Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow

Home , Musselshell River

Prepared in cooperation with the Montana Department of Transportation and Montana Department of Natural Resources and Conservation

Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing for Selected Long-Term Streamflow- Gaging Stations in or near Montana through Water Year 2011

Chapter B of Montana StreamStats

Scientific Investigations Report 2015–5019–B

U.S. Department of the Interior U.S. Geological Survey Cover photograph: Swiftcurrent Creek at Many Glacier, Montana. Photograph by Don Bischoff, U.S. Geological Survey, November 7, 2006. Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing for Selected Long-Term Streamflow-Gaging Stations in or near Montana through Water Year 2011

By Steven K. Sando, Peter M. McCarthy, Roy Sando, and DeAnn M. Dutton

Chapter B of Montana StreamStats

Prepared in cooperation with the Montana Department of Transportation and Montana Department of Natural Resources and Conservation

Scientific Investigations Report 2015–5019–B

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, Director

U.S. Geological Survey, Reston, Virginia: 2016

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Suggested citation: Sando, S.K., McCarthy, P.M., Sando, Roy, and Dutton, D.M., 2016, Temporal trends and stationarity in annual peak flow and peak-flow timing for selected long-term streamflow-gaging stations in or near Montana through water year 2011: U.S. Geological Survey Scientific Investigations Report 2015–5019–B, 48 p., http://dx.doi.org/10.3133/ sir20155019B.

ISSN 2328-0328 (online) iii

Contents

Acknowledgments...... vi Abstract...... 1 Introduction...... 2 Purpose and Scope...... 2 Selection of Streamflow-Gaging Stations...... 2 Methods of Analysis...... 7 Factors that Affect Interpretation of Results...... 8 Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing...... 9 Streamflow-Gaging Stations in the Saskatchewan River Basin...... 9 Streamflow-Gaging Stations in the Missouri River Basin...... 21 Missouri River Headwaters Tributaries...... 21 Upper Missouri River Tributaries...... 23 Musselshell River Basin...... 25 Upper Milk River Basin...... 25 Lower Missouri River Tributary...... 25 Yellowstone River Basin...... 26 Streamflow-Gaging Stations in the Columbia River Basin...... 33 Summary Observations...... 33 Discussion of Stationarity Issues for Low-Elevation Streamflow-Gaging Stations in Eastern Montana...... 37 Summary and Conclusions...... 39 References...... 40 Appendix 1. Information on Peak-Flow Frequency Analyses for Low-Elevation Streamflow- Gaging Stations in Eastern Montana...... 44

Figures

1. Map showing location of selected long-term streamflow-gaging stations in or near Montana...... 4 2. Graphs showing fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for streamflow-gaging stations in the Saskatchewan River Basin...... 20 3. Graphs showing fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for streamflow-gaging stations on Missouri River headwaters tributaries...... 22 4. Graphs showing fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for streamflow-gaging stations on upper Missouri River tributaries...... 24 5. Graphs showing fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for the streamflow-gaging station in the Musselshell River Basin...... 26 iv

6. Graphs showing fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for the streamflow-gaging station in the upper Milk River Basin...... 27 7. Graphs showing fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for the streamflow-gaging station on a lower Missouri River tributary...... 28 8. Graphs showing fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for streamflow-gaging stations in the Yellowstone River Basin...... 29 9. Graphs showing fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for streamflow-gaging stations in the Columbia River Basin...... 34

Appendix Figure

1–1. Graphs showing annual peak flows and peak-flow frequency curves for low-elevation streamflow-gaging stations in eastern Montana...... 48

Tables

1. Information for selected long-term gaging stations in or near Montana...... 5 2. Results of analysis of temporal trends in annual peak flow...... 10 3. Results of analysis of temporal trends in peak-flow timing...... 14 4. Statistical summaries of annual peak flow and peak-flow timing for summary time periods...... 18

Appendix Tables

1–1. Documentation regarding analytical procedures for peak-flow frequency analyses for low-elevation streamflow-gaging stations in eastern Montana...... 45 1–2. Peak-flow frequency results for low-elevation streamflow-gaging stations in eastern Montana...... 47 v

Conversion Factors

[U.S. customary units to International System of Units] Multiply By To obtain Length foot (ft) 0.3048 meter (m) mile (mi) 1.609 kilometer (km) Area square mile (mi2) 259.0 hectare (ha) square mile (mi2) 2.590 square kilometer (km2) Volume cubic foot (ft3) 28.32 cubic decimeter (dm3) cubic foot (ft3) 0.02832 cubic meter (m3) Flow rate cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Datum

Horizontal coordinate information is referenced to North American Datum of 1983 (NAD 83). Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88). Elevation, as used in this report, refers to distance above the vertical datum.

Supplemental Information

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 2011 is the period from October 1, 2010, through September 30, 2011.

Abbreviations

AEP annual exceedance probability GIS geographic information system LOWESS locally weighted scatterplot smooth NAVD 88 North American Vertical Datum of 1988 p-value statistical significance level USGS U.S. Geological Survey vi

Acknowledgments

Thanks are given to Greg Pederson of the U.S. Geological Survey for providing information on climatic processes in Montana. The authors would like to recognize the U.S. Geological Sur- vey hydrologic technicians involved in the collection of the peak-flow data for their dedicated efforts. The authors also would like to recognize the valuable contributions to this report chapter from the insightful technical reviews by Dave Bender and Kirk Miller of the U.S. Geological Survey.

Special thanks are given to Mark Goodman and Dave Hedstrom of the Montana Department of Transportation, and Steve Story of the Montana Department of Natural Resources and Conserva- tion for their support of this study. Thanks also are given to Kelsey Jencson of the University of Montana for providing information on climatic processes in Montana. Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing for Selected Long-Term Streamflow- Gaging Stations in or near Montana through Water Year 2011

By Steven K. Sando, Peter M. McCarthy, Roy Sando, and DeAnn M. Dutton

Abstract are variable and not particularly strong. Statistical distributions generally are similar among the summary time periods. A large-scale study by the U.S. Geological Survey, in However, for two high-elevation gaging stations on a Mis- cooperation with the Montana Department of Transporta- souri River headwater tributary (Gallatin River near Gallatin tion and the Montana Department of Natural Resources and Gateway, Montana [gaging station 06043500] and Gallatin Conservation, was done to investigate general patterns in River at Logan, Montana [gaging station 06052500]) and for peak-flow temporal trends and stationarity through water year five high-elevation gaging stations in the Yellowstone River 2011 for 24 long-term streamflow-gaging stations (hereinafter Basin (Yellowstone River at Corwin Springs, Montana [gag- referred to as gaging stations) in Montana. Hereinafter, all ing station 06191500], Yellowstone River near Livingston, years refer to water years; a water year is the 12-month period Montana [gaging station 06192500], Clarks Fork Yellowstone from October 1 through September 30 and is designated by River near Belfry, Montana [gaging station 06207500], Clarks the year in which it ends. The primary focus of the study was Fork Yellowstone River at Edgar, Montana [gaging station to identify general patterns in peak-flow temporal trends and 06208500], and Yellowstone River at Billings, Montana [gag- stationarity that are relevant to application of peak-flow fre- ing station 06214500]) downward trends in peak-flow timing quency analyses within a statewide gaging-station network. during 1967–2011 generally were stronger than upward trends Temporal trends were analyzed for two hydrologic vari- during 1930–1976, and day-of-peak medians for 1979–2011 ables: annual peak flow and peak-flow timing. Annual peak were considerably less than medians for 1930–78. The down- flow is the maximum instantaneous discharge, in cubic feet ward trends in peak-flow timing for 1967–2011 indicate that per second, recorded each year a gaging station was operated. the timing of annual peak flows changed from later in the year Peak-flow timing is the day of the annual peak flow (herein- to earlier in the year. For the seven high-elevation gaging sta- after referred to as day of peak), recorded each year a gaging tions, the mean change during 1967–2011 was about 13 days station was operated. (range of 8 to 22 days). Study results provide evidence that annual peak flow for For most of the high-elevation gaging stations in the most of the long-term gaging stations can be reasonably con- Missouri River headwaters, Yellowstone River Basin, and sidered as stationary for application of peak-flow frequency Columbia River Basin, there was general correspondence analyses within a statewide gaging station network. Upward between trend patterns for annual peak flow and trend patterns trends in annual peak flow during 1930–76 generally were for peak-flow timing; that is, during periods when there were stronger than downward trends during 1967–2011 for most upward trends in annual peak flow, there generally also were long-term gaging stations. Statistical distributions of annual upward trends in peak-flow timing. Conversely, during periods peak flow generally were similar among three summary time when there were downward trends in annual peak flow, there periods (1930–78, 1979–2011, and the entire period of record). generally also were downward trends in peak-flow timing. However, for two low-elevation gaging stations in eastern The two low-elevation gaging stations in eastern Mon- Montana (Poplar River at international boundary [gaging tana (Poplar River at international boundary [gaging station station 06178000] and Powder River at Moorhead, Montana 06178000] and Powder River at Moorhead, Montana [gaging [gaging station 06324500]), substantial downward trends in station 06324500]) had considerable changes in annual-peak- annual peak flow during 1967–2011 were of similar or stron- flow characteristics after the mid-1970s, which might provide ger magnitude than the upward trends during 1930–76, and the evidence of potential nonstationarity in the peak-flow records. annual-peak-flow medians for 1979–2011 were substantially The two low-elevation gaging stations that have potential lower than the medians for the entire period of record. nonstationarity are located in drainage basins that are strongly For peak-flow timing for most long-term gaging sta- affected by agricultural activities that potentially affect the tions, differences in trends between 1930–76 and 1967–2011 hydrologic regimes. Primary agricultural activities that might 2 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana alter natural hydrologic conditions include construction of per second associated with given annual exceedance prob- small impoundments (primarily for stock-watering purposes) abilities (AEPs), in percent. Preliminary to the investigation and irrigation diversions. Temporal variability in these activi- of peak-flow frequency analyses, a large-scale study was done ties might contribute to the potential nonstationarity issues. to investigate general patterns in peak-flow temporal trends Changes in climatic characteristics after the mid-1970s also and stationarity for Montana gaging stations. Temporal trends possibly contribute to the potential nonstationarity issues. were analyzed for two hydrologic variables: annual peak flow Lack of considerable indication of potential nonstationarity and peak-flow timing. Annual peak flow is the annual series in annual peak flow for the other long-term gaging stations of maximum instantaneous discharge in cubic feet per second, in this study might indicate that climatic changes have been which is recorded for each water year that a gaging station is more pronounced with respect to effects on peak flows in low- operated. Peak-flow timing is the annual series of the day of elevation areas in eastern Montana than in areas represented the annual peak flow (hereinafter referred to as day of peak). by the other long-term gaging stations. Another possibility is The primary focus of the study was to identify general pat- that climatic changes after the mid-1970s are exacerbated in terns in peak-flow temporal trends and stationarity through low-elevation areas where small-impoundment development water year 2011 that are relevant to application of peak-flow and potential effects of irrigation diversions might be more frequency analyses within a statewide gaging-station network; extensive. a water year is the 12-month period from October 1 through September 30 and is designated by the year in which it ends. Emphasis is placed on annual peak flow because of direct relevance to peak-flow frequency analysis; however, peak-flow Introduction timing was included in the study because although peak-flow timing data are not directly relevant to peak-flow frequency Concerns about increasing global temperatures since the analysis, peak-flow timing is of interest to many users of peak- mid-1970s (National Aeronautics and Space Administration flow frequency data. Goddard Institute for Space Studies, 2013) have prompted extensive research on environmental effects of climate change. Investigators have reported hydrologic effects (for example, Purpose and Scope Wahl, 1992; McCabe and Clark, 2005; Pederson and others, 2011) associated with reported changes in climatic conditions. The study described in Chapter B of this Scientific Inves- Of particular note, several studies have reported declining tigations Report is part of a larger study to develop a Stream- trends in snowpack (Stewart and others, 2004; Mote and oth- Stats application for Montana, compute streamflow charac- ers, 2005; Pederson and others, 2013), earlier snowmelt runoff teristics at streamflow-gaging stations, and develop regional (Dettinger and Cayan, 1995; Cayan and others, 2001), and regression equations to estimate streamflow characteristics at declining trends in some streamflow characteristics (West- ungaged sites (as described fully in Chapters A through G of macott and Burn, 1997; Aziz and Burn, 2006) in the western this Scientific Investigations Report). The primary purpose United States and Canada. The reported changes in hydro- of Chapter B is to present the results of a large-scale study to logic regimes have the potential to affect the stationarity of investigate general patterns in peak-flow temporal trends and annual peak-flow records. Hirsch (2011) noted the importance stationarity through water year 2011 for Montana gaging sta- of repeated analysis of long-term datasets to assist in water- tions; hereinafter, all references to specific years refer to water resources management and structure-design activities that are years in this report chapter. Temporal trends in annual peak dependent on hydrologic variables. flow and peak-flow timing for 24 long-term gaging stations Stationarity is an important issue in the statistical analysis are reported and described. The primary focus of the study of hydrologic characteristics. For a given streamflow-gaging was to identify general patterns in peak-flow temporal trends station (hereinafter referred to as gaging station), stationarity and stationarity that are relevant to application of peak-flow of annual peak-flow requires that all of the data represent a frequency analyses within a statewide gaging-station network. consistent hydrologic regime within the same (albeit highly variable) fundamental climatic system. If the fundamental climatic system has substantially shifted such that a new Selection of Streamflow-Gaging fundamental system exists, appropriate statistical analysis of hydrologic characteristics might require restricting the analysis Stations to the data that represent the new system. The U.S. Geological Survey (USGS), in cooperation with More than 700 gaging stations with 10 or more years of the Montana Department of Transportation and the Montana annual peak-flow records have been operated by the USGS Department of Natural Resources and Conservation, com- in Montana and for which peak-flow frequency analyses are pleted an investigation of peak-flow frequency analyses for reported. Initially, 725 gaging stations were screened for inclu- gaging stations in Montana (Sando and others, 2016). Peak- sion in this study based on the following selection criteria: flow frequencies refer to peak-flow magnitudes, in cubic feet (1) at least 75 years of annual peak-flow records with largely Selection of Streamflow-Gaging Stations 3 unbroken series (that is, generally few missing years in the further described in the section “Methods of Analysis”). The systematic record), (2) at least 5 years of data in the 1930s (a long record-length requirement allows thorough evaluation of particularly dry period that can substantially affect the peak- potential changes in peak-flow characteristics after the mid- flow characteristics of an individual gaging station), and (3) 1970s in relation to temporal patterns in characteristics before generally small effects from urbanization or large reservoir the mid-1970s. storage. The screening process resulted in selection of 24 long- Although there is some hydrologic and topographic term gaging stations (fig. 1, table 1; map numbers assigned diversity among the 24 long-term gaging stations, they provide according to McCarthy and others, 2016) for inclusion in poor representation of the entirety of Montana. Most of the the study of peak-flow temporal trends and stationarity. The 24 gaging stations are high elevation (mean basin elevation selected 24 long-term gaging stations represent the only gag- greater than about 6,000 feet [ft]), whereas much of Montana ing stations out of the 725 screened gaging stations that met all is below 6,000 ft. Furthermore, most of the gaging stations of the selection criteria. have relatively large drainage basins (greater than about Several of the gaging stations with large drainage basins 1,000 square miles [mi2]). These large drainage basins serve contain large urban areas that have substantially increased as integrators of climatic effects over large areas but probably in size during the periods of data collection. Urbanization do not provide good representation of the larger variability can affect hydrologic characteristics in several ways, with in peak-flow characteristics that is typical for smaller drain- increases in impervious area and runoff potential being a age basins. This study represents an initial effort to evaluate primary factor. Geographic information system (GIS) analysis general patterns in peak-flow temporal trends and stationarity of the 2001 National Land Cover Dataset (Homer and others, that are relevant to application of peak-flow frequency analy- 2007) was done to estimate the urban area (as determined by ses within a statewide gaging-station network. As such, there the area of high-intensity residential development) within the was purposeful emphasis on long-term datasets to allow full drainage basin for each of the gaging stations. In no case did temporal representation within the period of peak-flow record the urban area account for more than about 3 percent of the collection in Montana; however, the rigorous dataset require- drainage basin of an individual gaging station; therefore, it ments result in poor representation of the entirety of Montana. was presumed that temporal variability in urbanization within Future studies on peak-flow temporal trends and stationarity relatively small areas would have small effects on temporal might include relaxing the dataset requirements to provide trends in streamflow characteristics. representation of a broader range in areal, hydrologic, and Reservoir storage and operations have the potential to topographic characteristics. affect temporal variability in streamflow characteristics. The The 24 long-term gaging stations are grouped according current (2015) criterion used by the USGS in this study classi- to the following major river basins: Saskatchewan River Basin fies a gaging station as affected by major dam regulation if the (2 gaging stations); Missouri River Basin (16 gaging stations); drainage area upstream from a single upstream dam exceeds and Columbia River Basin (6 gaging stations). Gaging stations 20 percent of the drainage area for the gaging station. Specific in the Missouri River are subgrouped according to the follow- methods used to determine the regulation classification of a ing descriptive classes: (1) Missouri River headwaters tributar- gaging station are described by McCarthy and others (2016). ies (three gaging stations); (2) upper Missouri River tributaries Based on the regulation-classification criterion, none of the (two gaging stations); (3) Musselshell River Basin (one gaging 24 long-term gaging stations included in this study are con- station); (4) upper Milk River Basin (one gaging station); sidered to be affected by major dam regulation. Furthermore, (4) lower Missouri River tributary (one gaging station); and in previous peak-flow frequency studies for Montana (for (5) Yellowstone River Basin (eight gaging stations). example, Parrett and Johnson, 2004), all of the selected long- Several factors contribute to difficulties in making rigor- term gaging stations were considered to be unregulated. ous statistical comparisons among gaging stations and among The datasets of the 24 gaging stations are somewhat groups of gaging stations. The 24 gaging stations represent diverse, both with respect to the represented hydrologic somewhat of a diversity in hydrologic regimes that have regimes and the temporal data-collection characteristics. The relatively large variability in temporal patterns in peak-flow study was restricted to long-term gaging stations to ensure characteristics. The numbers of gaging stations vary substan- representation of a substantial time period before and after the tially among groups. Within groups, there also is variation in mid 1970s. This key breakpoint (the mid-1970s) was based on the temporal data-collection characteristics among the gaging increasing global temperatures since the mid-1970s (National stations. In some cases, multiple gaging stations are located Aeronautics and Space Administration Goddard Institute for on the same channel. In most of these cases, there is at least Space Studies, 2013) and various reported hydrologic effects a two-fold increase in drainage area between the gaging sta- (for example, Wahl, 1992; Westmacott and Burn, 1997; tions; however, in a few cases, the increase in drainage area McCabe and Clark, 2005; Aziz and Burn, 2006; Pederson and between the gaging stations is less than two fold and there is others, 2011) associated with reported changes in climatic potential for introduction of redundant information. Given conditions. The key mid-1970s breakpoint also was generally these factors, the datasets are not well suited for a rigorous identified as a transition point in large-scale temporal pat- statistical analysis focused on detailed definition and evalu- terns of peak flows for long-term Montana gaging stations (as ation of temporal trends in peak-flow characteristics. Rather, 4 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

