Precipitation, Temperature, and Evapotranspiration

An east-west gradient in precipitation exists across North Dakota and the Northern Great Plains in general, as well as a north-south gradient in temperature (Knapp and others, 2023). In this transition zone, North Dakota’s climate has been highly variable. “Early explorers and settlers had the same complaints about weather as we do today: too dry, too wet, too cold, too hot, too windy” (Severson and Sieg, 2006, p. 37). In a more scientific manner, Thornthwaite (1941, p. 180) stated that “the Great Plains, so situated as to be inundated successively by moist and dry, cold and hot air masses, suffer meteorological excesses and in consequence experience large fluctuations in climate.”

The east-west divide represents a change from continental to semiarid climate between the 98th and 100th meridians. The 100th meridian has long been considered a dividing line from the international border with Canada to the international border with Mexico. John Wesley Powell stated:

Wallace Stegner reemphasized the 100th meridian as a dividing line when he published “Beyond the Hundredth Meridian—John Wesley Powell and the Second Opening of the West” (Stegner, 1954). This line of demarcation entered popular culture, not just in the United States, but in Canada as well, with the Canadian rock band The Tragically Hip recording “At the Hundredth Meridian,” a song that describes the crossroads between the Great Plains and the Canadian Shield, or eastern Canada and western Canada (The Tragically Hip, 1993; Holmes, 2015; Krajick, 2018).

More recent research has determined that this line of demarcation is real in terms of agriculture and population (more intense agriculture and human settlement east of the line) and that the line could be moving east with climate change (Krajick, 2018; Seager and others, 2018a, b). However, the 98th meridian has been used as the line of demarcation in the past (Webb, 1931), and it is incorrect to assume this line is fixed, especially considering the extreme natural climate variability in the Great Plains. Differences east and west of the 98th–100th zones have been evident as long as historians and scientists have been studying the Great Plains (Powell, 1879; Webb, 1931; Hirsch and Ryberg, 2012; Seager and others, 2018a, b; Norton and others, 2022; Sando and others, 2022; Knapp and others, 2023).

Annual average precipitation in North Dakota varies from year to year, and average annual precipitation from 1895 to 2020 ranges from less than 16 inches (in.) in the northwest to 24 in. in the southeast (Frankson and others, 2022). Because of the State’s northern latitude, winter storms can be accompanied by severe conditions, including heavy snows, high winds, and low wind chill temperatures; however, compared to other northern States, North Dakota receives less snowfall, 30–55 in. annually (Frankson and others, 2022). The probability of a blizzard occurring in any given year is greater than 50 percent for the State, one of the highest probabilities in the Nation (Frankson and others, 2022). Despite harsh winters, most of the State’s precipitation falls in late spring or early summer (Frankson and others, 2022). The wettest multiyear periods in the State were in the early 1940s, 1990s, and early 2010s; the driest periods were in the 1930s; and the frequency of extreme precipitation events of 2 in. or more has been greater than average since 1990 (Frankson and others, 2022). Average annual precipitation over the 30-year period of 1991 through 2020 is shown in figure 2.

Numerous studies have identified a decadal-scale signal in precipitation in North America (10–20 years; Ault and St. George, 2010), in western North America (greater than a 7-year period; Cayan and others, 1998), in the United States (in fall precipitation with a period of 12 years; Small and Islam, 2008, 2009), in the Great Plains (Garbrecht and Rossel, 2002), and in the central United States (interdecadal variations of annual precipitation on 12- and 20-year time scales; Hu and others, 1998). Causal mechanisms generating this signal are not fully understood. Yang and others (2007) determined that September, October, and November precipitation values were strongly related to the Niño-3.4 sea-surface temperatures index on a 5.5–8.5-year timescale, where the Niño-3.4 sea-surface temperatures index considers temperature anomalies over a region between 5° N. and 5° S., 120° W. to 170° W. Precipitation increases have been reported in all seasons (Karl and Knight, 1998; Wang and others, 2009), and the largest changes were observed in fall (Garbrecht and Rossel, 2002; Small and Islam, 2008, 2009; Wang and others, 2009).

North Dakota is far from the temperature moderating effects of the oceans and as a result has one of the most variable temperature regimes in the United States (Frankson and others, 2022). Average (1991–2020) January temperatures range from 4 degrees Fahrenheit (°F) in the northeast to 18 °F in the southwest; average July temperatures range from 65 °F in the northeast to 72 °F in the south, and extreme temperatures of 100 °F are most prevalent in the southwestern and south-central areas (Frankson and others, 2022). Average annual temperature over the 30-year period of 1991 through 2020 is shown in figure 3.

Changes in temperature also exist in the region, but in a manner different from the changes in precipitation. Wang and others (2009) determined that the strongest U.S. surface air temperature warming in 1950–2000 was in the spring over the northwestern United States and the Northern Plains. North Dakota’s warming has been primarily in the winter and spring, with minimal warming in the summer months, a pattern like other States in the Great Plains and Midwest (Reidmiller and others, 2018; Frankson and others, 2022; Marvel and others, 2023). Since 1900, winter temperatures have risen by 4.5 °F per century, whereas summer temperatures have risen by 1.5 °F per century during the same period (Frankson and others, 2022). The period of 2000–20 has been one of the warmest recorded periods for North Dakota, and 2006, 2012, 2015, and 2016 are comparable to the heat of the Dust Bowl era in the 1930s (Frankson and others, 2022).

Water budgets provide a way to evaluate availability of water and balance the rate of change in water stored in an area against the rate at which water flows in and out of the area (Healy and others, 2007). After precipitation, the next key component of the water budget is ET (Hanson, 1991). ET is the sum of evaporation from the land surface and waterbodies plus transpiration from plants (Hanson, 1991; U.S. Geological Survey, 2018). On average, ET consumes about 70 percent of annual precipitation in the United States and more than 90 percent of the precipitation in the western and midwestern United States (Irmak, 2017). Weather conditions affect the evaporation from the land surface and plant transpiration. When net solar radiation increases, ET increases; when temperature increases, transpiration rates increase; when relative humidity increases around plants, transpiration decreases; increased wind increases evaporation and transpiration rates; and soil-moisture availability affects rates—when soils dry out, less moisture is evaporated and plants begin to senesce, transpiring less water (Hanson, 1991; U.S. Geological Survey, 2018). In North Dakota, potential evapotranspiration (PET) is greater in the west than the east, but actual ET depends on the moisture available during the year (Stoner and others, 1993). Increases in evaporation rates because of rising temperatures could increase the rate of soil-moisture loss and the intensity of naturally occurring droughts (Frankson and others, 2022).

