Sediment-Transport and Bed-Sediment Measurements at Gaging Stations

Suspended-sediment, bedload, and bed-sediment measurements were made at six of the principal gaging and monitoring stations in figure 1. These measurements were used to compute continuous mass-balance sediment budgets for three distinct river segments or areas, as described below in the “Analytical Methods” section. The suspended-sediment measurements were made continuously during ice-free periods at 15-minute intervals using bank-mounted arrays of side-looking acoustic-Doppler profilers (ADPs) utilizing the two-frequency or single-frequency acoustical method of Topping and Wright (2016), depending on the station (table 1). These acoustical measurements were augmented by episodic 10-vertical equal-width-increment (EWI) measurements made using depth-integrating samplers (Edwards and Glysson, 1999), and calibrated-pump measurements as described in Topping and others (2018). Depending on the water depth, the EWI measurements were made using US DH-81, US D-74, or US D-96-A1 samplers (Edwards and Glysson, 1999; Davis and others, 2005). The EWI measurements were made by wading at a tagline at low Q, and typically from a boat at a tagline at high Q, except at the LS-Lily station, and during water years 2013–2016 at the original Green-Jensen station, where these measurements were made from bridges at high Q. During May, August, and October 2016, back-to-back EWI measurements were made at the new upstream Green-Jensen station and at the original Green-Jensen station; these measurements confirmed that sediment transport was equivalent between these two locations of the Green-Jensen station, thus indicating that only negligible erosion or deposition occurred within the intervening 4.1-km-long reach. Moving the ADPs and pump sampler 4.1 km upstream at the Green-Jensen station in 2016 did therefore not affect the results from our study. The samples from all 10 sampling verticals in the EWI measurements made during our study were analyzed for the full sand grain-size distribution. This approach differs from that used to make EWI measurements during much of the historical period. During the historical period, only 1–3 verticals were sampled in the cross section, and the suspended-sand grain-size distribution was typically analyzed at only one of these verticals; refer to Text S1 in the Supporting Information document for Topping and others (2018) for the sources and sampling-methods for the historical EWI measurements. Refer to Text S2 in the Supporting Information document for Topping and others (2018) for the methods used to identify and remove the likely bed-contaminated EWI measurements.

The pump-sampler measurements made during our study were calibrated using the EWI measurements; the acoustical measurements were calibrated using primarily the EWI measurements and secondarily the calibrated-pump measurements, as described in Topping and Wright (2016). Following this calibration process, all three measurement types measured the velocity-weighted suspended-silt-and-clay concentration (C_SILT-CLAY), velocity-weighted suspended-sand concentration (C_SAND), and velocity-weighted suspended-sand median grain size (D_S) in the river cross section at each gaging station. The EWI measurements were used to verify the calibrated-pump measurements during the post-calibration period, and the EWI and calibrated-pump measurements were both used to verify the calibrated-acoustical measurements during the post-calibration period. Plots evaluating the calibrations of the pump and acoustical measurements are provided in Text S1 in the Supporting Information document for Topping and others (2018). Errors in the acoustical suspended-sediment measurements are described in Topping and Wright (2016); field and laboratory errors associated with the pump and EWI measurements are described in Topping and others (2010, 2011, 2021). Data from all stations are available at the USGS Grand Canyon Monitoring and Research Center (GCMRC) website, https://www.gcmrc.gov/discharge_qw_sediment/ (described by Sibley and others, 2015).

Sand bedload measurements were made episodically using the bedform-migration methods described in Topping and others (2018) and elaborated upon in Dean and others (2020); these methods were pioneered by Simons and others (1965). High-Q bedform-migration bedload measurements were made using repeat multibeam sonar surveys, whereas low-Q measurements were generally made using a method employing a stationary echosounder mounted to a pole driven into the riverbed or, in a few cases at low Q in the Little Snake River, using repeat photographs or direct observations. In the stationary-echosounder method, the measurements of bedform height and migration rate made by the stationary echosounder were combined with the average bedform wavelength calculated from either direct measurements or longitudinal acoustic-Doppler-current-profiler (ADCP) measurements to estimate bedload. The stationary-echosounder bedload measurements were made concurrently with those using physical bedload samplers at three gaging stations in March 2018 to allow comparison with historical bedload measurements made in our study area. These historical measurements were made using Helley-Smith samplers (Edwards and Glysson, 1999) by Elliott and others (1984), Martin and others (1998), and Elliott and Anders (2005) and were used in the analyses of Topping and others (2018).

Bed-sediment measurements were made on the same days as the EWI measurements at the gaging stations where sand-bedded conditions existed at least some of the time (table 1). These bed-sediment measurements generally consisted of 10 individual samples collected at the EWI verticals using a US BMH-60 bed-material sampler (Edwards and Glysson, 1999), a “can” on a pole, or hand grabs, depending on flow depth. The median grain sizes and percent of very fine sand among these 10 samples were both averaged to allow analysis of the cross-section-averaged median grain size of the bed sand (D_B) and the cross-section-averaged fractional amount of very fine sand on the bed (f_VF). To ensure that D_B and f_VF were calculated based on a sufficient amount of sampled bed sediment distributed across the cross section to be representative of the average bed-sand conditions in the cross section, we imposed thresholds for the minimum sampled sand mass at each sampling location and the minimum number of such sampled locations in the cross section. D_B and f_VF were thus calculated for only those bed-sediment measurements where samples containing ≥20 grams (g) of sand were collected at ≥50 percent of all verticals; this method follows Topping and others (2021) and uses their threshold for the minimum amount of sampled sediment mass at each vertical but uses a slightly lower threshold for the minimum number of samples in the cross section (≥50 percent instead of ≥60 percent), because of the much larger number of bed-sediment sampling verticals at each gaging station in our study than in the historical measurements analyzed by Topping and others (2021). We also used the bed-sediment measurements at the post-2015 location of the Green-Jensen station (table 1) to estimate changes in the areal coverage of sand. This station was the one station in our study where we observed the amount of sand overlying the cobbles on the bed to vary over time. At this station, we estimated the bed-sand area as the fraction of the 10 sampling verticals where a bed-sediment sample was possible and contained ≥20 g of sand.