BRITISH St Mary 116o COLUMBIA River 115° Milk 49° 698 114° 105° SASKATCHEWAN 113° 106° 386 14 271 112° ALBERTA 111° 110° 109° 108° 107° North CANADA F Poplar River Lodge r Battle enchman MONTANA River UNITED STATES NORTH DAKOTA Lake 9 Milk River Creek River Koocanusa Fork Creek

Yaak Creek River Bank Troy Cut Kootenai Havre Milk CONTINENTAL 700 Two River Shelby Libby Marias s n i a t n u o M y k c o R Medicine Medicine Middle 161 River Lake River Malta Cr Kalispell River Clark Flathead R. Birch Fork Glasgow Missouri River 48° 728

Fork Flathead River IDAHO Lake Swan South Teton Sidney

River

DIVIDE River River Fort Peck Fork

River Reservoir Sun River Redwater River Great Creek Flathead Falls Dry 697 Dearborn Boxelder Big Jordan River Glendive Missouri Creek Smith Lewistown 47° Mosby Judith Missoula River River 688 Blackfoot River 665 Clark

Helena Tenmile Cr. Creek River Harlowton 212 Miles City River 101 Fork DIVIDE Yellowstone Hamilton Musselshell

Armells

Rock Butte Creek 46° Bitterroot River River Big 88 Big Timber River ° CONTINENTAL Hole River EXPLANATION River SOUTH DAKOTA Billings Hardin Little Jefferson 458 River Ashland Basin Bozeman Livingston River Yellowstone Bighorn Saskatchewan River River River 45 Ruby 443 80 425 Pryor Tongue R 448 River Broadus

Missouri River River Bighorn Stillwater Fork Powder Columbia River Madison Dillon

Boulder Beaverhead Gallatin 14 Long-term streamflow-gaging station (number River Bighorn 424 Clarks 542 corresponds to map number in table 1) Lake 45° 445 Base modified from U.S. Geological Survey State base map, 1968 WYOMING North American Datum of 1983 (NAD 83)

0 10 20 30 40 50 MILES 0 10 20 30 40 50 KILOMETERS 414

Yellowstone Lake Figure 1. Location of selected long-term streamflow-gaging stations in or near Montana. Selection of Streamflow-Gaging Stations 5 Annual peak record through flows period of water year 2011 1909–2011 1902–04, 1906– 07, 1911–46, 1948–2011 1915–94, 1997–2011 1895–1900, 1902–05, 1929– 33, 1935–2011 1890–1894, 1931–81, 1985–2011 1931, 1933–2011 1924–40, 1942–2011 1903–71, 1973, 1975–2011 1931–38, 1940–2011 1913–2011 95 92 83 80 87 80 99 103 105 107 records Number of years of an - nual peak-flow 7,111 5,713 4,509 6,541 6,635 7,894 2,885 5,745 4,734 6,435 NAVD 88 NAVD feet above Mean basin elevation, in 5.5 6.8 3.8 1.5 0.6 0.6 0.0 0.0 0.0 13.8 dams Percent of affected by drainage basin 33.0 31.2 819 358 462 405 1,108 2,716 1,789 2,472 Contributing drainage area, in square miles degrees (NAD 83) -111.8898 -111.4383 -111.2707 -112.2566 -112.7017 -113.2995 -112.5453 -113.6567 -109.8412 -105.6969 Longitude, in decimal . Upper Milk River Basin Musselshell River Basin Lower Missouri River tributary 46.4288 48.4272 46.5239 45.8854 45.5266 45.4973 48.9903 49.0114 49.0075 48.7988 degrees Latitude, (NAD 83) Upper Missouri River tributaries in decimal Missouri River headwaters tributaries Streamflow-gaging stations in the Missouri River Basin Streamflow-gaging stations in the Saskatchewan River Basin Station name boundary Milk River at western crossing of international Musselshell River at Harlowton, Montana Marias River near Shelby, Montana Marias River near Shelby, Tenmile Creek near Rimini, Montana Tenmile Gallatin River at Logan, Montana Big Hole River near Melrose, Montana Gallatin River near Gallatin Gateway, Montana Gallatin River near Gateway, Poplar River at international boundary St. Mary River at international boundary Swiftcurrent Creek at Many Glacier, Montana Swiftcurrent Creek at Many Glacier, Station number 06133000 06120500 06099500 06062500 06052500 06025500 06043500 06178000 05020500 05014500 Information for selected long-term gaging stations in or near Montana identification

271 212 161 101 88 45 80 386 14 9 Map (fig. 1) number Table 1. Table Datum of 1988] Vertical American 88, North American Datum of 1983; NAVD [NAD 83, North 6 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana Annual peak record through flows period of water year 2011 1923, 1929–72, 1975–2011 1904–05, 1918, 1929–2011 1922–2011 1905–13, 1922– 32, 1934–2011 1911–17, 1911–17, 1929–2011 1922–2011 1929–94, 2001–2011 1911–14, 1911–14, 1935–2011 1911–23, 1911–23, 1929–2011 1897–1905, 1929–32, 1938–2011 1930–2011 1890–1893, 1911–2011 1908, 1930–2011 1923–82, 1984– 86, 1989–2011 82 86 90 98 90 90 77 81 96 87 82 83 86 105 records Number of years of an - nual peak-flow 5,250 6,544 5,012 6,322 5,399 7,761 5,753 7,204 5,571 8,012 5,742 8,343 5,765 8,699 NAVD 88 NAVD feet above Mean basin elevation, in 0.0 1.8 0.0 0.2 0.0 0.0 0.0 5.0 4.4 0.3 5.2 0.0 7.8 0.0 dams Percent of affected by drainage basin 672 429 976 995 8,029 2,034 1,556 1,152 3,551 9,017 2,616 6,021 11,414 10,728 Contributing drainage area, in square miles degrees (NAD 83) -113.9788 -114.1268 -114.4757 -115.0869 -110.5665 -114.1277 -110.7937 -113.9319 -110.3804 -105.8784 -108.4680 -108.8441 -109.0654 -109.3880 Longitude, in decimal Yellowstone River Basin Yellowstone 45.0572 45.8001 48.0242 45.4657 48.4958 45.0099 49.0012 45.5514 47.3016 45.5972 46.8686 45.1121 46.8772 44.5671 degrees Latitude, (NAD 83) in decimal Streamflow-gaging stations in the Columbia River Basin Streamflow-gaging stations in the Missouri River Basin—Continued Station name tana Montana Montana Yellowstone National Park, Wyoming National Park, Yellowstone Clark Fork above Missoula, Montana Powder River at Moorhead, Montana Yellowstone River at Billings, Montana Yellowstone Swan River near Bigfork, Montana Clarks Fork Yellowstone River at Edgar, Mon - River at Edgar, Yellowstone Clarks Fork North Fork Flathead River near Columbia Falls, Clarks Fork Yellowstone River near Belfry, River near Belfry, Yellowstone Clarks Fork Flathead River at Flathead, British Columbia Stillwater River near Absarokee, Montana Stillwater River near Clark Fork at St. Regis, Montana Yellowstone River near Livingston, Montana Yellowstone Clark Fork below Missoula, Montana Yellowstone River at Corwin Springs, Montana Yellowstone Yellowstone River at Yellowstone Lake outlet, Yellowstone River at Yellowstone Station number 12340500 06324500 06214500 12370000 06208500 12355500 06207500 12355000 06205000 12354500 06192500 12353000 06191500 06186500 Information for selected long-term gaging stations in or near Montana.—Continued identification

665 542 458 728 448 700 445 698 443 697 425 688 424 414 Map (fig. 1) number Table 1. Table Datum of 1988] Vertical American 88, North American Datum of 1983; NAVD [NAD 83, North Methods of Analysis 7 this study is intended to provide an initial assessment of known as the Kendall-Theil robust line, is a nonparametric general large-scale patterns in peak-flow temporal variability estimator of trend slope for a univariate time series when the and stationarity for long-term gaging stations in Montana. time interval is constant (equally spaced). The fitted trend line Primary considerations in the study were whether the analyses produced by the Sen slope estimator provides an estimate of for the long-term gaging stations indicate potential changes in the change in the median value of a variable through time. peak-flow characteristics after the mid-1970s and whether the Null hypothesis significance testing was done using the non- potential changes might be relevant to stationarity issues in the parametric Mann-Kendall test (Mann, 1945) to identify sig- application of peak-flow frequency analyses within a statewide nificant trends; however, it is notable that much discussion in gaging-station network. recent literature has focused on problems with null hypothesis significance testing (Nichols, 2001) and the issue of long-term persistence (Cohn and Lins, 2005) that might be misinter- preted as significant trends. Thus, the statistical significance of Methods of Analysis trend results are reported but are qualified as being potentially misleading if considered as a primary factor in interpreting Hydrographic information presented in this report chapter trend patterns. Descriptions of trend results in this report chap- (including drainage area, basin-elevation data, and percent- ter focus more heavily on patterns in trend magnitudes than age of basin greater than 6,000 ft) was determined by GIS statistical significance. analysis of medium resolution (1:100,000 scale and 30 meter) Statistical distributions of peak-flow characteristics were digital datasets. The digital datasets include National Elevation compiled for selected data summary periods for each gag- Dataset (Gesch and others, 2002), the National Hydrography ing station. The data summary periods were (1) 1930–78, Dataset (U.S. Geological Survey, 2015), and the National (2) 1979–2011, and (3) the entire period of record. The Hydrography Dataset Plus Version 2 (Horizon Systems Corpo- 1930–78 summary period was selected to represent peak- ration, 2013). flow characteristics during a period before the mid-1970s that Extensive preliminary exploratory analyses were done generally ranged from an unusually dry period to an unusually to develop a consistent general approach for investigating wet period and typically encompassed the full range in histori- peak-flow temporal characteristics among the diverse gag- cal variability; the summary period purposely extends slightly ing stations. Initially, for each gaging station, scatterplots of past the mid-1970s to include transition years. The 1979–2011 the annual peak-flow time series in conjunction with locally summary period was selected to represent the period after weighted scatterplot smooths (LOWESS; Cleveland, 1985) the mid-1970s that might be affected by reported changes in were investigated to assist in identifying dominant trend hydrologic regimes associated with changes in climatic condi- periods. Also, all possible 10-, 20-, 30-, 40-, and 50-year tions. The entire period of record (including any pre-1930 trends were plotted and examined for each gaging station. The data) also was statistically summarized. For annual peak flow, exploratory analyses indicated that peak flows for most gaging the entire period of record represents the data that are typically stations generally were lower than median peak flow (deter- used to calculate peak-flow frequencies. mined for the entire period of record through 2011) from about The data summary periods purposely differ from the 1930 to the early 1940s and generally were higher than median trend-analysis periods, based on the specific objectives of the peak flow from about the mid- to late 1960s to the mid- to late analyses applied to the periods. The data summary periods 1970s. These generally consistent large-scale patterns served were selected to allow characterization and comparison of as the basis for defining four trend analysis periods that were peak flows before and after the key mid-1970s breakpoint. The applied for each gaging station: (1) from the start of system- data summary period before the key breakpoint was extended atic data collection through 1940 (for gaging stations with at slightly past the mid-1970s to include transition years. Assign- least 15 years of systematic record during the period); (2) from ing the transition data into the data summary period before 1930 to 1976; (3) from 1967 to 2011; and (4) from the start of the mid-1970s would presumably accentuate the differences systematic data collection through 2011. The trend-analysis between the two summary periods. This conservative approach periods were purposely overlapped to better define the full was applied to avoid the possibility of not distinguishing extent of temporal changes from dry periods to wet periods or, actual changes in peak-flow characteristics after the mid- conversely, from wet periods to dry periods. Definition of the 1970s. In contrast, the trend-analysis periods were selected trend-analysis periods primarily was based on examination of to quantify and statistically evaluate changes in peak-flow annual peak flow with less consideration given to peak-flow characteristics from dry periods to wet periods or, conversely, timing; however, for many gaging stations, the defined trend from wet periods to dry periods. The trend-analysis periods analysis periods also provided reasonable representation of were purposely overlapped to better define the full extent of dominant trend periods for peak-flow timing. temporal changes from dry periods to wet periods or, con- For the defined trend analysis periods, trend magnitudes versely, from wet periods to dry periods. were computed using the Sen slope estimator (Sen, 1968), For a given gaging station, stationarity of annual peak generally following methods used by Hodgkins and others flow requires that all the data represent a consistent hydrologic (2007) and Holmes and others (2010). The Sen slope, also regime within the same (albeit highly variable) fundamental 8 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana climatic system. As such, a primary consideration in this study temperature and precipitation characteristics in Montana is whether annual-peak-flow data after the mid-1970s are (PRISM Climate Group, 2015), as well as principles described substantially different from data for the entire period of record by Mock (1996), Zelt and others (1999), Knowles and others and thus might result in substantially different peak-flow fre- (2006), Pederson and others (2011), and Shinker (2010). quencies. Peak-flow timing data are not directly incorporated In much of Montana, especially areas east of the Rocky in calculation of peak-flow frequencies and have less direct Mountain front, May and June typically have higher mean relevance than annual-peak-flow data in this study. The non- monthly precipitation than most other months, and the May parametric Wilcoxon rank sum procedure (Wilcoxon, 1945) and June precipitation typically (primarily depending on was used to test for significant differences between the annual- elevation) is in the form of rainfall. During the spring (typi- peak-flow median for 1979–2011 in relation to medians for cally May and June), two major sources provide moisture for 1930–78 and for the entire period of record. The nonparamet- the region: (1) warm moist air masses are advected into the ric Wilcoxon rank sum procedure (Wilcoxon, 1945) also was region because of the formation of the low-level jet, which used to test for significant changes in peak-flow timing, with advects moisture northward from the Gulf of Mexico (Mock, the test applied to the day-of-peak median for 1979–2011 in 1996; Shinker, 2010); and (2) northwesterly flows of mois- relation to medians for 1930–78 and for the entire period of ture from the northern Pacific Ocean in conjunction with the record. In this study, a significance level p( -value) less than formation of major frontal systems and unstable air masses, 0.05 indicates statistical significance. all of which result from cool season atmospheric circulation patterns (Mock, 1996; Shinker, 2010). Convective storms also can develop behind the cyclonic frontal systems and further contribute to spring precipitation. Runoff from spring rainfall Factors that Affect Interpretation of is a major causal factor contributing to many peak flows in Results Montana. Monthly mean precipitation typically decreases (sometimes sharply) as warm stable air masses build across The fitted trend lines provide estimates of the changes the Pacific Northwest and northern Rocky Mountains from in median values through time. Trend-magnitude values are June through September (Mock, 1996; Shinker, 2010). considered semiquantitative estimates determined by statisti- In the western part of Montana, cyclonic systems com- cal analysis. Throughout this report chapter, trend-magnitude monly referred to as atmospheric rivers can deliver large values (reported to two significant figures) sometimes are amounts of moisture from the Pacific Ocean in the late referred to in discussion of temporal changes in peak-flow summer and fall, occasionally resulting in flooding. In high- characteristics. Reference to specific trend-magnitude values elevation areas of western Montana, the cool season (fall and is intended to facilitate discussion of temporal changes, but is winter) precipitation totals usually exceed the spring (May and not intended to represent absolute accuracy at two significant June) precipitation totals, which can result in large accumu- figures. The discussion of trend results focuses on the trend- lated mountain snowpacks. Much lower precipitation totals magnitude values. The p-values associated with the trend and smaller amounts of accumulated snowpack, however, are results are indicated in the tables and figures that present trend common in lower elevation areas. The timing and relative con- results but not emphasized in the discussion. tribution of snowmelt runoff to streamflow is strongly depen- In the discussion of temporal trends in annual peak dent on spring temperatures, which reflect the importance of flow, qualitative observations on trend magnitudes are made. elevation and, to a lesser extent, latitude on snowmelt timing Trend magnitudes are considered to be (1) substantial, if the (Pederson and others, 2011). In low-elevation areas, snowmelt deviation from zero was larger than about 1 percent per year; runoff generally is in late winter through early spring (Zelt and (2) moderate, if the deviation from zero was about 0.2–1 per- others, 1999), typically before May, and the timing of annual cent per year; and (3) small, if the deviation from zero was peaks that result from low-elevation snowmelt runoff typically less than about 0.2 percent per year. The qualitative descrip- is somewhat distinctly separated from the timing of annual tions were subjectively defined and are intended to facilitate peaks that result from spring precipitation or summer con- discussion of trend patterns among gaging stations and groups vective storms. With increase in elevation, the time of snow- of gaging stations. melt runoff is later in the year. In high-elevation areas, most Among the diverse gaging stations, trend magnitudes for snowmelt typically is from May through mid-July (Pederson peak-flow timing are more difficult to consistently interpret and others, 2011); the typical snowmelt runoff period and the than trend magnitudes for annual peak flow. Multiple distinct typical spring rainfall period are somewhat synchronized, and populations of day-of-peak values for some individual gaging the relative contributions of snowmelt and rainfall runoff are stations contribute to this issue. A brief overview of major difficult to distinguish. Difficulties in distinguishing the effects causal factors of peak flows is relevant to understanding mul- of snowmelt and rainfall on peak flows in high-elevation areas tiple populations in day-of-peak data. Throughout this report also have been noted by Pederson and others (2011). chapter, general observations are made on relations among For most of the long-term gaging stations in this study causal factors of peak flows and peak-flow timing. The obser- that have relatively high mean basin elevations (that is, vations generally are based on consideration of mean monthly greater than about 6,000 ft) peak flows typically are during Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 9 the snowmelt runoff period and result from snowmelt only low-elevation gaging stations focuses on general patterns in or a combination of rainfall on snowmelt. Peak flows that are directions of trends. outside of the snowmelt runoff period (May through mid-July) A detailed analysis of causal factors for individual and result from rainfall only are somewhat infrequent. For the peak flows was not done for this study; however, results are high-elevation gaging stations, the day-of-peak data typically described based on principles that peak flows in high-elevation are well (approximately continuously and normally) distrib- areas (greater than about 6,000 ft) generally occur during the uted within the snowmelt period. Among the high-elevation high-elevation snowmelt runoff period (May through mid- gaging stations, trend magnitudes for peak-flow timing can July) and primarily are affected by snowmelt runoff. Peak be reasonably consistently interpreted and compared. Upward flows in low-elevation areas (less than about 6,000 ft) some- trends in peak-flow timing indicate that the timing of annual what frequently occur outside of the low-elevation snowmelt peak flows changed from earlier in the year to later in the year. runoff period (late winter through early spring, typically Conversely, downward trends in peak-flow timing indicate that before May), and rainfall-only events account for a larger the timing of annual peak flows changed from later in the year proportion of peak flows in low-elevation areas than in high- to earlier in the year. In the discussion, trend magnitudes for elevation areas. However, in both high- and low-elevation peak-flow timing for high-elevation gaging stations are quali- areas, a combination of rainfall and snowmelt events can occur tatively considered to be (1) substantial, if the deviation from within the snowmelt runoff period. zero was larger than about 0.20 percent per year; (2) moderate, if the deviation from zero was about 0.10–0.20 percent per year; and (3) small, if the deviation from zero was less than about 0.10 percent per year. The criteria for qualitative obser- Temporal Trends and Stationarity in vations on trend magnitudes for peak-flow timing purposely differ from the criteria for trend magnitudes for annual peak Annual Peak Flow and Peak-Flow flow because of large differences in units of measurement and Timing scaling between day of peak and annual peak flow. Many of the long-term gaging stations in this study that Results of analysis of temporal trends are presented in have relatively low mean basin elevations (less than about table 2 for annual peak flow and in table 3 for day of peak. 6,000 ft) have bimodal (and sometimes trimodal) distributions Statistical summaries of annual peak flow and peak-flow of day-of-peak data. The multiple populations of day-of-peak timing for summary time periods are presented in table 4. values for individual low-elevation gaging stations primarily Study results are discussed according to the groups of gaging result from the following major causal factors: low-elevation stations. snowmelt (possibly with associated rainfall) and rainfall only For stations that have at least 15 years of peak-flow outside of the snowmelt period. Furthermore, rainfall-only events can result from cyclonic storms (and convective storms records before 1940, trend results for the period from the start that sometimes follow behind cyclonic systems) that typically of systematic data collection to 1940 are presented in tables are in May and June and intense convective and cyclonic sum- and figures for informational purposes. However, because less mer storms that typically are from July through September. than 50 percent of the gaging stations have adequate pre-1940 Each of these causal factors might account for a considerable data, trend results for the period from the start of systematic proportion of the day-of-peak values in the annual series. For data collection to 1940 are not discussed. some gaging stations, there is somewhat distinct and relatively large separation in the ranges of day-of-peak values between Streamflow-Gaging Stations in the the various causal factors. Rigorous statistical analysis of day-of-peak data for gaging stations with multiple populations Saskatchewan River Basin would involve segregating the data into the individual populations for separate analysis; however, this detailed approach Fitted trends for annual peak flow and peak-flow tim- was beyond the scope of this study. In the simplified approach ing, and statistical distributions for summary time periods for of this study, all day-of-peak data for an individual gaging the two gaging stations in the Saskatchewan River Basin are station were treated as coming from a single population. The presented in figure 2. The two gaging stations in the Saskatch- fitted trend lines generally are within or near the day-of-peak ewan River Basin (Swiftcurrent Creek at Many Glacier, Mon- values representing the dominant causal factor population. tana [gaging station 05014500; map number 9; fig. 1, table 1] The temporal changes in median peak flow indicated by the and St. Mary River at international boundary [gaging station fitted trend lines might represent changes in timing within the 05020500; map number 14; fig. 1, table 1]) have mean basin dominant causal factor or shifts in dominance between causal elevations of 6,435 and 5,745 ft, respectively. For both gaging factors. As such, trend magnitudes for peak-flow timing for stations, nearly all peak flows are during May and June, likely low-elevation gaging stations are somewhat variable and more caused by snowmelt runoff (possibly with associated spring difficult to interpret than for high-elevation gaging stations. rainfall). Day-of-peak values generally are uniformly distrib- Discussion of trend magnitudes for peak-flow timing for uted during May and June (fig. 2). 10 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Table 2. Results of analysis of temporal trends in annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second).