Hydrologic Soil Groups

The dominant hydrologic soil groups, defined by the U.S. Department of Agriculture Natural Resources Conservation Service (2009), in North Dakota are shown in figure 4. The hydrologic soil groups are classified into four groups based on the soil’s runoff potential (U.S. Department of Agriculture Natural Resources Conservation Service, 2009, p. 7). Soil group A (isolated areas in northwestern, central, and southeastern North Dakota) has low runoff potential or high permeability. Soil group B (detected throughout North Dakota) has moderately low runoff potential or moderately high permeability. Soil group C (detected mainly in southwestern and eastern North Dakota) has moderately high runoff potential or moderately low permeability. Soil group D (detected mainly in southwestern and eastern North Dakota) has high runoff potential or low permeability because of high proportions of clay (greater than 40 percent; U.S. Department of Agriculture Natural Resources Conservation Service, 2009).

Some soils are categorized as dual hydrologic soil groups. These groups have two letters, such as the B/D group in northeastern North Dakota. The first letter applies when the drainage of the soil has been modified, and the second letter applies to the undrained or natural condition of the soil (U.S. Department of Agriculture Natural Resources Conservation Service, 2009). Following the convention of chapter A, the dual hydrologic soil groups are in shades of pink to distinguish them from the other soil groups (in shades of brown). The pink areas have a water table within 24 in. of the surface, and the darker the shade of pink, the higher the amount of clay in the soil.

Ecoregions and Land Cover

Ecoregions are areas of similar ecosystems in type, quality, and quantity of environmental resources. Five levels of ecoregions have been defined, and the levels are increasingly specific—level I separates North America into 15 regions, whereas level III distinguishes 182 regions (Wiken and others, 2011; U.S. Environmental Protection Agency, 2021; Commission for Environmental Cooperation, undated). Thus, higher levels are more ideal for State or local projects because they delineate finer variations in landscape, precipitation, or vegetation. North Dakota is categorized into four level III ecoregions (fig. 5). The level III ecoregions—the Northwestern Great Plains, Northwestern Glaciated Plains, Northern Glaciated Plains, and Lake Agassiz Plain—span the State with a north-south orientation, although they bend to conform to the shape of the Missouri River in the western and central regions of the State, which represents the boundary of the last glaciation (Bryce and others, undated).

The Northwestern Great Plains, with some small areas of exception, lie in southwestern North Dakota (fig. 5). This area encompasses the Missouri Plateau and is semiarid with rolling plains and buttes and badlands (U.S. Environmental Protection Agency, 2013). Land use includes farming and cattle ranching; rain is a limiting factor in agriculture productivity (U.S. Environmental Protection Agency, 2013; Bryce and others, undated).

The Northwestern Glaciated Plains ecoregion (fig. 5) lies on the northern and eastern sides of the Missouri River and coincides with the extent of continental glaciation (U.S. Environmental Protection Agency, 2013). The topography is characterized by moraines (where moraines are glacial till, or sediments, deposited by glaciers; Molnia, 2004) and has a high concentration of wetlands and glacial potholes, semipermanent and seasonal wetlands known as prairie potholes (U.S. Environmental Protection Agency, 2013; Bryce and others, undated). The Northwestern Glaciated Plains are defined by a rise in elevation from the Northern Glaciated Plains to the east and mark the beginning of the Great Plains (Bryce and others, undated). Land-use in this ecoregion is split between the farming common in the Northern Glaciated Plains to the east and the cattle ranching and farming more prevalent on the Northwestern Great Plains to the west (Bryce and others, undated).

The Northern Glaciated Plains ecoregion (fig. 5) extends across most of the northern part of the State and southward between the Lake Agassiz Plain and Northwestern Great Plains ecoregions to the southern border of North Dakota and into South Dakota. The landscape in this region is composed of glacial drift, has flat to gently rolling topography, has a subhumid climate, and lies in the transition zone between the tall and shortgrass prairies (U.S. Environmental Protection Agency, 2013). Like the Lake Agassiz Plain to the east, the soil in this ecoregion is fertile, but because of climatic factors, agricultural productivity is more variable (Bryce and others, undated).

The easternmost ecoregion of North Dakota, the Lake Agassiz Plain (fig. 5), is composed of glacial till overlain by thick lacustrine sediment layers. Formed by the Glacial Lake Agassiz at the end of the last ice age, the region is extremely flat (Upham, 1895; U.S. Environmental Protection Agency, 2013). Although this ecoregion is a glacial lake plain, it is commonly called the Red River Valley. The flat land with lacustrine sediments has made this region agriculturally productive but prone to overland flooding, and much of the original tallgrass prairie has been converted to intensive agriculture (Bryce and others, undated).

The major land-cover classes in North Dakota are shown in figure 6. Cultivated crops, hay, and pasture are most common throughout the State. Forest cover (deciduous and mixed) is minimal and is detected in isolated areas. Herbaceous area is mainly in the western areas of the State. High intensity developed land is isolated to North Dakota’s largest cities and most notable on the eastern edge of the State.

Autocorrelation

Autocorrelation, also called serial correlation, dependence, or persistence, is a state in which values in a time series are not random but are correlated with each other. Autocorrelation can be on short time scales, such as wet or dry periods of several years, or on much longer times scales because of persistent climatic forces. Autocorrelation violates the underlying assumptions of many statistical methods and can negatively affect flood-frequency analysis because it violates the assumption of independent, identically distributed data. One effect is that for a times series with autocorrelation, the analyst does not have as much independent data as the length of the record would imply. The Red River of the North in Canada was used as an example in a study that looked at flood frequency and the effect of autocorrelation. Burn and Goel (2001, p. 355) detected “persistence in the data series can lead to a slight increase in the expected flood magnitude for a given return period” and “persistence is shown to dramatically increase the uncertainty associated with estimated flood quantiles. The 117-year flood series for the Red River at Winnipeg is demonstrated to be equivalent to roughly 45 years of independent data.”

Two statistical tests for autocorrelation in peak flow were evaluated at streamgages for the four analysis periods. The rank von Neumann test for lag-1 autocorrelation was used to investigate short-term persistence, and the Hurt exponent was used to investigate long-term persistence. Details about these two tests are described in chapter A.

A peak-flow series can indicate persistence when high peak flows are followed by high peak flows or low peak flows are followed by low peak flows. Time series with persistence are nonstationary, which means that the data are not independent, random occurrences. Short-term persistence (rank von Neuman test for lag-1, p-value less than [<] 0.05) was detected at 3 streamgages, and long-term persistence (Hurst coefficient greater than 0.6) was detected at 12 streamgages in the four analysis periods (table 4, fig. 11A, B). Whether a streamgage indicated short- or long-term persistence was not dependent upon the size of the drainage area. Two streamgages in the 75- and 50-year analysis periods (USGS streamgages Wild Rice River near Rutland, North Dakota, [05051600], and Rush River at Amenia, North Dakota, [05060500], respectively) indicated evidence of short- and long-term persistence. In the 50-year analysis period, USGS streamgage 05051600 has short- and long-term persistence (fig. 11A, B). The peak-flow series is shown in figure 11A, and the autocorrelation plot is shown in figure 11B. The short-term persistence (rank von Neuman test) was statistically significant with a p-value of 0.018, and long-term persistence (Hurst exponent) has a value of 0.644, indicating that long-term persistence (autocorrelation at lags greater than 1) exists in the series of peak flow.