We initiated continuous suspended-sediment monitoring in our study area at five gaging stations (fig. 1A, B, stations 1–5) on the Green, Yampa, and Little Snake Rivers during water year 2013 (beginning either in October 2012 or March 2013), and then expanded this effort with data collection at a new station on the middle Green River in Ouray National Wildlife Refuge in March 2017 (fig. 1C, station 19). The start dates for the continuous suspended-sediment measurements and the acoustical method used at each gaging station are listed in table 1. Data from the first five stations were originally published and analyzed in Topping and others (2018). During 2020–2021, several aspects of the acoustical calibrations at these original five stations were revised. All aspects of the acoustical calibrations were rederived for the LS-Lily station on the Little Snake River in December 2020; the previous calibration, used in Topping and others (2018), was poorly constrained owing to a relative paucity of EWI measurements made at higher flows when the ADP was submerged and making measurements. In addition, the correction for the excess backscatter arising from silt and clay (described in Topping and Wright, 2016) was recalculated at all five original stations in 2021 using the larger amount of data available post publication of Topping and others (2018). This recalculation used a silt-and-clay median grain size of 5 microns (μm), a silt-and-clay geometric standard deviation of 1.5ϕ, and a silt-and-clay wet density of 2.8 grams per cubic centimeter (g/cm³) (a density slightly higher than the quartz density of 2.65 g/cm³ owing to the likely presence of illite); ϕ units are defined as ϕ = −log₂D, where D is the sediment grain diameter in millimeters (mm) (Krumbein, 1934). These recalibrations caused slight changes in the annual loads at these five stations (appendix 1), and only slightly affected the sediment budgets in Topping and others (2018).

Cross-Section Resurveys

In October 2020, we resurveyed 27 cross sections in the Uinta Basin segment of the middle Green River that were last surveyed between 1994 and 1996 by FLO Engineering (1996, 1997) or Rakowski (1997). These cross sections provide reasonable coverage of the downstream half of this river segment and are located between river kilometer (RK) 196.4 and RK 252.6 (fig. 1); river kilometers in our study are measured downstream from Flaming Gorge Dam. As part of this effort, we resurveyed all 20 of the cross sections at the Bonanza Bridge (BB), Horseshoe Bend (HB), Stirrup (ST), Baeser Bend (BA), and Above Brennan (AB) study sites of FLO Engineering (1997), located between RK 196.4 and 231.5. Each of these study sites contained four cross sections that were originally surveyed in June 1996. In addition, we resurveyed 2 of the 13 cross sections at Leota Bottom (LEB; at RKs 244.3 and 246.6) and one of the six cross sections at Wyasket Bottom (WYB; at RK 252.6) originally surveyed by FLO Engineering (1996) in March, May, and September 1995. We resurveyed 4 of the 12 cross sections established in 1992 by Rakowski (1997) at her study site, which we refer to as “Cindy’s Bar” (CB). These four cross sections at Cindy’s Bar are located between RK 251.4 and 252.1. In addition to the three Leota Bottom and Wyasket Bottom cross sections that we resurveyed, FLO Engineering (1996) established 33 other tightly spaced cross sections along this part of the river segment, from approximately RK 236.5 to 263.5, that we did not resurvey. Rakowski (1997) resurveyed each of the Cindy’s Bar cross sections seven times during 1994, from before the rise through after the recession of the annual flood: March 17, April 30, May 14, May 28, June 16, July 16, and October 8. We used these multiple repeat surveys spanning the annual floods in 1994 at Cindy’s Bar and in 1995 at Leota and Wyasket bottoms in conjunction with our October 2020 resurvey of these cross sections to compare the magnitudes and styles of seasonal and long-term cross-section change. Though Rakowski (1997) also surveyed the Cindy’s Bar cross sections in November 1992 and four times during and following the recession of the 1993 flood, we did not include those surveys in our analyses because they did not provide the greater resolution throughout the rise and fall of the annual flood captured by Rakowski’s 1994 repeat surveys. We used the last (most recent) of the repeat surveys at Leota Bottom, Cindy’s Bar, and Wyasket Bottom in 1994–1995 and the surveys of the other 20 cross sections in 1996 in conjunction with our October 2020 resurvey of all 27 cross sections to evaluate the long-term (that is, 1990s–2020) cross-section change in the Uinta Basin segment of the middle Green River.

The 2020 resurvey was conducted during October 11–16, 2020, using the Real-Time-Kinematic Global-Positioning-System (RTK-GPS) method with one permanent base station that we deployed at the Ouray National Wildlife Refuge headquarters, one local base station moved between each cross-section cluster, and one rover. We also incorporated data in this resurvey from the U.S. National Geodetic Survey Continuously Operating Reference Station CNC1 in Rangely, Colorado (https://www.ngs.noaa.gov/CORS/Sites/cnc1.html). Based on an analysis of the 1,342 RTK-GPS vectors in our survey, the 95-percent-confidence-level error in the 2020 survey was found to be ±2.0 centimeters (cm) in the horizontal dimension and ±2.4 cm in the vertical dimension. During the 2020 survey, we also collected one bed-sediment sample in the center of the main flow in each cross section for comparison with bed-sediment measurements collected by FLO Engineering (1996); these 2020 bed-sediment measurements are available from the USGS GCMRC website at https://www.gcmrc.gov/discharge_qw_sediment/ under the “Ancillary Sediment Data” link for the Dinosaur network, or directly from the USGS ScienceBase website at https://www.sciencebase.gov/catalog/item/5c002a4fe4b0815414cbb856.