[All years refer to water year, which is the 12-month period from October 1 through September 30 and is designated by the year in which it ends. Gray shading indicates statistical significance p( -value less than 0.05). p-value, statistical significance; —, not applicable]

Trend results for the period from the start of systematic data collection through 1940 (for stations with at least 15 years of systematic record during the period) Map Station Fitted trend Fitted trend Trend number identification Station name Number Start- value, in End- value, in magnitude, (fig. 1) number of years p-value year cubic feet year cubic feet in percent with data per second per second per year Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 28 1913 1,050 1940 1,120 0.21 0.57 14 05020500 St. Mary River at international boundary 26 1915 5,460 1940 3,100 -1.66 0.06 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana — — — — — — — 80 06043500 Gallatin River near Gallatin Gateway, Montana — — — — — — — 88 06052500 Gallatin River at Logan, Montana — — — — — — — Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 26 1915 317 1940 78 -2.90 0.03 161 06099500 Marias River near Shelby, Montana 35 1902 8,300 1940 3,230 -1.57 0.01 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 32 1909 1,712 1940 898 -1.49 0.14 Upper Milk River Basin 271 06133000 Milk River at western crossing of international — — — — — — — boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary — — — — — — — Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 18 1923 4,590 1940 3,800 -0.97 0.54 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 30 1911 19,100 1940 12,500 -1.15 0.09 425 06192500 Yellowstone River near Livingston, Montana — — — — — — — 443 06205000 Stillwater River near Absarokee, Montana — — — — — — — 445 06207500 Clarks Fork Yellowstone River near Belfry, Montana 19 1922 7,560 1940 7,900 0.24 0.86 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 18 1922 7,590 1940 7,410 -0.12 0.97 458 06214500 Yellowstone River at Billings, Montana — — — — — — — 542 06324500 Powder River at Moorhead, Montana — — — — — — — Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana — — — — — — — 688 12353000 Clark Fork below Missoula, Montana — — — — — — — 697 12354500 Clark Fork at St. Regis, Montana 25 1911 41,100 1940 23,400 -1.43 0.04 698 12355000 Flathead River at Flathead, British Columbia — — — — — — — 700 12355500 North Fork Flathead River near Columbia Falls, — — — — — — — Montana 728 12370000 Swan River near Bigfork, Montana 19 1922 5,860 1940 4,420 -1.29 0.10 Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 11

Table 2. Results of analysis of temporal trends in annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second).–Continued

Trend results for the period from 1930 through 1976 Map Station Fitted trend Fitted trend Trend mag- Number of number identification Station name Start- value, in End- value, in nitude, in years with p-value (fig. 1) number year cubic feet year cubic feet percent per data per second per second year Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 47 1930 1,020 1976 1,060 0.06 0.80 14 05020500 St. Mary River at international boundary 45 1930 2,900 1976 4,660 1.29 0.05 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana 46 1930 5,560 1976 10,100 1.73 0.01 80 06043500 Gallatin River near Gallatin Gateway, Montana 46 1931 3,350 1976 6,690 2.17 0.00 88 06052500 Gallatin River at Logan, Montana 46 1930 3,180 1976 6,400 2.15 0.00 Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 46 1931 161 1976 276 1.55 0.05 161 06099500 Marias River near Shelby, Montana 45 1931 4,980 1976 7,000 0.88 0.23 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 47 1930 850 1976 1,310 1.15 0.24 Upper Milk River Basin 271 06133000 Milk River at western crossing of international 45 1931 696 1976 1,290 1.86 0.12 boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary 45 1931 496 1976 935 1.92 0.18 Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 47 1930 3,370 1976 6,010 1.67 0.00 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 47 1930 14,100 1976 22,100 1.20 0.00 425 06192500 Yellowstone River near Livingston, Montana 42 1930 15,200 1976 24,800 1.34 0.00 443 06205000 Stillwater River near Absarokee, Montana 42 1935 6,105 1976 7,805 0.66 0.17 445 06207500 Clarks Fork Yellowstone River near Belfry, Montana 47 1930 6,840 1976 8,800 0.61 0.03 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 46 1930 6,921 1976 8,838 0.59 0.10 458 06214500 Yellowstone River at Billings, Montana 47 1930 33,200 1976 49,600 1.05 0.00 542 06324500 Powder River at Moorhead, Montana 45 1930 6,420 1976 8,050 0.54 0.41 Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana 47 1930 11,100 1976 20,500 1.82 0.01 688 12353000 Clark Fork below Missoula, Montana 47 1930 21,400 1976 39,600 1.80 0.00 697 12354500 Clark Fork at St. Regis, Montana 47 1930 28,700 1976 49,900 1.57 0.00 698 12355000 Flathead River at Flathead, British Columbia 47 1930 6,220 1976 9,840 1.24 0.01 700 12355500 North Fork Flathead River near Columbia Falls, 47 1930 16,200 1976 25,200 1.19 0.01 Montana 728 12370000 Swan River near Bigfork, Montana 47 1930 4,470 1976 5,790 0.63 0.11 12 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Table 2. Results of analysis of temporal trends in annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second).–Continued

Trend results for the period from 1967 through 2011 Map Station Fitted trend Fitted trend Trend mag- Number of number identification Station name Start- value, in End- value, in nitude, in years with p-value (fig. 1) number year cubic feet year cubic feet percent per data per second per second year Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 45 1967 1,010 2011 1,070 0.12 0.81 14 05020500 St. Mary River at international boundary 43 1967 3,700 2011 3,830 0.08 0.83 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana 45 1967 9,020 2011 6,080 -0.72 0.18 80 06043500 Gallatin River near Gallatin Gateway, Montana 42 1967 6,000 2011 4,970 -0.38 0.22 88 06052500 Gallatin River at Logan, Montana 45 1967 6,430 2011 4,770 -0.58 0.11 Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 43 1967 231 2011 183 -0.47 0.27 161 06099500 Marias River near Shelby, Montana 45 1967 6,400 2011 4,760 -0.57 0.40 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 45 1967 1,086 2011 686 -0.82 0.25 Upper Milk River Basin 271 06133000 Milk River at western crossing of international 45 1967 1,000 2011 1,100 0.21 0.84 boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary 45 1967 934 2011 296 -1.52 0.04 Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 42 1967 5,330 2011 4,840 -0.21 0.72 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 45 1967 19,300 2011 19,700 0.06 0.87 425 06192500 Yellowstone River near Livingston, Montana 45 1967 23,600 2011 22,400 -0.11 0.73 443 06205000 Stillwater River near Absarokee, Montana 45 1967 7,411 2011 5,449 -0.59 0.08 445 06207500 Clarks Fork Yellowstone River near Belfry, Montana 45 1967 8,320 2011 7,880 -0.12 0.74 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 45 1967 8,455 2011 7,205 -0.33 0.29 458 06214500 Yellowstone River at Billings, Montana 45 1967 43,900 2011 35,900 -0.41 0.20 542 06324500 Powder River at Moorhead, Montana 43 1967 6,840 2011 2,440 -1.43 0.01 Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana 45 1967 16,200 2011 11,400 -0.66 0.07 688 12353000 Clark Fork below Missoula, Montana 45 1967 33,300 2011 23,700 -0.64 0.16 697 12354500 Clark Fork at St. Regis, Montana 45 1967 42,900 2011 30,300 -0.65 0.12 698 12355000 Flathead River at Flathead, British Columbia 39 1967 7,520 2011 6,060 -0.43 0.27 700 12355500 North Fork Flathead River near Columbia Falls, 45 1967 20,300 2011 16,900 -0.37 0.29 Montana 728 12370000 Swan River near Bigfork, Montana 45 1967 5,280 2011 4,440 -0.35 0.16 Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 13

Table 2. Results of analysis of temporal trends in annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second).–Continued

Trend results for the period from the start of systematic data collection through 2011 Map Station Fitted trend Fitted trend Trend mag- number identification Station name Number of Start- value, in End- value, in nitude, in (fig. 1) number years with p-value year cubic feet year cubic feet percent per data per second per second year Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 99 1913 1,010 2011 1,070 0.06 0.57 14 05020500 St. Mary River at international boundary 95 1915 4,050 2011 3,900 -0.04 0.79 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana 87 1924 7,570 2011 7,430 -0.02 0.93 80 06043500 Gallatin River near Gallatin Gateway, Montana 78 1931 4,440 2011 5,780 0.37 0.03 88 06052500 Gallatin River at Logan, Montana 82 1929 4,160 2011 5,780 0.47 0.02 Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 95 1915 241 2011 186 -0.23 0.20 161 06099500 Marias River near Shelby, Montana 105 1902 6,480 2011 5,160 -0.19 0.29 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 103 1909 1,300 2011 840 -0.34 0.09 Upper Milk River Basin 271 06133000 Milk River at western crossing of international 80 1931 919 2011 1,130 0.28 0.51 boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary 80 1931 698 2011 490 -0.37 0.25 Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 86 1923 4,160 2011 5,340 0.32 0.09 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 101 1911 16,000 2011 19,600 0.22 0.08 425 06192500 Yellowstone River near Livingston, Montana 78 1929 17,600 2011 22,800 0.35 0.04 443 06205000 Stillwater River near Absarokee, Montana 77 1935 6,818 2011 6,162 -0.12 0.48 445 06207500 Clarks Fork Yellowstone River near Belfry, Montana 90 1922 7,280 2011 8,270 0.15 0.20 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 89 1922 7,723 2011 7,935 0.03 0.77 458 06214500 Yellowstone River at Billings, Montana 83 1929 37,600 2011 41,800 0.14 0.34 542 06324500 Powder River at Moorhead, Montana 81 1929 7,870 2011 3,470 -0.67 0.00 Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana 82 1930 15,000 2011 13,400 -0.13 0.55 688 12353000 Clark Fork below Missoula, Montana 82 1930 27,700 2011 28,300 0.03 0.89 697 12354500 Clark Fork at St. Regis, Montana 96 1911 38,200 2011 34,200 -0.10 0.46 698 12355000 Flathead River at Flathead, British Columbia 77 1929 7,180 2011 7,150 -0.01 0.96 700 12355500 North Fork Flathead River near Columbia Falls, 83 1929 19,700 2011 18,900 -0.05 0.72 Montana 728 12370000 Swan River near Bigfork, Montana 90 1922 5,310 2011 4,730 -0.12 0.25 14 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Table 3. Results of analysis of temporal trends in peak-flow timing (the annual series of the day of the annual peak flow).

