. Also, the 95-percent confidence intervals of the trend magnitudes of calcium, SAR, and alkalinity for site 12 do not overlap with confidence intervals of those constituents for site 11 (table 4.3). The 95-percent confidence interval of the trend magnitudes of sodium and sulfate for site 12 only slightly overlap with the confidence intervals of those con­ stituents for site 11. Thus, patterns in trend results for period 2 for site 12 are much different from site 11 and consistent with relative differences between stream water and CBM-produced water, with the exception of the significant increase in median chloride concentration, which is similar between sites 12 and 11. Chloride concentration is higher in stream water relative to CBM-produced water for site 12 and based on this relation, chloride concentration might have been expected to decrease during period 2. However, trend results for site 12 indicate a significant increase in chloride concentration during period 2 (37 percent; 95-percent confidence interval 21-55 percent) similar to a significant increase in chloride concentration indi­ cated for site 11 (44 percent; 95-percent confidence interval 24-67 percent). The significant increase in chloride concen­ tration for site 11 during period 2 might have contributed to the significant increase in chloride concentration for site 12 during period 2. Also, chloride can increase in concentration between CBM-produced water discharges and holding ponds and groundwater beneath holding ponds (Healy and others, 2008; Healy and others, 2011). Thus, geochemical processes relating to interaction of CBM-produced water with soil and rock materials in holding ponds and ephemeral channels in the site 12 watershed might have affected chloride concentrations. Significant decreases in median concentrations of calcium and magnesium during period 2 for site 12 might have been affected by dilution by calcium-and magnesium-poor CBMproduced water and also increased precipitation of carbonate minerals in the presence of higher alkalinity concentration. Differences in patterns of fitted trends, and unadjusted and flow-adjusted concentrations of estimated alkalinity between sites 12 and 11 also provides evidence of differences in waterquality characteristics between the sites during period 2 and potential effects of CBM-extraction activities on site 12 water quality (figs. 11A, 11B, 4.11, 4.12). Before the start of the oil-brine reinjection in 1990 (Lindner-Lunsford and others, 1992), unadjusted and flow-adjusted estimated alkalinity con­ centrations at site 12 were high and unadjusted concentrations were highly variable (characterized by generally high annual maxima; fig. 11B), similar to site 11. After the response to the oil-brine reinjection, unadjusted and flow-adjusted concentra­ tions of estimated alkalinity at both sites indicated general stationarity in estimated alkalinity concentrations during water years 1992-2000. However, during period 2, unadjusted and flow-adjusted estimated alkalinity concentrations at site 12 increased, unadjusted concentrations became more variable (generally similar to variability in unadjusted concentrations before oil-brine reinjection), and the TSM detected a signifi­ cant increase in median estimated alkalinity (fig. 11B). Unad­ justed and flow-adjusted estimated alkalinity concentrations at site 11 indicated general stationarity during period 2, similar to the period water years 1992-2000, and the TSM did not detect a significant trend in median estimated alkalinity (fig. 11A). Thus, during period 2, water-quality characteristics of the Powder River differed between the site upstream from and the first site downstream from substantial CBM-extraction activi­ ties, which provide evidence of potential effects of CBMextraction activities on Powder River water quality at site 12. FACs and fitted trends for period 2 for site 12 generally are within ranges of those for period 1 before substantial CBMextraction activities. In the Powder River watershed, period 1 encompasses time periods before and after the Salt Creek oil-brine reinjection. It is notable that the estimated alkalinity fitted trend and unadjusted and flow-adjusted concentrations (figs. 11B, 4.12) at the end of period 2 were similar in mag­ nitude to the fitted trend and unadjusted and flow-adjusted concentrations at the start of period 1, which was before the Salt Creek oil-brine reinjection. For period 1, trend results for Powder River at Moorhead (site 13; determined by using the TSM) indicate generally small to moderate significant decreases in median values of potassium, SAR, sodium, estimated alkalinity, chloride, fluoride, specific conductance, and dissolved solids (table 4; table 4.3; fig. 4.13). For period 2, trend results indicate gener­ ally large significant increases in median concentrations of potassium, SAR, sodium, estimated alkalinity, and fluoride, and small significant decreases in median concentrations of calcium and sulfate (table 4; table 4.3; fig. 4.13). ANNC and SEASC coefficients for site 13 (table 4.3) are highly significant for most constituents. For most constituents (and especially potassium, SAR, sodium, estimated alkalinity, chloride, and fluoride), ANNC has stronger magnitude than SEASC, which indicates that interannual effects on concentration and stream­ flow relations generally were of greater importance than seasonal effects in the trend analysis. Patterns in trend results

46    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds for site 12 for period 1 are consistent with those of Powder River at Sussex (site 11) and Powder River at Arvada (site 12), and also indicate effects of the Salt Creek oil-brine reinjection; however, magnitudes of significant trends generally decreased in a downstream direction from site 12 to site 13, probably because of moderating effects of intervening tributary contri­ butions. There are substantial CBM-extraction activities in the site 13 watershed; mean CBM pumping rate was 28 percent of 2001-10 median streamflow (table 1.3). Significant trends during period 2 (increases and decreases) in median values of calcium, SAR, sodium, estimated alkalinity, and sulfate are consistent with relative differences between stream water and CBM-produced water for site 13 (table 1.5). The significant trends during period 2 for site 13 also generally are consistent with significant trends for site 12; however, the significant decrease in median magnesium concentration and the signifi­ cant increase in median chloride concentration during period 2 for site 12 are not indicated for site 13. For constituents with significant trends during period 2 for sites 13 and 12, trend magnitudes generally are similar among the sites, and for all constituents 95-percent confidence intervals for site 13 overlap with those for site 12. However, the magnitude of the signifi­ cant increase in median estimated alkalinity concentration during period 2 for site 13 (75 percent; 95-percent confidence interval 56-97 percent) is larger than for site 12 (51 percent; 95-percent confidence interval 40-64 percent). The differ­ ence in estimated alkalinity trend results for period 2 between sites 12 and 13 might relate to the large data gap (water years 1990-2001) in the site 13 dataset, which might have affected the capability of the TSM to define concentration and stream­ flow relations after Salt Creek oil-brine reinjection as accu­ rately for site 13 as for site 12. Similar to site 12, the 95-per­ cent confidence intervals of the trend magnitudes of SAR and alkalinity for site 13 do not overlap with confidence intervals of those constituents for site 11 (table 4.3). Further, differences in patterns of fitted trends and unadjusted and flow-adjusted concentrations of estimated alkalinity between sites 13 and 11 (figs. 11A, 11C, 4.11, 4.13) are similar to differences between sites 11 and 12 discussed in the previous paragraph of this section of the report. Thus, significant trends during period 2 for site 13 are: consistent with relative differences between stream water and CBM-produced water (table 1.5); similar to those for site 12; and much different from those for site 11 (table 4). These factors indicate potential effects of CBMextraction activities on site 13 water quality. FACs and fitted trends for period 2 for site 13 generally are within ranges of those for period 1 before substantial CBM-extraction activi­ ties. It is notable that the estimated alkalinity fitted trend and unadjusted and flow-adjusted concentrations (figs. 11C, 4.13) at the end of period 2 were similar in magnitude to the fitted trend and unadjusted and flow-adjusted concentrations at the start of period 1, which was before the Salt Creek oil-brine reinjection. For period 1, trend results for Powder River near Locate (site 16; determined by using the TSM) indicate generally small to moderate significant decreases in median values of potassium, SAR, sodium, estimated alkalinity, chloride, fluoride, specific conductance, and dissolved solids (table 4; table 4.3; fig. 4.16). For period 2, trend results indicate gener­ ally moderate significant increases in median concentrations of potassium, SAR, sodium, estimated alkalinity, chloride, and fluoride (table 4; table 4.3; fig. 4.16). ANNC and SEASC coefficients for site 16 (table 4.3) are highly significant and of similar magnitude for most constituents, which indicates that interannual and seasonal effects on concentration and stream­ flow relations were important in the trend analysis, but neither interannual nor seasonal effects was more strongly dominant. Patterns in trend results for site 16 for period 1 are consis­ tent with those of Powder River at Sussex (site 11), Powder River at Arvada (site 12), and Powder River at Moorhead (site 13), and also indicate effects of the Salt Creek oil-brine reinjection; however, magnitudes of significant trends gener­ ally decreased in a downstream direction from site 13 to site 16, probably because of moderating effects of intervening tributary contributions, and groundwater and surface-water interactions. Although site 16 is a long distance (greater than 150 mi) downstream from the other main-stem Powder River sites, similarities in significant fitted trends between site 16 and sites 11, 12, and 13 for period 1 provide evidence that factors affecting water quality in the upstream part of the watershed also can affect water quality at site 16; however, other land-use activities in the watershed between sites 13 and 16 also might affect water quality downstream. There are substantial CBM-extraction activities in the site 16 watershed; mean CBM pumping rate was 34 percent of 2001-10 median streamflow (table 1.3). Some of the significant trends dur­ ing period 2 (including increases in median values of SAR, sodium, and estimated alkalinity) are consistent with relative differences between stream water and CBM-produced water for site 16 (table 1.5). The significant trends during period 2 for site 16 also generally are consistent with significant trends for site 13. However, magnitudes of significant trends gener­ ally decreased in a downstream direction from site 13 to site 16. Further, a significant decrease in median calcium concen­ tration during period 2 for site 13 is not indicated for site 16, and a significant increase in median chloride concentration for site 16 during period 2 is not indicated for site 13. Causes of differences in significant trends during period 2 between sites 16 and 13 are unknown, but might relate to effects of contribu­ tions from intervening tributaries, groundwater and surfacewater interactions, or geochemical interaction of stream water with geologic materials in the long channel reach between the sites. Thus, some significant trends during period 2 for site 16 are consistent with relative differences between stream water and CBM-produced water (table 1.5) and also are similar to, but generally of smaller magnitude than trends for site 13. Unlike sites 12 and 13, fitted trends for all constituents for site 16 for period 2 have 95-percent confidence intervals that overlap with confidence intervals for site 11. Trend charac­ teristics for site 16 might indicate potential effects of CBMextraction activities on site 16 water quality, but of smaller magnitude than potential effects on sites 12 and 13. FACs

Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds    47 and fitted trends for period 2 for site 16 generally are within ranges of those for period 1 before substantial CBM-extraction activities. It is notable that the estimated alkalinity fitted trend and unadjusted and flow-adjusted concentrations (figs. 11C, 4.13) at the end of period 2 were similar in magnitude to the fitted trend and unadjusted and flow-adjusted concentrations at the start of period 1, which was before the Salt Creek oil-brine reinjection. For main-stem Powder River sites analyzed by using the TSM [Powder River at Sussex (site 11), Powder River at Arvada (site 12), Powder River at Moorhead (site 13), and Powder River near Locate (site 16)], significant or large magnitude decreases in median values of SAR, sodium, estimated alkalinity, chloride, fluoride, specific conductance, and dissolved solids are indicated for period 1. Patterns in trend results for period 1 for main-stem Powder River sites are consistent with effects of Salt Creek oil-brine reinjection that started in 1990. Trend results for all of the main-stem Pow­ der River sites downstream from substantial CBM-extraction activities (sites 12, 13, and 16) indicate evidence of potential effects of CBM-extraction activities on stream water quality, although evidence is stronger for sites 12 and 13 than for site 16. Evidence in support of potential CBM effects includes significant increases during period 2 in median values of SAR, sodium, and estimated alkalinity for sites 12, 13, and 16 that are consistent with relative differences between stream water and CBM-produced water. Significant increases during period 2 in median values of these constituents are not indicated for site 11 upstream from substantial CBM-extraction activities. For sites 12, 13, and 16, mean CBM pumping rates were 26, 28, and 34 percent of 2001-10 median streamflows, respec­ tively. In interpreting the trend results, it is notable that the fit­ ted trends evaluate changes in median concentrations and that changes in the median concentrations that might be attributed to CBM-extraction activities probably are more strongly evi­ dent during low-flow conditions than during average to highflow conditions. This observation is relevant in assessing trend results in relation to specific water-quality concerns, including effects of water-quality changes on irrigators and effects on stream biota and ecology. Trend Results for Selected Sampling Sites on the Little Powder River Trend results for Little Powder River sites are variable among sites. Trend results for Little Powder River above Dry Creek (site 14; determined by using the TSM) indicate minor significant increase in median fluoride concentration during period 1 and large significant increases in median chloride concentration during period 1 and period 2 (table 4; table 4.3; fig. 4.14). ANNC coefficients for site 14 generally are positive and nonsignificant (table 4.3). SEASC coefficients are nega­ tive and highly significant for most constituents. The ANNC and SEASC coefficients indicate unusual concentration and streamflow relations for site 14, and seasonal effects on the relations were more important than interannual effects in the trend analysis. Site 14 exhibits ephemerality (with periods of zero streamflow in about 52 percent of years with continuous streamflow records during water years 1980-2010), which might have contributed to the unusual patterns in ANNC and SEASC coefficients. There are substantial CBM-extraction activities in the site 14 watershed; mean CBM pumping rate was about 360 percent of 2001-10 median streamflow (table 1.3). CBM-extraction activities in the site 14 watershed started in 1989, much earlier than most other sites, and might affect trend results during period 1 and period 2. Annual mean CBM pumping rates during period 1 were small (ranging from 0.05 to 0.50 ft3/s during water years 1989-95; table 1.3), but because of the low-streamflow characteristics of site 14, the small CBM pumping rates were in some years large in relation to annual median streamflow (for example, 84 percent in water year 1991). Significant increases in median chloride concen­ tration during period 1 and period 2 are difficult to interpret, but are not consistent with relative differences between CBMproduced water and stream water for site 14 (table 1.5). Chlo­ ride can increase in concentration between CBM-produced water discharges and holding ponds and groundwater beneath holding ponds (Healy and others, 2008; Healy and others, 2011). Thus, geochemical processes relating to interaction of CBM-produced water with soil and rock materials in holding ponds and ephemeral channels in the site 14 watershed might have affected chloride concentrations. However, significant trends are not indicated for any other constituent, except fluoride, during either period 1 or period 2 for site 14, which contributes to difficulty in interpreting chloride trend results; the chloride trend results should be used with caution. With the exception of chloride, FACs and fitted trends for period 2 for site 14 are within ranges of those for period 1 before sub­ stantial CBM-extraction activities. Trend results for Little Powder River near Broadus (site 15; determined by using OLS) indicate moderate to large significant increases in median values of specific conductance, sodium, chloride, sulfate, and dissolved solids during water years 2005-10 (table 5; table 4.4; fig. 4.15). Site 15 exhib­ its ephemerality (with periods of zero streamflow in about 35 percent of years with continuous streamflow records during water years 1980-2010) and might have unusual concentra­ tion and streamflow relations similar to Little Powder River above Dry Creek (site 14). There are substantial CBMextraction activities in the site 15 watershed, but there are no additional CBM-extraction activities in the intervening watershed between sites 14 and 15. Significant increases in sodium, chloride, and sulfate during water years 2005-10 are not consistent with relative differences between CBM-pro­ duced water and stream water for site 15 (table 1.5). Sodium, chloride, and sulfate can increase in concentration between CBM-produced water discharges and holding ponds, ground­ water beneath holding ponds, and ephemeral channels (Healy and others, 2008; Healy and others, 2011; Patz and others, 2004). Thus, geochemical processes relating to interaction of CBM-produced water with soil and rock materials in holding

