Historical Flood Information from Streamflow Records and High-Water Marks

USGS streamgage operations in Montana began in the 1890s, but a peak flow determined from a high-water mark in 1872 near Wibaux, Mont., is the earliest recorded Montana peak flow in the peak-flow data available in the USGS National Water Information System database (U.S. Geological Survey, 2023). Thus, the discussion of historical flood information primarily relates to the period of 1872–2020; however, there is discussion of extensive flooding in parts of the Yellowstone River Basin in 2022.

Sando and McCarthy (2018) provided a brief overview of unusually large floods in Montana, and much of the following discussion is taken directly from that report. These selected large floods are generally described in the following paragraphs to facilitate understanding of various conditions that contribute to floods in Montana. Work by O’Connor and Costa (2003) indicates that the spatial distribution of large floods is related to specific combinations of regional climatology, topography, and proximity to oceanic moisture sources such as the Pacific Ocean and Gulf of America (Gulf of Mexico); these observations are relevant to the occurrence of large floods in Montana. The selected large floods frequently rank in the top 10 percent of peak flows for individual streamgages in Montana and often are used in frequency analyses that incorporate historical information.

In northwestern and west-central Montana, particularly in areas near or adjacent to the Continental Divide and Rocky Mountain Front, there have been several notable large regional floods with generally similar climatic conditions. The floods were in May or June and interaction of large, moist air masses advected from the Gulf of America (Gulf of Mexico) in conjunction with Pacific frontal systems and orographic effects produced intense rainfall in periods near the peak of snowmelt runoff. The antecedent snowpacks typically were near or greater than average. The large regional floods of 1908 (National Weather Service, 2016), 1948 (Rantz and Riggs, 1949), 1953 (Wells, 1957), 1964 (Boner and Stermitz, 1967), and 1975 (Johnson and Omang, 1976b) provide the best representation of the described conditions. Boner and Stermitz (1967) also note large floods with similar conditions to 1964 in 1894 and 1916.

In southeastern Montana, an unusually large flood occurred on the Powder River in late September 1923 (Follansbee and Hodges, 1925). The rain that generated the unusual fall flood primarily fell in the Wyoming part of the Powder River drainage basin, but the flooding reached into Montana.

In north-central Montana, primarily in low-elevation plains areas in the Milk River Basin, a notable large regional snowmelt flood occurred in April 1952 (Wells, 1955). The flood was associated with an unusually large snowpack that rapidly melted during unusually warm spring temperatures; rainfall was not a contributing factor. The flooding was amplified by frozen-soil conditions and ice-jam releases, factors sometimes associated with late-winter and early-spring breakup events in association with transition from ice-cover to open-channel conditions.

Mostly in the western part of Montana, atmospheric rivers can deliver large amounts of moisture from the Pacific Ocean typically in early fall through late winter. Atmospheric rivers are moisture-laden narrow bands that spin off Pacific cyclonic systems and, under specific conditions, result in intense precipitation (Zhu and Newell, 1998; Dettinger, 2004; Ralph and others, 2004; Barth and others, 2017). When atmospheric rivers are associated with greater than average temperatures, intense rainfall can produce unusual cool-season flooding. Examples of large atmospheric river floods include the January 1974 flood in northwestern Montana (Johnson and Omang, 1974), the September 1986 flood in north-central Montana (Montana Department of Military Affairs, 2010), and the November 2006 flood in northwestern Montana (Barth and others, 2017). Cool-season flooding can be amplified by frozen-soil conditions and ice-jam releases (U.S. Army Corps of Engineers, 1991, 1998), factors sometimes associated with breakup events that are more typical in late winter and early spring.

Unusually wet winters and springs in 1978 and 2011 resulted in large accumulated snowpacks throughout much of Montana (Parrett and others, 1978; Holmes and others, 2013; Vining and others, 2013; National Weather Service, 2016). Flood conditions generally were greater than normal statewide, but intense rainfall in May 1978 in southeastern Montana and in May 2011 in north-central and southeastern Montana produced unusually large floods.

In May 1981, intense rainfall combined with snowmelt produced severe flooding in west-central Montana focused in the upper Missouri River Basin from near Helena (not shown on fig. 1) to near Bozeman (not shown on fig. 1) and in the upper Clark Fork Basin near Deer Lodge (not shown on fig. 1; Parrett and others, 1982). The antecedent snowpack generally was less than to near normal. In May 1984, intense rainfall combined with snowmelt produced severe flooding in southwestern Montana (U.S. Army Corps of Engineers, 1985; Montana Department of Military Affairs, 2010).

Parrett and others (2004) described flooding and debris flows in 2000 and 2001 in three burned areas of Montana after wildfires. At several streamgages near these three burned areas, the estimated recurrence intervals of the recorded peak flows were substantially larger than the estimated recurrence intervals of the precipitation events that caused the flooding, indicating increased runoff because of changes in the soil hydrophobicity after the fires.

Unprecedented flooding inundated parts of the Yellowstone River Basin in June 2022 just as analyses for this report were concluding. A wet, cool spring led to a large late season snowpack (as much as 200 percent of mean in some areas). The snow quickly melted as intense rainfall (about 1 to more than 5 in.) fell over the Absaroka Range and Beartooth Mountains (not shown on fig. 1) from June 10 through June 13, 2022 (Peters and others, 2022; National Weather Service, 2023). Provisional peak-flow data indicate that flood peaks at three streamgages on the Yellowstone River and streamgages on the Lamar, Gardner, Boulder, Stillwater Rivers (not shown on fig. 1), and Clarks Fork Yellowstone River were the highest on record (Peters and others, 2022; U.S. Geological Survey, 2023) and had annual exceedance probability values that ranged from 1 to less than 0.2 percent. The 2022 peak-flow data are not included in the data and results presented in this paper.