Horizontal positions and elevations in the original FLO Engineering (1996, 1997) and Rakowski (1997) cross sections were determined by digitizing the cross-section plots. By convention, the left and right directions in a river cross section are defined facing downstream. Comparison of the reported endpoint coordinates in FLO Engineering (1997) and Rakowski (1997) with our digitized horizontal and vertical coordinates of the endpoints of these cross sections indicate that the error in our digitization of the cross-section topography was generally sub-decimeter. Our digitized horizontal positions of the endpoints were, on average, only 0.04 meter (m) less than (that is, to the left of) the reported positions in FLO Engineering (1997); the standard deviation about this mean discrepancy in horizontal position was 0.15 m. Our digitized elevations of the endpoints were, on average, only 0.02 m higher than the reported elevations in FLO Engineering (1997); the standard deviation about this mean discrepancy in elevation was 0.03 m. During this step, we detected 12 outliers in the endpoint coordinates and two outliers in endpoint elevations reported by FLO Engineering (1997) that we excluded from the error analysis. These exclusions were justified because the endpoints digitized from the cross-section plots in FLO Engineering (1997) agreed with our 2020 field-surveyed positions and elevations of these endpoints but were not consistent with the tabular-reported coordinates of these endpoints in FLO Engineering (1997). Likely because of the smaller size of the cross-section plots in Rakowski (1997), the absolute value of the discrepancy between the digitized and reported horizontal endpoints were greater for Rakowski’s (1997) cross sections than for FLO Engineering’s (1997) cross sections. Our digitized horizontal positions of the endpoints were, on average, 0.41 m greater than (that is, to the right of) the reported positions in Rakowski (1997); the standard deviation about this mean discrepancy was 0.42 m. Despite the small figure size, our digitized elevations of the endpoints were, on average, only 0.01 m higher than the reported elevations in Rakowski (1997); the standard deviation about this mean discrepancy was 0.04 m. We could not conduct an error analysis for our digitization of the FLO Engineering (1996) cross-section plots because of insufficient information in that report. The digitizing errors associated with FLO Engineering’s (1996) cross sections are assumed to be similar in magnitude to those associated with FLO Engineering’s (1997) cross sections because the style and size of the cross-section plots in these reports are identical.

The original cross-section endpoints were found in the field during our 2020 resurvey using the reported coordinates and (or) maps in FLO Engineering (1996, 1997) and Rakowski (1997), and a magnetic detector (table 2). The FLO Engineering (1996, 1997) endpoints consisted of aluminum-capped rebar driven flush with the ground surface, stamped with the cross-section abbreviation and riverbank, left (L) or right (R). FLO Engineering (1996, 1997) placed a T-post 10–40 cm from the capped rebar in line with the cross section, typically, but not always, closer to the bank than the rebar endpoint. FLO Engineering (1996, 1997) drove these T-posts into the ground so that the top of the post was typically 0.3–0.6 m above the ground surface. The Rakowski (1997) endpoints consisted of uncapped rebar driven to within several centimeters of the ground surface, with T-posts placed in line with the cross section, several centimeters closer to the bank than the rebar. In the seven cases where a cross-section-endpoint rebar or T-post was not found (table 2), we used triangulation from nearby located endpoints to reoccupy the missing endpoint. Once the endpoints of each cross section were located, we surveyed between these endpoints and collected points at each topographic breakpoint. We resurveyed the subaerial part and shallower subaqueous parts of each cross section using an RTK-GPS rover mounted on a 1.8-m survey rod. For the subaqueous parts of each cross section with water depths exceeding 1.8 m, we used a boat-mounted single-beam sonar in combination with the RTK-GPS rover.

Orthometric elevations in the 2020 resurvey were referenced to the North American Vertical Datum of 1988 (NAVD 88) using the Geoid 18 model. Though FLO Engineering (1996, 1997) reported their surveyed elevations above sea level, we could not determine whether they used the National Geodetic Vertical Datum of 1929 (NGVD 29) or NAVD 88; Rakowski (1997) used a local vertical datum. We thus converted the elevations in the FLO Engineering (1996, 1997) and Rakowski (1997) surveys to the NAVD 88 datum by applying a vertical offset unique to each cross section, determined from our 2020 resurveyed elevations of FLO Engineering’s (1996, 1997) capped rebar and Rakowski’s (1997) uncapped rebar (table 2). The 2020 resurvey data are available from the USGS data release that accompanies this report (Griffiths and others, 2024).

Silt-and-Clay Load and Suspended-Sand Load

The cross-sectionally integrated suspended-silt-and-clay flux (Q_SILT-CLAY) and suspended-sand flux (Q_SS) at each 15-minute timestep were respectively calculated by multiplying C_SILT-CLAY and C_SAND by Q, the same method used by Topping and others (2018). The values of C_SILT-CLAY and C_SAND used to calculate these fluxes primarily were those measured by ADPs; in cases where the ADPs were out of the water (as happened during low Q at the LS-Lily, Yampa-Maybell, and Yampa-Deerlodge stations) or buried and (or) blocked by sandbars (as happened episodically at the Green-Ouray station), the values of C_SILT-CLAY and C_SAND from the calibrated-pump and EWI measurements were linearly interpolated to the 15-minute timesteps. These instantaneous values of Q_SILT-CLAY and Q_SS were then integrated over time to compute the silt-and-clay load and the suspended component of the sand load through the river cross section over a given time interval (Porterfield, 1972). At the two stations where the ADPs were located upstream from the streamflow gaging station (that is, the post-2015 Green-Jensen station and the Green-Ouray station) discharge travel-time relations were developed using 15-minute stage measurements at the locations of the ADP array and the streamflow gaging station. This method resulted in best-fit average times of −45 minutes at Green-Jensen and −150 minutes at Green-Ouray that were then applied to the Q timestamps at the gaging stations. The worst period of ADP burial and (or) blockage at the Green-Ouray station occurred from June 3 through October 1, 2021, when C_SILT-CLAY and C_SAND had to be estimated based on previous measurements at similar Q and based on the continuous measurements made during this period at the Green-Jensen station. During prior episodes of ADP burial at this station, sufficient calibrated-pump measurements were available to interpolate reasonably accurate values of C_SILT-CLAY and C_SAND at the 15-minute timestamps. Given that Q was mostly very low during the 2021 period of ADP burial at the Green-Ouray station, however, these estimations of C_SILT-CLAY and C_SAND did not introduce unacceptably high levels of uncertainty in the values of Q_SILT-CLAY, Q_SS, or Q_SB integrated to compute the loads during the annual-flood period of March–July (appendix 1) that were used in the sediment-budget analyses herein.

Sand Bedload and Sand Total Load

The cross-sectionally integrated bedload-sand flux (Q_SB) at each timestep was calculated using log-linear relations between Q and T (following Topping and others, 2018). T is defined as the ratio T = Q_SB/Q_SS; the sand bedload thus dominates over the suspended-sand load when T is >1, whereas the suspended-sand load dominates over the sand bedload when T is <1. The instantaneous values of Q_SB were then integrated over time to compute the bedload component of the sand load through the river cross section over a given time interval (also as in Topping and others, 2018). The cross-sectionally integrated total sand flux (Q_SAND) at each timestamp was calculated by summing Q_SS and Q_SB; these instantaneous values of Q_SAND were then integrated over time to compute the sand total load through the river cross section over a given time interval (also as in Topping and others, 2018).