48    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds ponds and ephemeral channels in the site 15 watershed might have affected concentrations of these constituents. However, independent from potential effects of CBM-extraction activi­ ties, plains streams in Montana and Wyoming are affected by complex interactions between surface water, groundwater, and geologic materials in a semiarid environment and can exhibit large temporal variability in major-ion constituents (Lambing and Cleasby, 2006; Clark, 2012; Clark and Mason, 2007). Trend results for Little Powder River sites downstream from substantial CBM-extraction activities [Little Powder River above Dry Creek (site 14) and Little Powder River near Broadus (site 15)] do not allow confident conclusions concerning detection of effects of CBM-extraction activi­ ties on stream water quality. CBM-extraction activities in the site 14 watershed started much earlier than most other sites and might potentially affect trend results during period 1 and period 2. Significant increases in median chloride concen­ tration during period 1 and period 2 for site 14 are difficult to interpret, but are not consistent with relative differences between CBM-produced water and stream water for site 14 (table 1.5). Geochemical processes relating to interaction of CBM-produced water with soil and rock materials in holding ponds and ephemeral channels in the site 14 watershed might have affected chloride concentrations. However, significant trends are not indicated for any constituent other than chloride during either period 1 or period 2 for site 14, which contrib­ utes to difficulty in interpreting chloride trend results; the chloride trend results should be used with caution. Significant increases in sodium, chloride, and sulfate during water years 2005-10 for site 15 are not consistent with relative differences between CBM-produced water and stream water for site 15 (table 1.5), but also might have been affected by interaction of CBM-produced water with soil and rock materials. However, independent from potential effects of CBM-extraction activi­ ties, plains streams in Montana and Wyoming can exhibit large temporal variability in major-ion constituents, which contrib­ utes to difficulty in interpreting trend results for site 15. Selected Trend Results in Relation to Results of Previous Studies This section of the report presents selected trend results from this study and discusses those results in relation to find­ ings of previous studies. Comparisons are made between trend results from this study and those of Clark (2012). Trend results from this study also are discussed with respect to results of Kinsey and Nimick (2011) relating to potential qualitative effects of CBM-produced water on stream water. Clark (2012) analyzed trends in flow-adjusted concentra­ tions for 40 sites in the Tongue and Powder River watersheds (and also in the Cheyenne and Belle Fourche River watersheds; not shown in fig. 1) by using the robust seasonal Kendall test. For sites analyzed in this study and by Clark (2012) for period 2, statistically significant trend results (p-value less than 0.01) determined by using the TSM or statistically significant trend results (p-value less than 0.05) of Clark (2012) determined by using the seasonal Kendall test are presented in table 6. Significant trend results for potassium and fluoride determined by using the TSM are not included in table 6 because those constituents were not analyzed by Clark (2012). The TSM trend results generally are similar in direction to trend results determined by using the seasonal Kendall test (Clark, 2012). However, magnitudes and significance of the trend results varied between the trend methods in some cases. An important consideration in evaluating differences between the TSM and seasonal Kendall trend results is that the TSM incorporates interannual and seasonal effects on concentration and stream­ flow relations and allows evaluation (by comparison of ANNC and SEASC coefficients ) of relative contributions of these effects on trend results. The seasonal Kendall analysis does not account for interannual effects on concentration and streamflow relations. Thus, consideration of ANNC and SEASC coefficients and relative contributions of interannual and seasonal effects on trend results is relevant to evaluating differences in trend results between the TSM and the seasonal Kendall test. Trend magnitude and significance for period 2 generally are stronger for the TSM compared to the seasonal Kendall test when ANNC is much more strongly negative than SEASC. Examples of this pattern include the following: chloride for Powder River at Sussex (site 11); SAR and sodium for Powder River at Arvada (site 12); and SAR, sodium, and alkalinity for Powder River at Moorhead (site 13). In these cases, the TSM trend magnitudes are much larger than the trend magnitudes estimated with the seasonal Kendall test and 95-percent confidence intervals about the TSM trends do not encompass or approach the seasonal Kendall trend magnitudes. In contrast, trend magnitudes and significance for period 2 generally are similar among the TSM and the seasonal Kendall test when ANNC is similar to or less strongly negative than SEASC. Examples of this pattern include the following: calcium, alkalinity, and sulfate for site 12; and calcium and sulfate for site 13. In these cases, the trend magnitudes of both methods generally are similar and 95-per­ cent confidence intervals about the TSM trends encompass or approach the seasonal Kendall trend magnitudes. In most of the cases, statistical significance is indicated for both methods. For specific conductance, calcium, and sulfate for Tongue River at State line (site 4), trend magnitude and significance for period 2 are stronger for the seasonal Kendall test compared to the TSM. For site 4, ANNC is similar to SEASC, indicating that interannual and seasonal effects on concentration and stream­ flow relations were of similar importance in the TSM analysis. Thus, incorporation of interannual effects on concentration and streamflow relations in the TSM does not explain differ­ ences between the methods for site 4. Percent differences in cation and anion balances (table 4.5) indicate less chemical consistency in the TSM trend results for site 4 than for other sites, which might indicate that concentration and streamflow relations for site 4 were not well defined by the TSM. The sea­ sonal Kendall analysis of Clark (2012) might have been more sensitive in detecting trends for site 4 for period 2.

Selected Trend Results in Relation to Results of Previous Studies    49 Table 6. Statistically significant trend results determined by using the time-series model (TSM; p-value 0.01) and statistically significant trend results from Clark (2012; p-value 0.05) for trend-analysis period 2 (water years1 2001-10). [Values in parentheses indicate 95-percent confidence intervals. Light gray shading indicates statistical significance at p-value 0.01. Dark gray shading indicates statistical significance at p-value 0.05. p-value, statistical significance level; less than; SEASC, seasonal concentration anomaly; ANNC, annual concentration anomaly; Mont., Montana; Wyo., Wyoming; NR, not reported; greater than] Constituent or property Results determined by using the TSM Results determined by using seasonal Kendall test (Clark, 2012) Estimated total percent change during trend-analysis period p-value for individual trend SEASC coefficient p-value for SEASC coefficient ANNC coefficient p-value for ANNC coefficient Estimated total percent change during trend-analysis period2 p-value for individual trend Tongue River at State line, near Decker, Mont. (site 4, fig. 1) Specific conductance 5 (-2, 12) Calcium 5 (-1, 11) NR3 Chloride 31 (18, 46) Sulfate 2 (-11, 17) NR3 Powder River at Sussex, Wyo. (site 11, fig. 1) Chloride 44 (24, 67) Powder River at Arvada, Wyo. (site 12, fig. 1) Calcium -23 (-29, -16) Magnesium -16 (-23, -8) Sodium adsorption ratio 53 (40, 66) Sodium 39 (25, 54) Alkalinity 51 (40, 64) Chloride 37 (21, 55) Sulfate -17 (-25, -9) Powder River at Moorhead, Mont. (site 13, fig. 1) Calcium -19 (-29, -8) Sodium adsorption ratio 41 (25, 59) Sodium 31 (13, 51) Alkalinity 75 (56, 97) Sulfate -16 (-27, -4) Little Powder River above Dry Creek, near Weston, Wyo. (site 14, fig. 1) Chloride 99 (52, 161) 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Trend magnitudes in Clark (2012) were reported as slopes that reflect relative changes (per year) in units after adjustment for streamflow variability (that is, slopes in fitted trends in flow-adjusted concentrations). For a given site and constituent combination, the slope (per year) was transformed into total percent change during the indicated trend-analysis period by dividing by the median concentration for 2001-10 (reported by Clark, 2012) and multiplying times the number of years in the trend-analysis period. 3p-value for individual trend period not reported because of nonsignificant overall trend analysis (p-value 0.01; table 4.1), as discussed in "Supplement 2: Summary of the Time-Series Model (TSM) as Applied in this Study."

50    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Statistically significant trend results (p-value less than 0.01) determined by using OLS or statistically significant trend results (p-value less than 0.05) determined by using the seasonal Kendall test (Clark (2012) for water years 2001-10 and 2005-10 are presented in table 7. Significant trend results for potassium and fluoride are not included in table 7 because those constituents were not analyzed by Clark (2012). Differ­ ences in results between OLS and the seasonal Kendall test would be expected to be less than between the TSM and the seasonal Kendall test. OLS and the seasonal Kendall test both use parametric regression procedures for defining concentra­ tion and streamflow relations, and neither method accounts for interannual effects. However, OLS and the seasonal Kendall test differ with respect to accounting for seasonal effects on concentration and streamflow relations, and also with respect to the use of parametric (OLS) or nonparametric (seasonal Kendall test) techniques for estimating trend magnitudes and significance. OLS trend results for Tongue River at Monarch (site 1), Goose Creek (site 2), and Prairie Dog Creek (site 3) generally are similar in direction, magnitude, and significance to results of the seasonal Kendall test, with the exception of results for Prairie Dog Creek (site 3) for water years 2001-10 (table 7). For site 2, OLS and the seasonal Kendall test indi­ cated no significant changes during water years 2005-10; thus, no results for site 2 are presented in table 7. For site 3, OLS results for water years 2001-10 are similar to OLS results for water years 2005-10. Also, OLS results for water years 2005- 10 are similar to Clark (2012) for water years 2005-10. How­ ever, seasonal Kendall test results for water years 2001-10 are different from OLS results and also are different from seasonal Kendall test results for water years 2005-10 (table 7). Factors responsible for these differences were not evaluated in detail; however, concentration and streamflow relations in Prairie Dog Creek are complex and affected by interbasin transfers for irrigation. This factor, combined with drought conditions dur­ ing the early part of water years 2001-10 might have affected trend results of OLS, the seasonal Kendall test, or both. Kinsey and Nimick (2011) reported results of two syn­ optic sampling trips, during September 2005 and April 2006, to provide spatially detailed profiles of specific conductance and SAR along the length of the upper Tongue River. A series of calculations were made to project potential increases in specific conductance and SAR that might be attributable to 12 primary discharges of CBM-produced water to the Tongue River upstream from Tongue River Reservoir. Streamflow for Tongue River at State line (site 4) during the September 2005 and April 2006 synoptic sampling trips (195 and 210 ft3/s, respectively) generally was similar to median streamflow during water years 2001-10 (177 ft3/s; table 1.3). Kinsey and Nimick (2011) projected that, at streamflows and discharge rates of CBM-produced water during the synoptic sampling trips, CBM-produced water would increase specific con­ ductance by about 4 percent. Estimated increases in specific conductance because of CBM-produced water (based on actual measurements made during the trips) generally agreed with projected increases, and ranged from about 4-6 percent. Kinsey and Nimick (2011) also projected that for the Septem­ ber 2005 synoptic sampling trip, the 12 primary discharges of CBM-produced water would increase SAR by about 34 per­ cent. The estimated increase in SAR because of CBM-pro­ duced water (based on actual measurements made during the trip) was smaller than the projected increase, and was about 18 percent. SAR data were not available for the April 2006 trip. Results of Kinsey and Nimick (2011) concerning poten­ tial effects of CBM-produced water on stream water cannot be directly compared to the TSM trend results because of funda­ mental differences in analytical approaches and the precise site locations on the Tongue River that were studied. Kinsey and Nimick (2011) investigated patterns in water quality upstream from and downstream from CBM-extraction activities within short time frames and made observations on potential effects of 12 primary discharges of CBM-produced water on spatial differences in water quality. The TSM results provide informa­ tion on long-term temporal changes in water quality that might relate to potential effects of CBM-produced water (contributed from the entire watershed) on stream water quality. However, there are some similarities in general findings of Kinsey and Nimick (2011) and the TSM trend results. Kinsey and Nimick (2011) indicated that projected and estimated increases in spe­ cific conductance because of CBM-produced water for Tongue River upstream from Tongue River Dam at near-median streamflow were small (about 4-6 percent). The TSM trend results indicate a nonsignificant increase in median specific conductance for period 2 for Tongue River at Tongue River Dam (site 5; 1 percent; 95-percent confidence interval -5 to 7 percent). Kinsey and Nimick (2011) indicated that projected and estimated increases in SAR (about 34 and 18 percent, respectively) for Tongue River upstream from Tongue River Dam were relatively larger than increases in specific conduc­ tance. The TSM trend results indicate a significant increase in median SAR for period 2 for site 5 (36 percent; 95-percent confidence interval 24-50 percent). Site 5 is 0.5 mi down­ stream from Tongue River Dam. Factors other than CBMextraction activities (including operations of Tongue River Reservoir, irrigation activities, and operations of the Decker coal mine) might affect the TSM trend results for site 5.

Selected Trend Results in Relation to Results of Previous Studies    51 Table 7.  Statistically significant trend results determined by using ordinary least squares regression (OLS) on time, streamflow, and season (p-value 0.01) and statistically significant trend results from Clark (2012; p-value 0.05). [Values in parentheses indicate 95-percent confidence intervals. Light gray shading indicates statistical significance at p-value 0.01. Dark gray shading indicates statistical significance at p-value 0.05. p-value, statistical significance level; less than; Wyo., Wyoming] Constituent or property Results determined by using OLS Results determined by using seasonal Kendall test (Clark, 2012) Estimated total percent change during trend-analysis period p-value for individual trend Estimated total percent change during trend-analysis period1 p-value for individual trend Tongue River atMonarch, Wyo. (site 1, fig. 1) Trend-analysis period water years 2005-10 Specific conductance 16 (7, 26) Calcium 16 (6, 26) Magnesium 15 (4, 28) Alkalinity 17 (9, 25) Chloride 42 (21, 66) Sulfate 26 (5, 52) Prairie Dog Creek near Acme, Wyo. (site 3, fig. 1) Trend-analysis period water years 2001-10 Specific conductance 17 (7, 28) Magnesium 24 (11, 38) Sodium adsorption ratio 32 (19, 46) Sodium 43 (24, 65) Alkalinity 12 (3, 21) Chloride 52 (34, 74) Sulfate 27 (11, 46) Trend-analysis period water years 2005-10 Specific conductance 17 (5, 32) Magnesium 19 (3, 38) Sodium adsorption ratio 32 (16, 51) Sodium 41 (17, 69) Alkalinity 10 (0, 21) Chloride 57 (36, 82) Sulfate 33 (12, 58) 1Trend magnitudes in Clark (2012) were reported as slopes that reflect relative changes (per year) in units after adjustment for streamflow variability (that is, slopes in fitted trends in flow-adjusted concentrations). For a given site and constituent combination, the slope (per year) was transformed into total percent change during the indicated trend-analysis period by dividing by the median con­ centration for 2001-10 (reported by Clark, 2012) and multiplying times the number of years in the trend-analysis period.