Historical Low- and High-Streamflow Periods from Streamflow Records

Merritt and others (1991) analyzed streamflow records from 20 Montana long-term streamgages to investigate the areal extent and severity of droughts in Montana. Merritt and others (1991) calculated annual departures from long-term mean monthly streamflows to determine low-streamflow periods. Merritt and others (1991) identified four major droughts in Montana based on analysis of streamflow records through 1988: 1929–42, 1944–47, 1949–62, and 1977. The 1929–42 drought encompassed all of Montana, but was less severe in southeastern Montana, in the lower Yellowstone River Basin. The 1944–47 drought was less severe than the 1929–42 drought and generally was restricted to western Montana. The 1949–62 drought also was less severe than the 1929–42 drought and generally was restricted to eastern Montana. The 1977 drought was less severe than the other droughts and generally was restricted to northern Montana.

In this report, the general approach of Merritt and others (1991) was used to expand and update their work based on analysis of streamflow records through 2020. For nine selected long-term streamgages on major river basins (table 8), annual mean streamflows (U.S. Geological Survey, 2023) were compared to the long-term mean annual streamflows to determine the annual departures from the long-term mean. Some of the nine selected streamgages are near the mouths of the three major rivers draining Montana (the Missouri and Yellowstone Rivers and the Clark Fork) and provide large-scale integrated representation for nearly all of Montana. For the nine selected streamgages, periods of at least 4 consecutive years of less than mean or greater than mean departures were subjectively identified as representing substantial low- or high-streamflow periods, respectively. For the nine selected streamgages, annual departures from long-term mean annual streamflow are summarized in table 8. For those nine streamgages plus 53 streamgages with at least 50 years of continuous streamflow records included in the nonstationarity analyses for this study, the annual departures from long-term mean annual streamflow are shown in figure 8 and the annual median departures (calculated from the variable number of streamgages operated in each year) of the annual departures are shown in figure 9A. The annual departures were standardized using Z-scores, which are the number and direction of standard deviations away from the long-term mean annual streamflow. The annual departures for peak flows in relation to the long-term mean peak flow are shown in figure 9B.

For the nine selected long-term streamgages on major river basins, two general periods are notable in terms of duration and mean departure from the long-term mean streamflows: 1929–41 (13 years) and 1999–2009 (11 years) (table 8); in those two low-streamflow periods, there is variability among the streamgages in terms of start and end years and the magnitude of the percentage departure, but nearly all the streamgages that were operated in the periods have strong, persistent less than mean departures. Most streamgages have less than mean departures in two other low-streamflow periods (the late 1950s through early 1960s and the late 1980s through early 1990s), but the duration, magnitude, and areal extent of these low-streamflow periods are not as severe or consistent as the 1930s and the early 2000s (figs. 8 and 9A; table 8).

Two of the nine selected USGS streamgages (06090800, Missouri River at Fort Benton, Mont., and 06329500, Yellowstone River near Sidney, Mont.) with streamflow records extending back to the 1890s have predominantly greater than mean departures in the 1890s through the 1920s (fig. 8; table 8). Most streamgages have predominantly greater than mean departures from the mid-1960s through the late 1970s (figs. 8 and 9A). Water year 2011 is notable because all of the streamgages operated in that year have greater than mean departures (figs. 8 and 9A), and 2011 is the maximum greater than mean departure for 5 of the 11 selected streamgages operated (table 8).

There is general correspondence between the annual mean streamflow and peak-flow standardized departures from long-term means with a Spearman correlation of 0.82 (statistical significance level [p-value] less than [<] 0.01). Thus, in general, higher peak flows tend to happen in higher streamflow years, and similarly, lower peak flows tend to happen in lower streamflow years.

Information on Historical Cool and Wet Periods and Warm and Dry Periods from Climatic Records

Frankson and others (2022) compiled data from 20 long-term climatic stations to report Montana statewide annual means of number of very hot days (daily maximum temperature greater than 95 °F), number of warm nights (minimum temperature of 70 °F or higher), precipitation, and number of 1-in. extreme precipitation events (days with precipitation of 1 in. or more) for the period of 1895–2020. To facilitate the discussion, refer to figure 10, which presents figure 2 from Frankson and others (2022).

Summary of Historical Flood and Drought Periods in Montana

Historical hydroclimatic data indicate several persistent periods of warm and dry conditions (with associated low-streamflow conditions) and also persistent periods of cool and wet conditions (with associated high-streamflow conditions) since the 1890s. Notable alternations between the most substantial warm and dry periods and wet and cool periods include (1) the cool and wet period of the mid-1890s through about 1920, (2) the extreme warm and dry period of the 1930s through early 1940s, (3) the cool and wet period of the mid-1960s through the early 1980s, (4) the warm and dry period of the mid-1980s through the early 1990s, (5) the cool and wet period of the mid- to late 1990s, (6) the extreme warm and dry period of the early 2000s, and (7) the cool and wet period of the 2010s. Consideration of the alternations in relation to the 30-, 50-, 75-, and 100-year analysis periods used in this study might be important in interpreting the results. Further, consideration of the alternations in relation to periods of record of individual streamgages might be important in evaluating the adequacy of a given peak-flow dataset to represent a reasonable range of hydroclimatic conditions and help provide a robust frequency analysis.

Monotonic Trends in Temperature Variables

For the 30-year annual temperature monotonic trends (fig. 13A), 36.9 percent of the streamgages have neutral results (table 11). No streamgages have combined downward results, and 63.0 percent have combined upward results. Thus, with respect to likelihood directional proportions, the 30-year annual temperature trends are strongly upward. The neutral streamgages have a median drainage area of 2.66 mi² and mostly are on small basins in the East-Central Plains, Northeast Plains, and Southeast Plains hydrologic regions of eastern Montana. The climate data used in this study were presented in grids of about 3 mi by 3 mi (Ryberg and others, 2024), which might contribute to variability and uncertainty for small-basin streamgages. The 77 streamgages with likely upward monotonic trends (hereinafter, likely upward streamgages) have a median drainage area of 391 mi² (table 11) and predominantly are in the mountainous areas of western Montana and northern Wyoming (fig. 13A).