Human interventions, such as land-use or land-cover change and construction of upstream dams, can result in a peak-flow series having a Hurst coefficient greater than 0.5 (Villarini and others, 2009a). Nonregulated sites were used in this study to control for some of these factors and, based on research on past climatic persistence described earlier in this chapter, the short-term and long-term persistence detected here is related to climate.

In a national study that included sites in North Dakota, Hodgkins and others (2019) detected statistically significant (p-value<0.05) lag-1 autocorrelation in 7.8 percent of 1,465 peak-flow series (that included regulated streams) for 1941–2015; therefore, autocorrelation was not a concern nationwide. The result was similar for North Dakota; however, analysis of Devils Lake and the Red River indicates that the region is subject to long-term climatic persistence. Analysis of naturalized peak flows for the Red River at James Avenue Pumping Station, Winnipeg, Manitoba, Canada, indicated statistically significant autocorrelation on the scale of 1 to 14 years (Ryberg and others, 2020b). The record was longer than 100 years (1892–2016), making it useful for detecting long-term persistence. Because the Red River at Winnipeg integrates streamflow from a substantial part of North Dakota, long-term persistence could be present to a greater extent than indicated and might be evident if streamgage records were longer.

Monotonic Trends

Monotonic trends are defined by a monotonic function that is always increasing or always decreasing (never changing sign), but the relation is not necessarily linear. The slope of the monotonic trends was determined using the Theil-Sen estimate, and the relation was tested for statistical significance using the Mann-Kendall test (Kendall, 1938; Sen, 1968; Theil, 1992; Helsel and others, 2020; Ryberg and others, 2024). This form of trend is nonparametric; that is, it does not have assumptions that the explanatory or response variables or the residuals can be approximated by a specific statistical distribution, although it has an assumption that the data are independent and identically distributed, and the distribution is possibly unknown (Hollander and others, 2014; Helsel and others, 2020). Nonparametric monotonic trends are more robust to outliers because the slope estimate is less affected by outliers than linear regression. For this reason, nonparametric monotonic trend methods are often a better choice for environmental data than trends based on linear regression. Because of the independence assumption, the autocorrelation results informed this analysis. If autocorrelation was not detected, then a Mann-Kendall test for trend in R (Millard, 2013) was used. If autocorrelation was detected, then a modified Mann-Kendall test for trend was completed (refer to chapter A).

An example of upward monotonic trend, hereafter referred to as a “trend,” in the peak flow at USGS streamgage Pembina River at Neche, North Dakota (05100000), in the 100-year analysis period is shown in figure 12A. The Theil-Sen slope and Mann-Kendall test for trend indicate a statistically significant upward trend at this site. An example of a downward trend in the peak flow at USGS streamgage Bear Den Creek near Mandaree, North Dakota (06332515), in the 50-year analysis period is shown in figure 12B. The Theil-Sen slope and Mann-Kendall test for trend indicate a statistically significant downward trend at this site.

The percentage of streamgages per likelihood category of detected trends in the peak flow in each analysis period is listed in table 5. The likelihood and normalized magnitude of trends for the streamgages in each analysis period are shown in figure 13. In the 100-, 75-, and 50-year analysis periods, likely upward trends in peak flow generally were detected in the eastern part of the State, and slightly larger magnitudes were detected in the 50-year analysis period. In the 30-year analysis period, likely upward trends generally were detected in the western part of the State. Likely upward trend magnitudes were larger in the 30-year analysis period than those in the 100-, 75-, and 50-year analysis periods. Likely downward trends were detected in the western part of the State in the 75- and 50-year analysis periods and, in the northeast, in the 30-year analysis periods. The largest likely downward trend magnitude was detected in the 50-year analysis period, whereas the rest of the likely downward trend magnitudes remained about the same in the 75-, 50-, and 30-year analysis periods.

The long-term pattern (as determined in the 100-, 75-, and 50-year periods) of decreasing peak flow in the west and increasing peak flow in the east is a pattern of opposing signals on either side of the 100^th meridian, and this pattern has been noted in the Third National Climate Assessment (water resources chapter, fig. 3.5, Georgakakos and others, 2014), the Fifth National Climate Assessment (Northern Great Plains chapter, fig. 25.4, Knapp and others, 2023), in other studies (Hirsch and Ryberg, 2012; Peterson and others, 2013; Hodgkins and others, 2019; Sando and others, 2022), and in the results for South Dakota presented in another chapter and the data release (Barth and Sando, 2024; Marti and others, 2024).

Many of the sites included here were used in an attribution study of changes in peak flow that indicated sites in eastern North Dakota with increased peak flow were also experiencing positive trends in annual precipitation (Ryberg, 2022; Sando and others, 2022). Eastern North Dakota and surrounding areas in Manitoba, Canada; Minnesota; and South Dakota have been extensively studied because of rising lake levels, increases in streamflow, and large, costly floods in Devils Lake, the Red River, the Souris River, and the James River Basins (Wiche, 1986; Macek-Rowland, 1997, 2001; Thorleifson and others, 1998; Wiche and others, 2000a, b, 2002; Burn and Goel, 2001; St. George and Nielsen, 2002, 2003; Vecchia, 2002, 2008, 2011; Brooks and others, 2003; Ryberg and others, 2007a, b, 2014, 2016a, b; Regorrah and Todhunter, 2008; Government of Canada, 2013; Gupta and others, 2015; Ryberg, 2015; Kolars and others, 2016, 2019; Nustad and others, 2016; Todhunter and Fietzek-DeVries, 2016; Todhunter and others, 2020; Van Hoy and others, 2020; Norton and others, 2022; Archambault and others, 2023; Atashi and others, 2023). Because of the supporting studies and the concurrent trends in precipitation that were identified in the attribution study, increasing long-term precipitation was recently attributed as the reason for nearly all the trends in peak flow in eastern North Dakota (Sando and others, 2022). Land-use and land-cover changes play a role, and numerous studies have attributed differing degrees of land-use effect on streamflow (Zhang and Schilling, 2006; Regorrah and Todhunter, 2008; Ryberg and others, 2014; Gupta and others, 2015; Todhunter and others, 2020). Increased magnitude of peak flow in recent years means that the exceedance probability of floods affecting infrastructure in eastern North Dakota could be increasing (Salas and Obeysekera, 2014), highlighting why advancements in flood-frequency analysis of nonstationary series would be beneficial.

