Hydrology

Buffalo Bill Dam is approximately 350 ft tall and generally acts as a complete barrier to natural passage of upstream water and sediment. The dam is operated to maximize water storage during the snowmelt runoff season and release it during irrigation season, and dam operations would be expected to have substantial effects on the natural timing and magnitude of annual peak streamflows (Williams and Wolman, 1984; Schmidt and Wilcock, 2008). Data available from 1902 to 1909 at Shoshone River at Cody, Wyo. (USGS streamgage 06282500; U.S. Geological Survey, 2023a), indicates that prior to dam completion, annual peak discharge ranged from 7,850 to 22,200 cubic feet per second (ft³/s), with a mean of about 12,680 ft³/s (fig. 2).

Peak streamflows recorded at Shoshone River below Buffalo Bill Reservoir, Wyo. (USGS streamgage 06282000; U.S. Geological Survey, 2023d), from water years 1921 to 2015 indicate that annual peak streamflow magnitudes likely declined after closure of the dam in 1910 and again after raising the height of the dam in 1993 (a water year is the 12-month period from October 1 through September 30 and is designated by the calendar year for which it ends). From 1921 to 1993, peak streamflows ranged from 1,290 to 17,300 ft³/s, with a mean of about 6,520 ft³/s; from 1994 to 2015, peak streamflows ranged from 1,330 to 8,550 ft³/s, with a mean of about 4,900 ft³/s (fig. 2). Examination of the 10-year moving average during the period of record (1921–2015) also indicates that peak streamflows declined after the 1930s (fig. 2), which may be associated with natural declines in peak streamflows observed in river basins elsewhere in the Western United States, changes in dam operations, or both (Stockton and Jacoby, 1976; Van Steeter and Pitlick, 1998; Allred and Schmidt, 1999; Grams and Schmidt, 2002).

Buffalo Bill Dam operations also alter the natural timing and magnitude of daily streamflows The upstream exceedance hydrograph (fig. 3) was constructed by summing the daily statistics for the South Fork Shoshone River above Buffalo Bill Reservoir, Wyoming (U.S. Geological Survey streamgage 06281000; U.S. Geological Survey, 2023b) and the North Fork Shoshone River at Wapiti, Wyo. (U.S. Geological Survey streamgage 06279940; U.S. Geological Survey, 2023c). A comparison of daily streamflow statistics upstream and downstream from Buffalo Bill Dam indicates the dam reduces daily mean streamflows relative to upstream during the spring runoff season from about late February through early May and elevates daily mean streamflows relative to upstream in late winter and summer to make room for spring runoff and to release water for irrigation demands, respectively (fig. 3). When the reservoir is releasing water for irrigation, daily flows are generally kept below 1,450 ft³/s, which is the current maximum flow capacity of Buffalo Bill Dam’s hydropower facilities (Mahonri Williams, Reclamation, oral commun., 2024); however, there are times during runoff when releases may be higher. Finally, the timing of elevated spring runoff flows appears to be later than the natural runoff pattern upstream from the dam, extending into July (fig. 3).

Fluvial Sediment Transport

Buffalo Bill and other large dams in the Bighorn River watershed accumulate sediments in their respective reservoirs, blocking fluvial sediment from being transported downstream and reducing storage capacities (Minear and Kondolf, 2009). Bathymetric reservoir surveys collected by Reclamation indicate mean unit sediment yields vary from 191 to 924 tons per year per square mile (tons/yr/mi²; table 1). Resurveys of Buffalo Bill Reservoir have shown that the combined sediment yields (annual mean sediment yields) of the North Fork Shoshone River and South Fork Shoshone River deliver between about 1 and 1.4 million tons per year (tons/yr) of sediment (table 1). Bathymetric surveys of Bighorn Lake, which receives sediment from the Shoshone and Bighorn Rivers, have shown that these rivers deliver a combined total of between about 2.0 and 4.2 million tons/yr of sediment (table 1).

Estimates of basin sediment yields made from reservoir surveys are dependent on assumptions of sediment density, which can vary with time because of compaction and reservoir operations (Strand and Pemberton, 1982), but daily fluvial suspended-sediment records available for the Shoshone River at Kane, Wyo. (USGS streamgage 06286200; U.S. Geological Survey, 2023e), and the Bighorn River at Kane, Wyo. (USGS streamgage 06279500; U.S. Geological Survey, 2023f), corroborate the sedimentation rates calculated from bathymetry. The suspended-sediment records were computed using the method of Porterfield (1972), which uses a combination of frequent suspended-sediment measurements and the hydrograph to compute daily suspended-sediment loads. At the USGS streamgage 06286200, the USGS measured suspended sediment from 1960 to 1964 and reported annual sediment yields ranging from 0.7 to 2.7 million tons/yr, and an average of 1.6 million tons/yr (533 tons/yr/mi²; table 2). Measurements on the USGS streamgage 06279500 were made from 1949 to 1964 and resulted in annual sediment yield estimates ranging from about 1.6 to 8.6 million tons/yr, with an average of about 5.0 million tons/yr (319 tons/yr/mi²; table 2).

Bed material transport conditions were also estimated for the Shoshone River upstream and downstream from Willwood Dam in response to the sediment released from the dam in 2016. These estimates were centered on understanding the potential to mobilize fine sediment clogging the interstices of spawning gravels used by trout. McElroy (2017) used measurements of bed material grain sizes and channel hydraulic geometry to estimate the magnitude of streamflow necessary to mobilize the gravel streambed of the Shoshone River. McElroy (2017) estimated a minimum streamflow of about 4,000 ft³/s sustained for approximately 2 weeks was needed to mobilize the bed material and evacuate and fully remove the fine sediment deposited in the channel from the 2016 sediment release. Cotton (2020) used stream velocity measurements to measure bed shear stresses upstream from Willwood Dam, and estimated streamflows of approximately 5,300 ft³/s sustained for at least 2 days were needed to fully mobilize the gravel bed and transport fine sediment out of the study area. McElroy (2021) investigated bed-material grain sizes and mobilization in two side channels of the Shoshone River near Cody, Wyo., and concluded that the side channels had similar grain sizes as the main channel and thus would likely be fully mobile under the conditions determined by Cotton (2020).

