Introduction

Peak-flow frequency analysis is essential in numerous water-resources management applications, including the design of critical infrastructure and floodplain mapping. Standardized recommended guidelines for peak-flow frequency analyses are presented in “Guidelines for Determining Flood Frequency—Bulletin 17C” (England and others, 2019; hereafter referred to as “Bulletin 17C”). A basic assumption within Bulletin 17C is that, for basins without major hydrologic alterations (for example, regulation, diversion, or urbanization), statistical properties of the distribution of annual peak streamflows are stationary, including a constant mean, variance, and skew. Stationarity requires that all the data represent a consistent hydrologic regime within the same (albeit highly variable) fundamental climate system. From the onset of the U.S. Geological Survey (USGS) streamgage program and in peak-flow frequency estimation investigations through much of the 20th century, the stationarity assumption was widely accepted within the peak-flow frequency community. However, in recent decades, a better understanding of climatic persistence as well as concerns about potential climate change and land-use change have caused the stationarity assumption to be reexamined (Milly and others, 2008; Lins and Cohn, 2011; Stedinger and Griffis, 2011; Koutsoyiannis and Montanari, 2015; Serinaldi and Kilsby, 2015).

Nonstationarity is a statistical property of a peak-flow series such that the long-term distributional (for example, the mean, variance, or skew) or interannual dependence properties change one or more times either gradually or abruptly through time. Nonstationarities in a given peak-flow series may be attributable to one cause (for example, either regulation, land-use change, or climate) but often are the result of a mixture of those causes (Vogel and others, 2011), which makes the detection and attribution of nonstationarity challenging (Barth and others, 2022; Levin and Holtschlag, 2022; Sando and others, 2022). Nonstationarity can manifest as a gradual trend in peak streamflows over time (Hodgkins and others, 2019); abrupt changes in the central tendency (mean or median), variability, or skew of peak streamflows; or both (Ryberg and others, 2020). If observed trends are not incorporated into peak-flow frequency analysis, the result may be a poor representation of the true flood risk at a certain time. Bulletin 17C currently offers no methodology for estimating flood frequency in the presence of nonstationarity and, further, identifies that additional peak-flow frequency studies that incorporate changing climate or basin characteristics into the analysis are warranted (England and others, 2019).

Previous studies have identified hydroclimatic changes, land-use changes, and nonstationarity in peak streamflow in the Midwest, including Missouri (McCabe and Wolock, 2002; Mallakpour and Villarini, 2015; Ivancic and Shaw, 2017; Ryberg and others, 2020; Levin and Holtschlag, 2022). This report is part of a larger study intended to document peak-flow nonstationarity across a nine-State region consisting of Illinois, Iowa, Michigan, Minnesota, Missouri, Montana, North Dakota, South Dakota, and Wisconsin. The full scope of the study includes evaluating the combined effects of hydroclimatic and land-use changes on peak-flow frequency analysis across the nine-State region. A wide range of statistical analyses were applied to characterize temporal changes in peak streamflow and hydroclimatic variables at streamgages in each State. These analyses are intended to provide the foundation for future studies that can address nonstationarity in peak-flow frequency analysis.

Purpose and Scope

The purpose of this report is to characterize changes in annual peak streamflows in Missouri and their relation to changes in climate. Detailed methods of streamgage selection and streamflow and climate analyses are provided in the associated USGS report Ryberg and others (2024). Annual peak streamflow, daily streamflow, monthly observed climatic data, and modeled climate metrics, as published in the associated USGS data release Marti and others (2024), were examined for spatial and temporal patterns of change across the State of Missouri. Four trend periods ending in water year 2020 are analyzed for 60 total streamgages in Missouri and the adjacent States of Arkansas and Kansas (fig. 1; table 1). A water year is the period from October 1 to September 30 and is designated by the year in which it ends; for example, water year 2020 was from October 1, 2019, to September 30, 2020. These analyses provide the foundation for better understanding the nature and causes of nonstationarities in observed peak streamflows in the State of Missouri.

Table 1.    

U.S. Geological Survey streamgages used in the report.

[ID, identification; USGS, U.S. Geological Survey]

Table 1.    U.S. Geological Survey streamgages used in the report.

Figure ID	USGS streamgage number	Streamgage name	Included in 100-year trend period	Included in 75-year trend period	Included in 50-year trend period	Included in 30-year trend period
1	05495000	Fox River at Wayland, Missouri	True	True	True	True
2	05496000	Wyaconda River above Canton, Missouri	True	True	True	True
3	05500000	South Fabius River near Taylor, Missouri	False	True	True	True
4	05501000	North River at Palmyra, Missouri	False	True	True	True
5	05502300	North Fork Salt River at Hagers Grove, Missouri	False	False	False	True
6	05502500	North Fork Salt River near Shelbina, Missouri	False	True	False	True
7	05503800	Crooked Creek near Paris, Missouri	False	False	False	True
8	05504800	South Fork Salt River above Santa Fe, Missouri	False	False	False	True
9	05506800	Elk Fork Salt River near Madison, Missouri	False	False	True	True
10	05508805	Spencer Creek below Plum Creek near Frankford, Missouri	False	False	False	True
11	05514500	Cuivre River near Troy, Missouri	True	True	True	True
12	06813000	Tarkio River at Fairfax, Missouri	True	False	False	False
13	06817700	Nodaway River near Graham, Missouri	False	False	False	True
14	06819500	One Hundred and Two River at Maryville, Missouri	False	True	True	False
15	06820500	Platte River near Agency, Missouri	False	True	True	True
16	06821190	Platte River at Sharps Station, Missouri	False	False	False	True
19	06893500	Blue River at Kansas City, Missouri	False	True	True	True
20	06897500	Grand River near Gallatin, Missouri	False	True	True	True
21	06899500	Thompson River at Trenton, Missouri	True	True	True	True
22	06901100	Locust Creek at Reger, Missouri	False	False	False	True
23	06902000	Grand River near Sumner, Missouri	False	True	True	True
24	06906800	Lamine River near Otterville, Missouri	False	False	False	True
25	06908000	Blackwater River at Blue Lick, Missouri	False	True	True	True
28	06918440	Sac River near Dadeville, Missouri	False	False	True	True
29	06918460	Turnback Creek above Greenfield, Missouri	False	False	True	True
30	06918740	Little Sac River near Morrisville, Missouri	False	False	True	True
31	06919500	Cedar Creek near Pleasant View, Missouri	False	False	True	True
32	06921070	Pomme de Terre River near Polk, Missouri	False	False	True	True
33	06921200	Lindley Creek near Polk, Missouri	False	False	True	True
34	06930000	Big Piney River near Big Piney, Missouri	True	True	True	True
35	06932000	Little Piney Creek at Newburg, Missouri	False	True	True	True
36	06933500	Gasconade River at Jerome, Missouri	False	True	True	True
37	06934000	Gasconade River near Rich Fountain, Missouri	False	False	False	True
38	07013000	Meramec River near Steelville, Missouri	True	True	True	True
39	07014500	Meramec River near Sullivan, Missouri	True	True	True	True
40	07015720	Bourbeuse River near High Gate, Missouri	False	False	True	True
41	07016500	Bourbeuse River at Union, Missouri	True	True	True	True
42	07017200	Big River at Irondale, Missouri	False	False	True	True
43	07019000	Meramec River near Eureka, Missouri	True	True	True	True
44	07021000	Castor River at Zalma, Missouri	True	True	True	False
45	07035800	St. Francis River near Mill Creek, Missouri	False	False	False	True
46	07037500	St. Francis River near Patterson, Missouri	True	True	True	True
50	07050700	James River near Springfield, Missouri	False	False	True	True
51	07052500	James River at Galena, Missouri	True	True	True	True
52	07057500	North Fork River near Tecumseh, Missouri	False	True	True	True
53	07058000	Bryant Creek near Tecumseh, Missouri	False	True	True	False
54	07066000	Jacks Fork at Eminence, Missouri	True	True	True	True
55	07067000	Current River at Van Buren, Missouri	True	True	True	True
56	07068000	Current River at Doniphan, Missouri	True	True	True	True
57	07071000	Greer Spring at Greer, Missouri	True	True	True	True
58	07071500	Eleven Point River near Bardley, Missouri	True	True	True	True
59	07186000	Spring River near Waco, Missouri	False	True	True	True
60	07187000	Shoal Creek above Joplin, Missouri	False	True	True	True
17	06893080	Blue River near Stanley, Kansas	False	False	True	True
18	06893300	Indian Creek at Overland Park, Kansas	False	False	True	True
26	06910800	Marais Des Cygnes River near Reading, Kansas	False	False	True	True
27	06917000	Little Osage River at Fulton, Kansas	False	False	True	True
47	07048600	White River near Fayetteville, Arkansas	False	False	True	True
48	07049000	War Eagle Creek near Hindsville, Arkansas	False	False	True	True
49	07050500	Kings River near Berryville, Arkansas	False	True	True	True

Description of Study Area

The study area covers all of Missouri, including all drainage basins that flow into the State. Peak streamflows may be affected by many different conditions, including climate variables like precipitation and antecedent soil moisture and land-surface characteristics like land cover and topography (Sharma and others, 2018). Characteristics of the study area described in this section include rivers and lakes, climate, ecoregions, land cover, and soils.