In the attribution study, most streamgages in the Upper Plains with significant downward trends had nonsignificant positive trends in annual precipitation and significant positive trends in annual air temperature (Sando and others, 2022). The most common attribution for significant downward trends in western North Dakota was air temperature (Sando and others, 2022). Some streamgages in this area are in the USGS Hydro-Climatic Data Network 2009, which only includes streamgages that monitor drainage basins with minimal human alterations that are suitable for analyzing hydrologic nonstationarity caused by climatic changes (Lins, 2012). The inclusion of some of the streamgages in the USGS Hydro-Climatic Data Network 2009 provides additional support that the regional pattern could be caused by climatic changes. Air temperature as an attribution for trends is supported by other studies. In the Little Missouri River Basin of western North Dakota, Griffin and Friedman (2017) detected an increased winter and summer atmospheric evaporative demand in 1976–2012 when compared to 1939–75. Because atmospheric evaporative demand represents the potential amount of water transfer from land surface to the atmosphere, increases in winter and summer atmospheric evaporative demand are likely contributors to decreased runoff for a given amount of rain (Griffin and Friedman, 2017; Sando and others, 2022).

Griffin and Friedman (2017) determined that air temperature was the dominant cause of reduced runoff from rainfall. They also determined that surface‐water withdrawals in the Little Missouri River Basin had a noticeable effect on the hydrology in the area, although they accounted for less than 12 percent of the reduction in average annual streamflow volume. They detected no evidence of substantial streamflow reduction caused by groundwater pumping (Griffin and Friedman, 2017). The attribution study also analyzed data from the Bureau of Reclamation’s Missouri River Basin depletions database (Bureau of Reclamation, 2012). The database indicated some increases in depletions related to irrigated agriculture and surface-water public supply; however, depletions were not considered a primary attribution for downward trends in peak flow (Sando and others, 2022). Like eastern North Dakota, climate is the major driver of changes in western North Dakota, and land-use change is a secondary consideration. Long-term (periods greater than 30 years), downward trends in the magnitude of peak indicate that the exceedance probability of floods affecting infrastructure in western North Dakota could be decreasing (Salas and Obeysekera, 2014). As with the pattern of increasing magnitude in eastern North Dakota, this observation highlights the need for improved analysis methods for nonstationary series. However, these observed trends could change in the future, particularly if affected by low-frequency climatic variability driven by phenomena such as Pacific Decadal Oscillation and Atlantic Multidecadal Oscillation, and increased extreme precipitation events, even in areas that experience drying climates, will be complicating factors (Salas and Obeysekera, 2014; Knapp and others, 2023).

Change Points

Change points are abrupt changes in the median, mean, scale, or variance of a time series. Change points in the median and scale of the peak flow were evaluated in this study using two tests (the Pettitt and Mood tests), as described in chapter A. The Pettitt test finds a single change point in the distribution of a series and reports a p-value for a determination of statistical significance. The Mood test finds a single change in the scale, or spread, of a series. The p-values from the results were converted to likelihood values to provide the following tabular and graphical summaries. This likelihood approach, proposed by Hirsch and others (2015) as an alternative to simply reporting significant trends with an arbitrary cutoff point, facilitates mapping spatial patterns in the direction of change.

Change points in the median and scale of peak flows were detected at 11 of the 91 streamgages tested in the 4 analysis periods (table 6). Five of these streamgages had changes in the median and scale of peak flow. Also listed in table 6 are the year and direction of the median change points and the year of the scale change point. Most change points in the median were in a positive direction, the years of median change points ranged from 1972 to 2008, and most were detected in the early 1990s. The years of scale change points ranged from 1981 to 2012, and many change points were detected at a similar time to the change points in the median.

The percentage of streamgages per likelihood category with change points in the median of peak flow for the 100-, 75-, 50-, and 30-year analysis periods is listed in table 7. The likelihood of change points in median peak flows is shown in figure 14. The spatial patterns in change points were like those for trends. Likely upward change points were detected in the east, and likely downward change points were detected in the west. In the 30-year analysis period, the patterns differ; likely upward change points were detected in the west, and mixed results were detected in the east.

An example of change-point analysis for streamgage 05100000 is shown in figure 15. An upward change point in the median peak flow was identified in 1991 because the median flow for the period from 1992 to 2020 is larger than the median flow for the period from 1921 to 1991. A change point in the scale was identified in 1993 because the peak flows were less variable in scale before 1993 than after.

The attribution study discussed in the “Monotonic Trends” section also examined the change points in peak flow (Ryberg, 2022). In eastern North Dakota, change-point years were clustered around 1992, as they are in the results presented here, and have remarkably little variation around that year (Sando and others, 2022). The circa 1992 change point for eastern North Dakota is consistent with the findings of Williams-Sether (1999), who documented a sudden switch from drought to wet conditions in North Dakota around 1992–93 and the findings of Wiche and others (2000b) who determined that in the Devils Lake Basin of eastern North Dakota, unusually high precipitation amounts have been detected since the 1990s during May and June and again during the early fall. Excess moisture can carry over into the next year’s flood season (Ryberg and others, 2014), thereby priming basins in eastern North Dakota for increased runoff and flooding.

In western North Dakota, negative change points were attributed to decreases in precipitation, increases in temperature, and at one site, increases in depletions (Sando and others, 2022). Most change points in the attribution study were from 1972 to 1987 (in the 1970s for the 75-year period and in the 1980s for the 50-year period). The results are similar here (fig. 14). Sando and others (2022) determined the most common attribution for statistically significant change points in western North Dakota, and the trends, was air temperature, and the increases in evaporative demand and reduced runoff from rainfall were discussed in the “Monotonic Trends” section of this report. In the attribution study, three streamgages with significant change points for the 50-year period were attributed to long-term precipitation changes, and a drought was determined to be the most probable cause (Sando and others, 2022). The mean year of the change point for the three streamgages was 1987, and that coincided with a severe drought from 1988 to 1992 (Williams-Sether and others, 1994; Williams-Sether, 1999). The departure from normal monthly precipitation during 1988–92 for each climatic division in North Dakota and a substantial decline in precipitation starting in 1987 in some areas are shown in figure 2 of Williams-Sether and others (1994).

Annual Peak-Streamflow Timing Analysis

The peak-flow timing analysis, as described in chapter A, is used to identify potential shifts, earlier or later, in the timing of floods. Peaks were classified programmatically into an early period, usually representing snowmelt, and a later period, representing rain-generated peaks. An example of a density plot and peak-flow timing analysis at USGS streamgage 05051600 is shown in figure 16A and B. The density plot (fig. 16A) shows the frequency of occurrence of peak flows on days of the water year and illustrates a bimodal peak-flow occurrence. The earlier peak flows are likely snowmelt generated, and the later peak flows are rain generated. The dark red vertical line indicates that day 229 of the water year is a local minimum, or turning point, in the density function and is the breakpoint between the early and late periods for the timing analysis. The peak-flow timing analysis (fig. 16B) shows the magnitudes of each peak flow (circular marker size and color) and the trend lines of the peak flows in the early, later, and overall periods. The solid line is the trend for all peaks. The dotted lines are the trend lines for the early and late peaks (snowmelt or rain generated). Red lines indicate trends that are statistically significant with a p-value <0.05. The upward trend lines for this streamgage indicate that peak flow is happening later in the water year for the overall period, and this is driven by an increase in the 1990s in the occurrence of peaks after day 229 of the water year.