Willwood Dam

Willwood Dam was built with three sluice gates at the base of the dam intended to pass sediment. These gates are typically referred to as the “north,” “middle,” and “south” gates based on their location along the dam. Since the mid-20th century, excess accumulation of sediment behind the dam must occasionally be released through the sluice gates. Prior to 1982, sediment releases, often referred to as “sluicing” events, caused disruptions to municipal water-supply intakes (Bonner, 2002) and occasionally resulted in fish kills (Willwood Work Group 2, 2019). In 1982, WID and WYDEQ entered into an agreement whereby increases in water turbidity would be limited to no more than 10 nephelometric turbidity units (NTUs) between the upstream and downstream river reaches (Stone and Webster Engineering, 1982).

Bathymetric surveys of the pool behind Willwood Dam made in the late 1960s and sediment loading analyses made in the 1980s estimated that, in the absence of annual releases, the pool behind the dam accumulated approximately 200,000 to 210,000 yd³ (about 190,000 to 200,000 tons using a sediment density of 70 pounds per cubic feet) of sediment per year (Stone and Webster Engineering, 1982). An analysis of hydroelectric feasibility published in 1982 concluded that the turbidity limits would “quite likely…seriously restrict sluicing…resulting in a more filled-in reservoir” (Stone and Webster Engineering, 1982, p. III-2). Notes handwritten by WID staff indicate that the south gate was discovered to have a bent stem on August 8, 1974 (Travis Moger, WID, written commun., August 11, 2023). By 2009 a detailed inspection and assessment of Willwood Dam concluded that the south and middle sluice gates were “buried by siltation and have been nonoperable for some time” (Engineering Associates, 2009, p. 14). In 2014, an air injection method was used to mobilize sediment deposited against the back of the dam and allowed the middle gate to be repaired and operational again (Mathers, 2015; WYDEQ, 2022).

Willwood Dam has been in place for nearly a century and is an important component of Park County’s agricultural infrastructure and economy (DJ&A, 2021). The sediment accumulation and sluicing problem at the dam has been happening since at least the mid-20th century (Bonner, 2002) and continues to collide with the river’s legally designated and regulated uses, as well as with a growing recreation and tourism economy that benefits from the fishery in the Shoshone River. Previous work has indicated that siltation at the upstream face of Willwood Dam may pose long-term structural problems, and that the water quality restrictions in combination with siltation of the sluice gates impose operational limitations on the dam (Stone and Webster Engineering, 1982; Engineering Associates, 2009). Shih and others (2009) used a hydraulic and sediment transport model to examine the effects of different sediment removal and sluicing scenarios on the life of the dam. That study concluded that partial removal of sediment near the upstream dam face (approximately 255,000 yd³), combined with changes in seasonal sluice gate operations, could extend the life of the dam by 50 years. However, Shih and others (2009) did not examine upstream sources or variability of annual sediment volumes deposited behind the dam and, instead, assumed that nearly all the incoming sediment was derived from “channel bed erosion and bank erosion” (Shih and others, 2009, p. 2) on the main channel of the Shoshone River.

Operational Modes of Willwood Dam

Willwood Dam has two primary operational modes associated with irrigation season and nonirrigation season (hereafter referred to as “fallow” season). During the irrigation season, the sluice gates on the dam are adjusted such that the Shoshone River rises behind the dam and reaches the elevation of the Willwood Canal headgate to deliver water to irrigators (Shih and others, 2009). During the fallow season, the sluice gates are adjusted to bring the elevation of the Shoshone River behind the dam below the elevation of the canal headgate to protect it from winter ice formation (fig. 5). Previous reports have indicated that the typical water level during the fallow season is around 14 ft below the canal intake (Stone and Webster Engineering, 1982).

These operational modes were hypothesized to have differing effects on sediment transport. When the dam is spilling over the top, we hypothesized that sediments passing over the dam are likely the “washload,” which is the portion of the sediment load composed of fine sediments that are nearly always in suspension, often assumed to be those less than 0.0625 mm, and colloquially referred to as “mud” (Julien, 1995). When streamflow is passing only through the sluice gates of the dam, the water surface slope behind the dam is steeper, and it is hypothesized that the stream has enough energy to transport sand grains (particles with nominal diameters between 0.0625 and 2 mm) in suspension, and that sand and coarse grains rolling on the river bed (bedload) have the potential to move through the dam. Because the sluice gate openings are used to regulate pool elevation during the irrigation season, there are times when streamflow is spilling over the top of the dam and going through the sluice gates. Under these mixed conditions it is hypothesized that suspended-sediment load and bedload can pass through the dam.

Because the two operation modes of Willwood Dam likely have a substantial effect on upstream channel hydraulics and sediment transport, boundaries were defined on the typical irrigation and fallow season for analysis of data in the context of historical conditions. Reclamation (Mahonri Williams, Reclamation, written commun., 2023) provided data, with the first year of information in 1996, that were used to identify the first and last days when water was flowing into Willwood Canal. The median starting and ending days for the available period of record (1996–2018) rounded to the nearest fifth day in the month (1, 5, 10, 15, 20, 25, or 30), were used to define the typical irrigation and fallow season periods.

Precipitation and Temperature

Daily precipitation and temperature data were used to quantify hydroclimatic conditions in the study area during the study period relative to “normal” values, defined here as a median or mean value from data taken from a reference period of record. Daily precipitation was obtained using the AN81d dataset from the Parameter-Elevation Regressions on Independent Slopes Model (PRISM) available from the PRISM Climate Group at Oregon State University (PRISM Climate Group, 2021). The AN81d daily precipitation dataset is available in gridded format at a 4-kilometer resolution and has a daily period of record spanning from January 1981 to the present. Gridded estimates of mean daily precipitation from the PRISM dataset were subset to the study area basin. The spatially averaged mean daily precipitation for each subbasin was taken as the simple arithmetic mean of the data points within each subbasin using equation 2:

The spatially averaged data were then compiled for each day to create a daily mean precipitation (mean precipitation value for each day) record for the irrigation and fallow seasons for the 1981 to 2018 period of record preceding the study period.

In the same manner described previously for precipitation data, a daily record of average temperature was created by spatially averaging data subset to the watershed boundary (fig. 1A):

The daily precipitation and temperature records were used in tandem to build measures of precipitation and temperature hypothesized to be broad measures of the potential for the study area to yield sediment. The AN81d daily precipitation record from PRISM is reported in units of liquid precipitation, and the daily temperature record was used to determine if the precipitation on the landscape was likely falling as liquid, solid, or a mixture. For days with at least a trace of precipitation, if the daily mean temperature was less than 22 °F, precipitation was assumed to be all solid (snow), and if the daily mean temperature was greater than 42 °F, precipitation was assumed to be all liquid (rain); for mean daily temperatures between 22 °F and 42 °F, precipitation was assumed to be mixed snow and rain. The temperature assumptions, although arbitrary, incorporate the fact that daily mean temperatures in the AN81d data are the average of the estimated minimum and maximum temperatures, and that the precipitation phase is affected by air temperature at the point of origin and near-surface air temperature.