Rivers and Lakes

All river basins in Missouri contribute directly or indirectly to the Missouri and Mississippi Rivers. Major rivers in northern and western Missouri drain directly into the Missouri River and include the Grand, Chariton, Platte, and Nodaway Rivers in the north and the Osage River in the west (not shown). Most rivers in eastern and southern Missouri drain directly or indirectly into the Mississippi River including the Fabius, Salt, Meramec, and White Rivers (not shown). Flooding of tributaries to the Missouri and Mississippi Rivers result from heavy rains and convective storms that are most frequent in the spring and early summer although record peaks have occurred every month of the year. Flooding on the Missouri and Mississippi River main stems also generally occurs in the spring and early summer after heavy rains over large regions, particularly when main-stem crests coincide with local tributary peak streamflows (Decker, 2023).

The Missouri River main stem and many tributaries are regulated by impoundments, historically for flood control but more recently for water supply, thereby affecting the magnitude, frequency, timing, and duration of peak streamflows. The 2018 national inventory of dams lists nearly 5,400 tributary dams in Missouri in addition to the 6 main-stem dams on the upper Missouri River in Montana, North Dakota, South Dakota, and Nebraska that regulate streamflows (U.S. Army Corps of Engineers, 2018). Although the dams are distributed throughout the State, more have been constructed in the northern part of the State compared to other areas, particularly in recent years. The frequency of dams in the northern part of the State likely is a result of a reliance on surface-water resources for public drinking water supplies, resulting from a lack of potable groundwater in northern Missouri (Mesko and Berkas, 1987) and the need to protect against recent (1999–2000, 2003) drought conditions (Richards, 2013). Most of the dams and associated storage volume were completed in the 1960 to 1980 period.

Climate

Missouri’s climate is continental with humid, temperate conditions determined by the mid-latitude location. The topographic maximums and relief are not sufficient to result in substantial orographic effects on the climate. The seasons are well defined, with winter periodically affected by cold-dry air masses from the north and summers highly affected by warm, moist air masses from the Gulf of Mexico (Frankson and others, 2022).

Because of the continental climate, Missouri is open to frequent temperature changes in all seasons, with mean annual temperature following a diagonal gradation from the northwest corner to southeast corner of the State (fig. 2) ranging from about 50 to 65 degrees Fahrenheit (°F). Winters typically last from December through early March, with most days of each month having maximum temperatures exceeding 32 °F. Summers extend from June through September, with mean maximum temperatures in the warmest month of July exceeding 90 °F.

Mean annual precipitation in Missouri also varies along a diagonal gradient from a low of about 30 inches (in.) in the northwest to a high of about 55 in. in the southeast (fig. 3). Seasonality in precipitation is more pronounced in the northwest than in the southeast as a result of the moderating effect of moisture from the Gulf of Mexico in the southern portion of Missouri. Spring, summer, and fall precipitation is mainly frontal, resulting from the meeting of moist Gulf air and the cooler and drier air from the north, which causes showers and thunderstorms (Decker, 2023). More than 40 percent of total annual precipitation falls in the 10 wettest days of the year for most of the State (Frankson and others, 2022). The mean annual snowfall ranges from about 8 to 23 inches per year. Snowfall rarely is a substantial contributor to flooding in Missouri. The mean annual snowfall at Springfield, for example, is 15.9 in., representing about 3.5 percent of total precipitation (Decker, 2023).

Ecoregions, Land Cover, and Soils

Land-surface characteristics such as land cover and soils interact with climate to affect the hydrology of drainage basins, including floods (Andrés-Doménech and others, 2015; Vereecken and others, 2022). One integrative descriptor of land-surface characteristics is the ecoregion, which represents areas of relative similarity in environmental resources and identifies the spatial variability of ecosystems. The U.S. Environmental Protection Agency level III ecoregions of Missouri (fig. 4) consist of the Central Irregular and Western Corn Belt Plains covering the north and western part of the State (Chapman and others, 2002). The Ozark Highlands span most of the southern part of the State, the Interior River Valleys and Hills range along the Missouri and upper Mississippi Rivers, and the Mississippi Alluvial Plain and Mississippi Valley Loess Plains are present in the southeast bootheel region. These divisions, with the Central Irregular Plains, Western Corn Belt Plains, and Interior River Valleys and Hills combined, correspond to three regions of similar hydrologic response used in the development of rural flood-frequency equations for Missouri (Crippen and Bue, 1977; Alexander and Wilson, 1995; Southard and Veilleux, 2014). The Western Corn Belt Plains, Central Irregular Plains, and Interior River Valleys and Hills of north and western Missouri correspond to hydrologic region I and what is referred to as the “Central Lowlands” (Southard and Veilleux, 2014). This area covers about 49 percent of the State, and local relief is about 50 to 150 feet (ft). Hydrologic region II corresponds to the Ozark Plateaus (Ozark Highlands ecoregion) and covers about 46 percent of the State with local relief of about 100 to 500 ft. Hydrologic region III represents about 5 percent of the State and corresponds to the Mississippi Alluvial Plain and Mississippi Valley Loess Plains with local relief of less than (<) 30 ft.

Land use in the State is dominated by a mix of deciduous forest (32 percent), hay/pasture (30 percent), and cultivated crops (22 percent), a mix of which constitutes the northern half of the State (fig. 5) (Dewitz, 2019). The southern half of the State is largely a mix of pasture/hay and deciduous forest, with the southeast portion being the most forested part of the State. In the farthest southeast part of the State, in the Mississippi Alluvial Plain, land use is almost completely dominated by cultivated crops. Karst features in the Ozark region affect hydrology through the formation of sinkholes and development of numerous springs. These features contribute to the sustained base flows in the Ozarks compared to other areas of the State, particularly the northern and western plains regions (Rafferty, 2019).

The runoff potential of soils varies throughout Missouri (fig. 6). The U.S. Department of Agriculture Natural Resources Conservation Service has grouped soils into four main hydrologic soil groups based on their permeability and runoff potential (U.S. Department of Agriculture Natural Resources Conservation Service, 2009). Large parts of the southern half of Missouri and the northwestern corner of the State have soil with a low runoff potential (fig. 6). Soils with moderately high runoff potential are present throughout most of the State, and areas of high runoff potential, where water movement through the soil is restricted, are present in the southeast, west-central, and northeast parts of the State.

Brief History of U.S. Geological Survey Peak-Flow Data Collection in Missouri

The history of streamgage operations is relevant to nonstationarity analyses because it provides information on the temporal distribution of the data available for evaluating nonstationarity. Based on data through water year 2020, there are 602 active and discontinued streamgaging locations in Missouri, of which 401 are predominantly continuous record streamgages and 201 are predominantly partial-record streamgages (U.S. Geological Survey, 2022). For the 602 total streamgages, the earliest recorded peak streamflow was in 1862.

A history of streamflow data collection in Missouri through 1970 is provided in Skelton and Homyk (1970). They report that the total number of streamgages in Missouri has varied substantially since the earliest continuous streamflow streamgage was established at the Mississippi River at St. Louis, Missouri, in 1857 by Federal agencies. Other early continuous streamgages include stage streamgages along the Missouri and Mississippi Rivers beginning in the late 1870s and the collection of stage along the Osage River beginning in the 1880s. In 1921, the State of Missouri established the Bureau of Geology and Mines to survey water resources of the State in cooperation with the USGS and other agencies. The Bureau of Geology and Mines entered into an agreement with the USGS in 1922 to establish streamgages at 39 stream sites and 5 springs. The first collaborative effort between the U.S. Army Corps of Engineers and the USGS to collect streamgage information in Missouri began in 1928 on the Missouri River and in 1933 on the Mississippi River. The Missouri Highway Commission entered into an agreement with the USGS in 1947 with the primary objective to collect streamflow information in small (<10 square miles) basins in Missouri. During the first year of the program, 12 continuous streamgages were established along with five crest-stage streamgages (CSGs). In 1955 the program was expanded to include 33 continuous streamgages and 88 CSGs. In 1960, 200 low-flow partial-record streamgages were established, and by 1970 the low-flow partial-record program included 250 streamgages.