Dean and others (2022) showed that, under the moderate transport-stage conditions that are typically characterized by the presence of dunes on the riverbed, the Q-dependent T-ratio-based approach is a more accurate estimator of Q_SB than the typical method of using Q—Q_SB rating curves. Transport stage is defined as the ratio of the skin-friction boundary shear stress (τ_sf) to the critical shear stress (τ_cr) associated with D_B. Changes in Q, manifest through changes in shear velocity ($u_{\ast }$), and changes in bed-sand grain size exert roughly similar influence on Q_SB and Q_SS at moderate transport stage (after equation 2 in Dean and others, 2022). The shear velocity is a standard measure of the flow strength and is defined as $u_{\ast }=\sqrt{{\tau }_{\text{b}}/\rho }$, where τ_b is the boundary shear stress and ρ is the density of water. The Q-dependent T-ratio-based approach thus provides a more accurate method for estimating Q_SB because this approach incorporates both the influence of Q on Q_SB (which is included in the Q—Q_SB rating-curve approach) and the influence of changing bed-sand conditions on Q_SB (which is excluded from the rating-curve approach). Given that moderate transport-stage conditions likely dominate at the gaging stations in our study area, substantial changes in both Q and bed-sand grain size occur at these stations (Topping and others, 2018). Therefore, because our continuous suspended-sediment measurements capture the effects of changing bed-sand conditions on Q_SS, the Q-dependent T-ratio-based approach for estimating Q_SB is ideally suited to the rivers in our study.

As in Topping and others (2018), T was calculated using paired EWI and bedload measurements; the bedload measurements were made using either Helley-Smith samplers or bedform-migration methods. At the largely gravel-bedded Yampa-Maybell and Green-Jensen stations, we used the Q—T relations used in Topping and others (2018). These relations were derived by Topping and others (2018) using the historical EWI and Helley-Smith measurements of Elliott and Anders (2005) that were filtered to remove likely bed-contaminated measurements. At the sand-bedded Green-Lodore, LS-Lily, and Yampa-Deerlodge stations, we developed revised Q—T relations using the data in Topping and others (2018) augmented by new paired EWI and bedload measurements made during water years 2017–2019 (figs. 2–4). We also developed a new Q—T relation at the new Green-Ouray station installed in 2017 using paired EWI and bedload measurements made during water years 2017–2018 (fig. 5). One of the new bedload measurements made at the Green-Lodore, LS-Lily, and Green-Ouray stations was made using a Helley-Smith sampler, and the others were made using bedform-migration methods. Upon development of the revised Q—T relations, we recalculated Q_SB at the Green-Lodore, LS-Lily, and Yampa-Deerlodge stations for water years 2013–2016, which were originally analyzed in Topping and others (2018).

Equivalency of Helley-Smith and bedform-migration bedload measurements was evaluated in tests conducted at the Green-Lodore, LS-Lily, and Green-Ouray stations in March 2018. These tests were required to determine whether the Q—T relations developed in Topping and others (2018), and revised herein, were unbiased, given that both the historical Helley-Smith measurements of Martin and others (1998) and Elliott and Anders (2005), and the modern bedform-migration measurements of Topping and others (2018) were used in these relations. For additional context, these tests also included the US BLH-84 bedload sampler (Edwards and Glysson, 1999; Davis and others, 2005), a bedload sampler found to be generally more accurate than the Helley-Smith sampler (Gray and others, 2021). These tests consisted of sequential single-vertical bedload samples, alternating between the Helley-Smith and US BLH-84 samplers, collected adjacent to a pole-mounted echosounder used to make bedform-migration measurements. To be consistent with the historical bedload measurements, both samplers were deployed using bags with a 0.25-mm mesh size. These tests were conducted at verticals in the left and right parts of the cross sections at the Green-Lodore and Green-Ouray stations and at one vertical in the center of the cross section at the LS-Lily station. In addition, one 10-vertical Helley-Smith bedload measurement was made over the full width of the cross section at each of these stations during these tests. The sequential single-vertical bedload samples were collected minutes apart at each vertical. At the Green-Lodore and Green-Ouray stations, three sequential samples were collected, alternating between the two bedload sampler types, in two sampling sets spaced hours apart to allow improved comparison with the bedform-migration bedload measurements (which were made over many hours). At the Green-Lodore station, the sampling sets extended for ~30 minutes at each vertical and were spaced 6 hours apart. At the Green-Ouray station, the sampling sets extended for ~20 minutes at each vertical and were spaced 4.5 hours apart. Among the two sets, six samples were collected with each bedload sampler type at each vertical. At the LS-Lily station, five sequential samples were collected, alternating between the two bedload sampler types, in only one sampling set extending for 45 minutes.

Results from the bedload-sampler tests indicate that, despite Gray and others’ (2021) finding that the US BLH-84 sampler was more accurate than the Helley-Smith sampler, our Helley-Smith measurements were in better agreement with the bedform-migration measurements than were the US BLH-84 measurements (table 3, fig. 6). Substantial overlap between the Helley-Smith and bedform-migration measurements at the 95-percent confidence level occurred in three of the five tests, with near overlap occurring in one additional test and substantial disagreement occurring in only one test (table 3, fig. 6). In contrast, only slight overlap between the US BLH-84 and bedform-migration measurements at the 95-percent confidence level occurred in two of the five tests, with substantial disagreement occurring in two of the five tests and near overlap occurring in only one test. Substantial 95-percent-confidence-level overlap between the US BLH-84 and bedform-migration measurements never occurred. Thus, bedload measurements made using a Helley-Smith sampler appear to be equivalent to those made using bedform-migration methods in our study area, thereby verifying that the Q—T relations of Topping and others (2018) were derived using data that were internally unbiased. Given the equivalency of the Helley-Smith and bedform-migration bedload measurements, we included the 10-vertical Helley-Smith bedload measurements made during the 2018 tests at the Green-Lodore, LS-Lily, and Green-Ouray stations in the revised and (or) new Q—T relations used herein to estimate Q_SB.