52    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Summary and Conclusions The primary purpose of this report is to present informa­ tion relating to flow-adjusted temporal trends in major-ion constituents and properties for 16 sampling sites in the Tongue and Powder River watersheds based on data collected dur­ ing water years1980-2010. In association with this primary purpose, the report presents background information on water-quality characteristics of the sampling sites and CBMproduced water in the site watersheds, trend analysis methods, streamflow conditions, and factors that affect trend results. The Tongue and Powder River watersheds overlie the Powder River structural basin (PRB) in northeastern Wyoming and southeastern Montana. The PRB contains large deposits of energy resources (coal, oil, natural gas) and, since the late 1800's, extraction activities have been extensive. Limited extraction of coal-bed methane (CBM) from the PRB began in the early 1990's and increased dramatically during the late 1990's and early 2000's. CBM-extraction activities produce discharges of water with high concentrations of dissolved sol­ ids (particularly sodium and bicarbonate ions) relative to most stream water in the Tongue and Powder River watersheds. Water-quality of CBM-produced water (groundwater pumped from coal seams) is of concern because of potential effects on downstream agricultural producers who irrigate soils that can contain large amounts of clay. Another concern with respect to discharge of CBM-produced water to stream channels is effects on aquatic biota; primarily because of potential toxicity of bicarbonate. Water-quality and flow-rate characteristics of CBMproduced water were estimated to allow general comparisons with water-quality and streamflow characteristics of the sampling sites. The information on water-quality and flow-rate characteristics of CBM-produced water in relation to charac­ teristics of streams does not account for effects of disposal, treatment, or other remediation activities on the potential qualitative or quantitative effects of CBM-produced water on receiving streams. For all sites in the Tongue River watershed with substantial CBM-extraction activities in their watersheds [Prairie Dog Creek (site 3), Tongue River at State line (site 4), Tongue River at Tongue River Dam (site 5), Hanging Woman Creek (site 6), Tongue River at Birney Day School (site 7), and Tongue River at Miles City (site 10)], relative differences in individual constituents between CBM-produced water and stream water generally are similar: calcium, magnesium, and sulfate concentrations are higher, and SAR, sodium, alkalinity, and chloride values are lower in stream water than in CBMproduced water. Relations between streamflow and pumping rates of CBM-produced water are variable among sites in the Tongue River watershed. For site 4 mean annual pumping rate of CBM-produced water during water years 2001-10 (here­ inafter referred to as mean CBM pumping rate) was 6 percent of the mean of annual median streamflows during water years 2001-10 (hereinafter referred to as 2001-10 median stream­ flow). For main-stem Tongue River sites 5, 7, and 10, mean CBM pumping rate was 8-12 percent of 2001-10 median streamflow. For plains tributaries (sites 3 and 6), mean CBM pumping rates were 35 and about 700 percent of 2001-10 median streamflows, respectively. Relative differences in individual constituents between CBM-produced water and stream water generally are similar among main-stem Powder River sites with substantial CBMextraction activities in their watersheds [Powder River at Arvada (site 12), Powder River at Moorhead (site 13), and Powder River near Locate (site 16)]: calcium, magnesium, chloride, and sulfate concentrations are higher, and SAR, sodium, and alkalinity values are lower in stream water than in CBM-produced water. Relative differences are similar for Lit­ tle Powder River sites [Little Powder River above Dry Creek (site 14) and Little Powder River near Broadus (site 15)], except sodium concentrations are higher in stream water than in CBM-produced water. Relations between streamflow and pumping rates of CBM-produced water are variable among sites in the Powder River watershed. For main-stem Powder River sites (sites 12, 13, and 16), mean CBM pumping rates were 26, 28, and 34 percent of 2001-10 median streamflows, respectively. For site 14 in the Little Powder River watershed mean CBM pumping rate was about 360 percent of 2001-10 median streamflow. Two parametric trend-analysis methods were used in this study: the time-series model (TSM) and ordinary least squares regression (OLS) on time, streamflow, and season. In this study, the TSM was selected as the preferred trend-analysis method primarily because of detailed analysis of continuous streamflow data that provides better definition of concentration and streamflow relations through time and incorporation of interannual, seasonal, and short-term information in flowadjustment procedures. The TSM was used to analyze trends for 11 of the 16 study sites. For five sites, the data require­ ments of the TSM were not met. In these cases, OLS was used to analyze trends. Two primary 10-year trend-analysis periods were selected. Trend-analysis 10-year period 1 (water years 1986-1995; hereinafter referred to as period 1) was selected to represent variability in major-ion concentrations in the Tongue and Powder River watersheds before potential effects of substantial CBM-extraction activities. Trend analysis 10-year period 2 (water years 2001-10; hereinafter referred to as period 2) was selected because it encompassed substan­ tial CBM-extraction activities and therefore might indicate potential effects of CBM-extraction activities on water-quality of receiving streams in the Tongue and Powder River water­ sheds. These two 10-year trend analysis periods were used for all sites that satisfied requirements for the data-intensive TSM. For sites that did not satisfy data requirements for the TSM, OLS was used to analyze trends for period 2 (if complete data were available) or a 6-year period (2005-10) to provide information on water-quality characteristics that might have been affected by CBM-extraction activities. Additional data collection at these sites will increase record length for future analysis of temporal trends. For main-stem Tongue River sites analyzed by using the TSM and downstream from substantial CBM-extraction

Summary and Conclusions    53 activities [Tongue River at State line (site 4), Tongue River at Tongue River Dam (site 5), Tongue River at Birney Day School (site 7), and Tongue River at Miles City (site 10)], generally small significant or nonsignificant decreases in most constituents are indicated for period 1. For period 2 for these sites, the TSM trend results do not allow confident conclusions concerning detection of effects of CBM-extraction activities on stream water quality. Detection of significant trends in major-ion constituents and properties for period 2 generally was infrequent, and direction, significance, and magnitudes of fitted trends were not strongly consistent with relative differ­ ences between stream water and CBM-produced water. The TSM indicated significant or large magnitude increases in median values of sodium adsorption ratio, sodium, and alka­ linity for period 2 for sites 5 and 7, which are consistent with relative differences between stream water and CBM-produced water and might indicate potential CBM effects. However, other factors, including operations of Tongue River Reser­ voir, irrigation activities, and operations of the Decker coal mine, confound confident determination of causes of detected significant trends for sites 5 and 7. For all main-stem Tongue River sites, flow-adjusted concentrations (FACs) and fitted trends for period 2 generally are within ranges of those for period 1 before substantial CBM-extraction activities. Trend results for Tongue River tributary sites down­ stream from substantial CBM-extraction activities [Prairie Dog Creek (site 3) and Hanging Woman Creek (site 6)] are variable among sites. Significant increases in median values of SAR, sodium, alkalinity, and chloride during period 2 (deter­ mined by using OLS) are consistent with relative differences between stream water and CBM-produced water for site 3. Significant increases in median concentrations of magne­ sium and sulfate during period 2 for site 3 might have been affected by geochemical processes relating to interaction of CBM-produced water with soil and rock materials in holding ponds and ephemeral channels in the site 3 watershed. Thus, CBM-extraction activities might have affected the observed significant increases in some major-ion constituents and prop­ erties for site 3. The significant increase in estimated alkalin­ ity concentration during period 2 is consistent with relative differences between stream water and CBM-produced water for site 6, but the significant increase in estimated alkalinity is difficult to interpret with respect to CBM-extraction activities. Relative differences between stream water and CBM-produced water for site 6 generally are smaller than most other sites, and stream water for site 6 has slightly higher ionic strength than CBM-produced water. Significant changes during period 2 for site 6 were not indicated for any constituent other than estimated alkalinity. FACs and fitted trends for period 2 for site 6 generally are within ranges of those for period 1 before substantial CBM-extraction activities. For main-stem Powder River sites analyzed by using the TSM [Powder River at Sussex (site 11), Powder River at Arvada (site 12), Powder River at Moorhead (site 13), and Powder River near Locate (site 16)], significant or large magnitude decreases in median values of SAR, sodium, estimated alkalinity, chloride, fluoride, specific conductance, and dissolved solids are indicated for period 1. Patterns in trend results for period 1 for main-stem Powder River sites are consistent with effects of Salt Creek oil-brine reinjection that started in 1990. Trend results for all of the main-stem Pow­ der River sites downstream from substantial CBM-extraction activities (sites 12, 13, and 16) indicate evidence of potential effects of CBM-extraction activities on stream water quality, although evidence is stronger for sites 12 and 13 than for site 16. Evidence in support of potential CBM effects includes significant increases during period 2 in median values of SAR, sodium, and estimated alkalinity for sites 12, 13, and 16 that are consistent with relative differences between stream water and CBM-produced water. Significant increases during period 2 in median values of these constituents are not indicated for site 11 upstream from substantial CBM-extraction activities. For sites 12, 13, and 16, mean CBM pumping rates were 26, 28, and 34 percent of 2001-10 median streamflows, respec­ tively. In interpreting the trend results, it is notable that the fit­ ted trends evaluate changes in median concentrations and that changes in the median concentrations that might be attributed to CBM-extraction activities probably are more strongly evi­ dent during low-flow conditions than during average to highflow conditions. This observation is relevant in assessing trend results in relation to specific water-quality concerns, including effects of water-quality changes on irrigators and effects on stream biota and ecology. Trend results for Little Powder River sites downstream from substantial CBM-extraction activities [Little Powder River above Dry Creek (site 14) and Little Powder River near Broadus (site 15)] do not allow confident conclusions con­ cerning detection of effects of CBM-extraction activities on stream water quality. CBM-extraction activities in the site 14 watershed started substantially earlier than most other sites and might potentially affect trend results during period 1 and period 2. Significant increases in median chloride concen­ tration during period 1 and period 2 for site 14 are difficult to interpret, but are not consistent with relative differences between CBM-produced water and stream water for site 14. Geochemical processes relating to interaction of CBMproduced water with soil and rock materials in holding ponds and ephemeral channels in the site 14 watershed might have affected chloride concentrations. However, significant trends are not indicated for any constituent other than chloride during either period 1 or period 2 for site 14, which contributes to difficulty in interpreting chloride trend results; the chloride trend results should be used with caution. Significant increases in sodium, chloride, and sulfate during water years 2005-10 for site 15 are not consistent with relative differences between CBM-produced water and stream water for site 15, but also might have been affected by interaction of CBM-produced water with soil and rock materials. However, independent from potential effects of CBM-extraction activities, plains streams in Montana and Wyoming can exhibit large temporal variability in major-ion constituents, which contributes to dif­ ficulty in interpreting trend results for site 15.

54    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds References Cited American Public Health Association, American Water Works Association, and Water Environment Federation, 1998, Standard methods for examination of water and wastewater (20th ed.): American Public Health Association, part 3120, p. 3-37 to 3-43. Bartos, T.T., and Ogle, K.M., 2002, Water quality and environ­ mental isotopic analyses of ground-water samples collected from the Wasatch and Fort Union Formations in areas of coalbed methane development—Implications to recharge and ground-water flow, eastern Powder River Basin, Wyo­ ming: U.S. Geological Survey Water-Resources Investiga­ tions Report 02-4045, 88 p. Bates, B.L., McIntosh, J.C., Lohse, K.A., and Brooks, P.D., 2011, Influence of groundwater flowpaths, residence times and nutrients on the extent of microbial methanogenesis in coal beds—Powder River Basin, USA: Chemical Geology, v. 284, p. 45-61. Boelter, A.M., Lamming, F.N., Farag, A.M., and Bergman, H.L., 1992, Environmental effects of saline oil-field dis­ charges on surface waters: Environmental Toxicology and Chemistry, v. 11, p. 1,187-1,195. Brinck, E.L., Drever, J.I., and Frost, C.D., 2008, The geo­ chemical evolution of water coproduced with coalbed natural gas in the Powder River Basin, Wyoming: Environ­ mental Geosciences, v. 15, no. 4, p. 153-171. Bryner, Gary, 2002, Coalbed methane development in the intermountain west-Primer: Natural Resources Law Center, University of Colorado School of Law, Boulder, Colorado, 50 p. Campbell, C.E., Pearson, B.N., and Frost, C.D., 2008, Stron­ tium isotopes as indicators of aquifer communication in an area of coal bed natural gas production, Powder River Basin, Montana and Wyoming: Rocky Mountain Geology, v. 43, no. 2, p. 149-175. Cary, L.E., 1991, Trends in selected water-quality characteris­ tics, Powder River and tributaries, Montana and Wyoming, water years 1968-88 and 1975-88: U.S. Geological Survey Water-Resources Investigations Report 91-4029, 42 p. Chanat, J.G., Rice, K.C., and Hornberger, G.M, 2002, Con­ sistency of patterns in concentration-discharge plots: Water Resources Research, v. 38, 10 p. Clarey, K.E., Gribb, N.W., Hays, R.J., McLaughlin, J.F., 2010, 1993-2006 Coalbed natural gas regional groundwater moni­ toring report—Powder River Basin—Wyoming: Wyoming State Geological Survey, Open File Report 2010-02, 96 p. Clarey, K.E., and Stafford, J.E., 2008, Water production and quality, in Copeland, D.A., and Ewald, M.L., eds., Water associated with coal beds in Wyoming's Powder River Basin—Geology, hydrology, and water quality: Wyoming State Geological Survey Exploration Memoir No. 2, p. 111-155. Clark, M.L., 2012, Water-quality characteristics and trend analyses for the Tongue, Powder, Cheyenne, and Belle Fourche River drainage basins, Montana and Wyoming, for selected periods, water years 1991 through 2010: U.S. Geo­ logical Survey Scientific Investigations Report 2012-5117, 82 p. Clark, M.L., and Mason, J.P., 2007, Water-quality character­ istics for sites in the Tongue, Powder, Cheyenne, and Belle Fourche River drainage basins, Montana and Wyoming, water years 2001-05, with temporal patterns of selected long-term water-quality data: U.S. Geological Survey Sci­ entific Investigations Report 2007-5146, 65 p. Daddow, P.B., 1986, Potentiometric-surface map of the Wyodak-Anderson coal bed, Powder River structural basin, Wyoming, 1973-84: U.S. Geological Survey WaterResources Investigations Report 85-4305, 1 sheet, scale 1:250,000. Decker, M. K. (General Chairman), 2001, Potential supply of natural gas in the United States—Report of the Potential Gas Committee, December, 2000: Golden, Colorado, Poten­ tial Gas Agency, Colorado School of Mines Report, 346 p. Edwards, T.K., and Glysson, G.D., 1999, Field methods for measurement of fluvial sediment: U.S. Geological Survey Techniques of Water-Resources Investigations, book 3, chap. C2, 89 p. Farag, A.M., and Harper, D.D., eds., 2012, The potential effects of sodium bicarbonate, a major constituent from coal-bed natural gas production, on aquatic life: U.S. Geo­ logical Survey, Scientific Investigations Report 2012-5008, 101 p. Fishman, M.J., ed., 1993, Methods of analysis by the U.S. Geological Survey National Water Quality Laboratory— Determination of inorganic and organic constituents in water and fluvial sediments: U.S. Geological Survey OpenFile Report 93-125, 217 p. Fishman, M.J., and Friedman, L.C., 1989, Methods for determination of inorganic substances in water and fluvial sediments: U.S. Geological Survey Techniques of WaterResources Investigations, book 5, chap. A1, 545 p.