The number of daily streamflow streamgages and CSGs in Missouri has varied as a result of funding availability, hydrologic events and conditions, and the changing data needs among a variety of State and Federal cooperators. The CSG network peaked in the 1980s, was eliminated between 1984 and 1994 but resumed in 1995, grew to about 50 streamgages in the late 1990s, and has remained relatively consistent through 2020. A notable development in the daily streamgage network in Missouri was the addition of data collection platforms in 1982 to transmit stage data and compute streamflow data in near real time (Blakey and others, 2005). Numbers of daily streamflow streamgages declined in the 1970s through the early 1990s, but daily streamgage network numbers rebounded in the late 1990s and have remained consistent since the early 2000s at about 230 daily record and 280 total streamgages.

The temporal variability in the number of streamgages may contribute to potential bias in evaluating nonstationarity in peak streamflows in Missouri. An additional limitation in evaluating nonstationarity in the streamgage record is the lack of streamgages in small drainage basins. The lack of long-term streamgages in small drainage basins is reflected in the distribution of drainage areas of 602 streamgage basins with any number of peak streamflows (fig. 7). Streamgages were split into groups by peak flow record length, showing that streamgages with longer peak-flow records generally have larger drainage basin areas (fig. 8).

History of Statistical Analysis of Peak Streamflows

Previous studies of the flood characteristics of rural and urban Missouri streams include the determination of annual exceedence probabilities (AEPs) of 90 to 2 percent completed by Searcy (1955) using data through 1952 from 112 streamgages. Sandhaus and Skelton (1968) used data through water year 1965 at 208 streamgages with AEPs computed for selected intervals from 83 to 2 percent. Hauth (1974) used data through water year 1970 at 152 streamgages to calculate AEPs for selected intervals from 50 to 1 percent. Alexander and Wilson (1995) used data through water year 1993 from 278 streamgages to update rural regression equations. Peak-flow estimates in this study were computed for selected intervals from 50- to 0.2-percent AEP. The same independent variables (drainage area and main channel slope) were used by Sandhaus and Skelton (1968), Hauth (1974), and Alexander and Wilson (1995) to develop regression equations. Southard and Veilleux (2014) used data through water year 2012 from 278 streamgages to compute AEPs of 50 to 0.2 percent for ungaged rural basins using the independent variables of drainage area or drainage area and basin shape depending on hydrologic region. Studies to determine flood-frequency estimates for urban basins in Missouri used regression equations that include variables accounting for development and impervious area (Spencer and Alexander, 1978; Sauer and others, 1983; Becker, 1986; Southard and Veilleux, 2014). Peak-flow frequency statistics were updated for selected Missouri streamgages after flooding in the Meramec River Basin in 2016 (Holmes and others, 2016) and throughout southern Missouri after record flooding in April 2017 (Heimann and others, 2018). Peak-flow frequency statistics for selected streamgages in the White River Basin in southern Missouri were calculated using a basin-specific skew for the White River in Missouri and Arkansas (Wagner and others, 2021).

The Missouri peak-flow frequency studies reviewed above assume stationary peak-flow series. Despite the assumption of stationarity, there is wide-ranging evidence for trends in peak streamflows, and in streamflow more generally, in and near Missouri. An upward trend in the number of days above flood categories has been observed across most of Missouri and the Midwest region, driven by precipitation and overall basin wetness (Slater and Villarini, 2016). An analysis of simulated global water-balance components indicates that changes in precipitation from 1905 to 2009 have been the main driver of changes in runoff globally (McCabe and Wolock, 2013). Despite an increase in actual evapotranspiration (ET) and potential evapotranspiration (PET) from 2000 to 2009, increases in runoff are observed as a result of increases in precipitation (McCabe and Wolock, 2013).

Characterizations and examination of trends of streamflows in Missouri commonly are in association with trend analysis of streamflows in the Mississippi River Basin or Missouri River Basin, which have included much of the State. Increasing streamflow has been observed in the Mississippi River Basin since the 1940s (Lins and Slack, 2005; Zhang and Schilling, 2006). Analysis of temporal changes in streamflows for the 1912–2011 period (Wise and others, 2018) indicated lower Mississippi River Basin flows are increasing. Increases in streamflow in the Mississippi River Basin have been attributed to increases in precipitation (Frans and others, 2013; Ivancic and Shaw, 2017) and changes in land use (Zhang and Schilling, 2006). Studies done on the upper Mississippi region indicate a strong consensus of observed streamflow increases (White and Arnold, 2015b; Reidmiller and others, 2018). Olsen and others (1999) examined the relation between the distribution of flood flows in the upper Mississippi River and lower Missouri River and climatic indices. They determined that global climate patterns explained little of the variation in flood peaks in the 1950–96 data period but determined significant upward trends in annual peak streamflows for the lower Missouri, Meramec, and Mississippi Rivers at St. Louis, Mo., streamgages. Olsen and others (1999) conclude that the results challenge the traditional assumptions in hydrology that floods are a sequence of random independently and identically distributed random variables and suggest that water management agencies may benefit from rethinking their paradigm for flood-frequency analysis to allow for flood risk variations with time. Wise and others (2018) determined that monthly mean streamflows of the Lower Missouri River Basin were significantly correlated with precipitation in almost every month of the year, with a peak correlation in the late spring and early summer. Norton and others (2014) examined trends in monthly, seasonal, and annual streamflow for the 1960–2011 period and determined significant upward trends at streamgages in the eastern Missouri River Basin, including Missouri.

Examination of the magnitude of the changes in median annual peak streamflows for streamgages in the southern Midwest affected by flooding in April 2017, including southern Missouri, indicated increases, in general, for each of the 1930–2017, 1956–2017, 1975–2017, and 1989–2017 analysis periods (Heimann and others, 2018). The median increase in peak streamflows was greatest in the 1975–2017 and 1989–2017 periods, with maximum increases of 8–10 percent per year. No streamgages in either the 1975–2017 or 1989–2017 analysis periods had decreases in median peak streamflows. Median changes in annual precipitation for the 1930–2017 period and 1956–2017 periods generally were small (<2 percent) and positive. Changes in annual precipitation, however, provided little explanation for the substantial increase in magnitude of streamflow peaks in the 1989–2017 analysis period and the increase in the frequency of larger magnitude rain events (greater than 2 in.) with time was suggested as a better explanatory variable for the greater positive changes in annual peak streamflows (Heimann and others, 2018). Wagner and others (2014) examined trends in precipitation, streamflow, reservoir pool volume, and reservoir releases at selected locations, including locations in southern Missouri, for 1951–2011. A statistically significant (probability value [p-value] less than or equal to 0.10) upward trend was observed in annual mean and autumn precipitation for the southern Ozark region of Missouri included in the study. Corresponding significant increases in annual mean and annual minimum streamflows were detected at most southern Missouri streamgages included in the study, and trends in annual maximum and seasonal mean daily streamflow were upward but not significant. Upward trends in the frequency of flooding, attributed to changes in seasonal rainfall and temperature (and subsequent increases in snowmelt), were identified in northern and southeastern Missouri by Mallakpour and Villarini (2015). Changes in annual peak streamflow were examined at streamgages across Missouri for a 50-year (water years 1966–2015) and 75-year (water years 1941–2015) period (Levin and Holtschlag, 2022; Sando and others, 2022; Tillery and others, 2022). Predominantly upward monotonic trends in annual peak streamflow were observed within the Missouri River Basin part of the State, many of which were attributed to changes in long-term precipitation and multidecadal climate variability (Sando and others, 2022). Of streamgages in the Upper Mississippi River Basin part of the State, most showed no trend in annual peak streamflow (Levin and Holtschlag, 2022), and no significant (p-value<0.10) monotonic trends in peak streamflow were determined in the southern region of the State (Tillery and others, 2022).