The percentage of streamgages per likelihood category for peak-flow timing trends in the 100-, 75-, 50-, and 30-year analysis periods for the complete, early, and late part of the water year is listed in table 8. The likelihood and magnitude of peak-flow timing trends for streamgages in the 100-, 75-, 50-, and 30-year analysis periods for the complete water year are shown in figure 17. Upward trends in the timing of peak flows were mainly in eastern part of North Dakota and were detected in the 100-, 75-, 50-, and 30-year analysis periods, indicating that peak flows are happening later in the year. Downward trends were mainly in the western part of North Dakota in the most recent 30-year analysis period, indicating that peak flows are happening earlier in the year. The trend magnitudes are largest in the 30-year analysis period compared to the longer analysis periods.

These changes were studied earlier in Ryberg and others (2016a), who determined that for all of North Dakota, snowmelt peak flows were tending to happen earlier, by 8.7–14.3 days, over a period of 1910–2012. The 75-year trend period has preponderance of somewhat likely or likely downward trends in the early part of the water year (table 8), also indicating likely earlier snowmelt peak flows; however, the pattern changes for shorter periods, indicating snowmelt/spring peak flows coming later (table 8). More late spring rain could be the cause of this pattern because North Dakota receives most of its precipitation in late spring and early summer, and although total annual precipitation is highly variable, it has been greater than average since 1990 (Frankson and others, 2022).

The 75-year trend period has a preponderance of somewhat likely or likely upward trends for the late part of the water year, indicating that trends are happening later in the water year. Based on Ryberg and others (2016a), this is affected by later summer/fall peak flows in eastern and northern North Dakota. They happened, on average, 5.2 days later over a period of 1910–2012. Fall streamflow has been higher in recent decades in these areas because of increases in fall precipitation; for example, November 4, 2009, streamflow for the Red River at Fargo, North Dakota, was the highest streamflow recorded for the month of November since measurements started in 1901 and was so high that the USGS put out a press release because high fall streamflow increases flood risk for the next spring (Ryberg and others, 2007a, 2016a). The November 4, 2009, daily streamflow value (7,900 ft³/s) is still the daily streamflow value record for November and fall streamflow has remained at values greater than typical historical conditions (U.S. Geological Survey, 2023).

The raster seasonality plots described in a subsequent section, “Raster Seasonality Plots,” and available in the data release for each streamgage in the study (Marti and others, 2024) can help in visualizing these changes. Those plots use daily streamflow and show increases in fall streamflow since 1993 in eastern North Dakota.

Raster Seasonality Plots

The raster seasonality plot, as described in chapter A, depicts gridded daily mean streamflow for every day in a period of record. The color of the daily mean streamflow is graduated with the larger flows in blue and the smaller flows in tan. Days with no daily mean streamflow are depicted as white. Raster seasonality plots for all streamgages analyzed are available in the data release (Marti and others, 2024). An example raster seasonality plot at USGS streamgage 05100000 in the 100-year analysis period in northeastern North Dakota is shown in figure 18. Larger flows (wetter conditions) are depicted with the blue coloring, and smaller flows (drier conditions) are depicted with the tan coloring. Before 1940, larger flows were measured between April and mid-July, and smaller flows were measured in August–November. Between 1940 and 1990, larger flows generally were measured between mid-March and about September. Larger flows started to be measured for most of the water year after 1990. Since about 1940 and after 2000, conditions at this streamgage have gradually become wetter as shown by the increase in green to blue coloring. Periodic drier conditions, shown by tan coloring, have not been detected since about 1990.

Center of Volume Analysis

The center of volume analysis plot, as described in chapter A, depicts the date of the water year for which 25, 50, and 75 percent of the streamflow volume has passed a given streamgage. Monotonic trends in the percentiles can be an indicator of change in the streamflow over time. The center of volume analysis plots for streamgages in the study are available in the data release (Marti and others, 2024). Two example center of volume analysis plots in the 100-year analysis period are shown in figure 19A and B: the plot for USGS streamgage 05100000, in northeastern North Dakota, is shown in figure 19A, and the plot for USGS streamgage Cannonball River at Breien (06354000), in southwestern North Dakota, is shown in figure 19B. In figure 19A, no apparent trend was detected in the 25th (orange line) percentile, indicating that the date at which 25 percent of the total volume has passed has not changed. Upward trends in the 50th (green line) and 75th (blue line) percentiles indicate that the date at which 50 and 75 percent of the total volume has passed is getting later. In figure 19B, an apparent downward trend exists in the 25th, 50th, and 75th percentiles, indicating that the dates for the 25th, 50th, and 75th percentiles of the total volume are earlier in more recent years. The duration between the 25th and 75th percentile dates is shown as black triangles and is scaled to the y-axis on the right-hand side of the plots. An increase exists in the duration in figure 19B, indicating that the number of days between the 25th and 75th percentiles of flow volume is getting longer.

Peaks-Over-Threshold Analysis

POT analysis, as described in chapter A, analyzes the frequency of occurrence for daily mean streamflows over a set threshold. For a given threshold, the number of times a streamflow exceeds the threshold is counted for each year. Meeting the independence criterion among candidate streamflows is the primary challenge with the POT analysis. Thresholds for the POT analyses in this study were set at the daily mean streamflow magnitude for which there is an average of two (POT2) and four (POT4) events per year. Tests for change points in the number of events over the threshold were completed to find increases or decreases in the frequency of the candidate streamflows. The results of change points in the frequency of POT2 for USGS streamgage 05051600 in the 50-year analysis period are shown in figure 20A and B. The daily mean streamflow times series (in gray) is shown in figure 20A. The daily mean streamflow magnitudes greater than the POT2 determined threshold (red line) are shown as blue (fig. 20A). Larger daily mean streamflows are more prevalent after about 1990. The detected change point (1992) in the frequency of mean daily streamflow greater than the POT2 threshold is shown in figure 20B.

The results of change points in the frequency of POT4 for USGS streamgage 05051600 in the 50-year analysis period are shown in figure 21A and B. The POT4 results are like those of the POT2, indicating larger and more frequent mean daily streamflows after the detected change point in 1992. The main difference between the POT2 and POT4 results is that the threshold is lower in the POT4 analysis than the POT2 analysis.

The percentage of streamgages per likelihood category of detected change points in median frequency of POT2 and POT4 of daily mean streamflow in each analysis period is listed in tables 9 and 10, respectively. The likelihood of change points in the median frequency POT2 and POT4 for streamgages in the four analysis periods is shown in figures 22 and 23, respectively. Likely upward and somewhat likely upward changes are being detected in streamgages in the eastern areas of North Dakota in the 100-, 75-, and 50-year analysis periods. Likely downward and somewhat likely downward changes are being detected in streamgages in the western areas the 75- and 50-year analysis periods. Likely and somewhat likely upward and downward changes are being detected throughout North Dakota in the 30-year analysis period.