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56    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Meredith, Elizabeth, Wheaton, J.R., Kuzara, Shawn, 2012, Coalbed-methane basics ten years of lessons from the Pow­ der River Basin, Montana: Montana Bureau of Mines and Geology, Information Pamphlet 6. Montana Board of Oil and Gas Conservation, 2011, CBM Wells: Accessed August 15, 2011, at http://www.bogc.dnrc. mt.gov/WebApps/DataMiner/CBM/CBMWells.aspx. Montana Bureau of Mines and Geology, 2012, Groundwater Information Center (GWIC) database: accessed January 23, 2012, at http://mbmggwic.mtech.edu/sqlserver/v11/menus/ menuData.asp. Mount, D.R., Gulley, D.D., Hockett, J.R., Garrison, T.D., and Evans, J.M., 1997, Statistical models to predict the toxicity of major ions to Ceriodaphnia dubia, Daphnia magna, and Pimephales promelas (fathead minnows): Environmental Toxicology and Chemistry, v. 16, p. 2,009-2,019. National Research Council, 1989, Irrigation-induced water quality problems: Washington, D.C., National Academy Press, 157 p. National Research Council, 2010, Management and effects of coalbed methane development and produced water in the western United States: Washington, D.C., National Acad­ emies Press, 217 p. , accessed January 23, 2012, at http:// www.nap.edu/openbook.php?record_id=12915&page=R1. Omernik, J.M., 1987, Ecoregions of the conterminous United States: Annals of the Association of American Geographers, v. 77, no. 1, p. 118-125, scale 1:7,500,000. Patz, M.J., Reddy, K.J., and Skinner, Q.D., 2004, Chemistry of coalbed methane discharge water interacting with semiarid ephemeral stream channels: Journal of the American Water Resources Association, v. 40, no. 5, p. 1,247-1,255. Pearson, B. N., 2002, Sr isotope ratio as a monitor of recharge and aquifer communication, Paleocene Fort Union Forma­ tion and Eocene Wasatch Formation, Powder River Basin, Montana and Wyoming: Laramie, University of Wyoming, M.S. thesis, 151 p. Peck, Charles, 1999, Review of coalbed methane development in the Powder River Basin of Wyoming/Montana: Society of Petroleum Engineers Rocky Mountain Regional Meeting, May 1999, Gillette, Wyoming, paper SPE 55801, 7 p. Perry, W.J., and Flores, R.M., 1997, Sequential Laramide deformation and Paleocene depositional patterns in deep gas-prone basins of the Rocky Mountain Region: U.S. Geo­ logical Survey Bulletin 2146-E, 13 p. Peterson, D.A., Hargett, E.G., and Feldman, D.L., 2011, Assessment of potential effects of water produced from coalbed natural gas development on macroinvertebrate and algal communities in the Powder River and Tongue River, Montana and Wyoming, 2010: U.S. Geological Survey Open-File Report 2011-1294, 34 p. Peterson, D.H., Dettinger, M.D., Cayan, D.R., DiLeo, Jeanne, Riddle, Larry, and Smith, R.E., 1996, River salinity varia­ tions in response to discharge—Examples for the Western United States during the early 1900's, in Isaacs, C.M., and Tharp, V.M., eds., Proceedings, 12th Annual Pacific Climate (PACLIM) Workshop, 1995: Interagency Ecological Pro­ gram Technical Report 46, California Department of Water Resources, p. 145-153. Poppenga, S.K., and Worstell, B.B., 2008, Elevation-derived watershed basins and characteristics for major rivers of the conterminous United States: U.S. Geological Survey Scien­ tific Investigations Report 2008-5153, 27 p. PRISM Climate Group, 2012, PRISM Products Matrix: accessed January 23, 2012, at http://www.prism.oregonstate. edu/products/matrix.phtml?vartype=ppt&view=data. Quillinan, S.A., 2011, Geochemical and isotopic characteriza­ tion of water associated with Wyoming's coalbed natural gas development: Laramie, University of Wyoming, Lara­ mie, MS thesis, 205 p. Rantz, S.E., and others, 1982, Measurement and computation of streamflow (volumes 1 and 2): U.S. Geological Survey Water-Supply Paper 2175, 2 v., 631 p. Rice, C.A., Bartos, T.T., and Ellis, M.S., 2002, Chemical and isotopic composition of water in the Fort Union and Wasatch Formations of the Powder River Basin, Montana and Wyoming—Implications for coalbed methane develop­ ment, in Schwochow, S.D., and Nuccio, V.F. eds., Coalbed methane of North America, II: Rocky Mountain Association of Geologists Guidebook, p. 53-70. Rice, C.A., Ellis, M.S., and Bullock, J.H., Jr., 2000, Water coproduced with coalbed methane in the Powder River Basin, Wyoming—Preliminary compositional data: U.S. Geologi­ cal Survey Open-File Report 00-372, 20 p. Rice, C.A., and Nuccio, V.F., 2000, Water produced with coal-bed methane: U.S. Geological Survey Fact Sheet FS-156-00, 2 p. Schenk, C.J., Nuccio, V.F., Flores, R.M., Johnson, R.C., Rob­ erts, S.B., and Collett, T.S., 2001, Coal-bed gas resources of the Rocky Mountain Region: U.S. Geological Survey Fact Sheet FS-110-01, 2 p., accessed January 18, 2012, at http:// pubs.usgs.gov/fs/fs-0110-01/fs-0110-01.pdf.

References Cited     57 Sowder, J.T., Kelleners, T.J., and Reddy, K.J., 2010, The origin and fate of arsenic in coalbed natural gas-produced water ponds: Journal of Environmental Quality, v. 39, p. 1604-15, accessed January 23, 2012, at https://www.agronomy.org/ publications/jeq/tocs/39/5. Taylor, J.K., 1987, Quality assurance of chemical measure­ ments: Chelsea, Mich., Lewis Publishers, 328 p. U.S. Energy Information Administration, 2010, U.S. coal sup­ ply and demand-2009 review: accessed January 23, 2012, at http://www.eia.gov/coal/review/pdf/feature09.pdf. U.S. Geological Survey, 1984, Chemical and physical qual­ ity of water and sediment, chap. 5 of National handbook of recommended methods for water-data acquisition: Office of Water Data Coordination, p. 5-1 to 5-194. U.S. Geological Survey, variously dated, National field man­ ual for the collection of water-quality data: U.S. Geological Survey Techniques of Water-Resources Investigations, book 9, chaps. A1-A9, 2 v. [variously paged]. (Also available at http://pubs.water.usgs.gov/twri9A. Chapters originally were published from 1997-1999; updates and revisions are ongoing and are summarized at http://water.usgs.gov/owq/ FieldManual/mastererrata.html) U.S. Geological Survey, 2012, USGS groundwater data: accessed January 23, 2012, at http://water.usgs.gov/ogw/ data.html#quality. Van Voast, W.A., 2003, Geochemical signature of formation waters associated with coalbed methane: American Asso­ ciation of Petroleum Geologists Bulletin, v. 87, no. 4, p. 667-676. Vecchia, A.V., 2003, Water-quality trend analysis and sam­ pling design for streams in North Dakota: U.S. Geological Survey Water-Resources Investigations Report 03-4094, 79 p. Vecchia, A.V., 2005, Water-quality trend analysis and sam­ pling design for streams in the Red River of the North Basin, Minnesota, North Dakota, and South Dakota, 1970-2001: U.S. Geological Survey Scientific Investiga­ tions Report 2005-5224, 60 p. Wang, Xixi, Melesse, A.M., McClain, M.E., and Yang, Wan­ hong, 2007, Water quality changes as a result of coalbed methane development in a Rocky Mountain watershed: Journal of American Water Resources Association, v. 43, no. 6, p. 1,383-1,399. Ward, J.R., and Harr, C.A., 1990, Methods for collection and processing of surface-water and bed-material samples for physical and chemical analysis: U.S. Geological Survey Open-File Report 90-140, 71 p. Wegemann, C.H., 1918, The Salt Creek Oil Field, Wyoming: U.S. Geological Survey Bulletin 670, 57 p. Wheaton, J. R. and Donato, T. A., 2004, Ground-water moni­ toring program in prospective coalbed-methane areas of southeastern Montana: Year One: Montana Bureau of Mines and Geology Open-File Report 508, 91 p. Woods, A.J., Omernik, J.M., Nesser, J.A., Shelden, James, Comstock, J.A., and Azevedo, S.H., 2002, Ecoregions of Montana, (2d ed.): U.S. Environmental Protection Agency, Western Ecology Division, accessed May 5, 2012, at http:// www.epa.gov/wed/pages/ecoregions/mt_eco.htm. Wyoming Oil and Gas Conservation Commission, 2011, Coal bed methane wells: digital data,: accessed June 25, 2011, at http://wogcc.state.wy.us/. Zelt, R.B., Boughton, G.K., Miller, K.A., Mason, J.P., and Gianakos, L.M., 1999, Environmental setting of the Yellow­ stone River Basin, Montana, North Dakota, and Wyoming: U.S. Geological Survey Water-Resources Investigations Report 98-4269, 112 p. (Also available at http://pubs.water. usgs.gov/wri98-4269.

Supplement 1    59 Supplement 1.   Summary Tables Relating to Quality-Control, Water-Quality, Streamflow, and Coal-Bed Methane (CBM) Produced-Water Data Table 1.1.  Summary information relating to quality-control samples (equipment blank and replicate samples) collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years1 1980-2010.2 less than] Constituent Number of equipment blank samples Maximum concentration in equipment blank sample, in milligrams per liter 90th percentile concentration in equipment blank samples, in milligrams per liter Number of replicate sample pairs Mean relative percent difference Calcium, dissolved Magnesium, dissolved Sodium, dissolved Alkalinity, as calcium carbonate

acid neutralizing capacity, as calcium carbonate

Chloride, dissolved Sulfate, dissolved 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Prior to the early 1990's, quality-control data collected by the U.S. Geological Survey generally were not permanently archived in an electronic format and are difficult to document. The samples summarized were collected during water years 1993-2010 for blank samples and water years 1992-2010 for replicate samples.

60    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10). [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Tongue River at Monarch, Wyo. (site 1, fig. 1) Water years 2001-10 1/2004-9/2010 Streamflow, instantaneous, ft3/s 2,520 Specific conductance, µS/cm Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L Goose Creek below Sheridan, Wyo. (site 2, fig. 1) Water years 2001-10 10/2001-8/2010 Streamflow, instantaneous, ft3/s 1,790 Specific conductance, µS/cm Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L

Supplement 1    61 Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Prairie Dog Creek near Acme, Wyo. (site 3, fig. 1) Water years 2001-10 10/2000-9/2010 Streamflow, instantaneous, ft3/s Specific conductance, µS/cm 1,220 1,460 1,450 1,670 2,510 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,160 Dissolved solids (sum of constituents), mg/L 1,020 1,040 1,230 2,030 Tongue River at State line, near Decker, Mont. (site 4, fig. 1) Water years 1986-95 11/1985-7/1995 Streamflow, instantaneous, ft3/s 3,840 Specific conductance, µS/cm Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Acid-neutralizing capacity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L

62    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Water years 2001-10 10/2000-9/2010 Streamflow, instantaneous, ft3/s 5,430 Specific conductance, µS/cm 1,280 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L Tongue River at Tongue River Dam, near Decker, Mont. (site 5, fig. 1) Water years 1986-95 10/1985-8/1995 Streamflow, instantaneous, ft3/s 3,290 Specific conductance, µS/cm Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Acid-neutralizing capacity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L

Supplement 1    63 Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Water years 2001-10 1/2004-9/2010 Streamflow, instantaneous, ft3/s 3,250 Specific conductance, µS/cm Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L Hanging Woman Creek near Birney, Mont. (site 6, fig. 1) Water years 1986-95 10/1985-7/1995 Streamflow, instantaneous, ft3/s Specific conductance, µS/cm 2,200 2,735 2,483 3,165 3,600 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Acid-neutralizing capacity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,100 1,092 1,300 1,700 Dissolved solids (sum of constituents), mg/L 1,880 2,090 2,043 2,350 2,810

64    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Water years 2001-10 7/2003-7/2010 Streamflow, instantaneous, ft3/s Specific conductance, µS/cm 2,120 2,500 2,510 2,910 3,990 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,160 2,050 Dissolved solids (sum of constituents), mg/L 1,480 1,690 1,830 2,200 3,320 Tongue River at Birney Day School, near Birney, Mont. (site 7, fig. 1) Water years 1986-95 10/1985-6/1993 Streamflow, instantaneous, ft3/s 3,130 Specific conductance, µS/cm Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L

Supplement 1    65 Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Water years 2001-10 1/2004-9/2010 Streamflow, instantaneous, ft3/s 3,230 Specific conductance, µS/cm Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L Otter Creek at Ashland, Mont. (site 8, fig. 1) Water years 1986-95 12/1987-9/1995 Streamflow, instantaneous, ft3/s Specific conductance, µS/cm 2,550 2,750 2,682 3,000 3,960 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,100 1,071 1,200 1,700 Dissolved solids (sum of constituents), mg/L 1,915 2,030 2,062 2,245 3,020

66    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Water years 2001-10 7/2003-7/2010 Streamflow, instantaneous, ft3/s Specific conductance, µS/cm 1,730 2,560 2,860 2,880 3,150 3,820 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,070 1,110 1,280 1,750 Dissolved solids (sum of constituents), mg/L 1,230 1,840 2,110 2,110 2,300 3,040 Pumpkin Creek near Miles City, Mont. (site 9, fig. 1) Water years 2001-10 3/2004-7/2010 Streamflow, instantaneous, ft3/s 2,110 Specific conductance, µS/cm 1,040 1,500 2,180 5,100 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 2,140 Dissolved solids (sum of constituents), mg/L 1,050 1,460 3,550

Supplement 1    67 Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Tongue River at Miles City, Mont. (site 10, fig. 1) Water years 1986-95 12/1985-9/1994 Streamflow, instantaneous, ft3/s 2,630 Specific conductance, µS/cm 1,500 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L Water years 2001-10 6/2001-9/2010 Streamflow, instantaneous, ft3/s 3,560 Specific conductance, µS/cm 1,030 1,360 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L Dissolved solids (sum of constituents), mg/L

68    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Powder River at Sussex, Wyo. (site 11, fig. 1) Water years 1986-95 10/1985-9/1995 Streamflow, instantaneous, ft3/s 10,700 Specific conductance, µS/cm 1,920 2,365 2,580 3,018 6,200 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L 1,400 Alkalinity, mg/L as calcium carbonate Chloride, mg/L 1,200 Fluoride, mg/L Sulfate, mg/L 1,600 Dissolved solids (sum of constituents), mg/L 1,275 1,570 1,684 1,920 3,920 Water years 2001-10 11/2000-9/2010 Streamflow, instantaneous, ft3/s 1,410 Specific conductance, µS/cm 1,960 2,260 2,660 2,920 6,240 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L 1,130 Alkalinity, mg/L as calcium carbonate Chloride, mg/L 1,190 Fluoride, mg/L Sulfate, mg/L 1,630 Dissolved solids (sum of constituents), mg/L 1,290 1,500 1,750 1,920 3,880

Supplement 1    69 Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Powder River at Arvada, Wyo. (site 12, fig. 1) Water years 1986-95 10/1985-8/1995 Streamflow, instantaneous, ft3/s 5,450 Specific conductance, µS/cm 2,010 2,400 2,614 3,100 6,200 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L 1,300 Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,600 Dissolved solids (sum of constituents), mg/L 1,287 1,590 1,745 2,045 4,290 Water years 2001-10 10/2000-9/2010 Streamflow, instantaneous, ft3/s 2,260 Specific conductance, µS/cm 1,990 2,270 2,350 2,610 5,170 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 2,010 Dissolved solids (sum of constituents), mg/L 1,320 1,510 1,580 1,800 3,770

70    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Powder River at Moorhead, Mont. (site 13, fig. 1) Water years 1986-95 7/1986-11/1989 Streamflow, instantaneous, ft3/s 7,540 Specific conductance, µS/cm 1,460 1,770 1,785 2,180 2,880 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,100 Dissolved solids (sum of constituents), mg/L 1,220 1,397 1,363 1,610 1,830 Water years 2001-10 5/2001-9/2010 Streamflow, instantaneous, ft3/s 5,220 Specific conductance, µS/cm 1,560 1,820 1,820 2,100 3,660 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,770 Dissolved solids (sum of constituents), mg/L 1,060 1,240 1,250 1,450 2,700

Supplement 1    71 Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Little Powder River above Dry Creek, near Weston, Wyo. (site 14, fig. 1) Water years 1986-95 10/1985-9/1995 Streamflow, instantaneous, ft3/s Specific conductance, µS/cm 1,765 2,590 2,546 3,238 5,500 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,200 1,245 1,800 2,700 Dissolved solids (sum of constituents), mg/L 1,358 2,105 2,091 2,943 4,400 Water years 2001-10 10/2000-9/2010 Streamflow, instantaneous, ft3/s Specific conductance, µS/cm 2,610 3,380 3,150 3,810 5,250 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,060 1,460 1,370 1,730 2,560 Dissolved solids (sum of constituents), mg/L 1,800 2,540 2,370 2,960 4,590

72    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Little Powder River near Broadus, Mont. (site 15, fig. 1) Water years 2001-10 3/2002-9/2010 Streamflow, instantaneous, ft3/s Specific conductance, µS/cm 1,950 2,490 2,470 3,060 3,940 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,290 1,770 Dissolved solids (sum of constituents), mg/L 1,340 1,820 1,810 2,280 3,020 Powder River near Locate, Mont. (site 16, fig. 1) Water years 1986-95 12/1985-9/1994 Streamflow, instantaneous, ft3/s 5,350 Specific conductance, µS/cm 1,585 2,100 2,126 2,585 4,330 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 2,000 Dissolved solids (sum of constituents), mg/L 1,280 1,470 1,588 1,905 3,450

Supplement 1    73 Table 1.2.  Summary information relating to major-ion constituents and properties in stream-water samples collected at sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during selected periods1 (water years2 1986-95 and 2001-10).—Continued [Wyo., Wyoming; ft3/s, cubic feet per second; µS/cm, microsiemens per centimeter at 25 degrees Celsius; mg/L, milligrams per liter; Mont., Montana] Period of water-quality sampling during indicated summary period Constituent or property, units of measurement Number of samples Minimum 25th percentile Median Mean 75th percentile Maximum Water years 2001-10 10/2000-9/2010 Streamflow, instantaneous, ft3/s 7,880 Specific conductance, µS/cm 1,850 2,100 2,080 2,530 3,580 Calcium, mg/L Magnesium, mg/L Potassium, mg/L Sodium adsorption ratio, dimensionless Sodium, mg/L Alkalinity, mg/L as calcium carbonate Chloride, mg/L Fluoride, mg/L Sulfate, mg/L 1,280 Dissolved solids (sum of constituents), mg/L 1,290 1,500 1,490 1,820 2,590 1Data summary periods were selected based on two 10-year trend analysis periods (period 1, water years 1986-95; and period 2, 2001-10), as discussed in the section of this report "Selection of Trend-Analysis Time Periods." No data are presented for period 1 for sites without adequate data for trend analysis for period 1. 2Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009.