Daily precipitation normals during the period of record were defined as the median total precipitation and number of dry (no precipitation), rain, mixed, and snow days for the fallow and irrigation seasons. Temperature during the period of record was quantified as mean temperatures during the fallow and irrigation seasons, as well as extreme cold temperatures during the fallow season. Mean temperatures during irrigation and fallow seasons were taken as the median of daily mean temperatures for the selected period. Cold days and extremely cold days were arbitrarily defined as days with mean temperatures between 10 and 22 °F, and less than 10 °F, respectively. Because cohesion of sediments has been shown to be inversely related to air temperature (Levy and Cvijanovich, 2023), the number of extreme cold days was used as a relative measure of cohesion of sediment on the landscape behind the dam. All measures of daily precipitation and temperature were then quantified for the irrigation and fallow seasons in 2019, 2020, and 2021 and compared against the 1981 to 2018 period of record normal.

Quality Control of Continuous Monitoring

Biofouling and calibration checks of the deployed turbidity sensors were made by field personnel typically once every 6 weeks. These checks followed the methods described in Wagner and others (2006), and included removal of debris, light scrubbing to remove algae, and cleaning or replacement of the optical sensor lens wiper. A secondary field turbidity sensor was used to check the relative accuracy of the deployed sensors during site visits. Turbidity cross sections, which quantify any differences between turbidity observations at the continuous monitor relative to the complete channel, were taken twice a year to quantify any potential differences between the sediment concentrations at the sensors and the rest of the channel.

The LISST–ABS sensors were less sensitive to algae growth, but the signal could become compromised by debris interference. At the time of the deployments, there was no established method for checking calibrations on the ABS sensors, and the primary quality control method was to remove them and send them to the manufacturer for annual re-calibrations, resulting in gaps in the data record, which happened in the winter 2019–20 period. In the winter 2020–21 period, the ABS sensors that were removed for re-calibration were immediately replaced with calibrated sensors. Portable LISST–ABS sensors were not available for making cross-sectional measurements, and we relied on the turbidity cross sections as the primary indicator of sediment mixing.

Discrete Sampling of Suspended Sediment

Discrete suspended-sediment samples were taken by the USGS, WYDEQ, and WID at streamgages near Willwood Dam starting in 2018 using a variety of methods. Suspended-sediment sampling was targeted to represent the range of turbidity and ABS conditions observed in the continuous record. Under steady streamflow conditions (constant stage and turbidity), two suspended-sediment samples (A and B sets) were taken concurrently using a US DH-74 depth-integrating water-quality sampler (Davis, 2005) using the 10-station equal-width increment (EWI) or 4-station equal-discharge increment (EDI) methods (Edwards and Glysson, 1999). These sequential samples provided quality control on the resulting concentrations.

At both streamgages, a single SSC sample required approximately 10 minutes to collect under optimal performance with the bank-operated cableway. When conditions (stage or turbidity) were changing rapidly, only single sample sets (A set) were taken using the EWI or EDI methods. In some cases, field judgements indicated that sample conditions may have been noncompliant with the EWI or EDI methods and these samples were labeled as “multiple verticals” or “non-isokinetic” if an EWI or EDI station was not sampled because of local conditions (for example, debris or heavy wind) or a bottle was judged to be overfilled, respectively. If a storm caused a spike in turbidity or ABS, and USGS personnel could not be on site, WID personnel collected either a single, depth-integrated sample using the US D-74 at midchannel or collected a grab sample with a 1-liter plastic bottle along the bank.

Automatic pumping samplers were installed at both streamgages in the summer of 2019 and were on site through the summer of 2020. Pump samples were used to capture high-concentration events at each site, which often occurred rapidly and, in some cases, overnight when conditions were unsafe for personnel to be on site. The pump samples were typically triggered during turbidity conditions higher than 300 FNUs and were taken sequentially every 30 minutes until all sample bottles (24) were full or turbidity receded below the threshold. At the upstream streamgage, the pump intake was secured to the outside of the sensor tube housing; at the downstream streamgage, the pump intake was secured along an aluminum I-beam protruding approximately 6 ft into the channel.

Suspended-sediment samples were analyzed at the USGS Wyoming-Montana Water Science Center sediment laboratory in Helena, Montana, and the USGS Central Midwest Center Science Center Iowa sediment laboratory, in Iowa City, Iowa. Samples were analyzed for SSC, and some samples were also analyzed for percentage of sample composed of grain sizes finer than 0.0625 mm (silt and clay) using the methods described in Guy (1969).

Construction of Basic Sediment Budgets

Sediment budgets require that a sediment load estimation is available for inputs and outputs over a given time interval (eq. 1). Sediment moving into and out of Willwood Dam must travel nearly 2 mi between streamgages, and thus an estimate of sediment travel time was considered essential for the accuracy of sediment budgets calculated for shorter time intervals (days or less). Time-of-travel between streamgages was estimated using cross-correlation analysis of the turbidity time-series whereby the lag with maximum correlation was assumed to represent the strongest overlap in sediment behavior between streamgages. Sediment loads calculated for the upstream streamgage were subtracted from the sediment loads calculated for the downstream streamgage offset by the estimated travel time such that a negative value indicated more sediment entered the dam pool than exited through the dam.

Sediment Load Partitioning

Sediment loads calculated at 15-minute intervals were summed at each streamgage to build sediment budgets (eq. 1) during various larger time intervals of interest. To quantify the relative balance of sediment into and out of Willwood Dam, as well as to understand the relative contribution of various sediment sources, sediment loads were partitioned into three primary time intervals: seasonal, dam releases, and runoff events. These intervals were chosen to quantify sediment budgets from agricultural dam operations, scheduled sediment releases, and natural sediment runoff events, respectively.