Distinct seasonal patterns were detected in association with the annual results. For winter and spring temperature results, neutral results are predominant with 58.6 and 51.0 percent of streamgages, respectively (table 12); however, combined upward streamgages (31.8 and 32.5 percent of streamgages, respectively) are substantially more prevalent than combined downward streamgages (9.6 and 16.6 percent of streamgages, respectively). For summer temperature results, all streamgages have combined upward results. For fall temperature results, 24.2 percent of streamgages have neutral results, no streamgages have combined downward results, and 75.8 percent of streamgages have combined upward results. Thus, the strongly upward annual temperature results are associated with strongly upward summer and fall temperature results and predominantly neutral winter and spring temperature results.

For the 50-, 75-, and 100-year annual temperature monotonic trends (fig. 13B, C, and D, respectively), all streamgages have likely upward results (table 11). Also, all seasons have likelihood directional proportions that are strongly upward, and likely upward results generally account for more than 95 percent of the results (table 12).

Monotonic Trends in Precipitation Variables

For the 30-year annual precipitation monotonic trends (fig. 14A), 54.1 percent of the streamgages have neutral results, 14.0 percent of the streamgages have combined downward results, and 31.9 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 30-year annual precipitation trends are predominantly neutral; however, upward streamgages are more prevalent than downward streamgages. The nine streamgages with likely downward precipitation trends (hereinafter, likely downward streamgages) mostly are in the mountainous areas of western Montana and northern Wyoming, somewhat interspersed among other streamgages with different results. The 13 likely upward streamgages mostly drain small basins in the East-Central Plains and Northeast Plains in central Montana.

Distinct seasonal precipitation trend patterns were detected in association with the 30-year annual results (table 12). For winter precipitation trends, 18.5 percent of streamgages have neutral results, 1.3 percent have combined downward results, and 80.2 percent have combined upward results. For spring precipitation trends, 32.5 percent of streamgages have neutral results, 8.3 percent have combined downward results, and 59.3 percent have combined upward results. For summer precipitation trends, 3.2 percent of streamgages have neutral results, 96.8 percent have combined downward results, and no streamgages have combined upward results. For fall precipitation trends, 24.8 percent of streamgages have neutral results, 3.8 percent have combined downward results, and 71.3 percent have combined upward results. Thus, the predominantly neutral annual precipitation trends are associated with strongly or predominantly upward winter, spring, and fall precipitation results and strongly downward summer precipitation results.

For the 50-year annual precipitation monotonic trends (fig. 14A), 38.6 percent of the streamgages have neutral results, 48.6 percent of the streamgages have combined downward results, and 12.8 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 50-year annual precipitation trends are moderately downward. The 23 likely downward streamgages mostly are in the mountainous areas of western Montana and northern Wyoming. The five likely upward streamgages mostly are on small basins in the East-Central Plains, Northeast Plains, and Southeast Plains hydrologic regions of eastern Montana.

Distinct seasonal precipitation trend patterns were detected in association with the 50-year annual results (table 12). For winter precipitation, 30.0 percent of streamgages have neutral results, 52.9 percent have combined downward results, and 17.2 percent have combined upward results. For spring precipitation trends, 48.6 percent of streamgages have neutral results, 22.9 percent have combined downward results, and 28.5 percent have combined upward results. For summer precipitation trends, 25.7 percent of streamgages have neutral results, 68.5 percent have combined downward results, and 5.7 percent have combined upward results. For fall precipitation trends, 42.9 percent of streamgages have neutral results, 21.4 percent have combined downward results, and 35.7 percent have combined upward results. Thus, the moderately downward annual precipitation results are associated with predominantly and strongly downward winter and summer precipitation results, respectively, and predominantly and moderately neutral spring and fall precipitation results, respectively.

For the 75-year annual precipitation monotonic trends (fig. 14A), 31.3 percent of the streamgages have neutral results, 43.8 percent of the streamgages have combined downward results, and 25.0 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 75-year annual precipitation trends are predominantly downward. The 12 likely downward streamgages mostly are in the mountainous areas of western Montana and northern Wyoming, somewhat interspersed among other streamgages with different results. The four likely upward streamgages mostly are in the East-Central Plains, Northeast Plains, and Southeast Plains hydrologic regions of eastern Montana.

Distinct seasonal precipitation trend patterns were detected in association with the 75-year annual results (table 12). For winter precipitation, 41.7 percent of streamgages have neutral results, 54.2 percent have combined downward results, and 4.2 percent have combined upward results. For spring precipitation, 18.8 percent of streamgages have neutral results, 10.4 percent have combined downward results, and 70.9 percent have combined upward results. For summer precipitation, 27.1 percent of streamgages have neutral results, 72.9 percent have combined downward results, and no streamgages have combined upward results. For fall precipitation trends, 50.0 percent of streamgages have neutral results, 8.4 percent have combined downward results, and 41.7 percent have combined upward results. Thus, the predominantly downward annual precipitation results are associated with predominantly and strongly downward winter and summer precipitation results, respectively, strongly upward spring precipitation results, and moderately neutral fall precipitation results.

For the 100-year annual precipitation monotonic trends (fig. 14A), 33.3 percent of the streamgages have neutral results, 25.0 percent of the streamgages have combined downward results, and 41.7 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 100-year annual precipitation trends are moderately upward. Among the 12 streamgages included in the 100-year trend analyses, clear spatial patterns in the results are not readily apparent.

