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#           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 in *Montana StreamStats*

      April 5, 2016    

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A large-scale study by the U.S. Geological Survey, in cooperation with the Montana Department of Transportation and the Montana Department of Natural Resources and Conservation, was done to investigate general patterns in peak-flow temporal trends and stationarity through water year 2011 for 24 long-term streamflow-gaging stations (hereinafter referred to as gaging stations) in Montana. Hereinafter, all years refer to water years; a water year is the 12-month period from October 1 through September 30 and is designated by the year in which it ends. The primary focus of the study was to identify general patterns in peak-flow temporal trends and stationarity that are relevant to application of peak-flow frequency analyses within a statewide gaging-station network.

Temporal trends were analyzed for two hydrologic variables: annual peak flow and peak-flow timing. Annual peak flow is the maximum instantaneous discharge, in cubic feet per second, recorded each year a gaging station was operated. Peak-flow timing is the day of the annual peak flow (hereinafter referred to as day of peak), recorded each year a gaging station was operated.

Study results provide evidence that annual peak flow for most of the long-term gaging stations can be reasonably considered as stationary for application of peak-flow frequency analyses within a statewide gaging station network. Upward trends in annual peak flow during 1930–76 generally were stronger than downward trends during 1967–2011 for most long-term gaging stations. Statistical distributions of annual peak flow generally were similar among three summary time periods (1930–78, 1979–2011, and the entire period of record). However, for two low-elevation gaging stations in eastern Montana (Poplar River at international boundary [gaging station 06178000] and Powder River at Moorhead, Montana [gaging station 06324500]), substantial downward trends in annual peak flow during 1967–2011 were of similar or stronger magnitude than the upward trends during 1930–76, and the annual-peak-flow medians for 1979–2011 were substantially lower than the medians for the entire period of record.

For peak-flow timing for most long-term gaging stations, differences in trends between 1930–76 and 1967–2011 are variable and not particularly strong. Statistical distributions generally are similar among the summary time periods. However, for two high-elevation gaging stations on a Missouri River headwater tributary (Gallatin River near Gallatin Gateway, Montana [gaging station 06043500] and Gallatin River at Logan, Montana [gaging station 06052500]) and for five high-elevation gaging stations in the Yellowstone River Basin (Yellowstone River at Corwin Springs, Montana [gaging station 06191500], Yellowstone River near Livingston, Montana [gaging station 06192500], Clarks Fork Yellowstone River near Belfry, Montana [gaging station 06207500], Clarks Fork Yellowstone River at Edgar, Montana [gaging station 06208500], and Yellowstone River at Billings, Montana [gaging station 06214500]) downward trends in peak-flow timing during 1967–2011 generally were stronger than upward trends during 1930–1976, and day-of-peak medians for 1979–2011 were considerably less than medians for 1930–78. The downward trends in peak-flow timing for 1967–2011 indicate that the timing of annual peak flows changed from later in the year to earlier in the year. For the seven high-elevation gaging stations, the mean change during 1967–2011 was about 13 days (range of 8 to 22 days).

For most of the high-elevation gaging stations in the Missouri River headwaters, Yellowstone River Basin, and Columbia River Basin, there was general correspondence between trend patterns for annual peak flow and trend patterns for peak-flow timing; that is, during periods when there were upward trends in annual peak flow, there generally also were upward trends in peak-flow timing. Conversely, during periods when there were downward trends in annual peak flow, there generally also were downward trends in peak-flow timing.

The two low-elevation gaging stations in eastern Montana (Poplar River at international boundary [gaging station 06178000] and Powder River at Moorhead, Montana [gaging station 06324500]) had considerable changes in annual-peakflow characteristics after the mid-1970s, which might provide evidence of potential nonstationarity in the peak-flow records. The two low-elevation gaging stations that have potential nonstationarity are located in drainage basins that are strongly affected by agricultural activities that potentially affect the hydrologic regimes. Primary agricultural activities that might alter natural hydrologic conditions include construction of small impoundments (primarily for stock-watering purposes) and irrigation diversions. Temporal variability in these activities might contribute to the potential nonstationarity issues. Changes in climatic characteristics after the mid-1970s also possibly contribute to the potential nonstationarity issues. Lack of considerable indication of potential nonstationarity in annual peak flow for the other long-term gaging stations in this study might indicate that climatic changes have been more pronounced with respect to effects on peak flows in low elevation areas in eastern Montana than in areas represented by the other long-term gaging stations. Another possibility is that climatic changes after the mid-1970s are exacerbated in low-elevation areas where small-impoundment development and potential effects of irrigation diversions might be more extensive.

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#### Steve Sando 

##### Hydrologist (NDAA)

Wyoming-Montana Water Science Center

sksando@usgs.gov

406-457-5928

#### Roy Sando 

##### Physical Scientist (GIS) 

Wyoming-Montana Water Science Center

tsando@usgs.gov

406-594-9801

## Related Content

#### Steve Sando 

##### Hydrologist (NDAA)

Wyoming-Montana Water Science Center

sksando@usgs.gov

406-457-5928

#### Roy Sando 

##### Physical Scientist (GIS) 

Wyoming-Montana Water Science Center

tsando@usgs.gov

406-594-9801

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####               Wyoming-Montana Water Science Center - Helena Office          

3162 Bozeman AvenueHelena, MT59601United States

(406) 457-5900

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