Streamflow events often are associated with change points (abrupt changes in the streamflow time series; Villarini and others, 2009; Ryberg and others, 2020), and this general association also is present in and near Missouri. Upward change points (abrupt increases) in daily mean streamflow in northern Missouri were present in 1968 and 2006 (Ivancic and Shaw, 2017). Positive change points in the median of peak streamflows were observed in the Eastern and Midwestern United States for trend periods 1916–2015, 1941–2015, and 1966–2015 (Ryberg and others, 2020), clustered around the mid-1960s and early 1970s. Most of the trends observed in Missouri were likely or somewhat likely upward, and clustered mostly in the northern half of the State. The distinct spatial pattern in increasing and decreasing change points across the country indicated that regional climate changes were the driver of observed changes in peak streamflows. The clusters of upward change points in the Midwest and Northeast were coincident with areas of large increases in observed precipitation (Ryberg and others, 2020). Changes in annual peak streamflow were examined at streamgages across Missouri for a 50-year (water years 1966–2015) and 75-year (water years 1941–2015) period (Levin and Holtschlag, 2022; Sando and others, 2022; Tillery and others, 2022). Predominantly upward change points in annual peak streamflow were observed within the Missouri River Basin part of the State (Sando and others, 2022), although most of the identified change points were nonsignificant (p-value greater than 0.10). Of streamgages in the Upper Mississippi River Basin part of the State, most showed no change point, with a handful indicating upward change points and one downward change point in each time period (Levin and Holtschlag, 2022). No significant (p-value<0.10) change points in peak streamflow were present in the southern region of the State (Tillery and others, 2022).

Review of Research Relating to Climatic Variability and Change

This section discusses historical floods across Missouri and characteristics of the driving factors and landscape responses associated with these floods. The driving factors include climatic forces (temperature and precipitation) that affect large-scale streamflow patterns.

Effects of Projected Climate Changes on Streamflow and Floods

Streamflow and flooding are affected by many climate-dependent hydrologic conditions, including antecedent soil moisture, magnitude and frequency of precipitation, and snowpack processes (Sharma and others, 2018). Changes in climate leading to changes in these conditions may affect future streamflow. Increasing temperatures and changes in precipitation affect ET and soil moisture, and increases in magnitude and intensity of precipitation can increase the runoff potential and hydrologic response of soils throughout the State (Reidmiller and others, 2018). A study of the effects of a range of predicted climate change scenarios on a small (89 square miles) basin in central Missouri indicated ET increases from +7.2 to +19.4 percent, and annual streamflow decreases from −5.9 to −26.8 percent (Sunde and others, 2017). Simulations for 2040–69 and 2070–2100 also indicated substantial decreases to summer streamflow and large increases of fall, spring, and summer ET. Changes in temperature are expected to contribute to decreasing soil moisture across much of the Midwest, leading to drier soil levels and more intense droughts, particularly during summer (Walsh and others, 2014; Reidmiller and others, 2018; Frankson and others, 2022). Villarini and Zhang (2020) examined the projected changes in extreme runoff across the continental United States based on eight global climate change models. Extreme runoff was indicated to increase consistently in the southeastern United States, including Missouri, with the extremes strongest in March through May and December through January. Studies on the upper Mississippi region indicate a strong consensus of increase in mean, low, and peak streamflow, although projected streamflow levels are less clear (White and Arnold, 2015b). Studies on the Missouri River region reveal moderate increases in streamflow during the past century (White and Arnold, 2015a). Naz and others (2016) predict increases in runoff for spring and summer and a mix of increases and decreases in different parts of Missouri for winter and fall.

Data

The focus of the analysis presented in this report is on the temporal properties of annual peak streamflows from selected USGS streamgages in and near Missouri. To enhance understanding of the peak-flow data, analyses were supplemented with daily streamflow data for those streamgages where such data were available. Peak-flow data were also supplemented with data from a gridded monthly water-balance model with values that were averaged over the basin contributing to the selected streamgages. Details regarding the selection of the streamgages and the processing of these data are provided in Ryberg and others (2024). Streamflow and climate data used as input for analyses are provided in Marti and others (2024).

Annual peak-flow data compiled for all streamgages came from the USGS National Water Information System database (U.S. Geological Survey, 2022). Four periods were selected for analysis: (1) a 100-year period, water years 1921–2020; (2) a 75-year period, water years 1946–2020; (3) a 50-year period, water years 1971–2020; and (4) a 30-year period, water years 1991–2020. Streamgages included in the study have peak-flow data for at least 80 percent of the period of record and included peak streamflows in at least 1 of the first 2 years of record. Streamgages were screened for potential regulation by dams or water diversions using existing streamflow qualification codes within the National Water Information System database (U.S. Geological Survey, 2022) and a dam impact metric described in Marti and Ryberg (2023). Regulated streamgages identified by the screening process were removed from the study. After data screening, there remained 18 streamgages in the 100-year period, 33 streamgages in the 75-year period, 48 streamgages in the 50-year period, and 56 streamgages in the 30-year period. All streamgages in the 100-, 75-, and 50-year trend periods and 55 streamgages in the 30-year trend period have daily streamflow data. The climate data used in this report were compiled for each drainage basin from simulations of the monthly water-balance model (MWBM) (McCabe and Wolock, 2011) for the period 1900–2020 (Wieczorek and others, 2022). Climate data were assessed for the same trend periods as peak streamflow. These data consist of monthly time series estimates of the following hydroclimatic variables: temperature, precipitation, PET, actual ET, snowfall, soil moisture storage, snow water equivalent, and runoff on a nominally 5-kilometer by 5-kilometer grid for the conterminous United States. The precipitation and temperature values used in the MBWM simulations are observed data obtained from the nCLIMGRID dataset (Vose and others, 2015). All the other monthly time series are modeled output from the MWBM (McCabe and Wolock, 2011). The modeled streamflow incorporates the effects of all the main hydroclimatic processes, including precipitation as rain and snow, water storage in the snowpack and in the soil, and output as ET and streamflow, but does not reflect the effects of land use or other anthropogenic changes, and thus trends in its values are due to climate effects only. For use in this analysis, the mean of the gridded values for the basin upstream from each selected streamgage was used to create a time series for each hydroclimatic variable. Further details on the MWBM data and its processing for use in this study are available in Ryberg and others (2024).

Methods

The annual peak streamflow, daily streamflow, and climate data for the selected streamgages were analyzed separately for each streamgage and trend period. Analyses of the peak streamflows consisted of tests for autocorrelation, monotonic trends, change points, quantile trends, and seasonality. Statistical analysis of daily streamflow consisted of an evaluation of the flow regime, seasonality, center of volume, and peaks-over-threshold (POT) analysis. Analysis of the climate metrics included tests for monotonic trends and several different visualizations including raster-seasonality plots, boxplots, and Budyko plots (Budyko, 1974). The analysis methods applied are described in Ryberg and others (2024).

The significance of trend test results in this report are presented using a likelihood approach proposed by Hirsch and others (2015) as an alternative to simply reporting significant trends by using an arbitrary p-value cutoff point. Trend likelihood values were determined using the p-value reported by each test using the equation trend likelihood = 1−(p-value)/2. When the trend likelihood value is between 0.85 and 1.0 (that is, the chance of the trend occurring in the specified direction is at least 85 out of 100), it is considered to be likely upward or likely downward. When the trend likelihood value associated with the trend is between 0.70 and 0.85 (that is, the chance of the trend occurring in the specified direction is between 70 and 85 out of 100), it is considered to be somewhat likely upward or somewhat likely downward. When the trend is <0.70 (that is, the chance of the trend being either upward or downward is <70 out of 100), it is considered to be about as likely as not. The p-values of all statistical hypothesis tests are reported in the associated USGS data release Marti and others (2024). Record length affects the statistical significance of a trend. The statistical significance of an estimated trend with the same underlying statistical properties increases with record length. The primary way trends are evaluated in this report is through statistical significance but to provide an additional perspective, trend magnitudes are also considered.

Results

Changes in peak streamflow, daily streamflow, and climate metrics were determined for all study streamgages across Missouri during all four trend periods. The main focus of this report is investigating changes in peak streamflows in Missouri. The examination of daily streamflow data supports this focus by providing context on whether similar changes are reflected in daily streamflows, and provides an alternative way of evaluating peak streamflows using a POT analysis. The examination of climate metrics aids in potential attribution of peak-flow trends to climate effects. This section summarizes the results of these analyses and describes observed spatial and temporal patterns. Detailed results, which consist of plots of peak streamflow, daily streamflow, and climate metric trend analyses for individual streamgages and tables of trend analysis statistics, are available in Marti and others (2024).