Distinct seasonal precipitation trend patterns were detected in association with the 100-year annual results (table 12). For winter precipitation, 41.7 percent of streamgages have neutral results, 41.7 percent have combined downward results, and 16.7 percent have combined upward results. For spring precipitation, no streamgages have neutral results, 8.3 percent have combined downward results, and 91.6 percent have combined upward results. For summer precipitation, 25.0 percent of streamgages have neutral results, 66.6 percent have combined downward results, and 8.3 percent have combined upward results. For fall precipitation, 41.7 percent of streamgages have neutral results, 16.7 percent have combined downward results, and 41.7 percent have combined upward results. Thus, the moderately upward annual precipitation results are associated with equally neutral and downward winter precipitation results, strongly upward spring precipitation results, strongly downward summer precipitation results, and equally neutral and upward fall precipitation results.

Monotonic Trends in Annual Snow to Precipitation Ratio

For the 30-year annual snow:precipitation monotonic trends (fig. 15A), 31.2 percent of the streamgages have neutral results, 4.4 percent of the streamgages have combined downward results, and 64.3 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 30-year annual snow:precipitation trends are strongly upward. The one likely downward streamgage is in western Montana surrounded by other streamgages with different results. The 49 likely upward streamgages are reasonably well dispersed throughout Montana.

For the 50-year annual snow:precipitation monotonic trends (fig. 15B), 17.1 percent of the streamgages have neutral results, 82.9 percent of the streamgages have combined downward results, and no streamgages have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 50-year annual snow:precipitation trends are strongly downward. The 48 likely downward streamgages are reasonably well dispersed throughout Montana and northern Wyoming.

For the 75-year annual snow:precipitation monotonic trends (fig. 15C), no streamgages have neutral results, 97.9 percent of the streamgages have combined downward results, and 2.1 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 75-year annual snow:precipitation trends are strongly downward. The 43 likely downward streamgages are reasonably well dispersed throughout Montana and northern Wyoming.

For the 100-year annual snow:precipitation monotonic trends (fig.  5D), all streamgages have combined downward results (table 11). The nine likely downward streamgages are reasonably well dispersed throughout Montana and northern Wyoming.

Monotonic Trends in Annual Potential Evapotranspiration to Precipitation Ratio

For the 30-year annual PET:precipitation monotonic trends (fig. 16A), 65.6 percent of the streamgages have neutral results, 11.5 percent of the streamgages have combined downward results, and 22.9 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 30-year annual PET:precipitation trends are strongly neutral. The two likely downward streamgages are in north-central Montana, interspersed among other streamgages with different results. The six likely upward streamgages are throughout Montana and northern Wyoming, interspersed among other streamgages with different results, except in north-central Montana where downward streamgages are more prevalent.

For the 50-year annual PET:precipitation monotonic trends (fig. 16B), 18.6 percent of the streamgages have neutral results, 10.0 percent of the streamgages have combined downward results, and 71.4 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 50-year annual PET:precipitation trends are strongly upward. The two likely downward streamgages are in northeastern Montana, interspersed among other streamgages with different results. The 36 likely upward streamgages are in northwestern to southeastern Montana and northern Wyoming.

For the 75-year annual PET:precipitation monotonic trends (fig. 16C), 25.0 percent of the streamgages have neutral results, 2.1 percent of the streamgages have combined downward results, and 72.9 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 75-year annual PET:precipitation trends are strongly upward. No streamgages are likely downward. The 30 likely upward streamgages are in northwestern to southeastern Montana and northern Wyoming.

For the 100-year annual PET:precipitation monotonic trends (fig. 16D), 50.0 percent of the streamgages have neutral results, 8.3 percent of the streamgages have combined downward results, and 41.7 percent have combined upward results (table 11). Thus, with respect to likelihood directional proportions, the 100-year annual PET:precipitation trends are moderately neutral. No streamgages are likely downward. The three likely upward streamgages are in northwestern to south-central Montana and northern Wyoming.

Summary of Monotonic Trends in Climate Variables

Considering all monotonic trend analyses of climatic variables, the most consistent and conclusive pattern is upward monotonic trends in annual, summer, and fall temperatures (fig. 13A–D; tables 11 and 12), and no streamgages have likely or somewhat likely downward likelihoods in any of the 30-, 50-, 75-, and 100-year analyses. For the 75- and 100-year analyses, more than 95 percent of streamgages have likely upward annual temperature trends (fig. 13C, D; table 11) and winter, spring, summer, and fall temperature trends (table 12). For the 50-year analyses, all streamgages have likely upward annual temperature trends (fig. 13B; table 11) and 98.6, 71.4, 95.7, and 100.0 percent of streamgages have likely upward winter, spring, summer, and fall temperature trends, respectively (table 12). The 30-year temperature trend analyses had less consistency in upward temperature trends than the other analysis periods, except for the summer temperature trends with 95.5 percent of streamgages having likely upward trends (table 12). The 30-year annual, winter, spring, and fall temperature trends have substantial percentages of streamgages with neutral results (36.9, 58.6, 51.0, and 24.2 percent, respectively; tables 11 and 12), and most of those neutral streamgages are on small basins in the East-Central Plains, Northeast Plains, and Southeast Plains hydrologic regions of eastern Montana, which might contribute to greater variability and uncertainty in the trend analyses for those streamgages. For the 30-year winter and spring temperature trend analyses, some trend results were somewhat likely downward (9.6 and 15.3 percent, respectively, of streamgages included in the analyses; table 12), and most of those streamgages are on small basins in the East-Central Plains, Northeast Plains, and Southeast Plains hydrologic regions of eastern Montana. The generally consistent pattern of upward monotonic temperature trends of this study agrees with the findings of Frankson and others (2022) and White and Arnold (2015), which indicated rising temperatures in Montana and the Missouri River Basin, respectively, in the recent past (about the last 100 years). Those studies also reported projections of rising temperatures into the future.