Sediment Budgets

Continuous mass-balance sediment budgets for silt and clay and for sand were calculated using the same methods described in Topping and others (2018) for two sediment-budget areas and one river segment (fig. 1). The Deerlodge Park sediment-budget area includes the lower segment of the Little Snake River that extends from the LS-Lily station (fig. 1B, station 3) downstream to the confluence with the Yampa River, the segment of the upper Yampa River that extends from the Yampa-Maybell station (fig. 1B, station 2) downstream to the confluence with the Little Snake River, and the short sand-bedded reach of the lower Yampa River that extends from the confluence of the Little Snake and Yampa Rivers downstream to the Yampa-Deerlodge station (fig. 1B, station 4). The Dinosaur sediment-budget area includes the segment of the lower Yampa River that extends from the Yampa-Deerlodge station (fig. 1B, station 4) downstream to the Yampa-Green confluence in Echo Park, the segment of the upper Green River (mostly in the Canyon of Lodore) that extends from the Green-Lodore station (fig. 1B, station 1) downstream to the Yampa-Green confluence, and the segment of the middle Green River that extends from the Yampa-Green confluence downstream to the original pre-2016 location of the Green-Jensen station (at the USGS streamflow gaging station) (fig. 1B, station 5). The Uinta Basin sediment-budget river segment includes the Uinta Basin segment of the middle Green River that extends from the original location of the Green-Jensen station (fig. 1C, station 5) downstream to the Green-Ouray station (fig. 1C, station 19). The 4.1-km-long reach of the Green River between the current (post-2015) and original locations of the Green-Jensen station (fig. 1, stations 18 and 5) is mostly gravel bedded and relatively steep. Thus, changes in sand mass and in silt and clay mass within this short reach are negligible compared to the changes in mass over the much longer river segments within the Dinosaur sediment-budget area (fig. 1B), as confirmed by back-to-back EWI measurements made throughout 2016 at both locations of the Green-Jensen station that indicated equivalency of C_SAND and C_SILT-CLAY at both station locations. Therefore, it was not necessary to change the location of the downstream end of the Dinosaur sediment-budget area when the Green-Jensen station was moved. Because the continuous suspended-sediment measurements at the three gaging stations that bracket these sediment-budget areas started at different times, the periods of record for the Deerlodge Park and Dinosaur sediment budgets began at slightly different times during the early part of water year 2013 (table 1 and as described in Topping and others, 2018). The period of record for the Uinta Basin sediment budget began on March 25, 2017, upon the initiation of continuous suspended-sediment measurements at the Green-Ouray station (table 1). The periods of record for the two sediment-budget areas and the one sediment-budget river segment extend through at least the end of water year 2021.

As described in Topping and others (2018), the sediment input to each continuous mass-balance sediment budget is computed using the 15-minute silt-and-clay loads and sand loads at the gaging station(s) bracketing the upstream extent of that area or segment. The sediment export from each continuous mass-balance sediment budget is computed using the 15-minute silt-and-clay loads and sand loads at the gaging station bracketing the downstream extent of that area or segment. No tributary sediment inputs are estimated the two sediment-budget areas or the one sediment-budget river segment because most of the tributaries are small, mainly ephemeral, and likely supply mainly silt and clay. The ramification of this sediment-budgeting approach with respect to the tributaries is that, though the sand budgets are almost certainly accurate to within the uncertainties applied to the sand loads (as justified in Topping and others, 2018), the possibility exists that neglecting the small, but not zero, amounts of silt and clay supplied by the tributaries causes negative step changes in the silt-and-clay budgets that are not the result of erosion.

The uncertainties in the sediment budgets are calculated by applying uncertainties to the 15-minute cross-sectionally integrated sediment fluxes at the bracketing gaging stations. These applied uncertainties are then included in the integration of the fluxes over time that yield the loads over a selected period, and then finally propagated through the standard sediment-budget calculation (export minus input yields the change in sediment mass). As justified in Topping and others (2018), 10-percent uncertainties are applied to the 15-minute values of both Q_SILT-CLAY and Q_SAND. We applied a 50-percent uncertainty to the 15-minute estimations of Q_SB used in the sediment budgets. These levels of uncertainty were chosen based on the likely magnitudes of the persistent biases that could be present over longer timescales in the values of Q, C_SILT-CLAY, C_SAND, and Q_SB (Topping and others, 2018). As in Topping and others (2018), the sediment budgets are indeterminate when the propagated uncertainty is ≥2 times the absolute value of the zero-bias value; the sediment budgets are demonstrably positive (thus indicating deposition) or negative (thus indicating erosion) when the uncertainty is less than the absolute value of the zero-bias value; and the sediment budgets are likely positive (thus indicating likely deposition) or likely negative (thus indicating likely erosion) when the uncertainty falls between these bounds.

Bed Stage

The average elevation of the bed in the measurement cross section (that is, bed stage) was calculated for the EWI measurements at the four sand-bedded stations (Green-Lodore, LS-Lily, Yampa-Deerlodge, and Green-Ouray). These calculations of bed stage were used to evaluate changes in the bed-sand grain-size distribution as a function of elevation within the bed (by utilizing bed scour and fill to access different elevations within the bed). Bed stage is defined as the gage height measured at the gaging station at the midpoint time of the EWI measurement minus the mean flow depth among the 10 EWI verticals; flow depths at each vertical in each EWI measurement can be downloaded from the USGS GCMRC website at https://www.gcmrc.gov/discharge_qw_sediment/. Because this calculation of bed stage includes neither the water-surface slope nor the longitudinal distance between the gaging station and the EWI-measurement cross section, the calculated bed stage is relative to a sloping datum parallel to the water surface. Thus, bed stage is only approximately in the same datum as gage height, depending on the water-surface slope and longitudinal distance. However, because the EWI-measurement cross sections tend to be at similar longitudinal positions relative to each gaging or monitoring station, the bed stages at each station are internally consistent and thus can be analyzed for the purpose of relating bed-sand grain size to relative elevation within the bed. Except at the Green-Ouray station, the ADP arrays and EWI measurements are located near the stage sensor used to measure gage height at the associated USGS streamflow gaging station. Thus, the gage heights used to calculate bed stage at the Green-Lodore, LS-Lily, and Yampa-Deerlodge stations are those measured at these gaging stations. Because the gaging station associated with the Green-Ouray station (a monitoring station) is located 8.6 km downstream, gage heights were measured at the Green-Ouray station using a stage sensor mounted with the ADP array near the EWI measurement cross-section location.