74    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010. [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Tongue River at Monarch, Wyo. (site 1, fig. 1) Mean 2001-10 Goose Creek below Sheridan, Wyo. (site 2, fig. 1)

Supplement 1    75 Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Goose Creek below Sheridan, Wyo. (site 2, fig. 1)­—Continued Mean 2001-10 Prairie Dog Creek near Acme, Wyo. (site 3, fig. 1)

76    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Prairie Dog Creek near Acme, Wyo. (site 3, fig. 1)—Continued 2,794 4,768 4,487 4,329 4,780 5,698 5,916 6,029 5,237 4,488 Mean 2001-10 4,853 Tongue River at State line, near Decker, Mont. (site 4, fig. 1)

Supplement 1    77 Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Tongue River at State line, near Decker, Mont. (site 4, fig. 1)—Continued

3,145 5,873 10,670 9,977 8,861 8,571 8,866 8,837 8,636 7,018 5,825 Mean 2001-10 8,313 Tongue River at Tongue River Dam, near Decker, Mont. (site 5, fig. 1)

78    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Tongue River at Tongue River Dam, near Decker, Mont. (site 5, fig. 1)­—Continued

3,146 5,875 10,680 10,030 9,969 10,460 12,280 14,250 15,880 13,320 10,800 Mean 2001-10 11,354 Hanging Woman Creek near Birney, Mont. (site 6, fig. 1)

Supplement 1    79 Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Hanging Woman Creek near Birney, Mont. (site 6, fig. 1)—Continued 1,248 1,200 1,724 1,840 3,803 5,084 2,591 1,789 2,237 1,065 1,523 1,304 Mean 2001-10 1,205 Tongue River at Birney Day School, near Birney, Mont. (site 7, fig. 1)

80    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Tongue River at Birney Day School, near Birney, Mont. (site 7, fig. 1)—Continued 10,010 11,920 14,500 17,080 18,320 14,950 12,250 Mean 2001-10 12,568 Otter Creek at Ashland, Mont. (site 8, fig. 1)

Supplement 1    81 Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Otter Creek at Ashland, Mont. (site 8, fig. 1)—Continued Mean 2001-10 Pumpkin Creek near Miles City, Mont. (site 9, fig. 1) Mean 2001-10

82    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Tongue River at Miles City, Mont. (site 10, fig. 1)

3,146 5,877 10,720 10,050 10,010 11,920 14,500 17,080 18,320 14,950 12,250 Mean 2001-10 12,570 Powder River at Sussex, Wyo. (site 11, fig. 1)

Supplement 1    83 Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Powder River at Sussex, Wyo. (site 11, fig. 1)—Continued Mean 2001-10 Powder River at Arvada, Wyo. (site 12, fig. 1)

84    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Powder River at Arvada, Wyo. (site 12, fig. 1)—Continued

1,759 3,780 9,001 10,760 12,840 18,800 30,240 32,280 34,740 35,140 36,800 Mean 2001-10 22,440 Powder River at Moorhead, Mont. (site 13, fig. 1)

Supplement 1    85 Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Powder River at Moorhead, Mont. (site 13, fig. 1)—Continued

6,360 14,060 20,540 23,960 26,110 33,550 48,390 51,760 56,360 51,760 51,560 Mean 2001-10 37,810 Little Powder River above Dry Creek, near Weston, Wyo. (site 14, fig. 1)

86    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Little Powder River above Dry Creek, near Weston, Wyo. (site 14, fig. 1)—Continued 1,940 3,921 8,372 10,090 11,160 2,201 8,540 1,204 8,005 3,029 8,340 7,971 7,433 7,509 4,117 3,242 Mean 2001-10 7,640 Little Powder River near Broadus, Mont. (site 15, fig. 1) 1,940 3,921

Supplement 1    87 Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Little Powder River near Broadus, Mont. (site 15, fig. 1)—Continued 8,372 10,090 11,160 8,540 8,005 8,340 7,971 7,433 7,509 4,117 3,242 Mean 2001-10 7,640 Powder River near Locate, Mont. (site 16, fig. 1)

88    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.3.  Summary information relating to volumes and rates of streamflow and coal-bed methane (CBM) produced water in watersheds for sites in the Tongue and Powder River watersheds, based on data collected during water years1 1980-2010.—Continued [CBM, coal-bed methane; Wyo., Wyoming; --, no data; Mont., Montana; less than] Water year or summary statistic Annual mean streamflow, in cubic feet per second Annual median streamflow, in cubic feet per second Annual volume of CBM-produced water, in acre-feet Annual mean pumping rate of CBM-produced water, in cubic feet per second Annual mean pumping rate of CBM-produced water relative to annual mean streamflow, in percent Annual mean pumping rate of CBM-produced water relative to annual median streamflow, in percent Powder River near Locate, Mont. (site 16, fig. 1)—Continued 34,120 41,890 56,360 59,200 63,870 55,880 54,800 Mean 2001-10 45,450 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009.

Supplement 1    89 Table 1.4.  Summary information relating to major-ion constituents and properties in groundwater samples collected from coalbed methane (CBM) wells and monitoring wells in coal beds in the watersheds upstream from sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years1 2001-10. [mg/L, milligrams per liter; Wyo., Wyoming; Mont., Montana] Constituent or property, units of measurement Number of wells sampled2 Data sources3 Minimum 25th percentile Median Mean 75th percentile Maximum Samples collected in the site 3 watershed (Prairie Dog Creek near Acme, Wyo.) Calcium, mg/L 4, 7 Magnesium, mg/L 4, 7 Sodium adsorption ratio, dimensionless 4, 7 Sodium, mg/L 4, 7 Alkalinity, mg/L as calcium carbonate 4, 7 1,140 1,160 1,170 1,170 1,180 1,200 Chloride, mg/L 4, 7 Sulfate, mg/L 4, 7 Samples collected in the site 4 watershed (Tongue River at State line, near Decker, Mont.) Calcium, mg/L 3, 4, 7 Magnesium, mg/L 3, 4, 7 Sodium adsorption ratio, dimensionless 3, 4, 7 Sodium, mg/L 3, 4, 7 Alkalinity, mg/L as calcium carbonate 3, 4, 7 1,170 1,640 Chloride, mg/L 3, 4, 7 Sulfate, mg/L 3, 4, 7 Samples collected in the site 5 watershed (Tongue River at Tongue River Dam, near Decker, Mont.) Calcium, mg/L 3, 4, 7 Magnesium, mg/L 3, 4, 7 Sodium adsorption ratio, dimensionless 3, 4, 7 Sodium, mg/L 3, 4, 7 Alkalinity, mg/L as calcium carbonate 3, 4, 7 1,060 1,110 1,390 1,650 Chloride, mg/L 3, 4, 7 Sulfate, mg/L 3, 4, 7 Samples collected in the site 6 watershed (Hanging Woman Creek near Birney, Mont.) Calcium, mg/L 3, 6, 7 Magnesium, mg/L 3, 6, 7 Sodium adsorption ratio, dimensionless 3, 6, 7 Sodium, mg/L 3, 6, 7 Alkalinity, mg/L as calcium carbonate 3, 6, 7 1,090 1,210 1,250 1,350 1,760 Chloride, mg/L 3, 6, 7 Sulfate, mg/L 3, 6 Samples collected in the site 7 watershed (Tongue River at Birney Day School, near Birney, Mont.) Calcium, mg/L 3, 4, 6, 7 Magnesium, mg/L 3, 4, 6, 7 Sodium adsorption ratio, dimensionless 3, 4, 6, 7 Sodium, mg/L 3, 4, 6, 7 Alkalinity, mg/L as calcium carbonate 3, 4, 6, 7 1,150 1,150 1,380 1,760 Chloride, mg/L 3, 4, 6, 7 Sulfate, mg/L 3, 4, 6, 7

90    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.4.  Summary information relating to major-ion constituents and properties in groundwater samples collected from coalbed methane (CBM) wells and monitoring wells in coal beds in the watersheds upstream from sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years1 2001-10.—Continued [mg/L, milligrams per liter; Wyo., Wyoming; Mont., Montana] Constituent or property, units of measurement Number of wells sampled2 Data sources3 Minimum 25th percentile Median Mean 75th percentile Maximum Samples collected in the site 10 watershed (Tongue River at Miles City, Mont.) Calcium, mg/L 3, 4, 6, 7 Magnesium, mg/L 3, 6, 7 Sodium adsorption ratio, dimensionless 3, 4, 6, 7 Sodium, mg/L 3, 4, 6, 7 Alkalinity, mg/L as calcium carbonate 3, 4, 6, 7 1,160 1,130 1,300 1,760 Chloride, mg/L 3, 4, 6, 7 Sulfate, mg/L 3, 4, 6 Samples collected in the site 12 watershed (Powder River at Arvada, Wyo.) Calcium, mg/L 1, 4, 5, 7 Magnesium, mg/L 1, 4, 5, 7 Sodium adsorption ratio, dimensionless 1, 4, 5, 7 Sodium, mg/L 1, 4, 5, 7 1,310 Alkalinity, mg/L as calcium carbonate 1, 4, 5, 7 1,450 1,980 1,900 2,310 3,460 Chloride, mg/L 1, 4, 5, 7 Sulfate, mg/L 1, 4, 5, 7 Samples collected in the site 13 watershed (Powder River at Moorhead, Mont. ) Calcium, mg/L 1, 4, 5, 7 Magnesium, mg/L 1, 4, 5, 7 Sodium adsorption ratio, dimensionless 1, 4, 5, 7 Sodium, mg/L 1, 4, 5, 7 1,310 Alkalinity, mg/L as calcium carbonate 1, 4, 5, 7 1,180 1,710 1,720 2,230 3,460 Chloride, mg/L 1, 4, 5, 7 Sulfate, mg/L 1, 4, 5, 7 Samples collected in the site 14 watershed (Little Powder River above Dry Creek, near Weston, Wyo.) Calcium, mg/L 2, 4, 5, 7 Magnesium, mg/L 2, 4, 5, 7 Sodium adsorption ratio, dimensionless 2, 4, 5, 7 Sodium, mg/L 2, 4, 5, 7 Alkalinity, mg/L as calcium carbonate 2, 4, 5, 7 1,160 Chloride, mg/L 2, 4, 5, 7 Sulfate, mg/L 2, 4, 5, 7 Samples collected in the site 15 watershed (Little Powder River near Broadus, Mont.) Calcium, mg/L 2, 4, 5, 7 Magnesium, mg/L 2, 4, 5, 7 Sodium adsorption ratio, dimensionless 2, 4, 5, 7 Sodium, mg/L 2, 4, 5, 7 Alkalinity, mg/L as calcium carbonate 2, 4, 5, 7 1,160 Chloride, mg/L 2, 4, 5, 7 Sulfate, mg/L 2, 4, 5, 7

Supplement 1    91 Table 1.4.  Summary information relating to major-ion constituents and properties in groundwater samples collected from coalbed methane (CBM) wells and monitoring wells in coal beds in the watersheds upstream from sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years1 2001-10.—Continued [mg/L, milligrams per liter; Wyo., Wyoming; Mont., Montana] Constituent or property, units of measurement Number of wells sampled2 Data sources3 Minimum 25th percentile Median Mean 75th percentile Maximum Samples collected in the site 16 watershed (Powder River near Locate, Mont.) Calcium, mg/L 1, 2, 3, 4, 5, 6, 7 Magnesium, mg/L 1, 2, 3, 4, 5, 6, 7 Sodium adsorption ratio, dimensionless 1, 2, 3, 4, 5, 6, 7 Sodium, mg/L 1, 2, 3, 4, 5, 6, 7 1,310 Alkalinity, mg/L as calcium carbonate 1, 2, 3, 4, 5, 6, 7 1,090 1,610 1,640 2,190 3,460 Chloride, mg/L 1, 2, 3, 4, 5, 6, 7 Sulfate, mg/L 1, 2, 3, 4, 5, 6, 7 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Some wells were sampled more than once. In these cases, concentrations for all samples for the given well were averaged for each constituent to provide a single set of concentrations. 3Data sources are designated by numbers that correspond to the following references: 1. Campbell and others (2008). 2. Frost and others (2002). 3. Montana Bureau of Mines and Geology (2012). 4. Pearson (2002). 5. Quillinan (2011). 6. U.S. Geological Survey (2012). 7. Wyoming Department of Environmental Quality, published in Quillinan (2011).

92    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 1.5.  Relative differences (ratios) in mean values of major-ion constituents and properties between stream-water samples (table 1.2) and coal-bed methane (CBM) groundwater samples (table 1.4) for sites in the Tongue and Powder River watersheds, Montana and Wyoming, based on data collected during water years1 2001-10. [Wyo., Wyoming; Mont., Montana] Constituent or property Ratio2 Constituent or property Ratio2 Prairie Dog Creek near Acme, Wyo. (site 3, fig. 1) Powder River at Arvada, Wyo. (site 12, fig. 1)—Continued Calcium Sodium adsorption ratio Magnesium Sodium Sodium adsorption ratio Alkalinity Sodium Chloride Alkalinity Sulfate Chloride Powder River at Moorhead, Mont. (site 13, fig. 1) Sulfate Calcium Tongue River at State line, near Decker, Mont. (site 4, fig. 1) Magnesium Calcium Sodium adsorption ratio Magnesium Sodium Sodium adsorption ratio Alkalinity Sodium Chloride Alkalinity Sulfate Chloride Little Powder River above Dry Creek, near Weston, Wyo. (site 14, fig. 1) Sulfate Calcium Tongue River at Tongue River Dam, near Decker, Mont. (site 5, fig. 1) Magnesium Calcium Sodium adsorption ratio Magnesium Sodium Sodium adsorption ratio Alkalinity Sodium Chloride Alkalinity Sulfate Chloride Little Powder River near Broadus, Mont. (site 15, fig. 1) Sulfate Calcium Hanging Woman Creek near Birney, Mont. (site 6, fig. 1) Magnesium Calcium Sodium adsorption ratio Magnesium Sodium Sodium adsorption ratio Alkalinity Sodium Chloride Alkalinity Sulfate Chloride Powder River near Locate, Mont. (site 16, fig. 1) Sulfate Calcium Tongue River at Birney Day School, near Birney, Mont. (site 7, fig. 1) Magnesium Calcium Sodium adsorption ratio Magnesium Sodium Sodium adsorption ratio Alkalinity Sodium Chloride Alkalinity Sulfate Chloride 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Ratios greater than one indicate higher concentrations in stream water than in CBM-produced water and indicate the multiple of the relation. For example, a ratio of 22 for calcium at Prairie Dog Creek (site 3) indicates that the mean calcium concentration in the stream water is 22 times higher than in the CBM-produced water. Ratios less than one indicate lower con­ centrations in stream water than in CBM-produced water and the multiple of the relation is determined by dividing one by the ratio. For example, a ratio of 0.15 for sodium at Prairie Dog Creek (site 3) indicates that the mean sodium concentration in the stream water is 1/0.15 one-sixth of the concentration in CBM-produced water. Sulfate Tongue River at Miles City, Mont. (site 10, fig. 1) Calcium Magnesium Sodium adsorption ratio Sodium Alkalinity Chloride Sulfate Powder River at Arvada, Wyo. (site 12, fig. 1) Calcium Magnesium