Tributary Yields

Discrete sediment yields were quantified in select tributaries (fig. 7) to describe variability of loading to the Shoshone River. Ranges of tributary sediment yields defined here as a mass of sediment per unit of time were calculated using discrete measurements of streamflow, SSC, and bedload. The measurements and samples were taken between 2017 and 2023 and targeted two primary conditions, stable (nonevent) and precipitation runoff, in irrigation and fallow seasons, for a total stratification of four different conditions (irrigation season-stable, irrigation season-runoff, fallow season-stable, fallow season-runoff). Streamflow measurements were taken on each sampling visit using a Marsh-McBirney Flo-Mate following methods outlined in Turnipseed and Sauer (2010). Suspended-sediment measurements were taken using the EWI method using a US DH-48 or US DH-81 sampler (Edwards and Glysson, 1999). Bedload samples were taken using the EWI method using a Helley-Smith type trap sampler (Emmett, 1980) with a 3-in. nozzle width. The suspended-sediment and bedload quantities were reported as discrete values and were normalized by drainage area to compare with ranges of long-term averages observed in reservoir surveys and past fluvial sediment measurements.

Backwater Extent and Cross Sections

The backwater extent produced by Willwood Dam was digitized to evaluate the differences through time to help understand sediment deposition within the river channel. The backwater extents were manually digitized from georeferenced National Agriculture Imagery Program (U.S. Geological Survey, 2023i) aerial imagery in a geographic information system (GIS). Aerial images from irrigation seasons 2012, 2015, 2017, 2019, and 2022 were digitized to determine backwater extents (table 3). Images contained four bands and were viewed in true color, false color, and a normalized difference vegetation index raster for the digitizing process. Initial digitizing was performed using a scale ranging between 1:80 and 1:150 while switching between different views. Refinements were made from the initial digitized layer in an iterative process at scales ranging from 1:150 to 1:500, focusing on one view until the user was satisfied with all views. To help address human bias and keep the methodology as constant as possible, one individual digitized all images.

Images were obtained during irrigation season (table 3) when pool elevations behind the dam are relatively consistent between years (fig. 8B). Water extent was separated into active channel, island, and incipient floodplain classifications. The active channel is defined as obvious flow of water; these areas were easiest to identify in false color and the normalized difference vegetation index raster, as they appeared blue or black, respectively. Islands are defined as bars within the active channel that appear unsaturated and persist through time. Incipient floodplain surfaces or mud flats are defined as areas at the fringe of the active channel where it appears saturated, but it is less clear if there is flowing water or not. Incipient floodplain surfaces included areas with a mix of vegetation and water, saturated sediment, or algae, appearing as dissimilar in coloration compared to the surrounding area of distinct active channel or floodplain.

A channel centerline was created using the midpoint line tool in ArcGIS Pro (Esri, 2023) on the 2017 channel bounds and used for generating all cross-sections for every year. Cross sections were placed along the channel centerline at 100-ft intervals. Cross sections were then clipped to each year’s active channel and total channel of the backwater extent and their widths were calculated. Cross-section widths were exported for statistical analysis in Wilcoxon rank sum tests (Bauer, 1972; Hollander and Wolfe, 1973) were used to evaluate differences in mean cross-section widths for each year. Because the images were not perfectly coregistered, the test was performed using the unpaired sample assumption to account for the additional uncertainty.

Sources of Uncertainty

Digital aerial images do not perfectly overlap in space, resulting in a slight offset, causing uncertainty in the location of features between images. This error in positioning is known as registration errors, which is the error resulting from the translation of aerial images into GIS (Gurnell and others, 1994). This uncertainty is important when comparing differences in measurements made in images taken in different years. To quantify the registration error, the root-mean-square difference (RMSD) was calculated between colocated points of identical features in each of the five images, based on methods outlined in Schaepe and others (2016). The RMSD is the mean distance between all the colocated points in an image compared to another images’ colocated points and is used to determine if differences in measurements are a result of the coregistration error or true detectable differences. Features were located in one image and then cross checked to determine if they still appeared in all images, which resulted in a total of 13 colocated points for each image. The RMSD was calculated for each of the years as a reference using equation 7:

From the RMSD results, the 2019 image was chosen as the reference year because of its high spatial resolution and high contrast in all landscape features throughout the image. Using the 2019 image as the reference year, the RMSD was calculated between all the colocated points and the results were used in subsequent analyses.

The digitizing error or horizontal uncertainty, defined as the difference between the actual feature boundary and the digitized line drawn in GIS (Dunn and others, 1990), was estimated in two different ways. The first, again following the methods outlined in Schaepe and others (2016), summed the image resolution and the estimated uncertainty of choosing the feature boundary of 3 meters to determine the horizontal uncertainty. The second way, using the results of Dunn and others (1990), determined the percent area uncertainty, using a conservative epsilon band value of 3.1 meters, was between 3 and 10 percent.

Bathymetric Surveys

Bathymetric surveys were completed by Wyoming Game and Fish Department in November 2017 and WYDEQ in August 2019 and April 2022. The survey data contained x, y, z coordinates that were imported into ArcGIS Pro (Esri, 2023). The bathymetric survey data were taken using different instruments and survey designs and covered different extents of the backwater areas. The routing tools available in ArcGIS Pro were used to measure the distance of each survey point upstream from the dam along a common channel center line. The minimum bed elevation was then extracted from the surveys using 100-ft sampling intervals to construct a longitudinal profile of the thalweg behind Willwood Dam. Longitudinal profiles were only compared for overlapping areas, and the points nearest the dam were excluded because the resolution and overlap of the data were very different between each of the surveys.

Seasonal Operational Modes of Willwood Dam

Data from agricultural years 1996 to 2018 indicate that Willwood Dam began diverting water into the Willwood Canal between March 3 and May 9; diversions stopped between October 3 and as late as November 17. The median starting day of irrigation diversions was April 13, and the median ending day was October 23. For the purposes of examining historical hydroclimatic conditions, an irrigation season is defined as the period during which the Willwood Canal was in operation and was generally from April 15 to about October 24 of the same calendar year; the fallow season is defined as the nonirrigation period during which the Willwood Canal was generally not in operation and was commonly from about October 25 to about April 14 of the following calendar year. For the purposes of examining historical hydroclimatic and sediment-transport conditions, an agricultural year is thus defined as the 12-month period from October 25 through October 24 of the following year and is designated by the calendar year for which it ends.

Precipitation and Temperature Conditions

Median annual precipitation for the 1981 to 2018 period of record was 11.2 in., with a mean of 8.4 in. during the irrigation season and 2.8 in. during the fallow season (table 4). The study area had a median of 81 and 111 days with at least some precipitation during the fallow and irrigation seasons agricultural years 2019–21, respectively (table 4). During the 1981 to 2018 period of record, the fallow season had an average median of 25 cold and 10 extremely cold days, with a median mean temperature of 32 °F; the irrigation season had a median daily mean temperature of 58 °F (table 4).