Annual Peak Streamflow

The annual peak-flow series for each streamgage were analyzed using the statistical analyses discussed in Ryberg and others (2024) for each of the four trend periods. Results that were informative in Missouri were selected for presentation in this section and consist of testing for the presence of a monotonic trend, change point in the median, trend in peak-flow quantiles, and trend in seasonality.

Monotonic Trends in Peak Streamflow

The peak-flow series for each streamgage in a given trend period were evaluated for the presence of a monotonic trend using the Mann-Kendall test (Ryberg and others, 2024). A monotonic trend is one in which the direction of the trend does not reverse over time and, unlike a linear trend, may include nonlinearities as long as they are monotonic. For example, the peak-flow series at USGS streamgage 07019000 (Meramec River near Eureka, Mo.) for the 100-year trend period has a visually strong, upward trend of 212 cubic feet per second per year (fig. 9). Because the p-value of the trend test is 0.003, the trend likelihood value is approximately 1 and, therefore, the trend is considered likely upward. Although the trend test is for a monotonic trend, a linear trend line (Ryberg and others, 2024) is shown in figure 9 to visually demonstrate the direction and an estimate of the magnitude of the peak-flow trend.

Most streamgages in Missouri for the 100-,75-, and 50-year trend periods exhibit an increase in peak streamflow magnitude. Of streamgages in the 100-, 75-, and 50-year trend periods, 77 to 94 percent exhibit likely or somewhat likely upward trends (table 2). Only two streamgages in all three trend periods exhibits a downward trend, and both are in the 75-year trend period. The streamgages with upward trends are somewhat evenly distributed throughout the State (fig. 10). The 30-year trend period has the fewest upward trends, with only 37 percent of streamgages exhibiting an upward trend, and these streamgages are mostly concentrated in the southwestern part of the State (fig. 10). More streamgages exhibit no trend for the 30-year trend period than for any other period, and most of these are located in the northern half of the State and mixed with a small number of streamgages with likely or somewhat like downward trends (fig. 10).

To compare trend magnitudes across streamgage basins of different sizes, trend slopes were divided by the median peak streamflow and converted to a percentage. The resulting trend magnitude represents the yearly change in peak streamflow as a percentage of the median peak streamflow. The median trend magnitude is similar for the 100-, 75-, and 50-year trend periods, with the 30-year trend period exhibiting the smallest median but largest distribution (fig. 11). The median normalized trend magnitude values are 0.40 percent per year at the 100-year trend period, 0.53 percent per year at the 75-year trend period, 0.55 percent per year at the 50-year trend period, and 0.32 percent per year at the 30-year trend period. These values equate to a median increase in peak streamflow of 40 percent over 100 years, 40 percent over 75 years, 28 percent over 50 years, and 10 percent over 30 years. The largest percent increase in the median peak streamflow during any trend period is for USGS streamgage 06930000 (Big Piney River near Big Piney, Mo.) at the 30-year trend period, with a trend of approximately 3.1 percent over 30 years, equating to a 93-percent increase in the peak streamflow from 1991 to 2020.

Table 2.    

Percentage of Missouri streamgages in each likelihood category and trend periods for selected statistical results of peak-flow analysis.

[<, less than]

Table 2.    Percentage of Missouri streamgages in each likelihood category and trend periods for selected statistical results of peak-flow analysis.

Trend period	Total streamgages	Percent likely upward (likelihood value: 0.85–1.0)	Percent somewhat likely upward (likelihood value: 0.70–0.85)	Percent upward	Percent about as likely as not (likelihood value<0.70)	Percent likely downward (likelihood value: 0.85–1.0)	Percent somewhat likely downward (likelihood value: 0.70–0.85)	Percent downward
Monotonic trends
100	18	83	11	94	6	0	0	0
75	33	73	18	91	9	0	0	0
50	48	52	25	77	19	0	4	4
30	56	25	12	37	48	2	12	14
Median change points
100	18	72	11	83	17	0	0	0
75	33	55	27	82	18	0	0	0
50	48	23	31	54	44	0	2	2
30	56	18	20	38	57	5	0	5
90-percent quantile
100	18	28	28	56	28	0	17	17
75	33	33	18	51	48	0	0	0
50	48	25	17	42	42	8	8	16
30	56	23	12	35	41	7	16	23
Peak-flow seasonality
100	18	6	6	12	50	17	22	39
75	33	15	15	30	39	18	12	30
50	48	46	35	81	17	0	2	2
30	56	9	20	29	50	12	9	21

Peak-Flow Change Points in Median

Changes in peak streamflow with time may be gradual trends or caused at least in part by abrupt changes, or change points. In addition to evaluating the annual peak-flow series for the presence of a monotonic trend, the series were evaluated for the presence of a single change point (that is, the most significant such point) in the median peak streamflow using the Pettitt test (Ryberg and others, 2024). For example, at USGS streamgage 05495000 (Fox River at Wayland, Mo.), an upward change point in the median peak streamflow was found in 1975 for the 100-year trend period (fig. 12). Because the p-value of the test is 0.0141, the change point likelihood value is approximately 0.99 and is therefore considered likely upward.

Similar to the monotonic trend results, most of the streamgages in the 100- and 75-year trend period have likely or somewhat likely upward change points, with the extreme southeastern part of the State exhibiting the fewest likely upward change points (table 2; fig. 13). Of streamgages in the 50- and 30-year trend periods, 54 and 38 percent, respectively, exhibit likely or somewhat likely upward change points (table 2) in peak streamflows. Most of these streamgages are in the southern half of the State, with a small grouping of sites with likely upward change points in northwestern Missouri for the 50-year trend period (fig. 13).

Temporally, most of these change points for the 100- and 75-year trend periods occur in the 1970s and early 1980s (fig. 14). All upward change points at the 50-year trend period occur between 1980 and 2014, with two clusters from the late 1970s and early 1980s and from 2003 to 2014 (fig. 14). Of the 27 total change points in the 50-year trend period, 11 (41 percent) occur in either 2006 or 2007. All but one of the upward change points at the 30-year trend period occur between 2006 and 2015, with most (15 of 24 streamgages, 63 percent) occurring in 2006 and 2007 (fig. 14). These temporal results are consistent with the results of other studies that have determined upward change points in streamflow in the Midwest and Eastern United States (Ivancic and Shaw, 2017; Ryberg and others, 2020).

The magnitude of the median peak streamflow before and after a change point was evaluated, and to compare change point magnitudes across streamgage basins of different sizes, change point magnitudes were divided by the median peak streamflow and converted to a percentage. The resulting change point magnitude represents the change in peak streamflow as a percentage of the median peak streamflow. Medians of the normalized change point magnitudes vary with trend period, with the largest median change point of about 33 percent occurring in the 75-year trend period (fig. 15).

Linear Quantile Trends

In addition to identifying monotonic trends in the median peak streamflow over time, trends in other quantiles of the peak-flow series also were evaluated. A linear quantile regression on log-transformed peak streamflow was applied to compute linear trends of multiple quantiles, the results of which provide flow-normalized trends in units of years^-1 (Ryberg and others, 2024). The 90-percent quantile trend results were selected for analysis because this exceedance probability is close to design criteria. These results, which correspond to the 10-percent exceedance probability, are compared to the 50-percent quantile results, which are similar to the monotonic trends in the median presented in the “Monotonic Trends in Peak Streamflow” section. The 50-percent quantile results differ slightly from the monotonic trend results owing to different fitting methods (Ryberg and others, 2024). Consider USGS streamgage 06918440 (Sac River near Dadeville, Mo.) for the 50-year trend period, where the quantile trend slopes increase monotonically for all quantiles (fig. 16). The trend slope of the 50-percent quantile is approximately equal to the monotonic trend (73 and 64 cubic feet per second, respectively). The 90-percent quantile trend is 79 cubic feet per second.