Supplement 2    93 Supplement 2.  Summary of the Time-Series Model (TSM) as Applied in this Study The theory and parameter estimation for the time-series model (TSM) are described in detail in Vecchia (2005). In the TSM, log-transformed concentration data were partitioned into several components according to equation 1:

log denotes the base-10 logarithm;

is the concentration, in milligrams per liter;

MC is the long-term mean of the log-transformed concentration, as the base-10 logarithm of milligrams per liter;

ANNC is the annual concentration anomaly (dimensionless);

SEASC is the seasonal concentration anomaly (dimensionless);

TREND is the concentration trend (dimensionless); and

HFVC is the high-frequency variability of the concentration (dimensionless). In equation 1, the annual concentration anomaly (ANNC ), seasonal concentration anomaly (SEASC ), and high-frequency variability (HFVC ) terms represent natural variability in con­ centration for different time scales. ANNC is an estimate of the interannual variability in concentration that can be attributed to long-term (that is, the period of analysis) variability in streamflow. Extended droughts and wet periods can change the chemical composition of streamflow by changing the degree of contact between surface runoff and soil particles, and chang­ ing the relative composition of runoff among groundwater, overland flow, and subsurface flow (Vecchia, 2005). SEASC is an estimate of the seasonal variability in concentration that can be attributed to seasonal variability in streamflow or to factors other than variability in streamflow. For example, the seasonal snow-accumulation and snowmelt cycle causes seasonal fluctuations in streamflow and water quality. Seasonality also might affect the relative amount of streamflow that comes from natural sources as compared to CBM-related sources and thus might cause seasonal fluctua­ tions in concentration that are more complicated than a simple relation between concentration and streamflow could produce. HFVC is an estimate of the variability in concentration for time scales that are smaller than the seasonal time scale (time scales of several days to several weeks). Thus, high-frequency variability is the variability that remains after the removal of seasonal and annual anomalies and trends. Day-to-day changes in meteorological conditions might cause high-frequency vari­ ability in concentration and streamflow. The high-frequency variability depends on a time-series model, called a periodic autoregressive moving average model, that accounts for the presence of serial correlation among concentrations (for example, the tendency for high or low values to persist for several days to several weeks before returning to normal lev­ els) (Vecchia, 2005). TREND is an estimate of the long-term systematic changes in concentration during the study period that are unre­ lated to long-term variability in streamflow. For this report, a significant trend might indicate changes in CBM-extraction activities that change the chemical composition of surface water or changes in other activities, such as agricultural prac­ tices or irrigation, that can change the amount of major ions that reach the stream. TREND consists of piecewise monotonic trends during specified trend-analysis periods. The overall significance of TREND (determined by using the generalized likelihood ratio principle; Vecchia, 2005; appendix 1) speci­ fies whether there were any significant changes during any of the specified trend-analysis periods. For a given site and constituent combination, if TREND was determined to be nonsignificant, the trends for all of the specified trend-analysis periods were considered nonsignificant and p-values were not reported. Infrequently, overall significance of TREND could not be determined or was unusually small (and thus, TREND was assumed to be nonsignificant), but the individual trend coefficient for a specified trend-analysis period was highly sig­ nificant and of large magnitude. In these cases, with TREND included in the model, the numerical procedure for minimizing the likelihood function apparently converged to a local, rather than global, minimum and produced unrealistic results rela­ tive to the model without TREND included. However, trend directions and magnitudes for these infrequent cases generally were consistent with trends for other constituents that would be expected to behave in a similar manner, and with trends for upstream or downstream sites. Therefore, the TSM was presumed to provide reasonably accurate trend magnitudes for the specified trend-analysis period and overall trend patterns were not strongly affected. For a given site and constituent combination, if TREND was determined to be significant, the slope coefficient (γ; Vecchia, 2005; appendix 1) for the trend for each specified trend-analysis period was used to determine the significance and magnitude of the trend for the specified trend-analysis period. The null hypothesis in the test for trend significance in a given trend analysis period is that there is no trend (that is, γ 0). If the two-tailed p-value for γ was less than the selected alpha level (0.01 in this report), the null hypothesis was rejected and the trend was determined to be significant. Determination of a nonsignificant trend (that is, a p-value greater than 0.01) does not imply that the null hypoth­ esis is accepted (that is, that there is no trend). It indicates that

94    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds within the statistical framework of the analysis, a significant trend was not detected. The magnitude of the trend for a speci­ fied trend-analysis period is expressed as the percent differ­ ence between the geometric mean concentration at the end of the period and the geometric mean concentration at the start of the period and is determined by the equation

− Fac ( ) 

%∆FAC is the percent change in the geometric mean of the flow-adjusted concentration; and

γ is the slope coefficient of the trend for the specified trend-analysis period in logtransformed units. Log-transformed concentrations that have ANNC and SEASC removed are referred to in this report as flow-adjusted concentrations. Using equation 2, the flow-adjusted concentra­ tion is defined as:

FAC (3) where FAC is the flow-adjusted concentration, as the base-10 logarithm of milligrams per liter. The FACs defined by equa­ tion 3 are analogous to FACs defined in previous publications as the residuals from a regression model that relates concen­ tration to concurrent daily streamflow (Helsel and Hirsch, 2002); however, the TSM approach generally is more effective than a regression-based approach for removing streamflowrelated variability (Vecchia, 2005). Time series plots showing the FACs along with the fitted trend (MC+TREND) illustrate long-term changes in median concentration that might indicate effects of changing CBM development on water quality in the selected watersheds. The key to making TSM a powerful trend analysis tool is that the entire time series of daily streamflow data are used in the model, not just streamflow for the days when water-quality samples are available. The model assumes a three-per-month, or approximately 10-day, sampling frequency. Each month is divided into three intervals—days 1-10, days 10-20, and day 21 through the end of the month. If a water-quality sample is available for a particular interval, it is paired with daily streamflow for the same day of the water-quality sample. If no water-quality sample is available, the concentration value for the interval is missing and streamflow for the middle of the interval (day 5, 15, or 25) is used. If more than one water-quality sample is available for the interval, the sample nearest to the midpoint of the interval is used. The log-trans­ formed streamflow time series (consisting of three values per month) is divided into an annual anomaly, seasonal anomaly, and high-frequency variability according to the following equation,

Q is daily mean streamflow, in cubic feet per second;

MQ is the mean of the log-transformed streamflow for the entire trend analysis period, as the base-10 logarithm of cubic feet per second;

ANNQ is the annual streamflow anomaly, computed as the one-year lagged moving average of (dimensionless);

SEASQ is the seasonal streamflow anomaly, computed as the 3-month lagged moving average of (dimensionless); and HFVQ

is the high-frequency streamflow variability (dimensionless). The streamflow anomalies from equation 4 are used as predictor variables for concentration (eq. 3). For example, ANNC is assumed to equal a constant coefficient (estimated from the time series model) times ANNQ. The different scales of streamflow variability often affect concentration in different ways. The relation between HFVC and HFVQ can be particu­ larly complicated, changing depending on the time-of-year and the degree of serial correlation in the concentration data and cross-correlation between concentration and streamflow. The TSM residuals for each site and constituent combina­ tion were graphically examined to verify the model assump­ tions that the residuals had constant variance, were serially uncorrelated, and were approximately normally distributed. Because of the application of the TSM to the large number of site and constituent combinations, and practical consider­ ations to keep the trend periods comparable among sites and constituents, some minor deviations of the residuals from model assumptions [such as small changes in residual vari­ ance through time and short-term (about 1-2 years) unre­ solved trending in the residuals] was tolerated. In cases where unresolved residual trends were considered to be large enough to possibly affect the magnitudes and significance levels of reported fitted trends, more complicated trend models were tested, and in all cases the more complicated models did not change the general findings and conclusions of this report. Therefore, the reported TSM results were judged to provide acceptable fits representative of linearity through nearly all of the range in FACs for a given site and constituent combination. For each site and constituent combination, the fit of the TSM can be assessed by examination of the fitted trends in relation to the FACs that are shown in figures 4.4-4.8, 4.10-4.14, and 4.16. The distribution of the FACs about the fitted trend lines shows the extent to which the residuals might exhibit nonconstant variance or unresolved trends.

Supplement 3    95 Supplement 3.  Summary of Ordinary Least Squares Regression of WaterQuality Constituents on Time, Streamflow, and Season, as Applied in this Study Ordinary least squares regression of water-quality con­ stituents on time, streamflow, and season (OLS) was applied in this study following guidelines presented in Helsel and Hirsch (2002). The regression model used is represented by the equation:

log sin sin( ) b bT b Q b T b T b T t t t t t t ( ) + + + ( ) + ( ) +    cousin + + b T E t t cousin( ) 

log denotes the base-10 logarithm;

Ct is the value of the water-quality constituent or property, in indicated units of measurement, at time t;

b0 is the intercept;

b1 through b6 are the estimated slope b1 coefficients associated with the various explanatory variables;

Tt is decimal time at time t;

Qt is instantaneous streamflow at the time of sampling, in cubic feet per second and variously transformed; sin( ), ( ),sin( ), ( )     T T T T t t t t cousin and cousin

are periodic functions that describe seasonal variability; and

Et is an approximately normally distributed random error. Use of OLS for trend analysis involves regression of constituent concentration eq. (1)] on streamflow [Qt, eq. (1)], which inherently provides for flow adjustment and quantifies concentration and streamflow relations. The residu­ als from the regression of concentration on streamflow repre­ sent flow-adjusted concentrations (FACs; Helsel and Hirsch, 2002). Including periodic functions that describe seasonal variability [ sin( ), ( ),sin( ), ( )     T T T T t t t t cousin and cousin , eq. (1)] accounts for the effect of repetitive seasonal variability on concentration and streamflow relations. The residuals from the regression of concentration on streamflow and the periodic functions represent changes in concentration and streamflow relations through the trend-analysis period. Including decimal time [Tt, eq. (1)] in the model provides quantification of the change in concentration and streamflow relations through time and describes the temporal trend in FACs for the specified trend-analysis period. The slope coefficient for decimal time [b1, eq. (1)] is used to determine the significance and mag­ nitude of the trend. The null hypothesis in the test for trend significance is that there is no trend (that is, b2 0). If the twotailed p-value for b2 is less than the selected alpha level (0.01 in this report), the null hypothesis is rejected and the trend is determined to be significant. Determination of a nonsignifi­ cant trend (that is, a p-value greater than 0.01) does not imply that the null hypothesis is accepted (that is, that there is no trend). It indicates that within the statistical framework of the analysis, a significant trend was not detected. The magnitude of the trend is expressed as the percent difference between the geometric mean concentration at the end of the period and the geometric mean concentration at the start of the period and is determined by the equation

− FAC Nb

%∆FAC is the percent change in the geometric mean of the flow-adjusted concentration; and

N is the number of years in the trend-analysis period. Application of linear regression for flow-adjusted trend analysis requires that the data are normally distributed and that relations between the response variable (a given water-quality constituent) and the combined explanatory variables (time, streamflow, and periodic functions that describe seasonal variability) can be appropriately represented by a linear fit. Further, the relation between the water-quality constituent and streamflow must be statistically significant. Data for many water-quality constituents typically do not conform to a nor­ mal distribution because of positive skew (Helsel and Hirsch, 2002). To approximate normality, constituent concentrations were transformed to logarithm (base 10) units. Best-fit streamflow transformations were determined based on examination of 10 different logarithmic, power, and hyperbolic streamflow transformations. For a given site, the transformation that consistently produced the lowest standard errors among all constituents and properties was selected. Regression diagnostics (including influence and leverage statistics and examination of residuals for normality and homoscedasticity) were reviewed to confirm the acceptability of the selected streamflow transformation in the regression model. In accounting for seasonal variability, 2π and 4π sine and cosine terms were included in the regression model for all site and constituent combinations. During exploratory analysis, different multiples of π were evaluated for signifi­ cant influence in the regression model, and the 2π and 4π terms frequently, but not always, were significant. Inclusion of the periodic functions when they were not significant in the regression model for some site and constituent combinations probably had small effect on the trend analysis results.

96    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Accounting for serial correlation was important in the trend analysis. Most sites were sampled on a monthly or bimonthly basis during water years 2001-10 and significant serial correlation was present. Initially, all samples for a given site were included in the analysis and significant serial correla­ tion was determined if the Spearman's correlation coefficient on the lag-one residuals produced a p-value less than 0.05 (Helsel and Hirsch, 2002). When serial correlation was signifi­ cant, the original data were reduced until serial correlation was not significant. The data reduction was done in a systematic stepwise manner with testing of serial correlation at each of the following steps: Removing the second sample in months with more than one sample; Dividing each year into 10 equally spaced intervals and selecting the sample closest in time to the midpoint of each interval, with all other samples removed; Repeating step 2 with eight and six equally spaced inter­ vals until significant serial correlation was resolved. In a few cases, the selected sample nearest to the mid­ point of a given interval was determined to result in a large influential outlier and was replaced with the next closest sample to the midpoint of the interval. The regression model results for each site and constitu­ ent combination were evaluated by examining the significance of the concentration and streamflow relation, the standard error of prediction, influence and leverage statistics, and homoscedasticity and normality of residuals. For a given site and constituent combination, trend results were not reported if the concentration and streamflow relation was nonsignifi­ cant (p-value greater than 0.05) or the regression model had a standard error of prediction greater than 75 percent. None of the regression models were affected by significant influence. Because of the application of a consistent regression model to the large number of site and constituent combinations, and practical considerations to keep the trend periods comparable among sites and constituents, some minor deviations of the residuals from model assumptions were tolerated. However, the reported regression model results were judged to provide acceptable fits representative of linearity through nearly all of the range in FACs for a given site and constituent combina­ tion. For each site and constituent combination, the fit of the regression model can be assessed by examination of the fitted trends in relation to the FACs that are shown in figures 4.1, 4.2, 4.3, 4.9, and 4.15. For plotting purposes, the FACs were determined by adding the residuals from the regression of con­ centration on streamflow to the geometric mean concentration based on data collected during water years 2001-2010. The distribution of the FACs about the fitted trend lines shows the extent to which the regression model results were affected by factors such as residual heteroscedasticity and curvature.