Precipitation in agricultural year 2019 was near normal during the fallow season but was 5.6 in. above normal during the irrigation season (table 4). Irrigation season 2019 had 22 more days with at least some rainfall than normal. The median daily mean temperature for fallow season 2019 was 2 degrees less than normal, and there were 14 more cold and extremely cold days during the season than normal. In contrast to agricultural year 2019, agricultural year 2020 had 2.1 in. less total rainfall than normal, and 9 fewer days with any rainfall than normal (table 4). Similarly, agricultural year 2021 had 2.5 in. less rainfall than normal, and 20 fewer days with any rainfall than normal (table 4). The median daily mean temperatures during fallow seasons 2020 and 2021 were 1 degree less than normal, but the irrigation season temperatures were 4 degrees above normal (table 4).

Discrete Samples of Suspended Sediment

Paired sampling of suspended sediment and turbidity began in October 2018 at both streamgages, and paired ABS values were available starting in March 2019. At the upstream streamgage, a total of 147 suspended-sediment samples were paired with turbidity or ABS, or both. Of these samples, 107 were pump samples with SSCs ranging from 62 to 36,100 mg/L, 4 were grab samples with SSCs ranging from 46 to 3,330 mg/L, and 36 were depth- and (or) width-integrated samples with SSCs ranging from 9.5 to 23,200 mg/L (U.S. Geological Survey, 2023g). The SSC samples ranged from the 15th to 99.9th turbidity ECDF quantiles (fig. 10A), and from the 8th to the 99.9th ABS ECDF quantiles (fig. 10B). Analysis of five suspended-sediment samples taken with the pump sampler at the upstream streamgage indicated low bias (2 percent) relative to width- and depth-integrated samples. The 2-percent bias indicated by this comparison was considered acceptable given that it is less than the mean percent difference between A and B samples taken concurrently using cross-sectional integrated samples at that location (4 percent), and thus no bias correction was made to the pump samples. A complete description of the comparison between pump and cross-sectionally average suspended-sediment samples is available in appendix 3.

At the downstream streamgage, a total of 126 suspended-sediment samples were paired with turbidity or ABS, or both. Of these samples, 79 were pump samples spanning a range of SSCs from 22 to 13,300 mg/L, 1 was a grab sample of 8,395 mg/L, and 46 were depth- and (or) width-integrated samples spanning a range of SSCs from 6.0 to 13,500 mg/L (U.S. Geological Survey, 2023h). The SSC samples spanned from the 11th to 99.9th turbidity ECDF quantiles (fig. 10C), and from the 0 to the 99.9th ABS ECDF quantiles (fig. 10D). The ABS sensor at the downstream streamgage failed and was at the manufacturer in late May 2019 when the storm that produced SSCs of as much as 36,100 mg/L (U.S. Geological Survey, 2023h) at the upstream streamgage happened. Although numerous pump samples were collected at the downstream streamgage during that event, none could be paired with a turbidity or ABS values because the NEP–5000 had reached its operational limit, and no ABS sensor was in place. The maximum SSC measured at the downstream streamgage was 32,600 mg/L (U.S. Geological Survey, 2023h) from a pump sample taken during the storm on May 27, 2019. Analysis of six suspended-sediment samples taken with the pump sampler at the downstream streamgage indicated low bias (1 percent) relative to width- and depth-integrated samples. The 1-percent bias indicated by this comparison was considered acceptable given that it was nearly identical in magnitude to the mean percent difference between A and B samples taken concurrently using cross-sectional integrated samples at that location (−1 percent), and thus no bias correction was made to the pump samples.

Suspended-Sediment Statistical Models

Statistical modeling of SSC using paired values of turbidity and ABS produced four initial models that had poor model diagnostics including heteroscedastic and serially correlated model residuals (table 5). These models were improved by downsampling and accounting for bias from serial correlation using the method of Cochrane and Orcutt (1949). At the upstream streamgage, 117 pairs of SSC and turbidity values and 138 pairs of SSC and ABS values were used to produce the initial models; those sample pairs were downsampled to 43 and 52, respectively, again improving the explanatory power and diagnostics of both models (table 5), but both models failed the Durbin-Watson test (Durbin and Watson, 1950) for serially correlated residuals. The Cochrane-Orcutt method (Cochrane and Orcutt, 1949) was applied to both models and resulted in improved balance of diagnostics and performance (table 5).

At the downstream streamgage, 89 pairs of SSC and turbidity values, and 72 pairs of SSC and ABS values were used to produce the initial models; those sample pairs were downsampled to 51 and 45, respectively, which again improved the explanatory power and diagnostics of both models (table 5), but the turbidity model failed the Durbin-Watson test (Durbin and Watson, 1950). The turbidity model was bias-corrected using the Cochrane-Orcutt method (Cochrane and Orcutt, 1949), which resulted in improved model performance and diagnostics (table 5).

Model fits were generally good (fig. 11), with coefficients of determination indicating that more than 84 percent of the variance was explained by either turbidity or ABS, and the downsampled models had reasonable compliance with normality (table 5). The turbidity model at the upstream streamgage was excellent, explaining 94 percent of the variance, whereas the ABS model was the best of the two downstream, explaining 87 percent of the variance in SSC. The better fit of turbidity upstream likely reflects the more natural sediment supply system upstream whereby the grain sizes reaching the streamgage do not vary substantially over time; the better fit of the ABS model downstream likely reflects the wider range of grain sizes produced by the dam when it sluices sediment.

Slope and intercept values differed between turbidity and ABS models at each streamgage, and for turbidity and ABS models between upstream and downstream streamgages. At both streamgages, the ABS models had higher intercept terms, whereas the turbidity models had higher slope terms (table 5), likely reflecting the higher sensitivity of the turbidity sensor to suspended mud particles and poor precision of the ABS when sand concentrations are very low. Although these model diagnostics were generally sufficient, Duan’s bias correction factors (Duan, 1983) indicated that three of four models had bias corrections of more than 10 percent (table 5).