To obtain the 50-percent and 90-percent quantile trends in percent per year, the original trends in years^-1 were multiplied by the natural log of 10 and then multiplied by 100. The 50-percent quantile trends are larger than the 90-percent quantile trends for most streamgages in the 100-year trend period (fig. 17), meaning the 50-percent quantile peak streamflow increased proportionally more during the 100-year trend period than the 90-percent quantile peak streamflow at most streamgages. The 50-percent quantile trends for the 75-, 50-, and 30-year trend periods are larger than the 90-percent quantile trends for 39 to 58 percent of streamgages (fig. 17). Spatially, the patterns of trends in the 90-percent quantile somewhat reflect the spatial patterns of the monotonic trends (figs. 10 and 18), but with substantially more streamgages exhibiting downward trends or no trends (for example, in southeastern and central Missouri in the 75-year trend period).

Peak-Flow Seasonality

The analysis of peak-flow seasonality—when peak streamflows occur during the year—in this study identifies the distribution of and trends in the seasonal timing of peak streamflows. For example, USGS streamgage 05514500 (Cuivre River near Troy, Mo.; fig. 19A) has a median day of peak streamflows in late April for the 30-year trend period; the unimodal distribution and timing of the peak streamflows at this streamgage indicate that the driver of peak streamflows is primarily spring and early summer precipitation events.

Each peak-flow series was evaluated for a trend in the seasonality of peaks by using a Mann-Kendall test (Ryberg and others, 2024). The example analysis at Cuivre River near Troy, Mo, exhibits a likely trend in peak-flow seasonality shifting towards earlier peaks for the 30-year trend period (fig. 19B). Although this streamgage exhibits a likely earlier trend in peak-flow timing at this trend period, it does not exhibit a monotonic trend in median peak streamflows—the time at which peak streamflows occur has shifted during the same 30-year period during which the magnitudes have remained largely the same.

Results of the trend analysis in seasonality vary across trend periods, with one-half of the streamgages in the 100-year trend period exhibiting no trend in peak streamflow seasonality (table 2), and only 22 percent of streamgages (four streamgages) exhibiting a likely trend, three of which had timing of peaks trending towards later in the water year (fig. 20). Streamgages in the northern half of the State exhibit peak streamflows trending toward later in the water year for the 75-year trend period, with streamgages in the southern half of the State exhibiting peak streamflows trending toward earlier in the water year. The 50-year trend period, in contrast, exhibits a widespread trend towards peaks that occur later in the water year, with 81 percent of streamgages exhibiting a likely or somewhat likely trend towards later peaks (table 2; fig. 20). Streamgages in the 30-year trend period exhibit a cluster of trends towards later peaks in the northern part of the State, and a mix of earlier or no trend streamgages in the southern two-thirds of the State.

Although informative, the seasonality results presented here use the likelihood from a nonperiodic Mann-Kendall test to evaluate trends in peak-flow seasonality (Ryberg and others, 2024). The seasonality of annual peak streamflows has a continuous periodicity over time, and separating the date of occurrence based only on water year to evaluate linear changes over time may lead to spuriously large changes during a trend period. Further analyses evaluating the changes in peak-flow seasonality using analyses more suited for continuous, periodic time series data are warranted.

Daily Streamflow

Although the main focus of this report is investigating changes in peak streamflows in Missouri, the examination of daily streamflow data supports that focus by providing context on whether similar changes are reflected in daily streamflows, and by providing an alternative way of evaluating peak streamflows by using POT analysis. Daily streamflow records do not exist for every streamgage examined for peak streamflows, and some daily streamflow records are incomplete. Changes in daily streamflow were examined using several different analyses, as detailed in Ryberg and others (2024), and the following results are presented and discussed for the POT analysis. Other results not shown consist of raster-seasonality plots, regime plots, and center-of-volume analysis. Raster-seasonality plots display the mean daily streamflow for every day in the period of record, colored by the magnitude of the streamflow and as such enable the viewer to identify patterns of temporal change across the water year for the entire period of record. Regime plots provide a visual summary of various statistical properties of the annual peak streamflows at a streamgage during the period of analysis. The center-of-volume analysis identifies the days of the year in which the 25th, 50th, and 75th percentiles of annual streamflow have been reached. Linear trends in these percentiles over time indicate a change in the timing of the annual daily streamflow distribution, which can be helpful for understanding changes in hydrologic regime. All plots and results not presented in detail here can be viewed for individual streamgages in Marti and others (2024).

Peaks-Over-Threshold Analysis

The POT analysis presented in this report is a change point analysis that tests whether a change point is present in the number of streamflow events per year that exceed a certain threshold. As such, this analysis focuses on the frequency of high-flow events in addition to their magnitude. Two thresholds were used: (1) the daily streamflow value above which there are, on average, two events per year (POT2), and (2) the value above which there are four events per year (POT4); for both thresholds, no more than one event in a specific window of time was allowed to preserve the independence of events (Ryberg and others, 2024). For example, at USGS streamgage 07186000 (Spring River near Waco, Mo.), there is a change point in the median of peaks over the POT4 threshold in 1972 for the 75-year trend period (fig. 21). There is a change point in the POT2 in 1982 for this streamgage (not shown) and a change point in the median of peak streamflows in 1972 (Marti and others, 2024).

About one-half of the streamgages exhibit an upward change point at the 100-year trend period for POT2 and POT4, and 64 and 57 percent exhibit an upward change point at the 75-year trend period, respectively (table 3; figs. 22 and 23). The upward change points in the 75-year trend period, for POT2 and POT4, are present throughout the State, with fewer present in the southeast corner. Far fewer streamgages, only 17 to 27 percent, exhibit an upward change point at the 50- and 30-year trend periods (table 3; figs. 22 and 23), with 65–76 percent of streamgages exhibiting no trend. The POT analysis, therefore, reveals streamgages exhibiting increasing frequency of high flows for the 100- and 75-year trend periods, but not the 50- or 30-year trend periods.

Table 3.    

Percentage of streamgages in Missouri in each likelihood category for a given trend period for the peaks-over-threshold change point results.

[<, less than]

Table 3.    Percentage of streamgages in Missouri in each likelihood category for a given trend period for the peaks-over-threshold change point results.

Period	Total streamgages	Percent likely upward (likelihood value: 0.85–1.0)	Percent somewhat likely upward (likelihood value: 0.70–0.85)	Percent upward	Percent about as likely as not (likelihood value<0.70)	Percent likely downward (likelihood value: 0.85–1.0)	Percent somewhat likely downward (likelihood value: 0.70–0.85)	Percent downward
Two events per year
100	18	44	6	50	33	6	11	17
75	33	52	12	64	36	0	0	0
50	48	8	15	23	65	2	8	10
30	55	4	13	17	76	0	5	5
Four events per year
100	18	28	28	56	44	0	0	0
75	33	36	21	57	39	0	3	3
50	48	6	21	27	65	0	6	6
30	55	4	18	22	67	4	5	9

Climate

Observed and modeled climate data for the basin upstream from each streamgage in all four trend periods were analyzed using the methods discussed in Ryberg and others (2024). Results that were informative in Missouri were selected for presentation here, and consisted of trends in annual temperature, annual precipitation, seasonal precipitation, annual snow to precipitation ratio, annual PET, annual PET to precipitation ratio, annual modeled streamflow, and annual soil water storage. Precipitation and temperature data are observed, and all other climate data were modeled using the MWBM with the inputs of the observed temperature and precipitation data as described in the “Data” section. Modeled streamflow, referred to in the MWBM output and here as “runoff,” incorporates the effects of all the main hydroclimatic processes, including precipitation as rain and snow, water storage in the snowpack and in the soil, and outputs as ET and streamflow. However, modeled streamflow does not reflect the effects of land use or other anthropogenic changes, and thus trends in its values are due to climatic effects only. Annual temperature has generally increased in study basins across the State for all trend periods (fig. 24). The 100-year trend period is dominated by somewhat likely upward trends in temperature, with 56 percent of basins exhibiting a somewhat likely upward trend and 22 percent a likely upward trend (table 4). All other trend periods are dominated by likely upward trends, with 100 percent of basins in the 75- and 50-year trend periods exhibiting likely upward trends, and 70 percent exhibiting likely upward trends at the 30-year trend period (table 4). The somewhat likely upward trends that make up 27 percent of basins at the 30-year trend period are mostly in the northern third of the State (fig. 24). The median (50-percent quantile) of trend magnitudes of the basins is 0.00369 °F per year (0.369-°F increase over 100 years) for the 100-year trend period, 0.0184 °F per year for the 75-year trend period (1.38-°F per year over 75 years), 0.0378 °F for the 50-year trend period (1.89-°F per year over 50 years), and 0.0411 °F per year at the 30-year trend period (1.23-°F increase over 30 years) (table 5).