Supplement 4    97 Supplement 4.  Tables and Figures Presenting Detailed Trend-Analysis Results

98    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 4.1.  Trend-analysis results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010. [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEASC, seasonal concentration anomaly; ANNC, annual concentration anomaly; Mont., Montana; NR, not reported; greater than] Constituent or property Number of samples Estimated total percent change during water years 1986-95 (period 1) p-value for individual trend2 Estimated total percent change during water years 2001-10 (period 2) p-value for individual trend2 p-value for overall trend analysis2 SEASC coefficient p-value for SEASC coefficient ANNC coefficient p-value for ANNC coefficient Tongue River at State line, near Decker, Mont. (site 4, fig. 1) Specific conductance -17 (-22, -10) 5 (-2, 12) Calcium, dissolved -7 (-17, 5) NR3 5 (-1, 11) NR3 Magnesium, dissolved -12 (-28, 7) NR3 -4 (-10, 2) NR3 Potassium, dissolved 0 (-29, 20) NR3 7 (-4, 20) NR3 Sodium adsorption ratio 2 (-15, 24) NR3 7 (-5, 20) NR3 Sodium, dissolved -7 (-17, 21) NR3 7 (-7, 24) NR3 "Estimated alkalinity"4 -12 (-22, 1) NR3 -1 (-6, 4) NR3 Chloride, dissolved -2 (-43, 24) 31 (18, 46) Fluoride, dissolved 14 (-10, 44) NR3 17 (4, 31) NR3 Sulfate, dissolved -23 (-24, 4) NR3 2 (-11, 17) NR3 Solids, dissolved, (sum of constituents) -16 (-30, 3) NR3 -1 (-8, 6) NR3 Tongue River at Tongue River Dam, near Decker, Mont. (site 5, fig. 1) Specific conductance -16 (-19, -12) NR3 1 (-5, 7) NR3 Calcium, dissolved -13 (-16, -9) 0 (-6, 6) Magnesium, dissolved -22 (-26, -17) -1 (-9, 7) Potassium, dissolved -20 (-25, -15) 8 (-3, 19) Sodium adsorption ratio -16 (-20, -11) NR3 38 (28, 49) NR3 Sodium, dissolved -21 (-26, -16) 36 (24, 50) "Estimated alkalinity"4 -10 (-13, -6) 11 (5, 17) Chloride, dissolved -5 (-14, 4) NR3 13 (-1, 29) NR3 Fluoride, dissolved -10 (-17, -1) NR3 33 (19, 49) NR3 Sulfate, dissolved -34 (-39, -29) 8 (-3, 21) Solids, dissolved, (sum of constituents) -22 (-26, -18) 10 (3, 18) Hanging Woman Creek near Birney, Mont. (site 6, fig. 1) Specific conductance 10 (0, 20) 7 (-4, 18) Calcium, dissolved 3 (-5, 13) NR3 12 (0, 25) NR3

Supplement 4    99 Table 4.1.  Trend-analysis results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010.—Continued [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEASC, seasonal concentration anomaly; ANNC, annual concentration anomaly; Mont., Montana; NR, not reported; greater than] Constituent or property Number of samples Estimated total percent change during water years 1986-95 (period 1) p-value for individual trend2 Estimated total percent change during water years 2001-10 (period 2) p-value for individual trend2 p-value for overall trend analysis2 SEASC coefficient p-value for SEASC coefficient ANNC coefficient p-value for ANNC coefficient Hanging Woman Creek near Birney, Mont. (site 6, fig. 1)—Continued Magnesium, dissolved 10 (1, 20) 11 (0, 22) Potassium, dissolved 18 (8, 30) 8 (-3, 20) Sodium adsorption ratio 8 (-1, 18) NR3 -13 (-23, -2) NR3 Sodium, dissolved 13 (1, 27) NR3 -6 (-19, 9) NR3 "Estimated alkalinity"4 -2 (-10, 6) 18 (8, 30) Chloride, dissolved 7 (-8, 25) NR3 -8 (-23, 10) NR3 Fluoride, dissolved -9 (-17, -1) NR3 14 (3, 27) NR3 Sulfate, dissolved 6 (-8, 23) NR3 6 (-12, 28) NR3 Solids, dissolved, (sum of constituents) 5 (-5, 15) NR3 12 (0, 26) NR3 Tongue River at Birney Day School, near Birney, Mont. (site 7, fig. 1) Specific conductance -15 (-19, -10) -2 (-8, 5) Calcium, dissolved -19 (-25, -12) NR3 9 (-2, 21) NR3 Magnesium, dissolved -33 (-39, -26) 20 (6, 36) Potassium, dissolved -24 (-33, -14) 10 (-6, 29) Sodium adsorption ratio -27 (-34, -19) NR3 46 (28, 66) NR3 Sodium, dissolved -35 (-43, -25) NR3 50 (27, 77) NR3 "Estimated alkalinity"4 -12 (-17, -7) 10 (3, 18) Chloride, dissolved -15 (-26, -2) NR3 25 (5, 50) NR3 Fluoride, dissolved -15 (-26, -2) NR3 19 (1, 41) NR3 Sulfate, dissolved -39 (-49, -28) 22 (0, 49) Solids, dissolved, (sum of constituents) -30 (-36, -22) 21 (7, 37) Otter Creek at Ashland, Mont. (site 8, fig. 1) Specific conductance -10 (-14, -5) 15 (8, 22) Calcium, dissolved -14 (-21, -6) NR3 22 (10, 36) NR3 Magnesium, dissolved -11 (-19, -1) NR3 18 (4, 33) NR3 Potassium, dissolved 0 (-8, 9) NR3 -3 (-15, 11) NR3

100    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 4.1.  Trend-analysis results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010.—Continued [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEASC, seasonal concentration anomaly; ANNC, annual concentration anomaly; Mont., Montana; NR, not reported; greater than] Constituent or property Number of samples Estimated total percent change during water years 1986-95 (period 1) p-value for individual trend2 Estimated total percent change during water years 2001-10 (period 2) p-value for individual trend2 p-value for overall trend analysis2 SEASC coefficient p-value for SEASC coefficient ANNC coefficient p-value for ANNC coefficient Otter Creek at Ashland, Mont. (site 8, fig. 1)—Continued Sodium adsorption ratio 5 (0, 9) -2 (-7, 4) Sodium, dissolved -6 (-13, 2) NR3 17 (7, 29) NR3 "Estimated alkalinity"4 0 (-6, 6) 11 (4, 18) Chloride, dissolved 3 (-14, 23) NR3 -13 (-30, 9) NR3 Fluoride, dissolved 5 (-4, 15) NR3 11 (-1, 24) NR3 Sulfate, dissolved -16 (-24, -8) 35 (21, 51) Solids, dissolved, (sum of constituents) -11 (-18, -3) 26 (14, 39) Tongue River at Miles City, Mont. (site 10, fig. 1) Specific conductance -7 (-13, -2) NR3 1 (-6, 10) NR3 Calcium, dissolved -10 (-15, -5) NR3 4 (-2, 12) NR3 Magnesium, dissolved -25 (-31, -18) 14 (2, 27) Potassium, dissolved -21 (-27, -13) NR3 6 (-5, 17) NR3 Sodium adsorption ratio -4 (-13, 6) NR3 7 (-5, 21) NR3 Sodium, dissolved -9 (-19, 2) NR3 7 (-7, 22) NR3 "Estimated alkalinity"4 -3 (-9, 3) NR3 6 (-2, 14) NR3 Chloride, dissolved -14 (-22, -5) 22 (8, 39) Fluoride, dissolved -11 (-19, -2) NR3 20 (6, 35) NR3 Sulfate, dissolved -25 (-33, -17) 9 (-5, 24) Solids, dissolved, (sum of constituents) -14 (-21, -7) 5 (-5, 15) 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Determination of and distinction between p-value for individual trend and p-value for overall trend analysis are discussed in "Supplement 2: Summary of the Time-Series Model (TSM) as Applied in this Study." 3p-value for individual trend period not reported because of nonsignificant overall trend analysis (p-value 0.01), as discussed in "Supplement 2: Summary of the Time-Series Model (TSM) as Applied in this Study." 4"Estimated alkalinity" data were developed by selecting either alkalinity or acid neutralizing capacity (ANC), depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods."

Supplement 4    101 Table 4.2.  Trend-analysis results determined by using ordinary least squares regression (OLS) on time, streamflow, and season for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 2001-10. [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEE, standard error of estimate, in percent; Wyo., Wyoming; log10, logarithm (base 10); HYP, hyperbolic transformation described by 1/(1+(b*Q)), where b is a constant (as indicated) and Q is streamflow, in cubic feet per second; Mont., Montana; NR, not reported] Constituent or property Number of samples Estimated total percent change during trendanalysis period p-value for individual trend Streamflow transformation p-value for streamflow coefficient SEE of regression p-value for regression Tongue River at Monarch, Wyo. (site 1, fig. 1) Trend-analysis period water years 2005-10 Specific conductance 16 (7, 26)

Solids, dissolved, (sum of constituents) 16 (6, 28)

Goose Creek below Sheridan, Wyo. (site 2, fig. 1) Trend-analysis period water years 2001-10 Specific conductance 5 (-9, 21) HYP (b=0.01) Calcium, dissolved 6 (-9, 22) HYP (b=0.01) Magnesium, dissolved 5 (-12, 26) HYP (b=0.01) Potassium, dissolved 1 (-21, 29) HYP (b=0.01) Sodium adsorption ratio -1 (-11, 10) HYP (b=0.01) Sodium, dissolved 2 (-14, 20) HYP (b=0.01) Alkalinity 6 (-9, 22) HYP (b=0.01) Chloride, dissolved 29 (1, 64) HYP (b=0.01) Fluoride, dissolved -3 (-17, 13) HYP (b=0.01) Sulfate, dissolved 1 (-16, 22) HYP (b=0.01) Solids, dissolved, (sum of constituents) 4 (-10, 21) HYP (b=0.01) Trend-analysis period water years 2005-10 Specific conductance -3 (-20, 18) HYP (b=0.01) Calcium, dissolved 0 (-19, 22) HYP (b=0.01) Magnesium, dissolved -9 (-28, 16) HYP (b=0.01) Potassium, dissolved -6 (-31, 27) HYP (b=0.01) Sodium adsorption ratio -6 (-17, 7) HYP (b=0.01) Sodium, dissolved -8 (-26, 14) HYP (b=0.01) Alkalinity 0 (-18, 21) HYP (b=0.01) Chloride, dissolved 18 (-12, 58) HYP (b=0.01) Fluoride, dissolved -2 (-19, 19) HYP (b=0.01) Sulfate, dissolved -11 (-30, 14) HYP (b=0.01) Solids, dissolved, (sum of constituents) -4 (-22, 17) HYP (b=0.01)

102    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 4.2.  Trend-analysis results determined by using ordinary least squares regression (OLS) on time, streamflow, and season for major-ion constituents and properties for sites in the Tongue River watershed, Wyoming and Montana, based on analysis of data collected during water years1 2001-10.—Continued [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEE, standard error of estimate, in percent; Wyo., Wyoming; log10, logarithm (base 10); HYP, hyperbolic transformation described by 1/(1+(b*Q)), where b is a constant (as indicated) and Q is streamflow, in cubic feet per second; Mont., Montana; NR, not reported] Constituent or property Number of samples Estimated total percent change during trendanalysis period p-value for individual trend Streamflow transformation p-value for streamflow coefficient SEE of regression p-value for regression Prairie Dog Creek near Acme, Wyo. (site 3, fig. 1) Trend-analysis period water years 2001-10 Specific conductance 17 (7, 28) HYP (b=0.1) Calcium, dissolved 12 (2, 22) HYP (b=0.1) Magnesium, dissolved 24 (11, 38) HYP (b=0.1) Potassium, dissolved 13 (0, 29) HYP (b=0.1) Sodium adsorption ratio 32 (19, 46) HYP (b=0.1) Sodium, dissolved 43 (24, 65) HYP (b=0.1) Alkalinity 12 (3, 21) HYP (b=0.1) Chloride, dissolved 52 (34, 74) HYP (b=0.1) Fluoride, dissolved 5 (-2, 13) HYP (b=0.1) Sulfate, dissolved 27 (11, 46) HYP (b=0.1) Solids, dissolved, (sum of constituents) 22 (10, 36) HYP (b=0.1) Trend-analysis period water years 2005-10 Specific conductance 17 (5, 32) HYP (b=0.1) Calcium, dissolved 6 (-6, 20) HYP (b=0.1) Magnesium, dissolved 19 (3, 38) HYP (b=0.1) Potassium, dissolved 12 (-6, 33) HYP (b=0.1) Sodium adsorption ratio 32 (16, 51) HYP (b=0.1) Sodium, dissolved 41 (17, 69) HYP (b=0.1) Alkalinity 10 (0, 21) HYP (b=0.1) Chloride, dissolved 57 (36, 82) HYP (b=0.1) Fluoride, dissolved -3 (-12, 7) HYP (b=0.1) Sulfate, dissolved 33 (12, 58) HYP (b=0.1) Solids, dissolved, (sum of constituents) 23 (7, 41) HYP (b=0.1) Pumpkin Creek near Miles City, Mont. (site 9, fig. 1) Trend-analysis period water years 2005-10 Specific conductance 168 (56, 360) HYP (b=0.1) Calcium, dissolved NR2 NR2 HYP (b=0.1) Magnesium, dissolved NR2 NR2 HYP (b=0.1) Potassium, dissolved 123 (47, 239) HYP (b=0.1) Sodium adsorption ratio -3 (-27, 28) HYP (b=0.1) Sodium, dissolved 176 (49, 410) HYP (b=0.1) Alkalinity 85 (24, 178) HYP (b=0.1) Chloride, dissolved 176 (41, 439) HYP (b=0.1) Fluoride, dissolved -12 (-31, 12) HYP (b=0.1) Sulfate, dissolved NR2 NR2 HYP (b=0.1) Solids, dissolved, (sum of constituents) 269 (87, 627) HYP (b=0.1) 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Results not reported because of SEE greater than 75 percent.

Supplement 4    103 Table 4.3.  Trend-analysis results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Powder River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010. [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEASC, seasonal concentration anomaly; ANNC, annual concentration anomaly; Wyo., Wyoming; NR, not reported; Mont., Montana; greater than] Constituent or property Number of samples Estimated total percent change during water years 1986-95 (period 1) p-value for individual trend2 Estimated total percent change during water years 2001-10 (period 2) p-value for individual trend2 p-value for overall trend analysis2 SEASC coefficient p-value for SEASC coefficient ANNC coefficient p-value for ANNC coefficient Powder River at Sussex, Wyo. (site 11, fig. 1) Specific conductance -31 (-35, -26) NR3 8 (1, 16) NR3 Calcium, dissolved 21 (14, 29) NR3 2 (-5, 9) NR3 Magnesium, dissolved 9 (3, 16) NR3 -6 (-11, 0) NR3 Potassium, dissolved -10 (-17, -3) 28 (16, 40) Sodium adsorption ratio -43 (-49, -36) 7 (-8, 23) Sodium, dissolved -53 (-57, -48) NR3 17 (3, 32) NR3 "Estimated alkalinity"4 -37 (-42, -32) 9 (-1, 20) Chloride, dissolved -63 (-67, -58) 44 (24, 67) Fluoride, dissolved -25 (-30, -20) 20 (11, 29) Sulfate, dissolved 14 (6, 23) NR3 -7 (-15, 1) NR3 Solids, dissolved, (sum of constituents) -29 (-33, -24) 8 (0, 16) Powder River at Arvada, Wyo. (site 12, fig. 1) Specific conductance -30 (-34, -25) 9 (1, 18) Calcium, dissolved 14 (5, 22) -23 (-29, -16) Magnesium, dissolved 2 (-5, 11) -16 (-23, -8) Potassium, dissolved -8 (-15, -1) 60 (46, 75) Sodium adsorption ratio -51 (-55, -48) 53 (40, 66) Sodium, dissolved -50 (-55, -46) 39 (25, 54) "Estimated alkalinity"4 -32 (-36, -27) 51 (40, 64) Chloride, dissolved -62 (-66, -57) 37 (21, 55) Fluoride, dissolved -31 (-39, -22) 48 (27, 72) Sulfate, dissolved -2 (-9, 7) -17 (-25, -9) Solids, dissolved, (sum of constituents) -27 (-32, -21) 4 (-4, 13) Powder River at Moorhead, Mont. (site 13, fig. 1) Specific conductance -23 (-27, -18) 4 (-3, 12) Calcium, dissolved 4 (-7, 17) -19 (-29, -8)

104    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 4.3.  Trend-analysis results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Powder River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010.—Continued [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEASC, seasonal concentration C, annual concentration anomaly; Wyo., Wyoming; NR, not reported; Mont., Montana; greater than] Constituent or property Number of samples Estimated total percent change during water years 1986-95 (period 1) p-value for individual trend2 Estimated total percent change during water years 2001-10 (period 2) p-value for individual trend2 p-value for overall trend analysis2 SEASC coefficient p-value for SEASC coefficient ANNC coefficient p-value for ANNC coefficient Powder River at Moorhead, Mont. (site 13, fig. 1)—Continued Magnesium, dissolved -9 (-19, 1) -7 (-19, 5) Potassium, dissolved -14 (-22, -5) 45 (29, 63) Sodium adsorption ratio -39 (-45, -32) 41 (25, 59) Sodium, dissolved -39 (-46, -30) 31 (13, 51) "Estimated alkalinity"4 -36 (-42, -29) 75 (56, 97) Chloride, dissolved -46 (-52, -38) -6 (-18, 8) Fluoride, dissolved -15 (-25, -5) 44 (26, 65) Sulfate, dissolved -7 (-18, 5) -16 (-27, -4) Solids, dissolved, (sum of constituents) -21 (-30, -12) 3 (-9, 16) Little Powder River above Dry Creek, near Weston, Wyo. (site 14, fig. 1) Specific conductance 12 (0, 25) NR3 8 (-5, 22) NR3 Calcium, dissolved 6 (-4, 19) NR3 11 (-4, 27) NR3 Magnesium, dissolved 5 (-7, 20) NR3 6 (-9, 25) NR3 Potassium, dissolved 9 (1, 18) NR3 1 (-9, 11) NR3 Sodium adsorption ratio 6 (-1, 13) 10 (0, 20) Sodium, dissolved 12 (0, 25) 15 (-1, 33) "Estimated alkalinity"4 4 (-6, 15) NR3 13 (0, 27) NR3 Chloride, dissolved 220 (156, 300) 99 (52, 161) Fluoride, dissolved 13 (4, 23) 6 (-4, 18) Sulfate, dissolved 1 (-10, 13) 8 (-6, 24) Solids, dissolved, (sum of constituents) 11 (-1, 24) NR3 10 (-5, 27) NR3 Powder River near Locate, Mont. (site 16, fig. 1) Specific conductance -20 (-26, -14) 12 (2, 23) Calcium, dissolved -4 (-12, 4) -9 (-18, 1) Magnesium, dissolved -13 (-21, -5) NR3 7 (-5, 20) NR3 Potassium, dissolved -11 (-17, -5) 42 (31, 54) anomaly; ANN