Suspended-Sediment Loads

The goal of the statistical modeling was to produce the most accurate records of suspended-sediment loads in the Shoshone River. To calculate a complete sediment budget, an SSC value would need to be produced for every 15-minute time step during the entire chosen period of interest. As stated in the previous section, not all 15-minute observations were accepted in the final turbidity and ABS records at each streamgage, which resulted in some time stamps that had only turbidity, or ABS, or neither. Ideally, we could use the statistical model with the most explanatory power for a streamgage when that variable was available in the record, and default to a statistical model with less explanatory power when that was the only variable available. However, the best models and resolution of records for each variable differed between streamgages, and the final models demonstrate that ABS and turbidity respond differently to the same concentrations, with ABS producing higher values at low concentrations and turbidity producing higher values at higher concentrations (fig. 11). These factors imply that using the only model available to estimate a sediment load can be intractable because any imbalances between upstream and downstream could be attributable to differences in the models chosen for each streamgage.

Instead of using the model with the most explanatory power available to generate sediment loads, a system of rules was constructed to select the models used for each time step. The rules are based on the seasonal operations of Willwood Dam, assumptions about the grain sizes mobilized during these operations, and assumed accuracy of the models at the downstream streamgage under different operational conditions. Sediment samples taken at the downstream streamgage during the irrigation season were always dominated by mud (greater than [>] 80 percent mud), whereas sediment samples taken during the fallow season had much more variability and much larger proportions of sand (fig. 12). The primary goal of the rule-based system was to produce sediment load estimates at both streamgages that were calculated using the same method, while maximizing the number of observations with a load estimate. The system of rules devised for the load estimates is depicted in figure 13, with the fundamental rule being the pool elevation behind Willwood Dam, which dictates the assumptions about the best model to use. When the pool is less than 4,499 ft NAVD 88, it was assumed that sand could be leaving Willwood Dam at any time, and the ABS model was likely most accurate. Likewise, when the pool elevation exceeded 4,499 ft NAVD 88 and the dam was spilling, it was assumed that turbidity was the better model downstream. It was also assumed that turbidity was more accurate for lower concentrations (<100 mg/L). Once a method for load calculation was selected for the downstream streamgage based on the rules in figure 13, the same method was applied upstream for that time step.

The sediment budget between upstream and downstream estimates of loads was interpreted using the mean predicted values bound by their respective model prediction intervals. If the mean predicted loads of one streamgage were contained in the prediction intervals of the other streamgage, and vice-versa, difference in the sediment budget were interpreted as “indeterminate.” If the mean predicted load of one streamgage was outside the prediction intervals of the other, the sediment budget was interpreted to be “weakly significant.” Finally, if the mean predicted load for both streamgages was outside the respective prediction intervals of the other streamgage, the sediment budget was interpreted to be “significant.” It should be noted that an “indeterminate” sediment budget does not signify no net change in sediment storage behind Willwood Dam, but it does signify that any changes during a given time period were not large enough to measure given the precision of the sediment models.

Season Loads

Modeled sediment load balances demonstrate the depositional and erosional behaviors expected from the conceptual model of dam operations whereby sediment accumulation tends to happen during irrigation seasons when the dam is spilling mainly over the top (shown as “Deposit” on fig. 14), and sediment export tends to happen during the fallow seasons when it is flowing through the sluice gates (shown as “Export” on fig. 14). There are times during the irrigation season when the models show more sediment leaving the dam than entering, but this sediment may or may not be from tributary inputs and therefore may not necessarily be evacuating from storage. For all seasons, except for fallow season 2022, the model calculated that more sediment left the dam than entered the dam (table 6), but the modeled mean loads at each streamgage were nearly always within the prediction intervals of each other, making the sediment balance indeterminant (fig. 15). The one exception was fallow season 2020, when the predicted means were not contained by either prediction interval, indicating a conclusive signal that more sediment left the dam than entered during the coincident periods of record. Although most of the seasonal budgets are indeterminate, the pattern of sediment accumulation and transport through the dam is captured by the models, and within the scale of previous estimates of sediment loads for the Shoshone River.

The results presented in the subsections that follow reference the estimated sediment loads only for the overlapping records at the upstream and downstream streamgages because these are the sediment budgets for which there is the most certainty. The total suspended-sediment loads presented in table 6 are a more accurate measure of the total amount of suspended sediment that can move through the Shoshone River in an agricultural season but should be interpreted with caution in the context of understanding changes in storage behind Willwood Dam because they are incomplete relative to each other.

Event-Based Loads

Three types of human events took place during the period of study, including typical sluices, a sediment flush from Willwood Dam, and Iron Creek Dam sediment releases. One of the sluice events was an experimental sluice that was part of a separate study aimed at understanding effects of different sediment concentrations on fish spawning habitat (Pilkerton, 2024). The flushing event was also considered an experiment because it was the first attempt in this system to combine high-concentration sediment releases from Willwood Dam with a deliberate bed-mobilizing streamflow event from Buffalo Bill Dam designed to flush the fine sediment downstream to the next reservoir. All calculated event loads are shown in table 7 and figure 16. The sluicing and flushing events are used to remove sediment from the pool behind Willwood Dam, and therefore the expected load balance should indicate a greater amount of sediment exiting the dam than accumulating behind it. For the sluicing and flushing events during the study period, more sediment exited the dam than entered it. For the Iron Creek Dam sediment releases that happened during the study period, sediment was hypothesized to accumulate behind the dam because the pool behind the dam reduces the energy of the streamflow. Our load predictions indicated that more sediment entered the dam than exited during the Iron Creek Dam releases, as expected.

Sediment Yields from Selected Tributaries

Between August 2017 and July 2023, sediment samples were collected from 9 tributaries to the Shoshone River during 137 sampling events (National Water Quality Monitoring Council, 2024) (table 8; fig. 7). Tributaries were sampled between 1 and 27 times during this period. The tributary sites were located between Buffalo Bill Reservoir (not shown) and Willwood Dam (fig. 7), and samples were collected near the mouths of the tributaries. All tributaries in the sample program receive water from irrigation canals either through seepage or direct return flow. The drainage area of the sampling sites in the tributaries ranged from 3.05 to 98.4 mi² (table 8). Sediment yields at each site varied substantially (table 8), with the data range at each site spanning two to five orders of magnitude (fig. 17). The largest sediment yield, 1,005 tons per day, was calculated for a sample from Sulphur Creek with a drainage area of 46.4 mi² (table 8). The next highest yield, 655 tons per day, was from Dry Creek, with a drainage area of 17.3 mi² (table 8).