Trend results for the period from the start of systematic data collection through 1940 (for stations with at least 15 years of systematic record during the period) Map Station Fitted trend Fitted trend Trend number identification Station name Number Start- value, End- value, magnitude, (fig. 1) number of years p-value year calendar day year calendar day in percent with data (Julian day) (Julian day) per year Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 28 1913 May 30 (150) 1940 May 22 (143) -0.18 0.24 14 05020500 St. Mary River at international boundary 26 1915 June 19 (170) 1940 May 29 (149) -0.47 0.01 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana — — — — — — — 80 06043500 Gallatin River near Gallatin Gateway, Montana — — — — — — — 88 06052500 Gallatin River at Logan, Montana — — — — — — — Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 26 1915 June 1 (153) 1940 May 13 (133) -0.49 0.06 161 06099500 Marias River near Shelby, Montana 35 1902 May 30 (151) 1940 May 25 (146) -0.08 0.72 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 32 1909 June 1 (152) 1940 June 4 (156) 0.06 0.90 Upper Milk River Basin 271 06133000 Milk River at western crossing of international — — — — — — — boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary — — — — — — — Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 18 1923 July 1 (183) 1940 June 26 (177) -0.17 0.32 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 30 1911 June 13 (165) 1940 June 1 (152) -0.25 0.12 425 06192500 Yellowstone River near Livingston, Montana — — — — — — — 443 06205000 Stillwater River near Absarokee, Montana — — — — — — — 445 06207500 Clarks Fork Yellowstone River near Belfry, Montana 19 1922 June 15 (167) 1940 June 10 (161) -0.19 0.48 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 18 1922 June 15 (166) 1940 June 9 (161) -0.18 0.57 458 06214500 Yellowstone River at Billings, Montana — — — — — — — 542 06324500 Powder River at Moorhead, Montana — — — — — — — Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana — — — — — — — 688 12353000 Clark Fork below Missoula, Montana — — — — — — — 697 12354500 Clark Fork at St. Regis, Montana 25 1911 June 7 (158) 1940 May 13 (134) -0.52 0.01 698 12355000 Flathead River at Flathead, British Columbia — — — — — — — 700 12355500 North Fork Flathead River near Columbia Falls, — — — — — — — Montana 728 12370000 Swan River near Bigfork, Montana 19 1922 May 30 (150) 1940 May 25 (146) -0.16 0.70 Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 15

Table 3. Results of analysis of temporal trends in peak-flow timing (the annual series of the day of the annual peak flow).—Continued

Trend results for the period from 1930 through 1976 Map Station Fitted trend Fitted trend Trend Number number identification Station name Start- value, End- value, magnitude, of years p-value (fig. 1) number year calendar day year calendar day in percent with data (Julian day) (Julian day) per year Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 47 1930 May 27 (148) 1976 June 13 (164) 0.24 0.04 14 05020500 St. Mary River at international boundary 45 1930 June 7 (158) 1976 June 9 (160) 0.03 0.72 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana 46 1930 May 31 (151) 1976 June 7 (159) 0.10 0.35 80 06043500 Gallatin River near Gallatin Gateway, Montana 46 1931 June 4 (156) 1976 June 15 (166) 0.15 0.06 88 06052500 Gallatin River at Logan, Montana 46 1930 June 6 (158) 1976 June 17 (168) 0.14 0.06 Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 46 1931 May 22 (143) 1976 May 29 (149) 0.11 0.31 161 06099500 Marias River near Shelby, Montana 45 1931 May 27 (148) 1976 June 2 (154) 0.09 0.49 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 47 1930 June 3 (154) 1976 June 7 (158) 0.06 0.77 Upper Milk River Basin 271 06133000 Milk River at western crossing of international 45 1931 May 17 (137) 1976 April 25 (115) -0.34 0.21 boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary 45 1931 April 9 (99) 1976 March 28 (87) -0.27 0.29 Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 47 1930 June 26 (177) 1976 July 1 (183) 0.06 0.28 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 47 1930 June 7 (158) 1976 June 16 (168) 0.12 0.10 425 06192500 Yellowstone River near Livingston, Montana 42 1930 June 9 (160) 1976 June 15 (166) 0.08 0.31 443 06205000 Stillwater River near Absarokee, Montana 42 1935 June 13 (164) 1976 June 16 (167) 0.04 0.52 445 06207500 Clarks Fork Yellowstone River near Belfry, Montana 47 1930 June 10 (161) 1976 June 19 (171) 0.12 0.11 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 46 1930 June 9 (160) 1976 June 22 (173) 0.17 0.02 458 06214500 Yellowstone River at Billings, Montana 47 1930 June 13 (165) 1976 June 18 (169) 0.06 0.29 542 06324500 Powder River at Moorhead, Montana 45 1930 June 10 (162) 1976 June 7 (158) -0.04 0.81 Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana 47 1930 May 14 (135) 1976 June 2 (153) 0.29 0.04 688 12353000 Clark Fork below Missoula, Montana 47 1930 May 18 (138) 1976 June 4 (156) 0.27 0.05 697 12354500 Clark Fork at St. Regis, Montana 47 1930 May 20 (140) 1976 June 4 (156) 0.23 0.06 698 12355000 Flathead River at Flathead, British Columbia 47 1930 May 19 (139) 1976 May 28 (149) 0.15 0.17 700 12355500 North Fork Flathead River near Columbia Falls, 47 1930 May 20 (140) 1976 June 2 (154) 0.21 0.06 Montana 728 12370000 Swan River near Bigfork, Montana 47 1930 May 25 (146) 1976 June 5 (156) 0.15 0.12 16 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Table 3. Results of analysis of temporal trends in peak-flow timing (the annual series of the day of the annual peak flow).—Continued

Trend results for the period from 1967 through 2011 Map Station Fitted trend Fitted trend Trend Number number identification Station name Start- value, End- value, magnitude, of years p-value (fig. 1) number year calendar day year calendar day in percent with data (Julian day) (Julian day) per year Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 45 1967 June 1 (152) 2011 June 4 (156) 0.05 0.72 14 05020500 St. Mary River at international boundary 43 1967 June 4 (156) 2011 June 10 (162) 0.08 0.36 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana 45 1967 June 6 (157) 2011 June 6 (157) 0.00 0.93 80 06043500 Gallatin River near Gallatin Gateway, Montana 42 1967 June 13 (165) 2011 June 1 (153) -0.16 0.13 88 06052500 Gallatin River at Logan, Montana 45 1967 June 13 (165) 2011 June 6 (157) -0.10 0.30 Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 43 1967 May 24 (144) 2011 May 29 (150) 0.08 0.43 161 06099500 Marias River near Shelby, Montana 45 1967 May 24 (145) 2011 May 31 (151) 0.09 0.56 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 45 1967 May 28 (148) 2011 June 2 (154) 0.07 0.56 Upper Milk River Basin 271 06133000 Milk River at western crossing of international 45 1967 April 21 2011 May 10 (131) 0.38 0.45 boundary (111) Lower Missouri River tributary 386 06178000 Poplar River at international boundary 45 1967 March 26 2011 April 16 0.55 0.21 (85) (107) Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 42 1967 July 1 (183) 2011 June 26 (178) -0.06 0.30 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 45 1967 June 17 (168) 2011 May 26 (146) -0.29 0.01 425 06192500 Yellowstone River near Livingston, Montana 45 1967 June 15 (166) 2011 May 31 (152) -0.20 0.02 443 06205000 Stillwater River near Absarokee, Montana 45 1967 June 14 (165) 2011 June 7 (159) -0.09 0.17 445 06207500 Clarks Fork Yellowstone River near Belfry, Montana 45 1967 June 16 (168) 2011 June 3 (154) -0.18 0.06 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 45 1967 June 18 (169) 2011 June 3 (155) -0.19 0.07 458 06214500 Yellowstone River at Billings, Montana 45 1967 June 15 (166) 2011 June 6 (158) -0.12 0.13 542 06324500 Powder River at Moorhead, Montana 43 1967 June 8 (159) 2011 May 25 (145) -0.19 0.54 Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana 45 1967 May 27 (148) 2011 May 26 (146) -0.02 0.85 688 12353000 Clark Fork below Missoula, Montana 45 1967 June 2 (154) 2011 May 28 (148) -0.08 0.42 697 12354500 Clark Fork at St. Regis, Montana 45 1967 May 31 (151) 2011 May 24 (145) -0.09 0.41 698 12355000 Flathead River at Flathead, British Columbia 39 1967 May 25 (145) 2011 May 25 (145) 0.00 0.87 700 12355500 North Fork Flathead River near Columbia Falls, 45 1967 May 24 (145) 2011 May 29 (149) 0.06 0.47 Montana 728 12370000 Swan River near Bigfork, Montana 45 1967 May 31 (151) 2011 June 3 (155) 0.05 0.60 Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 17

Table 3. Results of analysis of temporal trends in peak-flow timing (the annual series of the day of the annual peak flow).—Continued

Trend results for the period from the start of systematic data collection through 2011 Map Station Fitted trend Fitted trend Trend Number number identification Station name Start- value, End- value, magnitude, of years p-value (fig. 1) number year calendar day year calendar day in percent with data (Julian day) (Julian day) per year Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 99 1913 May 27 (148) 2011 June 5 (156) 0.06 0.16 14 05020500 St. Mary River at international boundary 95 1915 June 8 (159) 2011 June 8 (159) 0.00 0.92 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana 87 1924 June 1 (153) 2011 June 6 (157) 0.03 0.32 80 06043500 Gallatin River near Gallatin Gateway, Montana 78 1931 June 11 (162) 2011 June 6 (158) -0.03 0.42 88 06052500 Gallatin River at Logan, Montana 82 1929 June 11 (162) 2011 June 7 (159) -0.03 0.47 Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 95 1915 May 22 (143) 2011 May 29 (150) 0.05 0.14 161 06099500 Marias River near Shelby, Montana 105 1902 May 28 (148) 2011 June 2 (154) 0.03 0.42 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 103 1909 June 1 (153) 2011 June 4 (155) 0.01 0.75 Upper Milk River Basin 271 06133000 Milk River at western crossing of international 80 1931 May 9 (130) 2011 April 26 (116) -0.13 0.30 boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary 80 1931 March 31 2011 April 5 (96) 0.07 0.70 (90) Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 86 1923 June 29 (181) 2011 June 28 (179) -0.01 0.60 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 101 1911 June 12 (164) 2011 June 3 (154) -0.06 0.03 425 06192500 Yellowstone River near Livingston, Montana 78 1929 June 15 (167) 2011 June 2 (154) -0.09 0.02 443 06205000 Stillwater River near Absarokee, Montana 77 1935 June 13 (165) 2011 June 10 (161) -0.02 0.55 445 06207500 Clarks Fork Yellowstone River near Belfry, Montana 90 1922 June 15 (167) 2011 June 8 (159) -0.05 0.14 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 89 1922 June 14 (166) 2011 June 9 (160) -0.04 0.28 458 06214500 Yellowstone River at Billings, Montana 83 1929 June 15 (166) 2011 June 8 (160) -0.05 0.14 542 06324500 Powder River at Moorhead, Montana 81 1929 June 8 (159) 2011 May 30 (150) -0.07 0.45 Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana 82 1930 May 20 (140) 2011 May 28 (148) 0.07 0.21 688 12353000 Clark Fork below Missoula, Montana 82 1930 May 25 (146) 2011 May 30 (150) 0.04 0.40 697 12354500 Clark Fork at St. Regis, Montana 96 1911 May 30 (150) 2011 May 26 (146) -0.03 0.41 698 12355000 Flathead River at Flathead, British Columbia 77 1929 May 24 (144) 2011 May 24 (144) 0.00 0.84 700 12355500 North Fork Flathead River near Columbia Falls, 83 1929 May 24 (144) 2011 May 30 (150) 0.05 0.21 Montana 728 12370000 Swan River near Bigfork, Montana 90 1922 May 27 (148) 2011 June 4 (156) 0.06 0.11 18 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Table 4. Statistical summaries of annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow) for summary time periods.

Results of Wilcoxon rank sum test1 Median for indicated period, for differences in medians among cubic feet per second periods (p-value) Map Station Median for number identification Station name Median for 1979– 1979–2011 (fig. 1) number Period of 2011 compared 1930–78 1979–2011 compared to record to median for median for period of record 1930–78 Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana 1,010 1,040 1,040 0.78 0.72 14 05020500 St. Mary River at international boundary 3,740 3,610 3,980 0.64 0.58 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana 7,760 6,610 7,500 0.20 0.39 80 06043500 Gallatin River near Gallatin Gateway, Montana 5,020 5,200 5,140 0.97 0.97 88 06052500 Gallatin River at Logan, Montana 4,820 5,580 4,980 0.25 0.54 Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana 218 202 214 0.50 0.36 161 06099500 Marias River near Shelby, Montana 5,950 5,160 5,700 0.56 0.48 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana 1,080 739 1,070 0.52 0.25 Upper Milk River Basin 271 06133000 Milk River at western crossing of international 1,000 1,050 1,020 0.74 0.83 boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary 720 350 592 0.07 0.24 Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, Yel- 4,690 4,780 4,730 0.77 0.83 lowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana 18,100 17,500 17,700 0.48 0.53 425 06192500 Yellowstone River near Livingston, Montana 20,500 20,100 20,600 0.84 0.95 443 06205000 Stillwater River near Absarokee, Montana 6,905 6,250 6,470 0.26 0.49 445 06207500 Clarks Fork Yellowstone River near Belfry, 7,820 7,470 7,780 0.85 0.84 Montana 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana 7,900 7,440 7,890 0.43 0.43 458 06214500 Yellowstone River at Billings, Montana 41,400 37,600 39,400 0.51 0.71 542 06324500 Powder River at Moorhead, Montana 7,200 3,730 5,730 0.00 0.00 Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana 15,500 13,400 14,200 0.12 0.27 688 12353000 Clark Fork below Missoula, Montana 30,500 27,200 28,000 0.27 0.48 697 12354500 Clark Fork at St. Regis, Montana 37,400 34,400 36,100 0.16 0.24 698 12355000 Flathead River at Flathead, British Columbia 7,960 6,710 7,170 0.17 0.33 700 12355500 North Fork Flathead River near Columbia Falls, 20,400 18,600 19,200 0.15 0.40 Montana 728 12370000 Swan River near Bigfork, Montana 5,130 4,820 5,020 0.29 0.34 Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 19

Results of Wilcoxon rank sum Median for indicated period,calendar day test1 for differences in medi- (Julian day) ans among periods (p-value) Map Station number identification Station name Median for Median for 1979–2011 1979–2011 com- (fig. 1) number Period of 1930–78 1979–2011 compared to pared to median record median for for period of 1930–78 record Streamflow-gaging stations in the Saskatchewan River Basin 9 05014500 Swiftcurrent Creek at Many Glacier, Montana June 5 (156) June 1 (152) June 1 (152) 0.99 0.84 14 05020500 St. Mary River at international boundary June 8 (159) June 7 (158) June 8 (159) 0.82 0.97 Streamflow-gaging stations in the Missouri River Basin Missouri River headwaters tributaries 45 06025500 Big Hole River near Melrose, Montana June 4 (156) June 3 (154) June 4 (155) 0.90 0.89 80 06043500 Gallatin River near Gallatin Gateway, Montana June 10 (161) June 3 (155) June 9 (160) 0.03 0.12 88 06052500 Gallatin River at Logan, Montana June 11 (162) June 5 (156) June 10 (161) 0.03 0.12 Upper Missouri River tributaries 101 06062500 Tenmile Creek near Rimini, Montana May 26 (146) May 28 (148) May 26 (146) 0.21 0.34 161 06099500 Marias River near Shelby, Montana May 30 (150) May 31 (151) May 31 (151) 0.73 0.76 Musselshell River Basin 212 06120500 Musselshell River at Harlowton, Montana June 5 (156) May 31 (151) June 3 (154) 0.92 0.93 Upper Milk River Basin 271 06133000 Milk River at western crossing of international May 1 (121) May 5 (125) May 3 (123) 0.50 0.67 boundary Lower Missouri River tributary 386 06178000 Poplar River at international boundary April 3 (93) April 9 (99) April 3 (93) 0.61 0.74 Yellowstone River Basin 414 06186500 Yellowstone River at Yellowstone Lake outlet, June 29 (180) June 28 (180) June 29 (180) 0.34 0.50 Yellowstone National Park, Wyoming 424 06191500 Yellowstone River at Corwin Springs, Montana June 11 (162) June 2 (153) June 8 (159) 0.00 0.02 425 06192500 Yellowstone River near Livingston, Montana June 11 (163) June 6 (157) June 9 (160) 0.01 0.07 443 06205000 Stillwater River near Absarokee, Montana June 14 (166) June 11 (162) June 11 (162) 0.47 0.73 445 06207500 Clarks Fork Yellowstone River near Belfry, June 14 (165) June 7 (158) June 12 (163) 0.03 0.14 Montana 448 06208500 Clarks Fork Yellowstone River at Edgar, Montana June 15 (166) June 9 (160) June 13 (164) 0.07 0.15 458 06214500 Yellowstone River at Billings, Montana June 15 (166) June 10 (161) June 12 (163) 0.08 0.22 542 06324500 Powder River at Moorhead, Montana June 7 (158) May 31 (151) June 5 (156) 0.74 0.75 Streamflow-gaging stations in the Columbia River Basin 665 12340500 Clark Fork above Missoula, Montana May 24 (144) May 25 (145) May 24 (144) 0.73 0.87 688 12353000 Clark Fork below Missoula, Montana May 27 (147) May 30 (150) May 28 (148) 0.66 0.78 697 12354500 Clark Fork at St. Regis, Montana May 28 (148) May 28 (148) May 28 (148) 0.48 0.38 698 12355000 Flathead River at Flathead, British Columbia May 24 (144) May 25 (145) May 24 (144) 0.51 0.66 700 12355500 North Fork Flathead River near Columbia Falls, May 27 (147) May 26 (146) May 27 (147) 1.00 0.70 Montana 728 12370000 Swan River near Bigfork, Montana May 31 (151) June 2 (153) June 1 (152) 0.54 0.62 1The Wilcoxon rank sum test was used to test for significant differences between the median for the period 1979 through 2011 and the medians for 1930 through 1978 and the entire period of record. 20 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 10,000 [Water year is defined as the 12-month period from October 1 through A. Swiftcurrent Creek at Many Glacier, Montana September 30 and is designated by the (station 05014500) year in which it ends] Annual peak flows and days of annual peak flows 1,000 Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second Start of systematic data collection through 1940 100 Nov. 15 1930 through 1976 Nov. 1 1967 through 2011 Oct. 1 Start of systematic data collection through 2011 Sept. 1 Bold lines indicate statistical Aug. 1 significance (p-value less than 0.05) July 1 Boxplots