The annual and seasonal precipitation monotonic trend results are substantially more variable and less conclusive than the temperature trend results. For the annual precipitation trends, the 30-, 50-, 75-, and 100-year analyses all have substantial percentages of streamgages with neutral results (54.1, 38.6, 31.3, and 33.3 percent, respectively; fig. 14A; table 11). For the annual precipitation trends, likely downward streamgages equal or exceed likely upward streamgages for the 50-, 75-, and 100-year analyses, and the likely downward streamgages account for 32.9, 25.0, and 16.7 percent of streamgages included in the analyses. However, for the 30-year analysis, likely upward streamgages exceed likely downward streamgages with the likely upward streamgages accounting for 8.3 percent of streamgages included in the analyses.

On a seasonal basis, the most consistent and conclusive pattern in the precipitation trend results is downward summer precipitation trends with 72.6, 31.4, 47.9, and 58.3 percent of streamgages in the 30-, 50-, 75-, and 100-year analyses, respectively, having likely downward trends and no streamgages having likely upward trends (fig. 14D; table 12). Winter precipitation trends are variable (fig. 14B; table 12). The 50-, 75-, and 100-year winter precipitation analyses have substantial percentages of neutral streamgages, equaling or exceeding about 30 percent of streamgages included in the analyses. For the 50-, 75-, and 100-year winter precipitation trends, likely downward streamgages substantially exceed likely upward streamgages, and the likely downward streamgages account for 34.3, 41.7, and 33.3 percent of streamgages included in the analyses. However, for the 30-year analysis, likely upward streamgages account for 67.5 percent of streamgages included in the analysis and no streamgages are likely downward. For spring and fall precipitation trends (fig. 14C, E; table 12), likely upward streamgages substantially exceed likely downward streamgages for the 30-, 50-, 75-, and 100-year analyses.

The annual snow:precipitation trends for the 50-, 75-, and 100-year analyses mostly are downward with likely downward streamgages accounting for 68.6, 89.6, and 75.0 percent of streamgages included in the analyses, respectively, and no streamgages are likely upward (table 11). In contrast, for the 30-year analysis, likely upward streamgages account for 31.2 percent of streamgages included in the analysis and substantially exceed likely downward streamgages.

The annual PET:precipitation trends for the 50-, 75-, and 100-year analyses mostly are upward with likely upward streamgages accounting for 51.4, 62.5, and 25.0 percent of streamgages included in the analyses, respectively, and likely downward streamgages account for less than 5 percent of streamgages (table 11). In contrast, the 30-year analysis has a substantial percentage of streamgages with neutral results (65.6 percent); likely downward and likely upward streamgages account for small percentages of streamgages included in the analysis (1.3 and 3.8 percent, respectively; table 11). The annual PET:precipitation trends might provide a general indication of the overall net interaction of the temperature and precipitation trends on various streamflow characteristics. In the 50-, 75-, and 100-year analysis periods, climatic variables generally have been trending toward reduced streamflow conditions, whereas in the 30-year trend analysis period, trending in climatic variables is less consistent and more uncertain.

Monotonic Trends in Annual Center of Volume Variables

Downward trends in COVDUR indicate that the COV period is compressing, and upward trends indicate it is expanding. Compression of the COV period might be associated with several factors, including tendency for more rapid snowmelt runoff, decrease in base flow, and decrease in high-streamflow events outside the COV period. Expansion of the COV period might be associated with slower snowmelt runoff, increase in base flow, and increase in high-streamflow events outside the COV period.

Downward trends in COVQ50 indicate that the centroid of the annual hydrograph is happening earlier, and upward trends indicate it is happening later. Earlier COVQ50 might be associated with earlier snowmelt runoff, and later COVQ50 might be associated with later snowmelt runoff.

Monotonic Trends in Annual Center of Volume Variables for the 30-Year Analysis

The locations of the 77 streamgages included in the 30-year analysis and associated COVDUR likelihood and magnitude results are shown in figure 17A, and statistical distributions of COVDUR and COVQ50 monotonic trend magnitudes by hydrologic regions are shown in figure 18A. With respect to likelihood directional proportions, the 30-year COVDUR results are predominantly downward, indicating compression of the COV period; 35.1 percent of the streamgages have neutral results, 54.6 percent have combined downward results, and 10.4 percent have combined upward results (table 13). With respect to likelihood directional proportions, the 30-year COVQ50 results are moderately neutral; 51.9 percent of the streamgages have neutral results, 42.9 percent have combined downward results, and 5.2 percent have combined upward results (table 14).

The 17 likely downward COVDUR streamgages for the 30-year analysis period are mostly in mountainous areas of western Montana, in the West, Northwest, and Southwest hydrologic regions with isolated streamgages also in the Northeast Plains and Southeast Plains hydrologic regions, and Wyoming (figs. 17A and 18A). The COVDUR likely downward streamgages have a median drainage area of 490 mi² and a median trend magnitude of −0.69 day per year (table 13). The 13 likely downward COVQ50 streamgages are mostly in mountainous areas of western Montana, in the West, Upper Yellowstone-Central Mountain, and Southwest hydrologic regions with isolated streamgages also in the Northeast Plains hydrologic region, and Wyoming (table 14; fig. 18A). The COVQ50 likely downward streamgages have a median drainage area of 227 mi² and a median trend magnitude of −0.36 day per year (table 14).

The two likely upward COVDUR streamgages are in the Upper Yellowstone-Central Mountain and Southwest hydrologic regions (fig. 17A) and have drainage areas of 435 and 976 mi² and trend magnitudes of 0.27 and 0.51 day per year (table 13). No streamgages have likely upward COVQ50 trends (table 14).