Comparison of area-normalized yields for tributaries without precipitation events (referred to as “nonevents”) showed larger normalized yields during the irrigation season, but most sites had a similar large variation of loading during the period of sampling (fig. 17). During the irrigation season, the mean normalized yields from all sites ranged from 0.06 to 0.77 ton/day/mi² for nonevents, whereas the mean normalized yields from all sites during fallow season nonevents ranged from 0.01 to 0.35 ton/day/mi². During irrigation season precipitation events, the mean normalized yields ranged from 0.33 to 9.51 tons/day/mi², with five of the nine sites having averages >2 tons/day/mi². During fallow season precipitation events, the mean normalized yields ranged from 0.04 to 0.95 ton/day/mi².

All sites sampled for irrigation season precipitation events had the highest median yield and mean normalized yield compared to all other season event types except for Dry Gulch, which had its highest mean normalized yield measured during a nonevent in irrigation season. The second highest median yields and mean normalized yields were observed half during irrigation season nonevents and half during fallow season precipitation events, except for Dry Gulch, which had its second highest mean normalized yields during irrigation season precipitation events. The third highest median yields were spread evenly between irrigation nonevents and fallow season precipitation events and nonevents. The third highest mean normalized yields were mostly seen during fallow season precipitation events, except for Sulphur Creek, Sage Creek, and Buck Creek. The smallest median yields took place during fallow season nonevents except for Cottonwood Creek and Sage Creek. The smallest mean normalized yields also took place during fallow season nonevents except for Dry Creek and Sage Creek. Buck Creek was not sampled during fallow season precipitation events and its smallest median yield and mean normalized yields were during fallow season nonevents.

The range of group mean daily sediment yield per unit area across all samples at each tributary site ranged from 0.26 to 3.08 tons/day/mi² (table 9). Data describing sediment accumulation for three large reservoirs (Buffalo Bill Reservoir, Bighorn Lake, and Boysen Reservoir) in the Bighorn River watershed (Blanton, 1991; Ferrari, 1996, 201024; Hilldale, 2020) were used to provide geologic context for sediment yields from the tributary sites. Mean daily unit sediment yields to the three reservoirs ranged from 0.5 to 2.5 tons/day/mi² (table 1). These data indicate that although individual events on the tributaries can produce higher than average sediment yields, the mean sediment loading from the tributary sites are in a similar range to data collected in other locations in the Bighorn River watershed. Tributaries with mean normalized yields higher than the mean range of background sediment yield included Sulphur Creek, Cottonwood Creek, Idaho Creek, and Dry Creek (fig. 17), which had a mean sediment yield higher than the upper limit of the range of background sediment yields from literature.

Sediment Loads During Irrigation Season Stable Flows

Under stable conditions during the irrigation season, streamflows in the Shoshone River upstream from Willwood Dam are dominated by clear water originating out of Buffalo Bill Dam. Additional contributions to flow between Buffalo Bill Dam and the study area come from tributary contributions, which likely originate in the complex systems of irrigation canals and are delivered either directly by way of diversion gates in the canals or through seepage losses to the groundwater system (Willwood Work Group 3, 2019). Although these tributary contributions may be expected to be a relatively small component of the total suspended-sediment loads, because they are persistent, they may contribute more sediment than first perceived.

To estimate the potential maximum contribution of suspended sediment from tributaries carrying irrigation water, the relative percent contribution of suspended-sediment loads was calculated during stable conditions for irrigation seasons 2019, 2020, and 2021. These loads were calculated by subtracting suspended-sediment loads during high flows and natural (rainfall-runoff) events from the total for each irrigation season. These estimates require the assumption that all suspended sediment being carried by the Shoshone River during stable conditions originates in tributaries carrying irrigation return flows. This assumption is likely incorrect, because other sources of sediment from bank erosion in tributaries and the main-stem Shoshone River, yields from tributaries without return flows (McCullough Peaks; fig. 1B–C), as well as urban runoff, are present in the system. Likewise, suspended sediment in the Shoshone River during runoff events includes sediment from tributaries that may be carrying irrigation water. Nonetheless, the estimates allow for inference on the maximum possible suspended-sediment contributions from irrigation return flows.

In the 2019 irrigation season, suspended-sediment loads during stable conditions were estimated at 35,500 and 51,300 tons at the upstream and downstream streamgages, respectively. These totals represent 21 and 14 percent of the respective upstream and downstream total coincident suspended-sediment loads (table 10). These percentages increased at both streamgages to approximately 30 percent for the 2020 and 2021 irrigation seasons, which had near average rainfall runoff conditions and lower overall streamflow conditions relative to the 2019 irrigation season. These data indicate that a maximum of about one-third of the suspended-sediment loads measured during the study period happened during stable conditions when tributary contributions were likely dominated by return flow from irrigation water. Interpreting this maximum value may be affected by assumptions stated earlier in the section.

Planimetric Analysis

Imagery from irrigation seasons 2012, 2015, 2017, 2019, and 2022 was used to determine the backwater extent of the pool area to calculate cross-sectional widths. Backwater extents were further divided into active channel, islands that persist through time, and incipient floodplain (Brown and others, 2025), and the areas for each were calculated (table 11; fig. 18). These areas were used as a proxy for storage within the channel corridor rather than to compare differences in classification or the areas directly. Cross-sectional widths were extracted for 100 cross sections using total backwater extent and active channel backwater extent data.

Total channel widths obtained from the imagery analysis ranged from 86.8 to 338.1 ft across all years (fig. 19). The total channel widths tended to be relatively similar between the years (fig. 19), with the only statistically significant differences in the populations appearing between irrigation seasons 2015 and 2017 (p-value=0.016), and irrigation season 2015 compared to irrigation season 2022 (p-value=0.036). Active channel widths obtained from imagery analysis ranged from 70.9 to 338.1 ft (fig. 19). Active channel widths were all similar between years except for irrigation season 2015, which was determined to be statistically different from all other irrigation seasons (all p-values <0.05).

Understanding uncertainty allows a frame of reference for evaluating data. First, the RMSD between all of the co-located features in the images was used to determine how comparable the images were to each other. Using the 2019 image as the reference image, the difference between co-located features ranged from 3.1 to 5.4 ft. These results indicated that cross sections created using GIS were not in the same physical location within the images requiring unpaired statistical analysis. Cross-sectional width error was analyzed using two methods: (1) the Wilcoxon rank sum test and (2) comparing the difference in mean width to the sum of the image resolution and human feature boundary drawing uncertainty (3 meters) (Schaepe and others, 2016). Both methods resulted in nearly the same statistically significant results, except for one difference in means resulting in a significant difference (2019 compared to 2015, p-value=0.068) and one Wilcoxon rank sum test resulting in no significant difference (2019 compared to 2015, difference of means >11.8 ft [sum of image resolution and human feature boundary drawing uncertainty]).