Supplement 4    105 Table 4.3.  Trend-analysis results determined by using the time-series model (TSM) for major-ion constituents and properties for sites in the Powder River watershed, Wyoming and Montana, based on analysis of data collected during water years1 1980-2010.—Continued [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEASC, seasonal concentration C, annual concentration anomaly; Wyo., Wyoming; NR, not reported; Mont., Montana; greater than] anomaly; ANN Constituent or property Number of samples Estimated total percent change during water years 1986-95 (period 1) p-value for individual trend2 Estimated total percent change during water years 2001-10 (period 2) p-value for individual trend2 p-value for overall trend analysis2 SEASC coefficient p-value for SEASC coefficient ANNC coefficient p-value for ANNC coefficient Powder River near Locate, Mont. (site 16, fig. 1)—Continued Sodium adsorption ratio -29 (-34, -24) 28 (17, 40) Sodium, dissolved -31 (-37, -24) 29 (14, 47) "Estimated alkalinity"4 -15 (-20, -9) 20 (11, 30) Chloride, dissolved -56 (-61, -51) 36 (16, 59) Fluoride, dissolved -15 (-22, -9) 33 (21, 47) Sulfate, dissolved -13 (-21, -3) NR3 6 (-6, 21) NR3 Solids, dissolved, (sum of constituents) -21 (-28, -13) 13 (1, 26) 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Determination of and distinction between p-value for individual trend and p-value for overall trend analysis are discussed in "Supplement 2: Summary of the Time-Series Model (TSM) as Applied in this Study." 3p-value for individual trend period not reported because of nonsignificant overall trend analysis (p-value 0.01), as discussed in "Supplement 2: Summary of the Time-Series Model (TSM) as Applied in this Study." 4 "Estimated alkalinity" data were developed by selecting either alkalinity or acid neutralizing capacity (ANC), depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods."

106    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Table 4.4.  Trend-analysis results determined by using ordinary least squares regression (OLS) on time, streamflow, and season for major-ion constituents and properties for Little Powder River near Broadus, Mont. based on analysis of data collected during water years1 2001-10. [Values in parentheses indicate 95-percent confidence intervals. Gray shading indicates statistical significance at p-value 0.01. p-value, statistical significance level; less than; SEE, standard error of estimate, in percent; Mont., Montana; log10, logarithm (base 10); HYP, hyperbolic transformation described by 1/(1+(b*Q)), where b is a constant (as indicated) and Q is streamflow, in cubic feet per second; NR, not reported; greater than] Constituent or property Number of samples Estimated total percent change during trendanalysis period p-value for individual trend Streamflow transformation p-value for streamflow coefficient SEE of regression p-value for regression Little Powder River near Broadus, Mont. (site 15, fig. 1) Trend-analysis period water years 2005-10 Specific conductance 36 (16, 59) HYP (b=0.01) Calcium, dissolved 30 (3, 64) HYP (b=0.01) Magnesium, dissolved NR2 NR2 HYP (b=0.01) Potassium, dissolved NR2 NR2 HYP (b=0.01) Sodium adsorption ratio 11 (-2, 26) HYP (b=0.01) Sodium, dissolved 34 (12, 59) HYP (b=0.01) Alkalinity 12 (-4, 31) HYP (b=0.01) Chloride, dissolved 61 (32, 98) HYP (b=0.01) Fluoride, dissolved -4 (-19, 13) HYP (b=0.01) Sulfate, dissolved 51 (22, 87) HYP (b=0.01) Solids, dissolved, (sum of constituents) 41 (17, 69) HYP (b=0.01) 1Water year is the 12-month period from October 1 through September 30 of the following calendar year. The water year is designated by the calendar year in which it ends. For example, water year 2009 is the period from October 1, 2008, through September 30, 2009. 2Results not reported because of nonsignificant relation between constituent and streamflow (p-value 0.05).

Supplement 4    107 Table 4.5.  Information on percent differences in cation and anion balances for fitted trends and flow-adjusted concentrations for selected sampling sites in the Tongue and Powder River watersheds, Montana and Wyoming. [Wyo., Wyoming; OLS, ordinary least squares regression on time, streamflow, and season; Mont., Montana; TSM, time-series model] Site number (fig. 1) USGS site name Trend analysis method Mean (and range) of percent differences in the cation and anion balances for fitted trends Mean (and range) of percent differences in the cation and anion balances (range) for flow-adjusted concentrations Tongue River watershed Tongue River at Monarch, Wyo. OLS -1.1 (-1.8 to -0.44) -1.0 (-2.4 to +0.24) Goose Creek below Sheridan, Wyo. OLS -0.08 (+0.02 to -0.06) +0.48 (+0.34 to +0.60) Prairie Dog Creek near Acme, Wyo. OLS +0.50 (+0.29 to +0.74) +0.48 (+0.37 to +0.63) Tongue River at State line, near Decker, Mont. TSM +5.6 (+3.4 to +7.0) +4.6 (-28 to +15) Tongue River at Tongue River Dam, near Decker, Mont. TSM +1.8 (+0.68 to +2.7) +0.68 (-7.0 to +10) Hanging Woman Creek near Birney, Mont. TSM +1.3 (-0.35 to +3.2) +0.48 (-6.1 to +11) Tongue River at Birney Day School, near Birney, Mont. TSM -1.7 (-3.0 to -0.35) -1.0 (-5.6 to +5.7) Otter Creek at Ashland, Mont. TSM +0.46 (-2.0 to +1.5) -0.07 (-6.4 to +7.1) Pumpkin Creek near Miles City, Mont. OLS +2.9 (-0.63 to +9.7) +0.24 (-0.60 to +2.5) Tongue River at Miles City, Mont. TSM -0.47 (-0.79 to -0.18) +0.05 (-11 to +7.3) Powder River watershed Powder River at Sussex, Wyo. TSM +0.23 (-2.3 to +3.8) -0.22 (-10 to +10) Powder River at Arvada, Wyo. TSM +0.28 (-1.6 to +2.1) -0.14 (-9.0 to +10) Powder River at Moorhead, Mont. TSM -0.60 (-1.1 to +0.90) 0.00 (-7.0 to +6.2) Little Powder River above Dry Creek, near Weston, Wyo. TSM -1.5 (-3.0 to +0.54) -1.5 (-15 to +6.7) Little Powder River near Broadus, Mont. OLS -1.8 (-2.6 to -0.98) -1.6 (-2.2 to -1.1) Powder River near Locate, Mont. TSM -0.34 (-0.49 to +0.08) +0.64 (-7.3 to +6.2)

108    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds No substantial CBM-extraction activities in watershed No substantial CBM-extraction activities in watershed Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Sodium (milligrams per liter) Chloride (milligrams per liter) Sulfate (milligrams per liter) Dissolved solids (milligrams per liter) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Alkalinity (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using ordinary least squares regression on time, streamflow, and season—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using ordinary least squares regression on time, streamflow, and season No substantial coal-bed methane-extraction activities in watershed No substantial coal-bed methane-extraction activities in watershed Figure 4.1.  Fitted trends determined by using ordinary least squares regression (OLS) on time, streamflow, and season for selected major-ion constituents and properties for site 1 (Tongue River at Monarch, Wyo.; station 06299980), based on analysis of available data collected during water years 2001-2010.

Supplement 4    109 No substantial CBM-extraction activities in watershed No substantial CBM-extraction activities in watershed Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Sodium (milligrams per liter) Chloride (milligrams per liter) Sulfate (milligrams per liter) Dissolved solids (milligrams per liter) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Alkalinity (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using ordinary least squares regression on time, streamflow, and season—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using ordinary least squares regression on time, streamflow, and season No substantial coal-bed methane-extraction activities in watershed No substantial coal-bed methane-extraction activities in watershed 1,000 Figure 4.2.  Fitted trends determined by using ordinary least squares regression (OLS) on time, streamflow, and season for selected major-ion constituents and properties for site 2 (Goose Creek below Sheridan, Wyo.; station 06305500).

110    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds No substantial CBM-extraction activities in watershed No substantial CBM-extraction activities in watershed Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Sodium (milligrams per liter) Chloride (milligrams per liter) Sulfate (milligrams per liter) Dissolved solids (milligrams per liter) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Alkalinity (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using ordinary least squares regression on time, streamflow, and season—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using ordinary least squares regression on time, streamflow, and season 1,000 1,000 1,500 2,000 2,500 Figure 4.3.  Fitted trends determined by using ordinary least squares regression (OLS) on time, streamflow, and season for selected major-ion constituents and properties for site 3 (Prairie Dog Creek near Acme, Wyo.; station 06306250).

Supplement 4    111 Figure 4.4. Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 4 (Tongue River at State line, near Decker, Mont.; station 06306300).

112    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Sodium (milligrams per liter) Chloride (milligrams per liter) Sulfate (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Specific conductance (microsiemens per centimeter at 25 degrees Celsius) EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000

Figure 4.5.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 5 (Tongue River at Tongue River Dam, near Decker, Mont.; station 06307500).

Supplement 4    113 Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 1,000 1,500 1,000 2,000 3,000 4,000 Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Chloride (milligrams per liter) Sulfate (milligrams per liter)

Figure 4.6.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 6 (Hanging Woman Creek near Birney, Mont.; station 06307600).

114    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Chloride (milligrams per liter) Sulfate (milligrams per liter) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 Specific conductance (microsiemens per centimeter at 25 degrees Celsius)

Figure 4.7.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site River at Birney Day School, near Birney, Mont.; station 06307616).

Supplement 4    115 Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Chloride (milligrams per liter) Sulfate (milligrams per liter) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 1,000 1,500 1,000 2,000 3,000 4,000 Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) No substantial coal-bed methane-extraction activities in watershed No substantial coal-bed methane-extraction activities in watershed

Figure 4.8.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 8 (Otter Creek at Ashland, Mont.; station 06307740).

116    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds No substantial coal-bed methane-extraction activities in watershed No substantial CBM-extraction activities in watershed Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Sodium (milligrams per liter) Chloride (milligrams per liter) Sulfate (milligrams per liter) Dissolved solids (milligrams per liter) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Alkalinity (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using ordinary least squares regression on time, streamflow, and season—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using ordinary least squares regression on time, streamflow, and season 1,000 2,000 3,000 4,000 5,000 6,000 1,000 OLS results not presented because of standard error of prediction greater than 75 percent. Graph included as a place holder to assist in comparison with other stations. OLS results not presented because of standard error of prediction greater than 75 percent. Graph included as a place holder to assist in comparison with other stations. OLS results not presented because of standard error of prediction greater than 75 percent. Graph included as a place holder to assist in comparison with other stations. Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Figure 4.9.  Fitted trends determined by using ordinary least squares regression (OLS) on time, streamflow, and season for selected major-ion constituents and properties for site 9 (Pumpkin Creek near Miles City, Mont.; station 06308400).

Supplement 4    117 Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Chloride (milligrams per liter) Sulfate (milligrams per liter) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 1,500 Specific conductance (microsiemens per centimeter at 25 degrees Celsius)

Figure 4.10.   Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 10 (Tongue River at Miles City, Mont.; station 06308500).

118    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Sulfate (milligrams per liter) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 1,500 1,000 2,000 3,000 4,000 No substantial coal-bed methane-extraction activities in watershed No substantial coal-bed methane-extraction activities in watershed Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Chloride (milligrams per liter) Chloride (milligrams per liter)

Figure 4.11.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 11 (Powder River at Sussex, Wyo.; station 06313500).

Supplement 4    119 Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Chloride (milligrams per liter) Sulfate (milligrams per liter) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 1,500 1,000 2,000 3,000 4,000 Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Specific conductance (microsiemens per centimeter at 25 degrees Celsius)

Figure 4.12.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 12 (Powder River at Arvada, Wyo.; station06317000).

120    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Chloride (milligrams per liter) Sulfate (milligrams per liter) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 1,000 2,000 3,000 Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Specific conductance (microsiemens per centimeter at 25 degrees Celsius)

Figure 4.13.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 13 (Powder River at Moorhead, Mont.; station 06324500).

Supplement 4    121 Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Chloride (milligrams per liter) Sulfate (milligrams per liter) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 2,000 3,000 4,000 1,000 1,500 2,000

Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Figure 4.14.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 14 (Little Powder River above Dry Creek, near Weston, Wyo.; station 06324970).

122    Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds No substantial CBM-extraction activities in watershed No substantial CBM-extraction activities in watershed Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Sodium (milligrams per liter) Chloride (milligrams per liter) Sulfate (milligrams per liter) Dissolved solids (milligrams per liter) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Alkalinity (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using ordinary least squares regression on time, streamflow, and season—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using ordinary least squares regression on time, streamflow, and season 1,000 2,000 3,000 1,000 2,000 3,000 4,000 5,000 1,000 Ordinary least squares regression on time, streamflow, and season results not presented because of nonsignificantrelation between constituent and streamflow. Graph included as a place holder to assist in comparison with other stations. Figure 4.15.  Fitted trends determined by using ordinary least squares regression (OLS) on time, streamflow, and season for selected major-ion constituents and properties for site 15 (Little Powder River near Broadus, Mont.; station 06325500).

Supplement 4    123 Water year Calcium (milligrams per liter) Magnesium (milligrams per liter) Sodium adsorption ratio (dimensionless) Chloride (milligrams per liter) Sulfate (milligrams per liter) Sodium (milligrams per liter) Dissolved solids (milligrams per liter) Estimated alkalinity* (milligrams per liter as calcium carbonate) Flow-adjusted values, in indicated units of measurement Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin Period 2 10-year trend-analysis period after substantial coal-bed methane-extraction activities in the Powder River structural basin Period 1 10-year trend-analysis period before substantial coal-bed methane-extraction activities in the Powder River structural basin EXPLANATION [Water year is defined as the 12-month period from October 1 through September 30, and is designated by the calendar year in which it ends] Fitted trend determined by using time-series model—Bold line segments indicate statistical significance at p-value less than 0.01 Flow-adjusted concentration determined by using the time-series model *Estimated alkalinity data were developed by selecting either alkalinity or acid neutralizing capacity measurements, depending primarily on which measurement was available for a given sample, as discussed in the section of this report "Sampling and Analytical Methods." 1,000 1,500 1,000 2,000 3,000 Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Specific conductance (microsiemens per centimeter at 25 degrees Celsius) Figure 4.16.  Fitted trends determined by using the time-series model for selected major-ion constituents and properties for site 16 (Powder River near Locate, Mont.; station 06326500).

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Sando and others—Trends in Major-Ion Constituents and Properties for Selected Sampling Sites in the Tongue and Powder River Watersheds—SIR 2013-5179 http://dx.doi.org.10.3133/sir20135179 ISSN 2328-031X (print) ISSN 2328-0328 (online) 3 3 7 5 9 6 7 8 1 4 1 1 ISBN 978-1-4113-3759-6

Plates & figures from the original