Day of annual peak flow June 1 Data value greater than 1.5 times the interquartile range May 1 Apr. 15 outside the quartile Data value less than or equal to 1.5 times the interquartile 50,000 range outside the quartile B. St. Mary River at international boundary (station 05020500) 75th percentile Inter- 10,000 median quartile range 25th percentile Annual peak flow, Annual peak flow, in cubic feet per second 1,000

500 Dec. 1

Nov. 1

Oct. 1

Sept. 1

Aug. 1

July 1 Day of annual peak flow June 1

May 1 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Figure 2. Fitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for streamflow-gaging stations in the Saskatchewan River Basin: A, Swiftcurrent Creek at Many Glacier, Montana (gaging station 05014500); and B, St. Mary River at international boundary (gaging station 05020500). Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 21

Peak flows for St. Mary River at international boundary by snowmelt runoff (possibly with associated spring rainfall). are potentially affected by the St. Mary diversion canal, which Day-of-peak values generally are uniformly distributed (cen- transfers water from the St. Mary River into the North Fork of tered at times that are variable among gaging stations and time the Milk River. The canal was constructed in 1915 and has a periods) within May and June (fig. 3). diversion capacity of 850 cubic feet per second (ft3/s; Bureau Fitted trends for annual peak flow and peak-flow timing, of Reclamation, 2013). Because of the potential effect of the and statistical distributions for summary time periods for the St. Mary diversion on the trend results, the trend analyses for three gaging stations on Missouri River headwaters tributar- this station were restricted to the post-diversion period (1915– ies are presented in figure 3. The study results for all gaging 2011); it was presumed that the operation of the diversion was stations indicate substantial upward trends in annual peak flow reasonably similar during the post-diversion period. during 1930–76 and moderate downward trends in annual Temporal trends in peak-flow characteristics are variable peak flow during 1967–2011 (fig. 3; table 2). Big Hole River among the two gaging stations in the Saskatchewan River near Melrose, Montana, has a small downward trend in annual Basin but generally are small to moderate. However, the study peak flow during the entire period of record, and the Gallatin results indicate a substantial upward trend in peak-flow tim- River gaging stations have moderate upward trends in annual ing during 1930–76 for Swiftcurrent Creek at Many Glacier, peak flow during the entire period of record. The study results Montana (fig. 2A; table 3), which indicates that the timing of also indicate moderate upward trends in peak-flow timing for annual peak flows changed from earlier in the year to later in all gaging stations during 1930–76, but variable changes (in the year. Also, the study results indicate a substantial upward trend direction and magnitude) among gaging stations during trend in annual peak flow during 1930–76 for St. Mary River 1967–2011 (fig. 3; table 3). The gaging stations have small at international boundary (fig. B2 ; table 2). changes in peak-flow timing during the entire period of record Differences between the medians for 1979–2011 and the that are variable in direction. medians for the other summary time periods were not signifi- Significant differences between the day-of-peak medians cantly different for annual peak flow and day of peak (table 4). for 1979–2011 and the medians for 1930–78 were determined For annual peak flow and day of peak, statistical distributions for Gallatin River near Gallatin Gateway, Montana, and Galla- among the summary time periods generally are similar (fig. 2). tin River at Logan, Montana (table 4). The day-of-peak medi- Study results provide evidence that annual peak flow for the ans for 1979–2011 (Julian day 155 and 156 for Gallatin River long-term gaging stations in the Saskatchewan River Basin near Gallatin Gateway, Montana, and Gallatin River at Logan, can be reasonably considered as stationary for application Montana, respectively) are significantly less than medians for of peak-flow frequency analyses within a statewide gaging- 1930–78 (Julian day 161 and 162, respectively; table 4). station network. For annual peak flow, statistical distributions among the summary time periods generally are similar (fig. 3). However, for the Bighole River near Melrose, Montana, (fig. A3 ), the Streamflow-Gaging Stations in the Missouri interquartile range of peak flows for 1979–2011 is consider- River Basin ably larger than the interquartile range for 1930–1978 and for the entire period of record. For day of peak, the statistical dis- Gaging stations in the Missouri River are subgrouped tributions for the Gallatin River gaging stations for 1979–2011 according to the following descriptive classes: (1) Missouri are shifted downward in relation to distributions for 1930–78. River headwaters tributaries (three gaging stations); (2) upper For annual peak flow for the Missouri River headwater Missouri River tributaries (two gaging stations); (3) Mus- tributaries, upward trends during 1930–76 generally were selshell River Basin (one gaging station); (4) upper Milk River stronger than downward trends during 1967–2011, and statisti- Basin (one gaging station); (4) lower Missouri River tributary cal distributions generally were similar among summary time (one gaging station); and (5) Yellowstone River Basin (eight periods. Study results provide evidence that annual peak flow gaging stations). Study results are discussed according to the for the long-term gaging stations can be reasonably considered descriptive classes. as stationary for application of peak-flow frequency analyses within a statewide gaging-station network. However, for peak- flow timing for the two Gallatin River gaging stations, moder- Missouri River Headwaters Tributaries ate upward trends during 1930–76 were generally similar in The three gaging stations on Missouri River headwaters magnitude to moderate downward trends during 1967–2011; tributaries (Big Hole River near Melrose, Montana [gaging also, day-of-peak medians for 1979–2011 were significantly station 06025500; map number 45; fig. 1, table 1], Galla- less than medians for 1930–78 (table 4). For the Gallatin River tin River near Gallatin Gateway, Montana [gaging station gaging stations, the moderate downward trends in peak-flow 06043500; map number 80; fig. 1, table 1], and Gallatin River timing for 1967–2011 indicate that the timing of annual peak at Logan, Montana [gaging station 06052500; map number flows changed (by 8 to 12 days) from later in the year to ear- 88; fig. 1, table 1]) have mean basin elevations that range lier in the year. from 6,635 to 7,894 ft. For all of the gaging stations, nearly all day-of-peak values are during May and June, likely caused 22 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 100,000 [Water year is defined as the 12-month A. Big Hole River near Melrose, Montana period from October 1 through (station 06025500) September 30 and is designated by the year in which it ends] Annual peak flows and days of annual peak flows Annual peak flow 10,000 Day of annual peak flow

Fitted trend lines Annual peak flow, Annual peak flow,

in cubic feet per second 1930 through 1976

1967 through 2011 1,000 July 15 Start of systematic data July 1 collection through 2011 Bold lines indicate statistical significance (p-value less than 0.05) June 1

Boxplots

May 1 Data value greater than 1.5 times the interquartile range outside the quartile Day of annual peak flow Apr. 1 Data value less than or equal to 1.5 times the interquartile Mar. 15 range outside the quartile

50,000 75th percentile Inter- B. Gallatin River near Gallatin Gateway, Montana median (station 06043500) quartile range 25th percentile 10,000 Annual peak flow, Annual peak flow, in cubic feet per second 1,000

500 July 15

July 1

June 1 Day of annual peak flow

May 1 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Figure 3. Fitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for streamflow-gaging stations on Missouri River headwaters tributaries: A, Big Hole River near Melrose, Montana (gaging station 06025500); B, Gallatin River near Gallatin Gateway, Montana (gaging station 06043500); and C, Gallatin River at Logan, Montana (gaging station 06052500). Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 23

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 50,000 [Water year is defined as the 12-month C. Gallatin River at Logan, Montana period from October 1 through (station 06052500) September 30 and is designated by the year in which it ends] 10,000 Annual peak flows and days of annual peak flows Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second 1,000 1930 through 1976

500 1967 through 2011 July 15 Start of systematic data July 1 collection through 2011 Bold lines indicate statistical significance (p-value less than 0.05)

Boxplots June 1 Data value greater than 1.5 times the interquartile range

Day of annual peak flow outside the quartile Data value less than or May 1 equal to 1.5 times the interquartile 1910 1930 1950 1970 1990 2010 Water Water All water range outside the quartile years years years Water year 1930–78 1979–2011 75th percentile Inter- median quartile range 25th percentile

Figure 3. Graphs showing fFitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for streamflow-gaging stations on Missouri River headwaters tributaries: A, Big Hole River near Melrose, Montana (gaging station 06025500); B, Gallatin River near Gallatin Gateway, Montana (gaging station 06043500); and C, Gallatin River at Logan, Montana (gaging station 06052500).—Continued

Upper Missouri River Tributaries 10 percent of peak flows; thus, most day-of-peak values are uniformly distributed during May and June (fig. 4). The two gaging stations on upper Missouri River tribu- Fitted trends for annual peak flow and peak-flow timing, taries (Tenmile Creek near Rimini, Montana [gaging station and statistical distributions for summary time periods for the 06062500; map number 101; fig. 1, table 1], and Marias two gaging stations on upper Missouri River tributaries are River near Shelby, Montana [gaging station 06099500; map presented in figure 4. The study results indicate moderate to number 161; fig. 1, table 1]) have relatively large variability substantial upward trends in annual peak flow for the gaging in mean basin elevations. For Tenmile Creek near Rimini, stations during 1930–76 and moderate downward trends in Montana (mean basin elevation 6,541 ft), nearly all peak flows annual peak flow during 1967–2011 (fig. 4; table 2). The gag- are during May and June, likely caused by snowmelt runoff ing stations have small downward trends in annual peak flow (possibly with associated spring rainfall). Day-of-peak values generally are uniformly distributed during May and June during the entire period of record. The study results also indi- (fig. 4). For Marias River near Shelby, Montana (mean basin cate small to moderate upward trends in peak-flow timing for elevation 4,509 ft; range in elevation from 3,096–9,472 ft), the gaging stations during 1930–76 and small upward trends most peak flows are during May and June, likely caused by in peak-flow timing during 1967–2011 (fig. 4; table 3). The high-elevation snowmelt runoff and spring rainfall. The few gaging stations have small upward trends in peak-flow timing peak flows that are during March and April likely are caused during the entire period of record. by low-elevation snowmelt runoff. The few peak flows that Differences between the medians for 1979–2011 and the are in November likely are caused by rainfall. Day-of-peak medians for the other summary time periods were not signifi- values that are outside of May and June account for less than cant for annual peak flow and day of peak (table 4). For both 24 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Annual peak flows, days of annual Statistical distributions for peak flows, and fitted trend lines indicated periods EXPLANATION 1,000 1981–3,290 cubic feet per second [Water year is defined as the 12-month period from October 1 through September 30 and is designated by the year in which it ends] Annual peak flows and days of annual peak flows 100 Annual peak flow Day of annual peak flow Annual peak flow, Annual peak flow, A. Tenmile Creek near Rimini, Montana Fitted trend lines in cubic feet per second (station 06062500) Start of systematic data collection through 1940 10 July 15 1930 through 1976

July 1 1967 through 2011

Start of systematic data collection through 2011 June 1 Bold lines indicate statistical significance (p-value less than 0.05)

May 1 Boxplots Day of annual peak flow Data value greater than 1.5 times the interquartile range outside the quartile Apr. 1 Data value less than or 100,000 equal to 1.5 times the interquartile B. Marias River near Shelby, range outside the quartile 1964–241,000 cubic feet per second; Montana (station 06099500) Dam break 75th percentile Inter- median quartile range 10,000 25th percentile Annual peak flow, Annual peak flow, in cubic feet per second

1,000 Nov. 15 Nov. 1 Oct. 1 Sept. 1

Aug. 1

July 1 June 1

May 1 Day of annual peak flow Apr. 1

Mar. 1 Feb. 15 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Figure 4. Fitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for streamflow-gaging stations on upper Missouri River tributaries: A, Tenmile Creek near Rimini, Montana (gaging station 06062500); and B, Marias River near Shelby, Montana (gaging station 06099500). Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 25 annual peak flow and day of peak, statistical distributions station 06133000; map number 271; fig. 1, table 1]) has a among the summary time periods generally are similar (fig. 4). mean basin elevation of 4,734 ft. Although the maximum For annual peak flow for the upper Missouri River basin elevation exceeds 8,500 ft, greater than 97 percent of the tributaries, upward trends during 1930–76 generally were basin is less than 6,000 ft in elevation. A considerable propor- stronger than downward trends during 1967–2011, and statisti- tion (about 35 percent) of peak flows that are during March cal distributions generally were similar among summary time through mid-April likely are caused by low-elevation snow- periods. Study results provide evidence that annual peak flow melt runoff (sometimes with associated early spring rainfall). for the long-term gaging stations can be reasonably considered A considerable proportion of peak flows (about 40 percent) as stationary for application of peak-flow frequency analyses during mid-May through mid-July likely also are caused by within a statewide gaging-station network. spring and summer rainfall (possibly with associated high-elevation snowmelt runoff). Day-of-peak values are considered bimodally distributed. Musselshell River Basin Fitted trends for annual peak flow and peak-flow timing, and statistical distributions for summary time periods for The gaging station in the Musselshell River Basin Milk River at western crossing of international boundary are (Musselshell River at Harlowton, Montana [gaging station presented in figure 6. The study results indicate a substantial 06120500; map number 212; fig. 1, table 1]) has a mean basin upward trend in annual peak flow during 1930–76 and a small elevation of 5,713 ft. About 85 percent of peak flows are dur- upward trend during 1967–2011 (fig. 6; table 2). There is a ing May and June, likely caused by snowmelt runoff (possibly moderate upward trend in annual peak flow during the entire with associated spring rainfall). The few peak flows that are period of record. The study results also indicate a downward during March and April likely are caused by low-elevation trend in peak-flow timing during 1930–76, and an upward snowmelt runoff (possibly with associated rainfall). The few trend in peak-flow timing during 1967–2011 (fig. 6; table 3). peak flows that are in July are caused by rainfall. Peak flows There is a downward trend in peak-flow timing during the that are outside of May and June account for less than 15 entire period of record. Day-of-peak values for Milk River percent of peak flows; thus, most day-of-peak values generally at western crossing of international boundary are considered are uniformly distributed during May and June (fig. 5). to be bimodally distributed. Thus, caution should be used in Fitted trends for annual peak flow and peak-flow timing, interpreting the temporal trends in peak-flow timing because and statistical distributions for summary time periods for Mus- of the simplified handling of the multiple populations. selshell River at Harlowton, Montana, are presented in fig- Differences between the median for 1979–2011 and the ure 5. The study results indicate a substantial upward trend in medians for the other summary time periods were not signifi- annual peak flow during 1930–76 and a moderate downward cant for annual peak flow and day of peak (table 4). For both trend during 1967–2011 (fig. 5; table 2). There is a moderate annual peak flow and day of peak, statistical distributions downward trend in annual peak flow during the entire period among the summary time periods generally are similar (fig. 6). of record. Study results also indicate a small upward trend in For annual peak flow for Milk River at western crossing peak-flow timing during 1930–76, and a small upward trend of international boundary, the upward trend during 1930–1976 in peak-flow timing during 1967–2011 (fig. 5; table 3). There was stronger than the upward trend during 1967–2011, and is a small upward trend in peak-flow timing during the entire statistical distributions generally were similar among summary period of record. time periods. Study results provide evidence that annual peak Differences between the median for 1979–2011 and the flow for the long-term gaging station can be reasonably con- medians for the other summary time periods were not signifi- sidered as stationary for application of peak-flow frequency cant for annual peak flow and day of peak (table 4). For both analyses within a statewide gaging-station network. annual peak flow and day of peak, statistical distributions among the summary time periods generally are similar (fig. 5). For annual peak flow for Musselshell River at Harlowton, Lower Missouri River Tributary Montana, the upward trend during 1930–1976 was stronger The gaging station on a lower Missouri River tribu- than the downward trend during 1967–2011, and statistical tary (Poplar River at international boundary [gaging station distributions generally were similar among summary time 06178000; map number 386; fig. 1, table 1]) has a mean basin periods. Study results provide evidence that annual peak flow elevation of 2,885 ft. Most peak flows are during March and for the long-term gaging station can be reasonably considered April and likely are caused by snowmelt runoff (possibly with as stationary for application of peak-flow frequency analyses associated spring rainfall). However, a considerable proportion within a statewide gaging-station network. of peak flows (greater than 20 percent) are during mid-May through August, likely caused by spring and summer rainfall. Upper Milk River Basin Day-of-peak values are considered bimodally distributed. Fitted trends for annual peak flow and peak-flow timing, The gaging station in the upper Milk River Basin (Milk and statistical distributions for summary time periods for Pop- River at western crossing of international boundary [gaging lar River at international boundary are presented in figure 7. 26 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 50,000 [Water year is defined as the 12-month Musselshell River at Harlowton, Montana period from October 1 through (station 06120500) September 30 and is designated by the 10,000 year in which it ends] Annual peak flows and days of annual peak flows Annual peak flow 1,000 Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second Start of systematic data 100 collection through 1940 50 Aug. 1 1930 through 1976 1967 through 2011 July 1 Start of systematic data collection through 2011 June 1 Bold lines indicate statistical significance (p-value less than May 1 0.05)

Apr. 1 Boxplots Day of annual peak flow Data value greater than 1.5 Mar. 1 times the interquartile range outside the quartile Feb. 15 1910 1930 1950 1970 1990 2010 Water Water All water Data value less than or years years years equal to 1.5 times the interquartile Water year 1930–78 1979–2011 range outside the quartile

75th percentile Inter- median quartile range 25th percentile

Figure 5. Fitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for the streamflow-gaging station in the Musselshell River Basin.