Annual and Seasonal Precipitation

The percentage of streamgages in each likelihood category of detected trends in annual precipitation for each analysis period is listed in table 11. The likelihood and magnitude of annual precipitation trends in each analysis period are shown in figure 24. In the 100-, 75-, and 50-year analysis periods, most trends were upward, and the largest magnitudes were in the 50-year analysis period. In the 30-year analysis period, somewhat likely upward trends were detected in the west. Likely downward trends were detected in the southwest in the 50-year analysis period and in the northeast in the 30-year analysis period, and larger magnitudes were detected in the 30-year analysis period.

Annual precipitation totals may not be the best indicators of potential flooding because antecedent conditions, such as wet falls, and accumulated moisture over the winter contribute to runoff (Ryberg and others, 2007a, 2014; Gupta and others, 2015). Therefore, seasonal metrics of precipitation were also analyzed. The percentage of streamgages per likelihood category of seasonal precipitation trends in the 100-, 75-, 50-, and 30-year analysis periods is listed in table 12.

The likelihood and magnitude of seasonal precipitation trends in each analysis period are shown in figure 25. During the winter season, likely upward trends were detected at most streamgages in 50- and 30-year analysis periods and were detected across the State. Likely downward trends were detected in all analysis periods and tended to be detected in the southwestern and northeastern areas of the State. During the spring season, likely upward trends were detected in all analysis periods, most in the western area of the State. Likely downward trends were detected mainly in the east in the 30-year analysis period. During the summer season, likely upward trends were detected in the 100-, 75-, and 50-year analysis periods in the eastern and northwestern to southeastern areas of the State. Likely downward trends were detected mainly in the southwest in the 75- and 50-year analysis periods and across the State in the 30-year analysis period. During the fall season, likely upward trends were detected in all analysis periods, and trend magnitudes were largest in the 30-year analysis period mainly in the northwestern and northern areas of the State. The significant seasonal increases in likely upward and likely downward trend magnitudes in the 30-year analysis period indicate that precipitation is increasing over much of the State during the fall season and decreasing across the State during the summer season. As discussed earlier in the peak-streamflow timing analysis and raster seasonality plots of daily streamflow, a key factor in change in North Dakota hydroclimatology is in the increase in fall precipitation, particularly in the most recent period, as shown in figure 25.

Annual Temperature

The percentage of streamgages in each likelihood category of detected trends in annual temperature is listed in table 13, and the likelihood and magnitude of annual temperature trends are shown in figure 26. As noted in the earlier “Precipitation, Temperature, and Evapotranspiration” section, temperatures have risen across North Dakota. The trends in the 30-year period are somewhat likely upward (have less statistical significance). Given the high degree of variability in temperature, as described earlier, a large sample size is required to detect a trend; therefore, the 30-year results are reasonable statistically and indicate the temperature change is in one direction.

Annual Potential Evapotranspiration

The percentage of streamgages per likelihood category of trends in the ratio of PET and precipitation in the 100-, 75-, 50-, and 30-year analysis periods is listed in table 14. The likelihood and magnitude of trends in the ratio of annual PET and precipitation in the 100-, 75-, 50-, and 30-year analysis periods are shown in figure 27. Likely downward trends were detected mainly in the eastern area of the State in the 75- and 50-year analysis periods with magnitudes not substantially changing. Likely upward trends were detected in the southwestern area of the State in the 75- and 50-year analysis periods, and in the western and northeastern areas of the State in the 30-year analysis period. Trend magnitudes were larger in the 30-year analysis period. Likely upward trends indicate that annual PET (the numerator in the ratio) could be increasing or total annual precipitation (the denominator in the ratio) could be decreasing. Likewise, likely downward trends indicate that annual PET could be decreasing, or annual precipitation could be increasing.

Given the widespread increases in temperature (fig. 26), the upward trends in the ratio of annual PET to precipitation are indicative of the effect of increased temperature on PET. Annual precipitation indicated the largest and most frequent trends in the 50-year trend period were in eastern North Dakota (fig. 24), and that increase in precipitation results in the downward trends in the ratio of annual PET to precipitation in eastern North Dakota in the 50-year period (fig. 27).

Annual Snowfall

The percentage of streamgages per likelihood category of trends in the ratio of annual snowfall to annual precipitation in the 100-, 75-, 50-, and 30-year analysis periods is listed in table 15. The likelihood and magnitude of trends in the ratio of annual snowfall to annual precipitation each analysis period are shown in figure 28. Likely downward trends were detected throughout most of the State in the 100-, 75-, and 50-year analysis periods. These downward trends indicate that amounts of snowfall (the numerator in the ratio) have been decreasing and (or) the amounts of total annual precipitation (the denominator in the ratio) have been increasing during these analysis periods. Few trends were detected in the 30-year period, and the trends that were detected indicated likely upward and somewhat likely upward trends in the northwestern and south-central areas of the State.

A decrease in snowfall or a decrease in the percentage of annual precipitation falling as snow could decrease the magnitude and frequency of snowmelt peaks and favor changes in flood regimes to a more bimodal distribution (fig. 16A), and more peaks would be generated by rain rather than accumulated snow. In an analysis of peak flow in the north-central United States, Ryberg and others (2016a) determined that the odds of peaks being in summer/fall, as opposed to peaks in spring/snowmelt, have increased.

Annual Soil Moisture

The percentage of streamgages per likelihood category of annual soil-moisture trends in the 100-, 75-, 50-, and 30-year analysis periods is listed in table 16. The likelihood and magnitude of annual soil-moisture trends in the 100-, 75-, 50-, and 30-year analysis periods are shown in figure 29. Likely upward trends were detected across the State in all analysis periods and were concentrated in the east in the 50-year analysis period and in the west in the 30-year analysis period. Likely downward trends were detected in the southwest in the 50-year analysis period (at one site) and in the northeast in the 30-year analysis period (two sites). Likely upward magnitudes increased slightly in the 50- and 30-year analysis periods. Likely downward magnitudes were largest in the 30-year analysis period. Likely upward trends indicate that annual soil moisture could be increasing because of increases in precipitation and decreases in PET and temperature. Likewise, likely downward trends indicate that annual soil moisture could be decreasing because of decreases in precipitation and increases in PET and temperature.

The trends in soil moisture closely match the trends in annual precipitation (fig. 24). Saturated soils can carry over surplus moisture into the next year and play a substantial role in runoff and flood risk (Ryberg and others, 2007a, 2014; Knapp and others, 2023). In fact, modeling of high-flow events in the Upper Missouri River Basin indicates “acute runoff sensitivity to soil moisture in eastern sections of the basin” and wet antecedent soil conditions contributed to the extreme flood event of 2011 (Livneh and others, 2016, p. 3).