Change Points in Annual Peaks Over Threshold

As described in Ryberg and others (2024), a partial-duration flood series is a compilation of all independent streamflows that exceed a selected base stage or discharge, regardless of the number of peaks resulting during a water year. A POT approach is based on the partial-duration flood series of mean daily streamflows greater than some threshold to model a dual domain of the magnitude and timing (frequency) of floods (Lang and others, 1999). A POT approach allows consideration of the frequency of large events, so even if significant changes in the magnitude of peak flows are not detected, a POT approach might indicate significant changes in the interannual frequency of large magnitude events (Mallakpour and Villarini, 2015). Because of a lack of general guidelines for setting a threshold for the floods greater than a base, the POT approach tends to be underused compared to analyses that use annual maximum discharge. The primary challenge with the POT approach is meeting the independence criterion between candidate daily flood events. In this study, the approach described in Neri and others (2019) was applied to complete a POT analysis with a mean of two events per year (POT2) and four events per year (POT4) and no more than one event in a time window defined as 5 days plus the natural logarithm of the drainage area, in square miles (U.S. Water Resources Council, 1976). The POT analyses (POT2 and POT4) determine temporal change points in the number of POT detections during the 30-, 50-, 75-, and 100-year analysis periods. For a given POT change-point analysis for a given streamgage, the primary outputs produced were the change-point year, the change in the mean annual number of POT detections between before and after the change point, and the statistical likelihood of the change. Exploratory analyses generally indicated general agreement between the POT2 and POT4 trend analyses. As such, only the POT4 results were selected for discussion in this report. The POT4 change-point results are summarized in table 15.

Change Points in Annual Peaks Over Threshold for the 30-Year Analysis

The locations of the 87 streamgages included in the 30-year POT4 analysis and associated POT4 change-point likelihoods are shown in figure 19A, and statistical distributions of POT4 change-point magnitudes by hydrologic regions are shown in figure 20A. With respect to likelihood directional proportions, the 30-year POT4 results are similarly distributed with little difference among neutral, downward, and upward; 34.5 percent of the streamgages have neutral POT4 results, 29.9 percent have combined downward results, and 35.6 percent have combined upward results (table 15).

The 12 likely downward streamgages are in the East-Central Plains, Southeast Plains, Upper Yellowstone-Central Mountain, and Southwest hydrologic regions and Wyoming (figs. 19A and 20A) and are somewhat interspersed among other streamgages with different results. The likely downward streamgages have a median drainage area of 4,341.5 mi²; the median POT4 change-point year is 1999, the mode is 1999, and the median change-point change is −2.0 events after the change point (table 15).

The 21 likely upward streamgages are reasonably well dispersed, and at least 1 likely upward streamgage is in all but 1 (Northwest Foothills) of the Montana hydrologic regions and Wyoming (figs. 19A and 20A). The likely upward streamgages have a median drainage area of 322 mi²; the median change-point year is 2007, the mode is 2008, and the median change-point change is 2.0 events after the change point (table 15).

Summary of Nonstationarities in Daily Streamflow

Overall, the results of the nonstationarity analyses for the daily streamflow variables (COVDUR and COVQ50 monotonic trends and POT4 change points) are variable (figs. 17A–D, 18A–D, 19A–D, and 20A–D; tables 13, 14, and 15). The 30-, 50-, and 75-year COVDUR analyses have substantial percentages of neutral streamgages, exceeding about 30 percent of streamgages included in the analyses (table 13). For the 30- and 50-year COVDUR trends, likely downward streamgages (indicating compression of the COV period; 17 and 13 streamgages, respectively) substantially exceed likely upward streamgages (two and five streamgages, respectively; table 13), and the likely downward streamgages are reasonably well dispersed throughout Montana (fig. 17A, B). However, for the 30- and 50-year COVDUR trends, some likely upward streamgages (indicating expansion of the COV period) are mostly in south-central Montana dispersed among streamgages with different results. In contrast, for the 75- and 100-year COVDUR trends, likely upward streamgages substantially exceed likely downward streamgages (table 13), and the likely upward streamgages generally are reasonably well dispersed throughout Montana and northern Wyoming (fig. 17C, D). The 30- and 50-year COVQ50 analyses have substantial percentages of neutral streamgages, exceeding about 30 percent of streamgages included in the analyses (table 14). For all the 30-, 50-, 75-, and 100-year COVQ50 trends, likely downward streamgages (indicating earlier occurrence of the date by which one-half of the streamflow for a water year has passed a streamgage) substantially exceed likely upward streamgages.

The 30- and 50-year POT4 change-point analyses have substantial percentages of neutral streamgages, exceeding about 30 percent of streamgages included in the analyses (table 15). For the 30-year analysis, likely upward streamgages (indicating an increase in secondary high streamflows) substantially exceed likely downward streamgages; the median change-point year for the likely upward streamgages is 2007 (table 15; after the extreme warm, dry, and low-streamflow period in the early 2000s). For the 50- and 75-year analyses, likely downward streamgages (indicating a decrease in secondary high streamflows) substantially exceed likely upward streamgages; the median change-point year for the likely downward streamgages (for the 50- and 75-year analyses) is 1984 (table 15; near the transition from the cool and wet period of the mid-1960s through the early 1980s to the warm and dry period of the late 1980s through early 1990s). For the 50- and 75-year analyses, the mostly downward change points were mostly in the late 1970s and early 1980s (table 15), before the start of the 30-year trend period in 1991, indicating that the mostly downward changes in the longer analysis periods are dominant in relation to the mostly upward changes in the 30-year analysis period. For the 100-year analyses, numbers of likely downward and likely upward streamgages are similar.

Analysis of Autocorrelation in Annual Peak-Streamflow Data

Many statistical procedures assume that individual values in the data are independent of each other. The presence of substantial temporal autocorrelation violates that basic assumption. The rank version of the von Neumann ratio test for randomness (hereinafter, rank von Neumann test) for lag-1 autocorrelation (von Neumann and others, 1941; Bartels, 1982) was used to investigate autocorrelation. The autocorrelation results are summarized in table 16 for the streamgages included in the 30-, 50-, 75-, and 100-year analysis periods.