The study results indicate a substantial upward trend in annual than the median for the period of record (592 ft3/s). Also, the peak flow during 1930–76 and a substantial downward trend interquartile range of day-of-peak values for 1979–2011 is during 1967–2011 (fig. 7; table 2). Poplar River at interna- considerably larger than for 1930–78. During 1979–2011, tional boundary has a moderate downward trend in annual spring and summer peak flows were more frequent than during peak flow during the entire period of record. The study results 1930–78. also indicate a downward trend in peak-flow timing during For annual peak flow for the Poplar River at international 1930–76, and an upward trend in peak-flow timing during boundary, the substantial upward trend during 1930–76 was 1967–2011 (fig. 7; table 3). There is an upward trend in peak- of similar magnitude to the substantial downward trend during flow timing during the entire period of record. Day-of-peak 1967–2011, and the annual-peak-flow median for 1979–2011 values for Poplar River at international boundary are consid- was substantially lower than the median for the entire period ered to be bimodally distributed. Thus, caution should be used of record. Thus, study results indicate some potential changes in interpreting the temporal trends in peak-flow timing because in peak-flow characteristics after the mid 1970s, which is fur- of the simplified handling of the multiple populations. ther discussed in the section “Discussion of Stationarity Issues Differences between the medians for 1979–2011 and the for Low-Elevation Gaging Stations in Eastern Montana.” medians for the other summary time periods were not significant for annual peak flow and day of peak (table 4); however, Yellowstone River Basin there is a downward shift in the statistical distribution of peak flows for 1979–2011 in relation to the distributions for 1930– The eight gaging stations in the Yellowstone River Basin 78 and for the entire period of record. The annual-peak-flow have relatively large variability in mean basin elevations median for 1979–2011 (350 ft3/s) is about 40 percent lower (ranging from 5,250 to 8,699 ft). Seven of the gaging stations Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 27

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 10,000 [Water year is defined as the 12-month Milk River at western crossing of period from October 1 through international boundary September 30 and is designated by the (station 06133000) year in which it ends] Annual peak flows and days of annual peak flows 1,000 Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second 1930 through 1976

100 1967 through 2011 July 15 July 1 Start of systematic data collection through 2011 Bold lines indicate statistical June 1 significance (p-value less than 0.05) May 1 Boxplots Apr. 1 Data value greater than 1.5 times the interquartile range Day of annual peak flow Mar. 1 outside the quartile Data value less than or Feb. 1 equal to 1.5 times the interquartile 1910 1930 1950 1970 1990 2010 Water Water All water range outside the quartile years years years Water year 1930–78 1979–2011 75th percentile Inter- median quartile range 25th percentile

Figure 6. Fitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for the streamflow-gaging station in the upper Milk River Basin. in the Yellowstone River Basin have mean basin elevations For all of these high-elevation gaging stations except Yel- greater than 6,000 ft (fig. 1, table 1): lowstone River at Yellowstone Lake outlet, Yellowstone National Park, Wyoming, nearly all peak flows are during • Yellowstone River at Yellowstone Lake outlet, Yel- May and June, likely caused by snowmelt runoff (possibly lowstone National Park, Wyoming (gaging station with associated spring rainfall). Day-of-peak values generally 06186500; map number 414); are uniformly distributed (centered at times that are variable • Yellowstone River at Corwin Springs, Montana (gaging among gaging stations) within May and June (fig. 8). The station 06191500; map number 424); high mean basin elevation (8,699 ft) for Yellowstone River at Yellowstone Lake outlet, Yellowstone National Park, Wyo- • Yellowstone River near Livingston, Montana (gaging ming, results in day-of-peak values being generally uniformly station 06192500; map number 425); distributed during mid-June through mid-July. One of the gaging stations in the Yellowstone River • Stillwater River near Absarokee, Montana (gaging sta- Basin (Powder River at Moorhead, Montana [gaging station tion 06205000; map number 443); 06324500; map number 542; fig. 1, table 1]) has a mean basin elevation of 5,250 ft and less than 20 percent of the basin area • Clarks Fork Yellowstone River near Belfry, Montana is higher than 6,000 ft. Day-of-peak values for Powder River (gaging station 06207500; map number 445); at Moorhead, Montana, are more variable than for the high- • Clarks Fork Yellowstone River at Edgar, Montana elevation gaging stations. Most peak flows are during May and (gaging station 06208500; map number 448); and June, likely caused by spring rainfall and high-elevation snowmelt runoff. A considerable proportion of peak flows (about • Yellowstone River at Billings, Montana (gaging station 15–20 percent) are during March and probably are caused 06214500; map number 458). by low-elevation snowmelt runoff (possibly with associated 28 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Annual peak flows, days of annual Statistical distributions for peak flows, and fitted trend lines indicated periods EXPLANATION 1954–12,700 cubic feet per second 10,000 [Water year is defined as the 12-month Poplar River at period from October 1 through international boundary September 30 and is designated by the (station 06178000) year in which it ends] 1,000 Annual peak flows and days of annual peak flows Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, 100 Fitted trend lines in cubic feet per second

1930 through 1976

10 1967 through 2011 Oct. 1 Start of systematic data Sept. 1 collection through 2011 Bold lines indicate statistical Aug. 1 significance (p-value less than 0.05) July 1

June 1 Boxplots

May 1 Data value greater than 1.5 times the interquartile range Day of annual peak flow Apr. 1 outside the quartile Data value less than or Mar. 1 equal to 1.5 times the interquartile Feb. 15 1910 1930 1950 1970 1990 2010 Water Water All water range outside the quartile years years years Water year 1930–78 1979–2011 75th percentile Inter- median quartile range 25th percentile

Figure 7. Fitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for the streamflow-gaging station on a lower Missouri River tributary. spring rainfall). Furthermore, a considerable proportion of per year) are notable. All of the high-elevation gaging stations peak flows (greater than about 20 percent) are after July 1 have small downward trends in peak-flow timing during the and are caused by summer rainfall. Day-of-peak values for entire period of record. Overall, trend results for the high-ele- Powder River at Moorhead, Montana, are considered trimod- vation stations in the Yellowstone River Basin are somewhat ally distributed. similar to results for the Missouri River headwaters tributaries. Fitted trends for annual peak flow and peak-flow tim- For annual peak flow for the seven high-elevation gaging ing, and statistical distributions for summary time periods stations in the Yellowstone River Basin, differences between for the eight gaging stations in the Yellowstone River Basin the medians for 1979–2011 and the medians for the other sum- are presented in figure 8. For the seven high-elevation gag- mary time periods were not significant (table 4), and statisti- ing stations, the study results indicate moderate to substantial cal distributions among the summary time periods generally upward trends in annual peak flow during 1930–76 and gener- are similar (fig. 8). However, for three of the high-elevation ally small to moderate downward trends in annual peak flow gaging stations, the day-of-peak medians for 1979–2011 were during 1967–2011 (fig. 8; table 2). The high-elevation gaging significantly less than the medians for 1930–78, and for all of stations generally have small to moderate upward trends in the high-elevation gaging stations, statistical distributions of annual peak flow during the entire period of record. The study day-of-peak values for 1979–2011 are shifted downward in results also indicate variable (small to moderate) upward relation to distributions for 1930–78. trends in peak-flow timing during 1930–76, and variable For the low-elevation gaging station in the Yellowstone (small to substantial) downward trends in peak-flow timing River Basin (Powder River at Moorhead, Montana), study during 1967–2011 (fig. 8; table 3). The substantial downward results indicate a moderate upward trend in annual peak flow trends in peak-flow timing during 1967–2011 for Yellowstone during 1930–76 and a substantial downward trend in annual River at Corwin Springs, Montana (-0.29 percent per year) and peak flow during 1967–2011 (fig. 8H; table 2). For Powder Yellowstone River near Livingston, Montana (-0.20 percent River at Moorhead, Montana, there is a moderate downward Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 29

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 50,000 [Water year is defined as the 12-month A. Yellowstone River at Yellowstone Lake outlet, Yellowstone period from October 1 through National Park, Wyoming (station 06186500) September 30 and is designated by the year in which it ends]

10,000 Annual peak flows and days of annual peak flows Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second 1,000 Start of systematic data collection through 1940 500 Aug. 1 1930 through 1976 1967 through 2011

Start of systematic data collection through 2011 July 1 Bold lines indicate statistical significance (p-value less than 0.05)

Boxplots

Day of annual peak flow June 1 Data value greater than 1.5 times the interquartile range May 15 outside the quartile Data value less than or equal to 1.5 times the interquartile 100,000 range outside the quartile B. Yellowstone River at Corwin Springs, Montana (station 06191500) 75th percentile Inter- median quartile range 10,000 25th percentile Annual peak flow, Annual peak flow, in cubic feet per second

1,000 July 15

July 1

June 1 Day of annual peak flow

May 1 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Figure 8. Fitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for streamflow-gaging stations in the Yellowstone River Basin: A, Yellowstone River at Yellowstone Lake outlet, Yellowstone National Park, Wyoming (gaging station 06186500); B, Yellowstone River at Corwin Springs, Montana (gaging station 06191500); C, Yellowstone River near Livingston, Montana (gaging station 06192500); D, Stillwater River near Absarokee, Montana (gaging station 06205000); E, Clarks Fork Yellowstone River near Belfry, Montana (gaging station 06207500); F, Clarks Fork Yellowstone River at Edgar, Montana (gaging station 06208500); G, Yellowstone River at Billings, Montana (gaging station 06214500); and H, Powder River at Moorhead, Montana (gaging station 06324500). 30 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 100,000 [Water year is defined as the 12-month C. Yellowstone River near Livingston, Montana period from October 1 through (station 06192500) September 30 and is designated by the year in which it ends] Annual peak flows and days of annual peak flows 10,000 Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second 1930 through 1976

1,000 1967 through 2011 July 15 Start of systematic data July 1 collection through 2011 Bold lines indicate statistical significance (p-value less than 0.05)

Boxplots June 1 Data value greater than 1.5 times the interquartile range

Day of annual peak flow outside the quartile Data value less than or May 1 equal to 1.5 times the interquartile range outside the quartile

100,000 75th percentile D. Stillwater River near Absarokee, Montana (station 06205000) Inter- median quartile range 25th percentile

10,000 Annual peak flow, Annual peak flow, in cubic feet per second

1,000 July 15

July 1

June 1 Day of annual peak flow

May 1 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 100,000 [Water year is defined as the 12-month E. Clarks Fork Yellowstone River near Belfry, Montana period from October 1 through (station 06207500) September 30 and is designated by the year in which it ends] Annual peak flows and days of annual peak flows 10,000 Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second Start of systematic data collection through 1940 1,000 July 15 1930 through 1976

1967 through 2011 July 1 Start of systematic data collection through 2011 Bold lines indicate statistical significance (p-value less than 0.05) June 1

Boxplots Day of annual peak flow Data value greater than 1.5 times the interquartile range May 1 outside the quartile Data value less than or equal to 1.5 times the interquartile 100,000 range outside the quartile F. Clarks Fork Yellowstone River at Edgar, Montana (station 06208500) 75th percentile Inter- median quartile range 10,000 25th percentile Annual peak flow, Annual peak flow, in cubic feet per second

1,000 July 15

July 1

June 1 Day of annual peak flow

May 1 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 500,000 [Water year is defined as the 12-month G. Yellowstone River at Billings, Montana period from October 1 through (station 06214500) September 30 and is designated by the year in which it ends] 100,000 Annual peak flows and days of annual peak flows Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second 10,000 1930 through 1976

5,000 1967 through 2011 July 15 Start of systematic data collection through 2011 July 1 Bold lines indicate statistical significance (p-value less than 0.05)

Boxplots June 1 Data value greater than 1.5 times the interquartile range

Day of annual peak flow outside the quartile Data value less than or May 1 equal to 1.5 times the interquartile range outside the quartile

50,000 1923–100,000 cubic feet per second 75th percentile H. Powder River at Moorhead, Montana Inter- (station 06324500) median quartile range 10,000 25th percentile Annual peak flow, Annual peak flow, in cubic feet per second 1,000

500 Nov. 15 Nov. 1

Oct. 1 Sept. 1

Aug. 1 July 1 June 1 May 1 Day of annual peak flow Apr. 1 Mar. 1 Feb. 15 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Figure 8. Graphs showing fFitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for streamflow-gaging stations in the Yellowstone River Basin: A, Yellowstone River at Yellowstone Lake outlet, Yellowstone National Park, Wyoming (gaging station 06186500); B, Yellowstone River at Corwin Springs, Montana (gaging station 06191500); C, Yellowstone River near Livingston, Montana (gaging station 06192500); D, Stillwater River near Absarokee, Montana (gaging station 06205000); E, Clarks Fork Yellowstone River near Belfry, Montana (gaging station 06207500); F, Clarks Fork Yellowstone River at Edgar, Montana (gaging station 06208500); G, Yellowstone River at Billings, Montana (gaging station 06214500); and H, Powder River at Moorhead, Montana (gaging station 06324500).—Continued Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 33 trend in annual peak flow during the entire period of record. • Clark Fork below Missoula, Montana (gaging station The study results also indicate a downward trend in peak-flow 12353000; map number 688); timing during 1930–76, during 1967–2011, and also during the • Clark Fork at St. Regis, Montana (gaging station entire period of record (fig. H8 ; table 3). Day-of-peak values 12354500; map number 697); for Powder River at Moorhead, Montana, are considered to be trimodally distributed. Thus, caution should be used in inter- • Flathead River at Flathead, British Columbia (gaging preting the temporal trends in peak-flow timing because of the station 12355000; map number 698); simplified handling of the multiple populations. For Powder River at Moorhead, Montana, the annual- • North Fork Flathead River near Columbia Falls, Mon- peak-flow median for 1979–2011 was significantly less than tana (gaging station 12355500; map number 700); and the medians for 1930–78 and for the entire period of record; • Swan River near Bigfork, Montana (gaging station statistical distributions for 1979–2011 are shifted downward in 12370000; map number 728). relation to distributions for 1930–78 and for the entire period of record (fig. 8H; table 4). The annual-peak-flow median For all of the gaging stations, nearly all peak flows are during for 1979–2011 (3,730 ft3/s) is about 35 percent lower than May and June, likely caused by snowmelt runoff (possibly with associated spring rainfall). Day-of-peak values generally the median for the period of record (5,730 ft3/s). For day of are uniformly distributed during May and June (fig. 9). peak, differences between the median for 1979–2011 and the Fitted trends for annual peak flow and peak-flow timing, medians for the other summary time periods were not signifi- and statistical distributions for summary time periods for the cant (table 4); however, the interquartile range of day-of-peak six gaging stations in the Columbia River Basin are presented values for 1979–2011 is considerably larger than the interquar- in figure 9. The study results indicate substantial upward tile range for 1930–78. trends in annual peak flow for most gaging stations during For annual peak flow for the high-elevation gaging sta- 1930–76 and moderate downward trends in annual peak flow tions in the Yellowstone River Basin, upward trends during for all gaging stations during 1967–2011 (fig. 9; table 2). Most 1930–76 generally were stronger than downward trends during gaging stations have small to moderate downward trends in 1967–2011, and statistical distributions generally were similar annual peak flow during the entire period of record. The study among summary time periods. Study results provide evidence results also indicate variable (moderate to substantial) upward that annual peak flow for the high-elevation long-term gag- trends in peak-flow timing for all gaging stations during ing stations can be reasonably considered as stationary for 1930–76, but small changes that are variable in trend direc- application of peak-flow frequency analyses within a statewide tion among gaging stations during 1967–2011 (fig. 9; table 3). gaging-station network. For peak-flow timing, all of the seven Most gaging stations have small changes in peak-flow timing high-elevation gaging stations have downward trends during during the entire period of record that are variable in trend 1967–2011, and three of those stations have day-of-peak medi- direction. ans for 1979–2011 that are significantly less than medians for Differences between the medians for 1979–2011 and the 1930–78 (table 4). medians for the other summary time periods were not signifi- For annual peak flow for the low-elevation gaging sta- cant for annual peak flow and day of peak (table 4). For both tion (Powder River at Moorhead, Montana), the upward trend annual peak flow and day of peak, statistical distributions during 1930–76 was weaker than the substantial downward among the summary time periods generally are similar (fig. 9). trend during 1967–2011, and the annual-peak-flow median For annual peak flow for the Columbia River Basin, for 1979–2011 was substantially lower than the median for upward trends during 1930–76 generally were stronger than the entire period of record. Thus, study results indicate some downward trends during 1967–2011, and statistical distribu- potential changes in peak-flow characteristics after the mid- tions generally were similar among summary time periods. 1970s, which is further discussed in the section “Discussion Study results provide evidence that annual peak flow for the of Stationarity Issues for Low-Elevation Gaging Stations in long-term gaging stations can be reasonably considered as sta- Eastern Montana.” tionary for application of peak-flow frequency analyses within a statewide gaging-station network. Streamflow-Gaging Stations in the Columbia River Basin Summary Observations For annual peak flow for most long-term gaging stations, The six gaging stations in the Columbia River Basin have upward trends during 1930–76 generally were stronger than mean basin elevations that range from 5,012 to 5,765 ft (fig. 1, downward trends during 1967–2011 and statistical distribu- table 1): tions generally were similar among summary time periods. • Clark Fork above Missoula, Montana (gaging station Study results provide evidence that annual peak flow for most 12340500; map number 665); of the long-term gaging stations can be reasonably considered 34 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 100,000 A. Clark Fork above Missoula, Montana [Water year is defined as the 12-month period from October 1 through (station 12340500) September 30 and is designated by the year in which it ends] Annual peak flows and days of annual peak flows 10,000 Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second 1930 through 1976