Synthesis of 50-Year Peak Streamflow and Climate Trends

The 50-year period is the period that balances the intersecting objectives of widespread spatial coverage for trends and the longest trend period possible. The pattern of monotonic (gradual) changes in peak flow in this period can be summarized as increased magnitude in the eastern half of the State and decreased magnitude in the western half of the State (fig. 13). For that same period, the ratio of annual snowfall to annual precipitation declined across the State. This pattern of decreased annual snowfall as a fraction of annual precipitation can be detected across the Northern Hemisphere; however, like in North Dakota, the resulting streamflow variation is complex (Han and others, 2024; Ryberg, 2024b).

Eastern parts of the State are in a snow climate (Köppen-Geiger classification system, major climate “snow”; Kottek and others, 2006) and typically have a pattern like that of figure 16, indicating that the highest frequency of occurrence of peak flow is in the spring, which is indicative of snowmelt (also refer to Ryberg and others, 2016a). Snowmelt peaks tend to be larger than rain-generated peaks (refer to figure 16 as an example and additional sites in the associated data release, Marti and others, 2024). However, in the eastern part of the State, flood magnitude increased, whereas snow as part of total precipitation declined. This can be explained by changes in annual and seasonal precipitation. In the 50-year trend period, annual precipitation increased (fig. 24); therefore, even if snow amounts held steady, the ratio of snow to total precipitation would still decline. In addition, summer and fall precipitation increased (fig. 25), but the ratio of annual PET and precipitation declined (fig. 27). Greater than normal precipitation in the fall and the resulting increase in soil moisture are factors that contribute to flooding in the eastern part of the State (Ryberg and others, 2007a), and increased soil moisture can be detected in the east (fig. 29). Moisture-surplus conditions carry over into the spring and can increase runoff and flood risk (Ryberg and others, 2014). Temperature and ET are important parts of the water balance as well, and results indicate that despite increased temperatures, the ratio of annual PET and precipitation has decreased (fig. 27), indicating that precipitation is a larger driver of observed peak-flow trends in the east than is temperature or ET. These results match those of Han and others (2024) for the Northern Hemisphere in that they determined that even though declining snowfall as a fraction of annual precipitation is often assumed to be related to changes in temperature, it is more closely related to changes in precipitation (Ryberg, 2024b).

For the western part of the State, annual and seasonal precipitation trends are mixed, temperature trends are upward, snowfall as a ratio of total precipitation is downward, and PET and snow moisture trends are mixed and have smaller magnitudes than the trends in the east. These factors combine to create conditions in which peak flow has declined. Central North Dakota is a transition zone to the arid climate on the western edge of the State (Köppen-Geiger classification system, major climate “arid”; Kottek and others, 2006), and in semiarid and arid basins, temperature plays a greater role in the water balance, as determined in a detailed study of the Little Missouri River of western North Dakota (Griffin and Friedman, 2017).

Monsters as Metaphor for the Stationary-Nonstationary Choice

The choice of analysts and decision makers between stationary assumptions and analyses and nonstationary assumptions and analyses is commonly represented as a choice with mutually exclusive options, one of them having a great deal more uncertainty (in choice of methods, distributions, or explanatory variables). This binary choice itself is a source of uncertainty, and these kinds of mutually exclusive choices have been described as “uncertainty monsters.” In the metaphor of monsters, “a monster is understood as a phenomenon that at the same moment fits into two categories that were considered to be mutually excluding, such as knowledge versus ignorance, objective versus subjective, facts versus values, prediction versus speculation, science versus policy” (Van der Sluijs, 2005, p. 87). “In terms of philosophical pragmatism, a monster should be read as a so-called ‘problematic situation,’ a confusing situation in which a new phenomenon severely challenges our preliminary categories of judgment” (Smits, 2006, p. 501).

This metaphor of monsters for uncertainty has evolved from research on premodern ideas of technological doom and salvation (Douglas, 1975) to a monster theory of technology (Smits, 2002, 2006), to a monster theory of the science-policy interface (Van der Sluijs, 2005), to a metaphor for coping with uncertainty in flood-risk management (Knotters and others, 2024). The metaphor applies well to the flood-frequency analysis question of using stationary or nonstationary assumptions and methods.

Uncertainty monsters may be dealt with in six ways: “denial,” “exorcism,” “adaptation,” “embracement,” “assimilation,” or “anesthesia” (Smits, 2002, 2006; Van der Sluijs, 2005; Knotters and others, 202490). Monster denial could entail ignoring the problem, clinging to past investments (Bulletin 17C, England and others, 2018), or not reporting uncertainties. These actions might be described as the ostrich or Concorde effect or sunk cost fallacy (Knotters and others, 2024). Monster exorcism would entail reducing all uncertainties (get rid of the monster), but the theory predicts that this option is futile in the long run (Smits, 2002, 2006; Van der Sluijs, 2005). Climate science is an example of attempts to reduce uncertainties. As one source of uncertainty is addressed in climate models, science finds new complexities in a chaotic system (Van der Sluijs, 2005).

In monster adaptation, attempts are made to change the monster into something that better fits existing categories (Smits, 2002, 2006; Van der Sluijs, 2005). Again, climate science has been used as an example of this adaptation because, rather than reducing all the uncertainties, climate science has turned to scenarios (Van der Sluijs, 2005). Various scenarios are fed into models, and the choice is changed from best model and model parameters to a choice of what scenario is preferred or likely; the multiple results can cause new uncertainties. In flood-frequency analysis, one could generate multiple potential peak-flow series and produce multiple realizations of annual exceedance probabilities.

In monster assimilation, the mutually exclusive categories are rethought and the lack of a single truth is acknowledged (Smits, 2002, 2006; Van der Sluijs, 2005). Smits uses an example from medicine to describe the rethinking of mutually exclusive categories.

In monster embracement, the complexities are fascinating, the uncertainties are to be pointed out to the detriment of a focus on the actual risk, and new methods are also embraced (Smits, 2002, 2006; Van der Sluijs, 2005). In monster anesthesia, consensus is key, and a panel or committee might decide the path forward, providing some psychological and organizational benefits, but the uncertainty remains (Knotters and others, 2024).

Knotters and others (2024) indicate that if the problem is well structured and simple, monster adaptation is the right choice. Statistical models can be applied, and uncertainties can be quantified. If a well-structured, complex problem exists, monster assimilation is the right choice. The uncertainties that can be quantified are quantified, the unquantifiable uncertainties are disclosed, and the uncertainties have a role in decision making (Knotters and others, 2024).

Implications for Flood-Frequency Analysis

Nonstationary flood-frequency analysis necessitates detailed exploratory data analysis and additional data and information about climate, land use, and other factors (Serinaldi and Kilsby, 2015). This study provides extensive exploratory analysis for peak flow and daily streamflow and climate data for North Dakota, setting the stage for informed nonstationary flood-frequency analysis. Attribution of the causes of nonstationarity is valuable because the driving mechanisms can be natural, such as long low-frequency climate signals; anthropogenic; or a mix (Khaliq and others, 2006; Vogel and others, 2011). One may be able to incorporate explanatory variables into a nonstationary model, and the types of models can depend on the distribution of or trends in the explanatory variable. An attribution study has been completed for streams in North Dakota (Sando and others, 2022), and that study informed this work and could be viewed in conjunction with the results here.