The rank von Neumann test generally resulted in infrequent detection of significant autocorrelation. The percentage of streamgages with significant autocorrelation ranged from 4.2 percent for the 75-year analysis to 16.7 percent for the 100-year analysis (table 16). Overall, the results of the rank von Neumann test indicate the presence of some autocorrelation but not to a large extent. Uncertainty on the issue of autocorrelation likely does not impact the study results because the zyp.trend.vector function in the “zyp” package (Bronaugh and Werner, 2013) for R (R Core Team, 2022) was used to compensate for, or prewhiten, the autocorrelation. The primary effect of substantial autocorrelation on results is to create greater uncertainty in the estimates of statistical significance of the nonstationarity analysis results. The likelihood approach used in this study for presentation of statistical probability (Ryberg and others, 2024) further assists in reducing the effect of autocorrelation issues because emphasis is placed on ranges in statistical probability rather than strict reliance on a threshold of statistical-significance values (for example, a p-value less than 0.05).

Monotonic Trends in Annual Peak-Streamflow Timing

For each streamgage, the time series of peak-flow timing is the Julian day of the peak flow for each year. The peak-flow timing monotonic trend analysis quantifies changes in the median Julian day of the peak flows as a function of time. Analysis of peak-flow timing in Montana is complicated by spatial variability in major hydroclimatic drivers, which results in monomodal, bimodal, and sometimes trimodal peak-flow timing distributions in different parts of the State (Sando and others, 2016a [fig. 2, p. 6], b; Sando and McCarthy, 2018). The complexity of the Montana peak-flow timing datasets might result in anomalies in the quantification of the trend magnitudes; however, the directional patterns of the timing trends (that is, downward [earlier] or upward [later]) provide useful information in understanding temporal changes in peak-flow characteristics. Further, changes in peak-flow timing might either be merely associated with changes in peak-flow magnitudes, or they might actually contribute to those changes. For example, in areas with multimodal peak-flow regimes, if the timing changes result in greater synchronization among major hydroclimatic drivers such as snowmelt runoff and spring rainfall, increasing peak-flow magnitudes might result. The peak-flow timing results are summarized in table 17.

Monotonic Trends in Annual Peak-Streamflow Timing for the 30-Year Analysis

The locations of the 157 streamgages included in the 30-year analysis and associated likelihood and magnitude results are shown in figure 21A, and statistical distributions of monotonic trend magnitudes by hydrologic regions are shown in figure 22A. With respect to likelihood directional proportions, the 30-year peak-flow timing trends are moderately downward; 34.4 percent of the streamgages have neutral results, 41.4 percent have combined downward results, and 24.2 percent have combined upward results (table 17). Among the hydrologic regions, the Northeast Plains, East-Central Plains, and Southeast Plains hydrologic regions have the largest variability in trend magnitudes (fig. 22A), which might be affected by disproportionate representation of small basins (fig. 11B) and that these hydrologic regions have greater variability in peak-flow characteristics in general (Sando, 2021).

The 38 likely downward streamgages (indicating earlier peak flows) are reasonably well dispersed, and at least 1 likely downward streamgage is in all but 1 (Northwest hydrologic region) of the Montana hydrologic regions and Wyoming (figs. 21A and 22A). The likely downward streamgages have a median drainage area of 26.3 mi² and a median trend magnitude of −1.39 days per year (table 17).

The 13 likely upward streamgages (indicating later peak flows) are in two groupings (figs. 21A and 22A). Seven likely upward streamgages are in the eastern plains of Montana (the Northeast Plains, East-Central Plains, and Southeast Plains hydrologic regions), generally on small basins with a median drainage area of 0.88 mi². Six likely upward streamgages are in the western mountainous areas of Montana in the West, Upper Yellowstone-Central Mountain, and Southwest hydrologic regions and Wyoming on moderately large basins with a median drainage area of 202 mi². For the eastern plains and the western mountains groupings, the likely upward streamgages are somewhat interspersed among other streamgages with different results. For both groupings combined, the median trend magnitude for the likely upward streamgages is 0.90 day per year (table 17).

Change Points in Annual Peak-Streamflow Magnitude and Scale

The change-point and scale results are summarized in table 18. The locations of the streamgages included in the 30-, 50-, 75-, and 100-year change-point analyses and associated likelihoods are shown in figure 23A–D. Statistical distributions of normalized change-point magnitudes by hydrologic regions are shown in figure 24A–D. The normalized magnitudes shown in figure 24A–D were estimated by subtracting the median of the peak flows in the period before the change-point year from the median of the peak flows in the period after the change-point year, dividing by the median of the peak flows in the period before the change-point year, and then multiplying by 100. The likely and somewhat likely downward and upward change-point years are shown in figure 25.

Monotonic Trends in Annual Peak Streamflow

The peak-flow monotonic trend results are summarized in table 19. The locations of the streamgages included in the 30-, 50-, 75-, and 100-year trend analyses and associated likelihoods and normalized trend magnitudes are shown in figure 26A–D. Statistical distributions of normalized trend magnitudes by hydrologic regions are shown in figure 27A–D.

Summary of Nonstationarities in Annual Peak Streamflow

Overall, the results of the nonstationarity analyses for the peak-flow variables (monotonic trend analyses for timing and magnitude and change-point analyses for magnitude and scale) are variable (figs. 21A–D, 22A–D, 23A–D, 24A–D, 25, 26A–D, and 27A–D; tables 17, 18, and 19). The 30-, 50-, 75-, and 100-year peak-flow timing results have substantial percentages of neutral streamgages, exceeding 25 percent of streamgages included in the analyses. For the 30-, 50-, and 75-year peak-flow timing trends (figs. 21A–C and 22A–C; table 17), likely downward streamgages (indicating earlier peak flows) substantially exceed likely upward streamgages, and the likely downward streamgages are reasonably well dispersed throughout Montana and northern Wyoming. For the 100-year peak-flow timing trends (figs. 21D and 22D; table 17), likely downward streamgages also exceed likely upward streamgages; the likely downward streamgages mostly are in mountainous areas near Yellowstone National Park, and the likely upward streamgages are in mountainous areas of western Montana.