1,000 1967 through 2011 July 1 Start of systematic data collection through 2011 Bold lines indicate statistical June 1 significance (p-value less than 0.05)

Boxplots

May 1 Data value greater than 1.5 times the interquartile range

Day of annual peak flow outside the quartile Data value less than or Apr. 1 equal to 1.5 times the interquartile range outside the quartile

500,000 75th percentile B. Clark Fork below Missoula, Montana Inter- (station 12353000) median quartile range 100,000 25th percentile Annual peak flow, Annual peak flow, in cubic feet per second 10,000

5,000 July 1

June 1

Day of annual peak flow May 1

Apr. 15 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 500,000 [Water year is defined as the 12-month C. Clark Fork at St. Regis, Montana period from October 1 through (station 12354500) September 30 and is designated by the year in which it ends]

100,000 Annual peak flows and days of annual peak flows Annual peak flow Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second 10,000 Start of systematic data collection through 1940 5,000 July 1 1930 through 1976 1967 through 2011

Start of systematic data collection through 2011 June 1 Bold lines indicate statistical significance (p-value less than 0.05)

Boxplots

Day of annual peak flow May 1 Data value greater than 1.5 times the interquartile range outside the quartile Apr. 15 Data value less than or equal to 1.5 times the interquartile 50,000 range outside the quartile D. Flathead River at Flathead, British Columbia (station 12355000) 75th percentile Inter- 10,000 median quartile range 25th percentile Annual peak flow, Annual peak flow, in cubic feet per second 1,000

500 July 1 November 7, 2007

June 1

Day of annual peak flow May 1

Apr. 15 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Annual peak flows, days of annual Statistical distributions for EXPLANATION peak flows, and fitted trend lines indicated periods 100,000 [Water year is defined as the 12-month E. North Fork Flathead River period from October 1 through near Columbia Falls, Montana September 30 and is designated by the (station 12355500) year in which it ends] Annual peak flows and days of annual peak flows Annual peak flow 10,000 Day of annual peak flow

Annual peak flow, Annual peak flow, Fitted trend lines in cubic feet per second Start of systematic data collection through 1940 1,000 July 1 1930 through 1976 November 8, 2007 1967 through 2011

Start of systematic data collection through 2011 June 1 Bold lines indicate statistical significance (p-value less than 0.05)

Boxplots

Day of annual peak flow May 1 Data value greater than 1.5 times the interquartile range outside the quartile Apr. 15 Data value less than or equal to 1.5 times the interquartile 50,000 range outside the quartile F. Swan River near Bigfork, Montana (station 12370000) 75th percentile Inter- 10,000 median quartile range 25th percentile Annual peak flow, Annual peak flow, in cubic feet per second 1,000

500 July 15 December 25, 1934 July 1

June 1

Day of annual peak flow May 1

Apr. 15 1910 1930 1950 1970 1990 2010 Water Water All water years years years Water year 1930–78 1979–2011

Figure 9. Fitted trends for annual peak flow (the annual series of maximum instantaneous discharge, in cubic feet per second) and peak-flow timing (the annual series of the day of the annual peak flow), and statistical distributions for summary time periods for streamflow-gaging stations in the Columbia River Basin: A, Clark Fork above Missoula, Montana (gaging station 12340500); B, Clark Fork below Missoula, Montana (gaging station 12353000); C, Clark Fork at St. Regis, Montana (gaging station 12354500); D, Flathead River at Flathead, British Columbia (gaging station 12355000); E, North Fork Flathead River near Columbia Falls, Montana (gaging station 12355500); and F, Swan River near Bigfork, Montana (gaging station 12370000).—Continued Temporal Trends and Stationarity in Annual Peak Flow and Peak-Flow Timing 37 as stationary for application of peak-flow frequency analyses Discussion of Stationarity Issues for Low- within a statewide gaging-station network; however, for two Elevation Streamflow-Gaging Stations in low-elevation gaging stations (Poplar River at international boundary [gaging station 06178000; map number 386; fig. 1, Eastern Montana table 1] and Powder River at Moorhead, Montana [gaging sta- The two low-elevation gaging stations in eastern Mon- tion 06324500; map number 542; fig. 1, table 1]), substantial tana (Poplar River at international boundary [gaging station downward trends in annual peak flow during 1967–2011 were 06178000; map number 386; fig. 1, table 1] and Powder River of similar or stronger magnitude than the upward trends during at Moorhead, Montana [gaging station 06324500; map number 1930–76, and the annual-peak-flow medians for 1979–2011 542; fig. 1, table 1]) had considerable changes in annual peak- were substantially lower than the medians for the entire period flow characteristics after the mid-1970s, which might provide of record. These issues are further discussed in the section evidence of potential nonstationarity in the peak-flow records. “Discussion of Stationarity Issues for Low-Elevation Gaging Although a small number of stations are represented, addi- Stations in Eastern Montana.” tional investigation was considered to be warranted. For peak-flow timing for most long-term gaging sta- Peak-flow frequencies for the two gaging stations based tions, differences in trends between the periods 1930–76 and on data collected during 1979–2011 were compared to peak- 1967–2011 are variable and not particularly strong, and sta- flow frequencies based on the entire period of record. Docu- tistical distributions generally are similar among the summary mentation concerning development of the peak-flow frequen- time periods. However, for two gaging stations on a Mis- cies is presented in appendix 1 (at the back of this report souri River headwater tributary (Gallatin River near Gallatin chapter). Documentation regarding analytical procedures for Gateway, Montana [gaging station 06043500; map number 80; the peak-flow frequency analyses is presented in table 1–1. fig. 1, table 1] and Gallatin River at Logan, Montana [gaging Peak-flow frequency results are presented in table 1-2 and station 06052500; map number 88; fig. 1, table 1]), and for figure 1–1. five of the seven high-elevation gaging stations in the Yel- For Poplar River at international boundary, peak-flow lowstone River Basin (Yellowstone River at Corwin Springs, frequencies for the period 1979–2011 were somewhat lower Montana [gaging station 06191500; map number 424; fig. 1, than peak-flow frequencies for the entire period of record (fig. table 1], Yellowstone River near Livingston, Montana [gaging 1–1A, table 1–2). For individual annual exceedance probabili- station 06192500; map number 425; fig. 1, table 1], Clarks ties (AEPs), peak-flow frequencies for the period 1979–2011 Fork Yellowstone River near Belfry, Montana [gaging station ranged from 19 to 50 percent lower than peak-flow frequen- 06207500; map number 445; fig.1, table 1], Clarks Fork Yel- cies for the entire period of record. For most AEPs, the peak- lowstone River at Edgar, Montana [gaging station 06208500; flow frequencies for the period 1979–2011 were lower than the map number 448; fig. 1, table 1], Yellowstone River at Bill- lower 95-percent confidence level of the peak-flow frequency ings, Montana [gaging station 06214500; map number 458; curve for the entire period of record. fig. 1, table 1]), downward trends in peak-flow timing during For Powder River at Moorhead, Montana, peak-flow 1967–2011 generally were stronger than upward trends during frequencies for the period 1979–2011 were substantially lower 1930–1976 and day-of-peak medians for 1979–2011 were than peak-flow frequencies for the entire period of record (fig. considerably less than day-of-peak medians for 1930–78. The 1–1B, table 1–1). For individual AEPs, peak-flow frequencies downward trends in peak-flow timing for 1967–2011 indicate for the period 1979–2011 ranged from 32 to 65 percent lower that the timing of annual peak flows changed from later in the than peak-flow frequencies for the entire period of record year to earlier in the year. For the seven high-elevation gaging (table 1–2). For all AEPs, the peak-flow frequencies for the stations, the mean change during 1967–2011 was about 13 period 1979–2011 were lower than the lower 95-percent con- days (range of 8 to 22 days). fidence level of the peak-flow frequency curve for the entire For most of the high-elevation gaging stations on the period of record. Furthermore, for all AEPs, the upper 95-per- Missouri River headwaters tributaries and in the Yellowstone cent confidence level for the period 1979–2011 was lower River and Columbia River Basins, there was general corre- than the lower 95-percent confidence level of the peak-flow spondence between trend patterns for annual peak flow and frequency curve for the entire period of record. trend patterns for peak-flow timing. That is, during periods The differences between peak-flow frequencies based on when there were upward trends in annual peak flow, there also 1979–2011 data and peak-flow frequencies based on the entire generally were upward trends peak-flow timing. Conversely, period of record provide additional information on potential during periods when there were downward trends in annual nonstationarity in annual peak flow for the two low-elevation peak flow, there generally were downward trends in peak- gaging stations in eastern Montana. The observed differences flow timing. Moore and others (2007) also reported general could have large effects on some uses of peak-flow frequency correspondence between trend patterns in runoff variables and information. timing variables. It is difficult to accurately determine the possible causes of the potential nonstationarity in annual peak flow. Con- sequently, it also is difficult to develop a clear approach for 38 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana handling this potential nonstationarity issue within the context affects about 20 percent of the intervening drainage area. Also, of application of peak-flow frequency analyses within a state- small-impoundment development probably was extensive in wide gaging-station network. the Powder River Basin in Wyoming during about 1997–2010 The two low-elevation gaging stations that exhibit when coalbed methane extraction activities were extensive potential nonstationarity are located in drainage basins that (National Research Council, 2010); therefore, small-impound- are strongly affected by agricultural activities that potentially ment development might be a contributor to nonstationarity affect the hydrologic regimes. Primary agricultural activities issues for Powder River at Moorhead, Montana. that might alter natural hydrologic conditions include con- The criteria used by the USGS for regulation classifica- struction of small impoundments (primarily for stock-watering tion do not incorporate assessment of irrigation diversions. purposes) and irrigation diversions. Because of the extensive Datasets for irrigation diversions are not readily available data requirements of the trend analysis, a small number of at sufficient scale and coverage for assessing effects on the stations in low-elevation agriculture-dominated basins are application of peak-flow frequency analyses within a statewide represented; however, the potential nonstationarity issues rep- gaging-station network. Compilation of a statewide dataset of resented by the two low-elevation gaging stations might have locations and capacities of irrigation canals would be impor- application to a large number of gaging stations in Montana. tant for better definition of regulation effects on streamflow As previously discussed in the section “Selection of characteristics. Lacking suitable data, it is difficult to assess Streamflow-Gaging Stations,” the current (2015) criterion potential effects of irrigation diversions on the potential non- used by the USGS classifies a gaging station as affected by stationarity issues for the two low-elevation gaging stations. major dam regulation if the drainage area upstream from a Changes in climatic characteristics after the mid-1970s single upstream dam exceeds 20 percent of the drainage area possibly contributed to the potential nonstationarity issues. for the gaging station. Additionally, the USGS classifies a gag- Lack of considerable indication of potential nonstationarity ing station as affected by minor dam regulation if the drainage in annual peak flow for the other long-term gaging stations area upstream from all upstream dams exceeds 20 percent of in this study might indicate that climatic changes have been the drainage area for the gaging station (McCarthy and oth- more pronounced with respect to effects on peak flows in low- ers, 2016). According to these criteria, the two low-elevation elevation areas in eastern Montana than in areas represented gaging stations are not classified as affected by major or minor by the other long-term gaging stations. Another possibility is regulation. However, for the two low-elevation gaging sta- that climatic changes after the mid-1970s are exacerbated in tions, additional considerations might affect their regulation low-elevation areas where small-impoundment development status. and potential effects of irrigation diversions might be more Much of the drainage basins of the two low-elevation extensive. gaging stations are located in either Saskatchewan, Canada Potential nonstationarity issues for peak flows have been (for Poplar River at international boundary) or Wyoming (for considered in other parts of the United States. Increasing peak Powder River at Moorhead, Montana). The geospatial data for flows have been observed in recent years (after the 1970s) in small impoundments used by the USGS for regulation clas- Maine (Hodgkins, 2010) and North Dakota (Williams-Sether, sification (McCarthy and others, 2016) were not available for 2015). In Maine, Hodgkins (2010) suggested a conservative Canada and Wyoming, and quantitative assessment of poten- approach of computing peak-flow frequencies from datasets tial effects of small-impoundment development was difficult. restricted to recent years and also datasets that include the However, some qualitative information might be relevant to entire period of record and then selecting the higher computed evaluating potential effects of small-impoundment develop- peak-flow frequencies. In North Dakota, peak-flow frequen- ment for the two gaging stations. cies have been calculated using generalized skew values For Poplar River at international boundary, a second determined from the truncated period 1960–2009 (Williams- gaging station (Poplar River near Bredette, Montana [gaging Sether, 2015). For the two low-elevation gaging stations in station 06180500]) is downstream. Within the intervening eastern Montana with indication of decreasing peak flows after drainage area in Montana between the two gaging stations, the mid-1970s, a conservative approach would be to compute there was small-impoundment development during about peak-flow frequencies based on the entire period of record. 1950–65 that affects about 13 percent of the intervening drain- The issue of potential nonstationarity of annual peak flow age area. The somewhat small amount of small-impoundment in low-elevation areas of eastern Montana might be clari- development in the intervening drainage area might indicate fied by additional future research. Research activities might that small-impoundment development was not a large contrib- include (1) detailed analysis of effects of changes in climatic utor to nonstationarity issues for Poplar River at international characteristics after the mid-1970s on hydrologic regimes in boundary. eastern Montana; (2) detailed documentation of locations and For Powder River at Moorhead, a second gaging sta- capacities of irrigation diversion canals in eastern Montana; tion (Powder River near Locate, Montana [gaging station (3) detailed documentation of locations, storage capacities, 06326500]) is downstream. Within the intervening drainage and operations of small impoundments in eastern Montana; area in Montana between the two gaging stations, there was (4) analysis of effects of irrigation diversion canals and small small-impoundment development during about 1940–61 that impoundments on peak-flow characteristics; and (5) analysis Summary and Conclusions 39 of the combined effects of changes in climatic characteristics, selected data summary periods for each gaging station. The diversions, and small impoundments on peak-flow character- data summary periods were (1) 1930–78, (2) 1979–2011, and istics in eastern Montana. A possible initial follow-up study (3) the entire period of record. The 1930–78 summary period might involve relaxing the rigorous dataset requirements that was selected to represent peak-flow characteristics during a were used in this study to include additional low-elevation period before the mid-1970s that generally ranged from an gaging stations in eastern Montana. This expanded study unusually dry period to an unusually wet period and typically might provide information on the areal extent of the observed encompassed the full range in historical variability; the sum- trend patterns for the two low-elevation gaging stations. mary period purposely extends slightly past the mid-1970s to include transition years. The 1979–2011 summary period was selected to represent the period after the mid 1970s that might be affected by reported changes in hydrologic regimes associ- Summary and Conclusions ated with changes in climatic conditions. The entire period of record (including any pre-1930 data) also was statistically The primary purpose of Chapter B of this Scientific summarized. For annual peak flow, the entire period of record Investigations Report is to present the results of a large-scale represents the data that are typically used to calculate peak- study by the U.S. Geological Survey, in cooperation with flow frequencies. For a given gaging station, stationarity of the Montana Department of Transportation and the Mon- annual peak flow requires that all of the data represent a con- tana Department of Natural Resources and Conservation to sistent hydrologic regime within the same (albeit highly vari- investigate general patterns in peak-flow temporal trends and able) fundamental climatic system. As such, a primary consid- stationarity through water year 2011 for 24 long-term stream- eration in this study is whether annual peak flow data after the flow-gaging stations (hereinafter referred to as gaging sta- mid-1970s are substantially different from data for the entire tions) in Montana. Hereinafter, all years refer to water years; period of record and thus might result in substantially different a water year is the 12-month period from October 1 through peak-flow frequencies. The nonparametric Wilcoxon rank sum September 30 and is designated by the year in which it ends. procedure was used to test for significant differences between Temporal trends were analyzed for two hydrologic variables: the annual-peak-flow median for 1979–2011 in relation to annual peak flow and peak-flow timing. Annual peak flow medians for 1930–78 and for the entire period of record. The is the annual series of maximum instantaneous discharge in nonparametric Wilcoxon rank sum procedure also was used to cubic feet per second. Peak-flow timing is the annual series of test for significant changes in peak-flow timing, with the test the day of the annual peak flow (hereinafter referred to as day applied to the day-of-peak median for 1979–2011 in relation of peak). to medians for 1930–78 and for the entire period of record. In The 24 long-term gaging stations are grouped according this study, a significance level p( -value) less than 0.05 indi- to the following major river basins: Saskatchewan River Basin cates statistical significance. (2 gaging stations); Missouri River Basin (16 gaging stations); For annual peak flow for most long-term gaging stations, and Columbia River Basin (6 gaging stations). Gaging stations upward trends during 1930–76 generally were stronger than in the Missouri River are subgrouped according to the follow- downward trends during 1967–2011, and statistical distribu- ing descriptive classes: (1) Missouri River headwaters tributar- tions generally were similar among summary time periods. ies (three gaging stations); (2) upper Missouri River tributaries Study results provide evidence that annual peak flow for most (two gaging stations); (3) Musselshell River Basin (one gaging of the long-term gaging stations can be reasonably considered station); (4) upper Milk River Basin (one gaging station); (4) as stationary for application of peak-flow frequency analyses lower Missouri River tributary (one gaging station); and (5) within a statewide gaging-station network. However, for two Yellowstone River Basin (eight gaging stations). low-elevation gaging stations in eastern Montana (Poplar Exploratory analyses indicated that peak flows for most River at international boundary [gaging station 06178000] sites generally were lower than median peak flow (determined and Powder River at Moorhead, Montana [gaging station for the entire period of record through 2011) from about 1930 06324500]), substantial downward trends in annual peak flow to the early 1940s and generally were higher than median peak during 1967–2011 were of similar or stronger magnitude than flow from the mid- to late 1960s to the mid- to late 1970s. the upward trends during 1930–76, and the annual-peak-flow These generally consistent large-scale patterns served as the medians for 1979–2011 were substantially lower than the basis for defining four trend analysis periods that were applied medians for the entire period of record. for each gaging station: (1) from the start of systematic data For peak-flow timing for most long-term gaging sta- collection through 1940 (for gaging stations with at least 15 tions, differences in trending between the periods 1930–76 years of systematic record during the period); (2) from 1930 to and 1967–2011 are variable and not particularly strong, and 1976; (3) from 1967 to 2011; and (4) from the start of system- statistical distributions generally are similar among the sum- atic data collection through 2011. mary time periods. However, for two gaging stations on a Mis- For the defined trend analysis periods, trend magnitudes souri River headwater tributary (Gallatin River near Gallatin were computed using the Sen slope estimator. Statistical Gateway, Montana [gaging station 06043500] and Gallatin distributions of peak-flow characteristics were compiled for River at Logan, Montana [gaging station 06052500]) and for 40 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana five high-elevation gaging stations in the Yellowstone River for the two low-elevation gaging stations in eastern Montana. Basin (Yellowstone River at Corwin Springs, Montana [gag- The observed differences could have large effects on some ing station 06191500], Yellowstone River near Livingston, uses of peak-flow frequency information. Montana [gaging station 06192500], Clarks Fork Yellowstone It is difficult to accurately determine the possible causes River near Belfry, Montana [gaging station 06207500], Clarks of the potential nonstationarity in annual peak flow. Conse- Fork Yellowstone River at Edgar, Montana [gaging station quently, it also is difficult to develop a clear approach for han- 06208500], and Yellowstone River at Billings, Montana [gag- dling this potential nonstationarity issue within the context of ing station 06214500]), downward trends in peak-flow timing application of peak-flow frequency analyses within a statewide during 1967–2011 generally were stronger than upward trends gaging-station network. The two low-elevation gaging stations during 1930–76, and day-of-peak medians for 1979–2011 that exhibit potential nonstationarity are located in drainage were considerably less than medians for 1930–78. basins that are strongly affected by agricultural activities that For most of the high-elevation gaging stations on the potentially affect the hydrologic regimes. Primary agricul- Missouri River headwaters tributaries and in the Yellowstone tural activities that might alter natural hydrologic conditions River and Columbia River Basins, there was general corre- include construction of small impoundments (primarily for spondence between trend patterns for annual peak flow and stock-watering purposes) and irrigation diversions. Temporal trend patterns for peak-flow timing. That is, during periods variability in these activities might contribute to the potential when there were upward trends in annual peak flow, there also nonstationarity issues. Changes in climatic characteristics after generally were upward trends in peak-flow timing. Con- the mid-1970s also possibly contribute to the potential nonsta- versely, during periods when there were downward trends in tionarity issues. Lack of considerable indication of potential annual peak flow, there generally were downward trends in nonstationarity in annual peak flow for the other long-term peak-flow timing. gaging stations in this study might indicate that climatic The two low-elevation gaging stations in eastern Mon- changes have been more pronounced with respect to effects tana (Poplar River at international boundary [gaging station on peak flows in low-elevation areas in eastern Montana than 06178000] and Powder River at Moorhead, Montana [gaging in areas represented by the other long-term gaging stations. station 06324500]) have had considerable changes in annual- Another possibility is that climatic changes after the mid- peak-flow characteristics after the mid-1970s, which might 1970s are exacerbated in low-elevation areas where small- provide evidence of potential nonstationarity in the peak-flow impoundment development and potential effects of irrigation records. Peak-flow frequencies for the two gaging stations diversions might be more extensive. based on data collected during 1979–2011 were compared to peak-flow frequencies based on the entire period of record. For Poplar River at international boundary, peak-flow frequencies for the period 1979–2011 were somewhat lower than References peak-flow frequencies for the entire period of record. For individual annual exceedance probabilities (AEPs), peak-flow Aziz, O.I., and Burn, D.H., 2006, Trends and variability in the frequencies for the period 1979–2011 ranged from 19 to 50 hydrological regime of the Mackenzie River Basin: Journal percent lower than peak-flow frequencies for the entire period of Hydrology, v. 319, p. 282–294. [Also available at http:// of record. For most AEPs, the peak-flow frequencies for the dx.doi.org/10.1016/j.jhydrol.2005.06.039.] period 1979–2011 were lower than the lower 95-percent confidence level of the peak-flow frequency curve for the entire Cayan, D.R., Kammerdiener, S.A., Dettinger, M.D., Caprio, period of record. For Powder River at Moorhead, Montana, J.M., and Peterson, D.H., 2001, Changes in the onset peak-flow frequencies for the period 1979–2011 were substan- of spring in the western United States: Bulletin of the tially lower than peak-flow frequencies for the entire period American Meteorological Society, v. 82, no. 3, p. 399– of record. For individual AEPs, peak-flow frequencies for the 415. [Also available at http://dx.doi.org/10.1175/1520- period 1979–2011 ranged from 32 to 65 percent lower than 0477(2001)082<0399:CITOOS>2.3.CO;2.] peak-flow frequencies for the entire period of record. 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Stewart, I.T., Cayan, D.R., and Dettinger, M.D., 2004, Zelt, R.B., Boughton, Greg, Miller, K.A., Mason, J.P., and Changes in snowmelt runoff timing in western North Amer- Gianakos, L.M., 1999, Environmental setting of the Yellow- ica under a ‘Business as Usual’ climate change scenario: stone River Basin, Montana, North Dakota, and Wyoming: Climatic Change, v. 62, no. 1, p. 217–232. [Also available at U.S. Geological Survey Water-Resources Investigations http://dx.doi.org/10.1023/B%3ACLIM.0000013702.22656. Report 98–4269, 113 p. [Also available at http://pubs.usgs. e8.] gov/wri/wri984269/.] Appendix 1 44 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