The many methodological choices for nonstationary flood-frequency analysis and the detailed additional analyses of explanatory data could become part of monster embracement if an analyst becomes overly enamored with the patterns in the data and the statistical intricacies of methods and overly focused on the minutiae of sources of uncertainty. However, the path through the data and methods may be one of monster assimilation, adaptation, or both. No one nonstationary flood-frequency analysis method is likely applicable to all studies, and multiple scenarios from multiple models and future estimates of peak flow may be useful in making design decisions.

Historical and paleoflood data can help place some nonstationarities in a broader context and improve flood-frequency analysis, and such data can represent floods from a different climate or different channel conditions and complicate flood-frequency analysis (Benito and others, 2004; Harden and others, 2011; Ryberg and others, 2020b). Bulletin 17C provided advancements for the inclusion of historical and paleoflood data (England and others, 2018), and these additional data can be used in a scenario approach (monster adaptation) to assess the fit of flood-frequency curves for rare floods (Ryberg and others, 2020b). This option is limited because historical and paleoflood data are available for a small subset of sites, and a comprehensive paleoflood study might require a team of geomorphologists, hydraulic modelers, hydrologists, and surveyors (Harden and others, 2021). Detailed analysis of past meteorological conditions is also essential and depends on reconstructions of data (Benito and others, 2004) that may be technically or cost prohibitive.

Numerous advanced techniques have been suggested (monster embracement; Cunderlik and Burn, 2003; Khaliq and others, 2006; Villarini and others, 2009b; Gilroy and McCuen, 2012; O’Brien and Burn, 2014; Machado and others, 2015; Tan and Gan, 2015; Debele and others, 2017; Luke and others, 2017; Razmi and others, 2017; Serago and Vogel, 2018; Yan and others, 2019; Hecht and Vogel, 2020; Vogel and Kroll, 2020; Awasthi and others, 2022; Hecht and others, 2022). Limited testing has determined that stationary analysis could still be preferred, and nonstationary models commonly are not an improvement, but the use of nonstationary models to update parameters for stationary models may be preferred for physically changing basins (Luke and others, 2017). This last possibility could be seen as monster assimilation: update the model parameters with new, current information and then use the stationary method, thereby blurring the stark stationary-nonstationary choice.

When embracing the monster, some of the suggested nonstationary methods are statistically complex, discouraging widespread adoption. In addition, when one goes outside the framework of Bulletin 17C, the method may require one to choose a different statistical distribution for the data or compare multiple distributions (Debele and others, 2017); this too is a discouragement to widespread adoption. A promising step toward addressing nonstationarity and assimilating the monster may be explaining the nonstationary behaver with an exogenous variable and then generating conditional mean, variance, and skew with which to complete stationary flood-frequency analysis (Khaliq and others, 2006; Serago and Vogel, 2018). Generalized additive models for location, scale, and shape (known as GAMLSS) can also incorporate explanatory variables and provide a flexible framework for modeling nonstationarities because they can model abrupt changes and trends (Villarini and others, 2009a, b; Machado and others, 2015). However, the flexibility comes with more choices for the analyst in terms of statistical distributions and explanatory variables.

Serially correlated, or dependent, peak flows violate the assumptions of conventional flood-frequency analysis. Several methods have been suggested to adjust for serial correlation, including decorrelation or prewhitening; modeling the short- and long-term persistence; or thinning the observations (Lettenmaier, 1976; Burn and Goel, 2001; Khaliq and others, 2006). One challenge is that serially correlated observations result in an effective record length that can be much shorter than the observed record length (Burn and Goel, 2001); therefore, thinning, or otherwise using fewer of the data in the series, results in small sample size problems (Khaliq and others, 2006).

The changes in seasonality and extended periods of high flow, as shown in raster plots, indicate that using only the annual maximum series, peak flow, leaves many floods out of the analysis. A POT approach would include multiple floods in some years (and none in others) that are greater than a particular threshold. A POT approach can have less bias for frequent floods, and using more of the data seems reasonable, making a POT approach seem like a way to have a well-structured and simple method, or monster adaptation. However, the POT approach has been underused mainly because of the challenge of selecting a threshold and a minimum separation time that ensure independent peaks that meet distributional assumptions and provide enough data for estimation of parameters (Khaliq and others, 2006; Pan and others, 2022).

Results of this study indicate that the patterns in nonstationarity have spatial or temporal cohesiveness, such as the opposing trends in North Dakota east and west of the 100th meridian and increases in peak flow in the 1990s in eastern North Dakota. These regional patterns can indicate linkages to low-frequency climate effects, such as El Niño-Southern Oscillation, Pacific Decadal Oscillation, North Atlantic Oscillation, or Atlantic Multidecadal Oscillation. Researchers have attempted to document these linkages, but they are complex given the varying time scales, differing seasonal patterns in precipitation and temperature, and their interactions (Wang and others, 2016; Dickinson and others, 2019; Collins and others, 2022). A panel regression model can incorporate explanatory variables that have fixed effects or vary across space and time and therefore could have a regional component (Khaliq and others, 2006; Ferreira and Ghimire, 2012; Over and others, 2016; Blum and others, 2020) and might be an example of monster assimilation. Modeling regional components of flood behavior can be particularly useful given short record lengths at some sites (Khaliq and others, 2006).

Some proposed methods can incorporate climate projections (such as Awasthi and others [2022]) and follow the monster adaptation approach of creating flood-risk scenarios. Parameters of a statistical distribution can be estimated using explanatory variables, such as rainfall and temperature. Once such a model is developed, projected precipitation and temperature could be used to project flood-frequency estimates under future climate scenarios. Awasthi and others (2022) developed a process to do this; however, they determined that model estimates were better in humid basins and did not work as well in arid basins. This finding is common in hydrologic modeling because rainfall runoff in arid and semiarid areas has a nonlinear relation; precipitation is more variable in space and time than in humid regions and hydrological processes differ (such as less base flow and more channel losses than in humid areas; Pilgrim and others, 1988; Jin and others, 2022). As determined by the natural state of Devils Lake being rising or falling and as described by Pilgrim and others (1988, p. 381), “arid zones (and especially semiarid zones) are often in a delicate hydrological balance. The whole nature of the hydrology (and hence values of model parameters) may be changed by a prolonged wet or dry sequence.”

Finally, if a causal mechanism for the nonstationarities cannot be identified, as is sometimes the case (Barth and others, 2022; Sando and others, 2022; York and others, 2022), a model other than the conventional stationary model introduces additional uncertainty (Serinaldi and Kilsby, 2015). When the cause of the nonstationarity is unknown, the stationary model can provide the best estimates provided uncertainty and other safety factors are taken into consideration (Serinaldi and Kilsby, 2015).