The 30- and 50-year peak-flow change-point results (figs. 23A–D and 24A–D; table 18) have substantial percentages of neutral streamgages, exceeding 25 percent of streamgages included in the analyses. For the 30-year results (figs. 23A and 24A; table 18), likely upward streamgages (38 streamgages) substantially exceed likely downward streamgages (14 streamgages), and the likely upward streamgages are reasonably well dispersed throughout Montana and northern Wyoming. The fewer likely downward streamgages are in two groupings: (1) nine likely downward streamgages in the eastern plains of Montana mostly on small basins with a median drainage area of 1.70 mi² and (2) five likely downward streamgages in the western mountainous areas of Montana mostly on moderately large basins with a median drainage area of 90.9 mi². For the eastern plains and the western mountains groupings, the likely downward streamgages are somewhat interspersed among other streamgages with different results. For the 50- and 75-year change-point results (figs. 23B–C and 24B–C; table 18), likely downward streamgages (14 and 21 streamgages, respectively) substantially exceed likely upward streamgages (4 and 4 streamgages, respectively). The likely downward streamgages are reasonably well dispersed throughout Montana and northern Wyoming. The fewer likely upward streamgages are variably located and are interspersed among other streamgages with different results. For the 100-year change-point results (figs. 23D and 24D; table 18), three streamgages are likely downward and three are likely upward. The three likely downward streamgages are in the East-Central Plains hydrologic region and northern Wyoming (figs. 23D and 24D); all the streamgages are in the lower Yellowstone River Basin and have headwater areas in mountainous ecoregions, but their drainage basins are predominantly in the Northwestern Great Plains ecoregion. The three likely upward streamgages are in the Upper Yellowstone-Central Mountain and Southwest hydrologic regions (figs. 23D and 24D); all the streamgages are in the headwaters of the Missouri and Yellowstone Rivers in or near Yellowstone National Park and have drainage basins that are entirely within mountainous ecoregions. The three likely upward streamgages in the mountainous headwaters of the Missouri and Yellowstone Rivers are in contrast to the three likely downward streamgages in the lower Yellowstone River Basin that are predominantly in the Northwestern Great Plains ecoregion.

With respect to the distribution of change-point years among the 30-, 50-, 75-, and 100-year analyses, the change-point years predominantly are before 1991 for the 50-, 75-, and 100-year analyses (the start year of the 30-year analysis; fig. 25). This pattern might be affected by the changes in the data structure among the analyses, monotonically decreasing from strong representation of small basins in the East-Central Plains, Northeast Plains, and Southeast Plains hydrologic regions in the 30-year analysis to virtually no representation of small basins and those hydrologic regions in the 100-year analysis. However, the pattern likely indicates that the nonstationarity patterns of the 30-year analysis, which generally are more variable than and less consistent with the 50-, 75-, and 100-year analyses, are not as influential as various hydroclimatic nonstationarities that happened before 1991. For the 50-, 75-, and 100-year analyses, the change points are predominantly downward and are concentrated in the 1970s and 1980s (fig. 25), which indicates general consistency among the longer trend periods.

The 30-, 50-, and 75-year peak-flow monotonic trend results (figs. 26A–C and 27A–C; table 19) all have substantial percentages of neutral streamgages, exceeding about 30 percent of streamgages included in the analyses. The general patterns of the peak-flow change-point results (figs. 23A–D and 24A–D) and the peak-flow monotonic trend results (figs. 26A–D and 27A–D) are quite similar, which might indicate that in many cases, likely downward or upward monotonic trends would be better described as change points.

For the 30-year peak-flow monotonic trend results (figs. 26A and 27A; table 19), likely upward streamgages (39 streamgages) substantially exceed likely downward streamgages (20 streamgages), and the likely upward streamgages are reasonably well dispersed throughout Montana and northern Wyoming. Similar to the peak-flow change-point results (figs. 23A and 24A), the fewer likely downward streamgages are in two groupings: (1) 12 likely downward streamgages in the eastern plains of Montana mostly on small basins with a median drainage area of 1.62 mi² and (2) 8 likely downward streamgages in the western mountainous areas of Montana mostly on moderately large basins with a median drainage area of 170 mi². For the eastern plains and the western mountains groupings, the likely downward streamgages are somewhat interspersed among other streamgages with different results. For the 50- and 75-year monotonic trend results (figs. 26B, C and 27B, C; table 19), likely downward streamgages (14 and 19 streamgages, respectively) substantially exceed likely upward streamgages (2 and 4 streamgages, respectively). The likely downward streamgages are reasonably well dispersed throughout Montana and northern Wyoming. The fewer likely upward streamgages are variably located and are interspersed among other streamgages with different results. For the 100-year monotonic trend results (figs. 26D and 27D; table 19), three streamgages are likely downward and five are likely upward. The three likely downward streamgages are in the East-Central Plains hydrologic region and northern Wyoming (figs. 26D and 27D); all the streamgages are in the lower Yellowstone River Basin and have headwater areas in mountainous ecoregions, but their drainage basins are predominantly in the Northwestern Great Plains ecoregion. The five likely upward streamgages mostly are in the Upper Yellowstone-Central Mountain and Southwest hydrologic regions (figs. 26D and 27D) in the headwaters of the Missouri and Yellowstone Rivers in or near Yellowstone National Park and have drainage basins that are entirely within mountainous ecoregions. The three likely upward streamgages in the mountainous headwaters of the Missouri and Yellowstone Rivers are in contrast to the three likely downward streamgages in the lower Yellowstone River Basin that are predominantly in the Northwestern Great Plains ecoregion.