Appendix 1. Information on Peak-Flow Frequency Analyses for Low-Elevation Streamflow-Gaging Stations in Eastern Montana

Peak-flow frequency analyses for Poplar River at international boundary (streamflow-gaging station 06178000; map number 386; fig. 1, table 1) and Powder River at Moorhead, Montana (streamflow-gaging station 06324500; map number 542; fig. 1, table 1) were done using procedures described by Sando and others (2016). Estimates of peak-flow magnitudes for 66.7-, 50-, 42.9-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (AEPs) are reported. These AEPs correspond to 1.5-, 2-, 2.33-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals. For each of the streamflow-gaging stations, peak-flow frequency analyses were done on two of the data summary periods: (1) 1979–2011, and (2) the entire period of record. Documentation regarding analytical procedures for the peak-flow frequency analyses is presented in table 1–1. Peak-flow frequency results are presented in table 1–2 and figure 1–1. Appendix 1 45 -0.400 -0.400 -0.005 -0.005 skew Generalized skew -0.251 -0.436 -0.324 -0.216 Station 0 0 ------10 10 1978 threshold threshold flow for user or Water year of peak Water peak flows less than historical high-outlier Number of systematic or equal to low-outlier sis Skew type 2 2 WEIGHTED WEIGHTED WEIGHTED WEIGHTED used in analy - user user default default default Type of Type default default default Type of Type threshold threshold high-outlier low-outlier 0.504 0.654 0.343 0.295 Low-outlier information Standard deviation Log-distribution information for peak-flow data 7.6 615.8 591.9 threshold, High-outlier and historical adjustment information threshold, per second per second 2.817 2.581 3.743 3.540 Low-outlier High-outlier Mean in cubic feet in cubic feet 160 19,174.0 31,385.2 20,348.5 33,000 1 1 1 ------low-end low-end low-end procedures procedures procedures Bulletin 17B Bulletin 17B Bulletin 17B for deviation for deviation for deviation from standard from standard from standard Primary reason Primary reason Primary reason years years years Analysis period Analysis period Analysis period of record, water of record, water of record, water 1979–2011 1931, 1933–2011 1931, 1933–2011 1979–2011 1979–2011 1931, 1933–2011 1923, 1929–72, 1975–2011 1979–2011 1923, 1929–72, 1975–2011 1979–2011 1923, 1929–72, 1975–2011 1979–2011 33 80 80 33 33 80 82 33 82 33 82 33 Number of Number of Number of years of peak- years of peak- years of peak- flow records in flow records in flow records in analysis period analysis period analysis period 358 358 358 miles miles miles 8,029 8,029 8,029 square square square area, in area, in area, in Drainage Drainage Drainage Station name Station name Station name Poplar River at international boundary Poplar River at international boundary Poplar River at international boundary Powder River at Moorhead, Montana Powder River at Moorhead, Montana Powder River at Moorhead, Montana Station Station Station number number number Documentation regarding analytical procedures for peak-flow frequency analyses low-elevation streamflow-gaging stations in eastern Montana. identification identification identification 06178000 06178000 06178000 06324500 06324500 06324500

386 386 386 542 542 542 Map Map Map (fig. 1) (fig. 1) (fig. 1) number number number Table 1–1. Table year is the 12-month period from October 1 through September 30 and designated by in which it ends. --, not applicable] [Water 46 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana ------End 2011 water period year of historic ------1919 Start water period year of historic ------93 period, historic in years Length of 0 0 1 0 threshold Number of or equal to systematic peak flows high-outlier greater than High-outlier and historical adjustment information Advisory Council on Water Data, 1982); user: outlier threshold Water Advisory Council on 0 0 1 0 flows Number of historical peak 1 ------low-end procedures Bulletin 17B for deviation from standard Primary reason years Analysis period of record, water 1931, 1933– 2011 1979–2011 1923, 1929–72, 1975–2011 1979–2011 80 33 82 33 Number of years of peak- flow records in analysis period 358 miles 8,029 square area, in Drainage Station name Poplar River at international boundary Powder River at Moorhead, Montana Station number Documentation regarding analytical procedures for peak-flow frequency analyses low-elevation streamflow-gaging stations in eastern Montana.—Continued identification 06178000 06324500

0 0 386 542 Map Standard Bulletin 17B (U.S. Interagency Advisory Council on Water Data, 1982) procedures are considered to be the use of weighted skew and single Grubbs-Beck low-outlier threshold. In Water Advisory Council on Standard Bulletin 17B (U.S. Interagency Definitions of types outler thresholds include: default: outlier threshold calculated using Bulletin 17B default procedures (U.S. Interagency (fig. 1) 1 2 number Table 1–1. Table year is the 12-month period from October 1 through September 30 and designated by in which it ends. --, not applicable] [Water based on a systematic peak flow selected by the user (peak-flow frequency analyst). cases where either the station skew or a user-selected low-outlier threshold was used, the frequency analysis was considered to deviate from standard Bulletin 17B procedures. The abbreviations for the reasons low-outlier threshold was used, the frequency analysis considered to deviate from standard Bulletin 17B procedures. cases where either the station skew or a user-selected for deviation from standard Bulletin 17B procedures are defined as follows: low-end: the probability plots of peak-flow records deviate typical patterns in lower end frequency curve at high annual exceedance probabilities (greater than about 50.0 percent). Appendix 1 47 10 0.2 2,990 4,120 2,280 2,420 4,740 1,450 8,190 6,490 11,200 15,400 19,100 12,800 6,530 27,200 49,700 16,900 13,500 38,200 61,900 91,700 45,400 21,600 36,900 15,200 869 20 0.5 1,710 2,230 1,350 1,380 2,460 9,120 6,180 8,000 5,010 10,700 12,800 5,090 11,400 17,500 30,200 10,100 26,800 47,200 67,400 35,600 18,100 29,600 13,100 1 763 956 620 555 878 359 42.9 6,240 7,250 5,420 3,990 4,890 3,270 8,260 7,860 4,100 11,500 12,300 20,200 19,700 37,800 52,400 29,200 15,600 24,600 in percent in percent 2 622 771 501 424 662 274 50 5,420 6,270 4,690 3,530 4,300 2,890 8,390 5,860 5,890 3,190 9,940 13,100 13,900 29,800 40,000 23,500 13,200 20,000 indicated annual exceedance probability, indicated annual exceedance probability, indicated annual exceedance probability, Annual peak flow, in cubic feet per second, for Annual peak flow, in cubic feet per second, for Annual peak flow, 4 382 475 302 218 337 135 66.7 3,880 4,490 3,310 2,630 3,190 2,100 5,550 8,230 4,030 4,210 9,220 2,380 8,440 11,000 22,900 29,800 18,500 15,900 Data type Data type lower 95-percent confidence level frequency-curve estimates upper 95-percent confidence level lower 95-percent confidence level frequency-curve estimates upper 95-percent confidence level lower 95-percent confidence level frequency-curve estimates upper 95-percent confidence level lower 95-percent confidence level frequency-curve estimates upper 95-percent confidence level upper 95-percent confidence level lower 95-percent confidence level frequency-curve estimates upper 95-percent confidence level lower 95-percent confidence level frequency-curve estimates upper 95-percent confidence level lower 95-percent confidence level frequency-curve estimates upper 95-percent confidence level lower 95-percent confidence level frequency-curve estimates 2011 2011 of record, of record, 1979–2011 1975–2011 1979–2011 1979–2011 1975–2011 1979–2011 water years water years 1931, 1933– 1931, 1933– 1923, 1929–72, 1923, 1929–72, Analysis period Analysis period 33 33 33 33 80 82 82 80 records in records in of peak-flow of peak-flow analysis period analysis period Number of years Number of years 358 358 miles miles 8,029 8,029 square square area, in area, in Drainage Drainage

Station name Station name international boundary Moorhead, Montana Moorhead, Montana international boundary Poplar River at Poplar River at Powder River at Powder River at Station Station number number Peak-flow frequency results for low-elevation streamflow-gaging stations in eastern Montana. 06178000 06178000 06324500 06324500 identification identification

386 386 542 542 Map Map (fig. 1) (fig. 1) number number Table 1–2. Table year is the 12-month period from October 1 through September 30 and designated by in which it ends] [Water 48 Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana

100,000 A. Poplar River at international boundary EXPLANATION (station 06178000) [Water year is defined as the 12-month period from October 1 through September 30 and is designated by the year in which it ends] 10,000 Annual peak flow—plotting positions determined using the Cunnane formulation; Helsel and Hirsch, 2002 Entire period of record Water years 1979 through 2 011

1,000 Peak-flow frequency curves Enitre period of record Water years 1979 through 2 011

Dashed lines indicate upper and lower 95-percent confidence 100 intervals

1,000,000 B. Powder River at Moorhead, Montana (station 06324500) Annual peak flow, in cubic feet per second Annual peak flow,

100,000

10,000

1,000 99.99 99.9 99.8 99.5 99 98 95 90 80 70 60 50 40 30 20 10 0.5 0.2 0.1 0.05 0.01 100 5 2 1

Annual exceedance probability, in percent

Figure 1–1. Annual peak flows and peak-flow frequency curves for low-elevation streamflow-gaging stations in eastern Montana. Publishing support provided by: Rolla Publishing Service Center

For more information concerning this publication, contact: Director, Wyoming-Montana Water Science Center U.S. Geological Survey 3162 Bozeman Ave Helena, MT 59601 (406) 457–5900

Or visit the Wyoming-Montana Water Science Center Web site at: http://wy-mt.water.usgs.gov/ Sando and others—Temporal Trends and Stationarity for Selected Long-Term Streamflow-Gaging Stations, Montana—Scientific Investigations Report 2015–5019–B ISSN 2328-0328 (online) http://dx.doi.org/10.3133/sir20155019B