Regulation of Suspended-Sand Concentration by Flow, Grain Size, and Other Processes

We used a modified version of the theory-derived parameter α of Rubin and Topping (2001, 2008) to evaluate the relative importance of changes in flow and changes in the bed-sand grain-size distribution in regulating C_SAND. The original version of α was used by Topping and others (2018) to evaluate the relative importance of historical changes in flow and bed-sand grain size in regulating sand transport in the Green, Little Snake, and Yampa Rivers. Changes in bed-sand grain size caused by downstream migration of sand waves were important in regulating sand transport in these rivers historically (Topping and others, 2018). For the analyses herein, we used the approach described in this section to calculate a modified version of |α| separately for the EWI, calibrated-pump, and acoustical suspended-sand measurements; the need for this separation resulted from the different error magnitudes between these three measurement types. In addition, we also investigated whether other processes, such as Q-independent changes in the shear velocity or changes in the area of the bed covered by sand (for example, Topping and others, 2007; 2021; Rubin and others, 2020) had important roles in regulating sand transport. The importance of these other processes in our study area was evaluated graphically.

As defined by Rubin and Topping (2001),

is a quantitative measure of the relative importance of the shear velocity ($u_{\ast }$) versus the median grain size of the bed sand (D_B) in regulating the depth-integrated suspended-sediment flux over a point on the bed, that is, the unit suspended-sand flux (q_SS). The numerator in α describes the variation in q_SS associated with a change in D_B, whereas the denominator in α describes the variation in q_SS associated with a change in $u_{\ast }$. $u_{\ast }$is a measure of the flow strength and is linearly related to velocity (von Karman, 1930), and thereby positively correlated with Q; D_B is the proxy used to simplify all changes in the bed-sand grain-size distribution. Δ signifies the ratio of a quantity at two different times. α is defined so that q_SS is equally regulated by $u_{\ast }$ and D_B when |α| equals the critical value of one, meaning that an observed change in q_SS is attributable to an equal change in $u_{\ast }$ and D_B. Moreover, $u_{\ast }$ is more important than D_B in regulating q_SS when |α| < 1, whereas D_B is more important than $u_{\ast }$ in regulating q_SS when |α| > 1. Changes in sand transport are caused entirely by changes in flow when |α| = 0 (that is, the flow-regulated case), whereas changes in sand transport are caused entirely by changes in the bed-sand grain-size distribution when |α| = ∞ (that is, the grain-size-regulated case).

The values of J, K, L, and M in equation 1 are derived from theory (Rubin and Topping, 2001) and depend on the sorting of the bed-sand grain-size distribution and whether dunes are present on the bed. These exponents are associated with the following proportionalities in Rubin and Topping (2001):

where, as defined early in this report, D_S is the median grain size of the suspended sand. Rubin and Topping (2001) determined the values of the exponents J, K, L, and M by contouring the results from a numerical suspended-sediment model based on McLean (1992) that was run for 129 size classes of sediment in more than 1,000 combinations of flow and bed-sediment conditions, with cases for dunes present and absent on the bed. In essence, this approach allowed Rubin and Topping (2001) to distill the complexities present in the full suspended-sediment theory of McLean (1992) to these simple proportionalities to allow easier, but still rigorous, physically based analyses of suspended-sediment data.

Analysis of our bed-sediment data indicates that the mean geometric standard deviations of the bed-sand grain-size distributions in our study area are intermediate to those used by Rubin and Topping (2001) for poorly and well-sorted beds. Consequently, and for consistency with Topping and others (2018), we set J = 3.5, K = −2.5, L = 0.35, and M = 0.75, values within the range of exponents in Rubin and Topping (2001) and the same as those used by Topping and others (2018). These values are slightly different from the well-sorted bed-sand values of J = 4.3, K = −2.8, L = 0.18, and M = 0.85 used by Dean and others (2020) on the lower Green River and Colorado River near Canyonlands National Park and by Topping and others (2021) on the Colorado River in Grand Canyon National Park. Use of these different sets of exponents can cause |α| to vary by over 20 percent for the same values of σ(log₁₀C_SAND) and σ(log₁₀D_S), where σ indicates standard deviation. Therefore, although the choice of exponents can affect interpretations of flow versus grain-size regulation of sand transport when |α| is close to unity, interpretations of clearly flow- or grain-size-regulated conditions based on |α| values much less than (<<) 1 or much greater than (>>) 1 are generally unaffected by the values of the exponents because of the behavior of α depicted in figure 4 in Rubin and Topping (2001).

Though Rubin and Topping (2001) derived |α| to evaluate the relative importance of $u_{\ast }$ versus D_B in regulating q_SS, |α| can also be used to evaluate the relative importance of Q versus D_B in regulating q_SS (Dean and others, 2016, 2020; Topping and others, 2018, 2021). Analysis of Q measurements from water years 2013–2021 using the method of Topping and others (2021) with appropriate ranges of the bed roughness parameter indicates that the relations between Q and $u_{\ast }$ are nonlinear described by the proportionality