Bathymetric Analysis

Bathymetric data provided by WYDEQ were used to assist with the evaluation of sediment retention in the pool behind Willwood Dam. Measurement of the bed elevation at three different times provided an indication of whether the overall bed elevation was increasing, indicating sediment deposition, or decreasing, indicating scour (fig. 20). Minimum and mean bed elevations were determined; however, the evaluation of bed changes used the minimum elevation because the minimum value is easier to determine and therefore is considered a more robust measurement. The number of measured points varied between surveys, with some intervals having far fewer points to determine mean bed elevation, introducing bias in some intervals and none in others. Analysis of the minimum bed elevations using unpaired Wilcoxon rank sum tests indicated no statistically significant differences in bed elevations between the years (all p-values >0.05).

Determination of Sediment Retention in Willwood Dam Pool

A direct examination of the sediment storage behind Willwood Dam was not explicitly evaluated during the study period. A planimetric and bathymetric survey was used as a proxy for storage, which supported the model findings and indicated that on an annual basis the system appears to be in a quasi-equilibrium. This difference between the upstream and downstream loads can be caused by sediment movement out of storage or into the area behind the dam and from sediment loads from unmeasured tributaries between the upstream streamgage and the dam. Additionally, hillslope erosion can contribute an unknown sediment load that could be moved through or stored behind the dam. These considerations help to explain the pool areas, cross-sectional widths, and longitudinal profiles not indicating any strong trends in either sediment accumulation or transport through the dam.

Results from the planimetric and bathymetric survey data provide multiple lines of evidence to show that the sediment accumulation behind the dam, on an annual basis, did not happen within the error of the methods. Both methods of measurement have inherent uncertainty; however, multiple methods used to evaluate the sediment accumulation support the idea that the current system operation is in a quasi-equilibrium on an annual basis. Although the sediment balance on an annual basis is a near equilibrium with dam operations, evaluation of the data over the course of a given year does indicate periods of accumulation during irrigation season and export during the fallow season, sluicing events, and flushing events.

Rainfall Runoff

Estimates of sediment loads for natural runoff events described in the “Natural Events” section for the upstream streamgage (table 6) were combined with daily average precipitation data from the PRISM AN81d dataset (PRISM Climate Group, 2021) for the Shoshone River watershed upstream from Willwood Dam. Total accumulated precipitation was summed from the day before the beginning of each event until the last day of the event. These data indicate that accumulated rainfall from the natural runoff events captured during the study period varied from a trace to as much as 4.26 in. (fig. 21). The turbidity suspended-sediment model predicted a range of sediment loads varying from 112 to 99,000 tons, whereas the ABS model predicted a range of 47 to 232,000 tons of suspended sediment from these events. The behavior of the sediment loads relative to accumulated precipitation did not appear to change depending on irrigation or fallow season (fig. 21A), but only a few runoff events were captured during fallow season, so any differences would not be expected to be apparent.

The plots in figure 21 show that the amount of sediment delivered to the Shoshone River during rainfall events varies substantially for a given rainfall accumulation. For the area of the plot near 0.1 in. of rain, there is a variation of nearly two orders of magnitude of suspended-sediment loads between events calculated using the ABS sensor (fig. 21A). This variation is weaker using the turbidity model (fig. 21B), but still covers approximately one order of magnitude. These data indicate that fine sediment runoff from the basin between Buffalo Bill Dam and Willwood Dam is complex and likely dependent on where the precipitation is concentrated on the landscape. However, the data in figure 21 also indicate that sediment loads begin to increase exponentially after about 0.3 in. of accumulated rainfall, suggesting the system begins to respond in unison to larger, more persistent storms.

Snowmelt Runoff

Snowmelt runoff events were identified as events when diel fluctuations in sediment loads were parallel and consistent with the hydrograph in the late winter and early spring. The beginning and end of these events were identified by examination of the simultaneous turbidity, ABS, and streamflow timeseries for the upstream streamgage. Estimates of suspended-sediment loads from snowmelt runoff event ranged from 9 to 562 tons for the ABS suspended-sediment model and 87 to 10,600 tons for the turbidity model (table 12). Snowmelt events constituted 7 percent and 6 percent of the total coincident fallow season suspended-sediment loads predicted with the ABS and turbidity models, respectively (table 6).

Precipitation Runoff Modeling

There are turbidity records for the upstream streamgage from March 2018 through October 2021 and an average turbidity-predicted SSC was determined for a total of 1,002 days at that streamgage. Of those, 254 had days with at least some precipitation recorded with an average temperature greater than 42 °F (rain); these days had rainfall totals ranging from a trace to 1.86 in. A plot of the modeled daily average SSC relative to 2-day accumulated precipitation (fig. 22) shows that days with snow had low SSC relative to days with rain or mixed precipitation, and mixed days had the greatest variability in SSC.

Exponential models were fitted to the 1-, 2-, and 3-day accumulated precipitation. All model coefficients were statistically significant at the 0.001 level, and the 2-day accumulated precipitation model explained the most variance (coefficient of determination=0.42; fig. 22). That model fits the data pattern well, effectively capturing the change in data behavior when 2-day precipitation exceeds 0.1 in., shown as 10⁻¹ in. on figures 22 and 23. The model slope constant (k, eq. 8) was estimated to be 2.3. The model intercept was estimated to be approximately 42 mg/L, which is a reasonable approximation of mean SSC values for days when accumulated precipitation was less than 0.1 in., shown as 10⁻¹ in. on figure 22.

Using the model to estimate the magnitude of 2-day accumulated precipitation required to double the intercept value resulted in a value of 0.3 in., indicating this is the threshold value when SSC in the Shoshone River begins to rapidly increase beyond slightly elevated levels associated with minor rainfall. Based on the empirical cumulative distribution function of the PRISM Climate Group (2021) rainfall record for days when precipitation exceeds 0 in., 0.3 in. of rain was approximately equal to the 90th percentile. These data indicate that days when the accumulated rainfall exceeded 0.3 in. occurred in 10 percent or less of all storms (fig. 23). Examination of the precipitation record from 1981 to 2021 indicates that rainstorms with accumulated precipitation greater than 0.3 in. occur on average 4.5 times a year in the Shoshone River watershed upstream from Willwood Dam and as many as 11 times in a single year.