Table 4.    

Percentage of Missouri basins in each likelihood category and trend period for selected climate trends.

[<, less than]

Table 4.    Percentage of Missouri basins in each likelihood category and trend period for selected climate trends.

Period	Total streamgages	Percent likely upward (likelihood value: 0.85–1.0)	Percent somewhat likely upward (likelihood value: 0.70–0.85)	Percent upward	Percent about as likely as not (likelihood value<0.70)	Percent likely downward (likelihood value: 0.85–1.0)	Percent somewhat likely downward (likelihood value: 0.70–0.85)	Percent downward
Annual temperature versus water year
100	18	22	56	78	11	0	11	11
75	33	100	0	100	0	0	0	0
50	48	100	0	100	0	0	0	0
30	56	70	27	97	4	0	0	0
Annual precipitation versus water year
100	18	100	0	100	0	0	0	0
75	33	100	0	100	0	0	0	0
50	48	54	38	92	8	0	0	0
30	56	16	39	55	45	0	0	0
Annual snow/precipitation ratio versus water year
100	18	0	0	0	33	39	28	67
75	33	0	0	0	0	88	12	100
50	48	0	0	0	0	96	4	100
30	56	0	0	0	9	59	32	91
Annual potential evapotranspiration/precipitation ratio versus water year
100	18	0	0	0	0	94	6	100
75	33	0	0	0	0	82	18	100
50	48	0	0	0	42	10	48	58
30	56	0	2	2	91	0	7	7
Annual modeled runoff versus water year
100	18	89	11	100	0	0	0	0
75	33	94	3	97	3	0	0	0
50	48	15	48	63	38	0	0	0
30	56	12	25	37	59	0	4	4

Table 5.    

The 25-, 50-, and 75-percent quantiles of climate trend magnitudes for all streamgage basins.

Table 5.    The 25-, 50-, and 75-percent quantiles of climate trend magnitudes for all streamgage basins.

Period	25-percent quantile	50-percent quantile	75-percent quantile
Annual temperature (degrees Fahrenheit per year)
100	0.00292	0.00369	0.00445
75	0.0166	0.0184	0.0214
50	0.0327	0.0378	0.0412
30	0.0359	0.0411	0.0491
Annual precipitation (inches per year)
100	0.0419	0.0558	0.0602
75	0.0754	0.0902	0.105
50	0.0622	0.0861	0.0996
30	0.0229	0.0942	0.137
Ratio of annual snow and total precipitation (percent per year)
100	−0.0157	−0.0108	−0.00605
75	−0.0457	−0.0389	−0.023
50	−0.0627	−0.0521	−0.0446
30	−0.0895	−0.0772	−0.0557
Annual potential evapotranspiration (inches per year)
100	−0.00287	−0.000709	0.000629
75	0.0114	0.013	0.0146
50	0.0218	0.0281	0.0319
30	0.0501	0.0548	0.0604
Ratio of annual potential evapotranspiration and precipitation (percent per year)
100	−0.117	−0.104	−0.0944
75	−0.174	−0.124	−0.11
50	−0.136	−0.0908	−0.0465
30	−0.0824	−0.0384	0.0656
Annual modeled runoff (inches per year)
100	0.0283	0.0393	0.0436
75	0.0569	0.0617	0.0713
50	0.0203	0.0388	0.0542
30	−0.0187	0.047	0.109

Trends in annual precipitation are generally upward across the State for the 100-, 75-, and 50-year trend periods and in the southern half of the State for the 30-year trend period (fig. 25). For the 100- and 75-year trend period, 100 percent of basins have a likely upward trend in annual precipitation (table 4). For the 50-year period, 92 percent of basins exhibit a likely or somewhat likely upward trend, with 55 percent exhibiting the same for the 30-year trend period (table 4). No study basins exhibit a downward trend in annual precipitation at any trend period. The median trend magnitude of the basins ranges from 0.0558 inch per year at the 100-year trend period (5.58-in. increase over 100 years) to 0.0942 inch per year at the 30-year trend period (2.826-in. increase over 30 years) (table 5).

Trends in precipitation across the State vary by season, generally increasing in most months and trend periods (fig. 26). Spring exhibits the largest increases, including in the southern half of the State at the 30-year trend period. Fall exhibits mostly upward trends at the 100- and 75-year trend periods, but mostly downward trends at the 50- and 30-year trend periods (fig. 26).

The proportion of precipitation falling as snow has largely decreased in study basins across the State, which is expected in response to increasing temperature (table 4, fig. 27). Less precipitation may fall as snow also because of seasonal shifts in timing, although precipitation trends presented previously indicate generally increasing precipitation trends across most seasons outside of fall at the shorter trend periods. The 75- and 50-year trend periods, in particular, are dominated by downward trends, with no basin exhibiting an upward trend. The median trend magnitude of the basins ranges from −0.0108 percent per year at the 100-year trend period (1.08-percent decrease over 100 years) to −0.0772 per year at the 30-year trend period (2.316-percent decrease over 30 years) (table 5).

Because PET is a modeled quantity that depends only on temperature for its climatological data input in many models, including MWBM, trends in PET across the State follow those in temperature and thus are largely positive for the basins in the 75-, 50-, and 30-year trend periods (not shown) (Marti and others, 2024). The 100-year trend period is the only trend period with negative trends in PET. The median trend magnitude for all basins ranges from −0.000709 inch per year at the 100-year trend period (0.709-in. decrease over 100 years) to 0.0548 inch per year at the 30-year trend period (1.644-in. increase over 30 years) (table 5).

Changes in the ratio of PET to annual precipitation vary by trend period (fig. 28). At the 100-year trend period, where changes in temperature are smaller and all basins experienced an increase in annual precipitation, the ratio has decreased. At the 30-year trend period, where temperature has increased across most of the State and annual precipitation has only increased in the southern half of the State, the PET to annual precipitation ratio exhibits mostly no trends. For the 75- and 50-year trend periods, despite the consistent and substantial upward trend in PET across the State (not shown), the ratio of PET to annual precipitation has decreased in every study basin for the 75-year trend period and 58 percent of the 50-year trend period basins (table 4, fig. 28). Decreasing PET to precipitation ratio trends approximately follow the spatial distribution of increasing precipitation trends across the State and trend periods (fig. 25), which indicates that increases in precipitation have overwhelmed the relatively smaller increases in PET over much of the State for the 75- and 50-year trend periods. According to the Budyko (1974) framework, a decreasing ratio of PET to precipitation indicates basins that are moving toward a wetter, more energy-limited hydrologic regime. This move is characterized by a decreasing ratio of actual ET to precipitation and an increasing ratio of runoff to precipitation. Where the precipitation is steady or increasing, an increasing ratio of runoff to precipitation implies an increase in streamflow.

As expected, according to the implications of the observed PET and precipitation trends within the Budyko (1974) framework, modeled annual runoff trends are generally positive across the State for the 100- and 75-year trend periods and in the southern half of the State for the 50- and 30-year trend periods (tables 4 and 5; fig. 29). Increases in modeled annual runoff are observed in the same geographic areas where there are observed increases in annual precipitation. The median trend magnitude of the basins ranges from 0.0388 inch per year at the 50-year trend period (1.94-in. increase over 50 years) to about 0.0617 inch per year at the 75-year trend period (4.63-in. increase over 75 years) (table 5). These trend magnitudes compare to the median of the mean annual modeled runoff of 15.9 in. for the 50-year trend period and 14.9 in. for the 75-year trend period (Marti and others, 2024).

Discussion and Implications for Peak-Flow Frequency Analysis

Peak streamflows have generally increased in magnitude across Missouri at the 100-, 75-, and 50-year trend periods, and the southern half of the State at the 30-year trend period (fig. 10). The typical magnitude of these trends is substantial at the longer trend periods, with a median trend magnitude (normalized by the median peak streamflow) that equates to a 40-percent increase in the median peak streamflow over 100 years, a 40-percent increase over 75 years, a 28-percent increase over 50 years, and a 10-percent increase over 30 years (fig. 11). Changes in the 90-percent quantile peak-flow magnitude are not as substantial, showing consistent increases mainly in the southern part of the State in the 50- and 30-year trend periods. Comparing the 90-percent quantile trends to the trends in median peak streamflow indicates that changes in peak streamflows closer to the magnitude of design peak streamflows may not be increasing as much as indicated by the median peak-flow trends. Clusters of upward change points in the median of peak streamflows were present in the 1970s and 1980s for the 100- 75-, and 50-year trend periods and around 2006 and 2007 for the 50- and 30-year trend periods (figs. 13 and 14). The timing of these change point clusters agrees with previous analyses of change points in Missouri, the Midwest, and the conterminous United States (McCabe and Wolock, 2002; Ivancic and Shaw, 2017; Ryberg and others, 2020).