where the exponent ε is estimated by regression, as described below. The value of $u_{\ast }$ in equation 3 is estimated using equation 1 in Text S3 in the Supporting Information document for Topping and others (2021). At the four sand-bedded stations (Green-Lodore, LS-Lily, Yampa-Deerlodge, and Green-Ouray), the range of the bed roughness parameter used in these $u_{\ast }$ estimations was 1 to 2 cm, based on the Columbia River measurements of Smith and McLean (1977). The bed roughness parameter includes the spatially averaged roughness of all bed-roughness elements (for example, bars and dunes) and is larger than the skin-friction roughness parameter that is mostly associated with grain-scale and bedload roughness (Smith and McLean, 1977; Wiberg and Rubin, 1989). At the two largely gravel-bedded stations (Yampa-Maybell and Green-Jensen), the range of the bed-roughness parameter used in these $u_{\ast }$ estimations was 0.1 to 0.2 cm, based on Wiberg and Smith (1991) and the observation that the 84th-percentile grain size (D₈₄) of the gravel comprising the bed at these stations was likely within the cobble size class (that is, 6.4–25.6 cm). The values of ε estimated by least-squares log-linear regression using these highly approximate ranges of the bed roughness parameter were ~0.2 at Green-Lodore, ~0.05 at LS-Lily, ~0.1 at Yampa-Deerlodge, ~0.2 at Green-Ouray, ~0.3 at Yampa-Maybell, and ~0.4 at Green-Jensen. Given these values of ε, a large change in Q will cause only a relatively small change in $u_{\ast }$ at all the gaging and monitoring stations in our study area. Though the value of the exponent ε is inversely related to the assumed value of the bed roughness parameter, this inverse dependence is relatively weak. Hence, the result that the relations between Q and $u_{\ast }$ are steeper at the largely gravel-bedded Yampa-Maybell and Green-Jensen stations than at the four sand-bedded stations is relatively insensitive to the chosen value of the bed roughness parameter. The steeper relations between Q and $u_{\ast }$ at the Yampa-Maybell and Green-Jensen stations will therefore cause C_SAND to increase more rapidly as a function of Q at these stations than at the other stations.

The correlations between Q and $u_{\ast }$ are positive and generally strong, thus indicating that we can effectively exchange Q for $u_{\ast }$ when interpreting |α| at the gaging and monitoring stations in our study area. The correlation coefficient (r) between Q and $u_{\ast }$ ranges from a low of ~0.6 at the Green-Ouray station to a high of almost 1.0 at the Green-Jensen station. Thus, we use the proportionality $u_{\ast }\propto Q^{\epsilon }$ and the above-derived station-specific values of ε to convert $u_{\ast }$ to Q for the analyses herein. Despite the strength of the correlations between Q and $u_{\ast }$, however, it is important to remember that, at especially the sand-bedded stations in our study area, substantial variation in $u_{\ast }$ exists at any given Q about the relation $u_{\ast }\propto Q^{\epsilon }$, and this variation can cause roughly a factor-of-2 variation in C_SAND at any given Q, as elaborated upon below.

Because we ultimately wanted to evaluate the relative importance of Q versus the bed-sand grain size in regulating C_SAND, not q_SS, we derived a new version of α for C_SAND to compare with the standard version of α derived for q_SS. As defined in Rubin and Topping (2001), $C_{\text{SAND}}\propto u_{\ast }^J{D}_{\text{B}}^K$ and $q_{\text{SS}}\propto u_{\ast }^{J+1}{D}_{\text{B}}^K$. After making the appropriate substitutions in equation 1, the C_SAND version of α thus becomes

where α_C is the measure of the relative importance of the shear velocity ($u_{\ast }$) versus the median grain size of the bed sand (D_B) in regulating C_SAND. For the values of J = 3.5 and K = −2.5 used herein, comparison of equations 1 and 4 indicates that α_C = 1.3α, and for the well-sorted-bed values of J = 4.3 and K = −2.8 used by Dean and others (2020) and Topping and others (2021), α_C = 1.2α. Consequently, the critical value of the standard version of |α| to evaluate whether C_SAND is regulated by flow or bed-sand grain size is roughly 1.2 to 1.3. It should be noted, however, that |α| and |α_C| can be used interchangeably when they are <<1 or >>1 because of the uncertainty in the choice of the values of J and K (because bed-sand sorting is not constant over time and dunes may not always be present on the bed), and because of the behavior of α depicted in figure 4 in Rubin and Topping (2001). It is only for cases where |α| or |α_C| are near unity that it is important to recognize the 20 to 30 percent difference between |α| and |α_C| when evaluating the relative importance of flow versus bed-sand grain size in regulating either q_SS or C_SAND.

To allow application of equation 4 to our datasets, with typically over 100,000 suspended-sediment measurements at each gaging station, we used the approximation of Rubin and Topping (2001):

We then used the method of Topping and others (2018) to evaluate the sign of log₁₀ΔC_SAND/log₁₀ΔD_S in equation 4 and calculate |α_C|. By this method, the sign of log₁₀ΔC_SAND/log₁₀ΔD_S was the sign of the slope of log₁₀C_SAND regressed on log₁₀D_S for cases where an F-test indicated that this regression was significant (that is, level of significance [p] < 0.05) and the correlation between log₁₀D_S and log₁₀C_SAND was at least moderate (that is, correlation coefficient [r] > 0.4). When this regression was insignificant or this correlation was weak, the sign of log₁₀ΔC_SAND/log₁₀ΔD_S was indeterminate, and |α_C| was set equal to the mean |α_C| calculated using positive and negative σ(log₁₀C_SAND)/σ(log₁₀D_S) ratios.

Bed-Sand Grain Size

Following Topping and others (2018), we used the nondimensional measure of bed-sand coarseness (β) of Rubin and Topping (2001, 2008) to link the suspended-sand transport to the bed-sand grain-size distribution, and thereby detect the changes in the upstream sand supply associated with sand-wave migration. Rubin and Topping (2001, 2008) derived β using the suspended-sediment theory of McLean (1992), and then tested β against the flume data of Einstein and Chien (1953) and data from the Colorado River. β utilizes suspended-sand measurements to back-calculate the relative coarseness of the spatially averaged bed-sand grain-size distribution in equilibrium with the suspended sand in the reach upstream from the location of the suspended-sediment measurements. β thereby takes advantage of the physical processes governing the suspension of sediment to spatially “sample” the bed sand in exactly the way the flow interacts with the bed. Consequently, β is more representative of the spatially averaged bed-sand grain-size distribution over the reach extending hundreds of meters upstream from a measurement cross section than are direct bed-sediment measurements made only at that cross section (Topping and others, 2021). In addition, β has the added benefit of allowing the calculation of the bed-sand grain size at the time of every suspended-sediment measurement. Because there are many more suspended-sediment measurements than bed-sediment measurements, β allows a more continuous estimation of bed-sand grain size than is possible using only the episodically made direct bed-sediment measurements.

where C_SAND is from a single measurement, C_SAND-REF is the reference C_SAND, D_S is from a single measurement, and D_S-REF is the reference D_S. Reference values are mean values over an entire dataset; hence, the bed sand is finer than the mean condition when β < 1. Unlike in Topping and others (2018), who used the entire period of suspended-sand record at each gaging station to calculate the reference values, we use only the water year 2013–2021 EWI measurements to calculate the reference values at each station; thus, the values of β herein are shifted slightly from those in Topping and others (2018). Our approach has the benefit of normalizing the bed-sand grain size to the modern sediment conditions observed during the period of our study. The reference values from the EWI measurements were used as the reference values for the other measurement types (acoustical and calibrated pump) so that the β values among the various measurement types would be consistent at each station.