Changes in peak streamflow seem to be driven by increasing precipitation as seen spatially in annual and seasonal precipitation (figs. 25 and 26), which increases soil water moisture and runoff (fig. 29). These increases in precipitation are occurring despite higher temperatures (fig. 24), which are driving increases in PET for the 75-, 50-, and 30-year trend periods (table 4). Similar conditions have been observed in other areas (McCabe and Wolock, 2013). Highly significant positive relations were observed between the peak-flow series and annual precipitation, winter and spring precipitation, and annual modeled runoff (table 6), especially at the 30-year trend period.

In addition to increases in the magnitude of peak streamflows, the frequency of high flows (as measured by daily streamflows above a threshold) has increased at many streamgages in Missouri during the 100- and 75-year trend periods. Of streamgages at the 100- and 75-year trend periods, 50 to 64 percent exhibit an upward change point for the POT2 and POT4 thresholds (table 3). However, most of the streamgages exhibit no change point in either threshold for the 50- and 30-year trend period. Although the frequency of high flows in some areas of Missouri has increased, these increases are not as widespread as increases in trend magnitude.

Whereas widespread increases in peak streamflow were observed across the State for the 100-, 75-, and 50-year trend periods and in southern Missouri for the 30-year trend period, changes in peak-flow seasonality follow different spatial patterns (fig. 20). This difference in pattern may indicate different drivers for the changes in peak-flow seasonality than for increases in peak streamflows, such as seasonal precipitation. For example, the nearly Statewide trend towards peaks occurring later in the water year at the 50-year trend period is likely related to the distinct decrease in fall precipitation at the same trend period (figs. 20 and 26). Decreases in fall precipitation, which occur mostly at the beginning of the water year, could result in changes to the distribution of peak streamflows throughout the water year.

The widespread prevalence of nonstationarity in peak streamflow in Missouri has important implications for peak-flow frequency analysis. Statistical methods used to estimate flood magnitude for a given AEP assume that peak streamflows are stationary (that is, they represent a sample from a stationary random hydrologic process). Observations of trends and change points in peak streamflow in Missouri challenge this assumption.

Long streamgage records are helpful in peak-flow frequency analysis owing to the length of data they can provide. However, because of the presence of trends with and without change points, a nonstationary analysis may be appropriate, depending on the expectation regarding future conditions. If past nonstationarities are expected to repeat or continue in the future and the peak-flow frequency estimates are being used for some purpose that extends far into the future, then the use of the entire nonstationary record may be the most reasonable. However, if the present trend (without a change point) or post-change point conditions are expected to continue, then those conditions warrant consideration for design.

Increases in peak streamflow in Missouri seem to be driven largely by increases in precipitation. Annual mean precipitation is projected to increase across the State, particularly for winter and spring, and the occurrence of extreme precipitation events also is expected to increase in the future (Frankson and others, 2022). If precipitation continues to increase as expected, peak-flow frequency estimates based on older records may no longer represent the hydrologic regime of today or the future.

In addition to changes in climate, land-use effects such as urbanization are an important factor to consider when investigating changes in peak streamflow, particularly for urban areas. An understanding of urbanization and its effects on peak streamflows may be crucial for better understanding nonstationary parts of the Missouri streamgaging network.

Summary

This report characterizes changes in peak streamflow in Missouri and the relation of these changes to climatic variability. It is part of a larger study undertaken by the U.S. Geological Survey to assess potential nonstationarity in peak streamflows in the Central United States. Various analyses and statistical approaches are employed to characterize potential changes. Annual peak streamflow, daily streamflow, and gridded climatic data were examined across four trend periods (water years 1921–2020, 1946–2020, 1971–2020, and 1991–2020) for trends, change points, and other statistical properties indicative of changing conditions. Peak streamflow magnitude has increased at most streamgages across the state in the 100-, 75-, and 50-year trend periods. At least 77 percent of streamgages in the 100-, 75-, and 50-year trend periods exhibit an upward monotonic trend in peak streamflow magnitude, with no streamgages exhibiting a downward trend. At the 30-year trend period, 37 percent of streamgages exhibit an upward trend, clustered mostly in southwestern Missouri, with the streamgages in northern and southeastern Missouri largely exhibiting no trend. The median trend magnitude (normalized by the median peak streamflow) equates to a 40-percent increase in the median peak streamflow over 100 years (1921–2020), a 40-percent increase over 75 years (1946–2020), a 28-percent increase over 50 years (1971–2020), and a 10-percent increase over 30 years (1991–2020). Changes in the 90-percent quantile peak streamflow magnitude are not as substantial, showing consistent increases mainly in the southern part of the State in the 50- and 30-year trend periods. Comparing the 90-percent quantile trends to the trends in median peak streamflow indicates that changes in peak streamflows closer to the magnitude of design peak streamflows may not be increasing as much as indicated by the median peak streamflow trends.

Change points in peak streamflow magnitude generally follow that of the monotonic trends, with upward change points throughout most of the State at the 100- and 75-year trend periods and southern Missouri at the 30-year trend period. Temporally, the clusters of change points in the 1970s through 1980s for the 100-, 75-, and 50-year trend periods and around 2006 and 2007 for the 50- and 30-year trend periods agree with other findings of upward change points in Missouri, the Midwest, and the conterminous United States.

Peaks-over-threshold (POT) analysis, which evaluates changes in the frequency of peak streamflows over a certain threshold, was applied using two thresholds: (1) the daily streamflow value above which there are, on average, two events per year (POT2); and (2) the daily streamflow value above which there are four events per year (POT4). About one-half of the streamgages exhibit an upward change point at the 100-year trend period for POT2 and POT4, and 64 and 57 percent, respectively, exhibit an upward change point at the 75-year trend period. Most streamgages in the 50- and 30-year trend periods do not exhibit a change point for POT2 or POT4. Although the frequency of high streamflows has increased at some streamgages and trend periods in Missouri, these increases are not as widespread as the increases in the magnitude of peak streamflow.

Observed (temperature and annual precipitation) and modeled climate data (all other variables) for each streamgage basin in all trend periods were used to relate changes in peak streamflow to changes in climate metrics. Likely or somewhat likely upward trends in temperature and annual precipitation dominated in all trend periods, with no downward trends in precipitation and only two somewhat likely downward trends in temperature at the 100-year trend period. Increases in annual precipitation are mostly limited to southern Missouri at the 30-year trend period. The proportion of precipitation falling as snow has largely decreased in streamgage basins across the State, which is expected in response to increasing temperature. Also expected in response to increasing temperature, an increase in potential evapotranspiration (PET) across the State and the 75-, 50-, and 30-year trend periods was exhibited. Despite this increase in PET, the PET-to-precipitation ratio decreased for much of the State outside the 30-year trend period, approximately mimicking the spatial distribution of increasing precipitation trends. Decreasing PET-to-precipitation ratios while PET increased indicates that increases in precipitation have overwhelmed the somewhat smaller increases in PET over much of the State; and that the basins are moving toward a wetter, more energy-limited hydrologic regime, which indicates, in turn, an increase in the fraction of precipitation becoming runoff, and thus increased streamflow in the presence of increasing precipitation. Upward trends in modeled annual runoff, which in this study incorporates only the effects of climatic variation, are observed in the same geographic areas where there are increases in observed annual precipitation.

Considering the peak streamflow and climate analyses together, the widespread increases in peak streamflows at the 100-, 75-, and 50-year trend periods and increases in southern Missouri at the 30-year trend period (encompassing gradual and abrupt change) seem to be driven largely by increases in annual precipitation. Spring and winter precipitation is projected to increase across the State, and the occurrence of extreme precipitation events also is expected to increase in the future. If precipitation continues to increase as expected, peak-flow frequency estimates from older records may no longer represent the hydrologic regime of today or the future.