Even though Rubin and Topping (2001, 2008) defined β to be a nondimensional measure of D_B, the bed-sand grain-size metric tracked by β in practice depends on the dominant transport mode of the bed sand. Rubin and Topping (2001, 2008) derived equation 6 using log-normal bed-sediment grain-size distributions in their McLean-based numerical model. They conducted two series of model runs for bed sediment with two different geometric standard deviations that remained constant among the runs in each series. Because the shapes of the bed-sediment grain-size distributions in these model runs remained fixed (that is, log-normal with a constant geometric standard deviation) no change in the bed-sediment grain-size distribution could occur without a change in D_B. In real rivers where the shape of the bed-sand grain-size distribution is free to change, however, and especially in rivers where a large part of the bed-sand grain-size distribution is transported as bedload, β can be uncorrelated with D_B and only relate to the amount of finer sand on the bed (Topping and others, 2018, 2021). Changes in the bed-sand grain-size distribution in these rivers typically involve changes mostly in the fine tail of the bed-sand grain-size distribution without necessarily a major change in D_B. Moreover, because the fractional amount (f, expressed as a percentage) of a sand size class on the bed surface required to support a given amount of sand in suspension increases nonlinearly with grain size (after McLean, 1992), relations between β and f in the fine tail of the bed-sand grain-size distribution are semi-logarithmic such that $\beta \propto -\log \left(f\right)$ (Topping and others, 2021). Small changes in the cross-section-averaged fractional amount of very fine sand (f_VF) on the bed thereby cause large changes in β. Consequently, changes in β are typically more sensitive to changes in log₁₀(f_VF) than they are to changes in D_B.

Changes in Cross-Sectional Sediment Area and Topographic Complexity

The change in cross-sectional sediment area between surveys was determined in each cross section by differencing the cross-sectionally integrated NAVD 88 elevations over the horizontal domains common to all surveys. By this approach, positive changes in cross-sectional sediment area corresponded to deposition between surveys and negative changes corresponded to erosion between surveys. Because of bank retreat between the last survey conducted in 1994–1996 and our 2020 resurvey, and the need to measure the erosion caused by this bank retreat, we had to estimate bank-top elevations in 1994–1996 at eight cross sections, as documented below in the “Cross-Section Resurveys” subsection in the “Results with Discussion” section. Of these eight cases, the horizontal extents of these estimations were short except at two cross sections, HB-1B and HB-2B, where large-scale bank retreat had occurred between 1996 and 2020 on the right side of an island (table 2). In addition, we had to estimate the 2020 floodplain topography over relatively short horizontal distances at two cross sections, HB-3 and AB-4, as documented below in the “Cross-Section Resurveys” subsection in the “Results with Discussion” section. At cross section HB-3, this estimation was required because we terminated the left-bank survey near where the 2020 ground surface merged with the 1996 ground surface at the edge of an extremely dense willow thicket; the capped-rebar endpoint and T-post on the left bank could not be found in this thicket. At cross section AB-4, this estimation was required because we terminated our left-bank survey at an apparently misreported capped-rebar endpoint and T-post that we found 20.2 m closer to the bank than was reported in FLO Engineering (1997) (table 2). The channel width in each cross section was measured at the elevation associated with the top of the lower of the two banks (the approximate floodplain elevation), at the lowest elevation of this bank top among the 1990s and 2020 surveys.

The topographic complexity in each cross section during each survey was evaluated by resampling the surveyed elevations at 0.5-m intervals over the domain used to compute changes in cross-sectional sediment area and then computing the topographic variance among the elevations at these fixed intervals, that is, nodes. We used the topographic variance among these nodes as a measure of the cross-section channel complexity. Changes in the topographic variance between surveys could then be used to evaluate our hypothesis that erosion of sediment corresponds to an increase in channel complexity and conversely that sediment deposition corresponds to a decrease in channel complexity. There is an important caveat that must be first acknowledged, however, when using topographic variance to detect changes in channel complexity. In the case where only a small part of the analyzed domain includes the higher elevations associated with the tops of floodplains or terraces, as in the resurveyed cross sections presented herein, changes in topographic variance provide an accurate measure of changes in channel complexity only when minimal change in channel width occurs. When only a small part of the domain is at higher elevation, the transfer of nodes between high and low elevations caused by changes in channel width can dominate over the signal in topographic variance arising from the bed-elevation variability across the channel that is associated with channel complexity (fig. 7). Thus, cross sections with substantial changes in channel width must be segregated from those exhibiting minimal changes in width when analyzing relations between sediment erosion or deposition and cross-section topographic variance.

Controls on Sediment Transport

Grain-Size Evidence for Sand Waves During the Annual Flood

In addition to the episodic sand waves generated by tributary floods during other times of the year (the most notable example of which are the large Sand Creek floods of 1956–1966), annual sand waves are also generated during the annual snowmelt flood. Bed-sand grain-size data indicate that these annual sand waves originate in the Yampa River basin as the result of the flow accessing finer bed sand as Q increases. The most likely mechanism responsible for the bed-sand fining with increasing Q differs between the sand- and gravel-bedded parts of the rivers in the Yampa River basin. At the sand-bedded LS-Lily and Yampa-Deerlodge stations, the most likely mechanism is scour through an inversely graded bed (figs. 15–16). At the gravel-bedded Yampa-Maybell station, the most likely mechanism is access to finer sand stored at higher elevations in sandy point bars (fig. 19). Both mechanisms result in the generation of a sand wave that migrates downstream in the middle Green River, as evidenced by β calculated from our annual high-flow EWI measurements (fig. 25). Although bed-sand grain size tends to be inversely related to Q at the Yampa-Maybell, LS-Lily, Yampa-Deerlodge, and Green-Ouray stations, no relation exists between bed-sand grain size and Q at the Green-Jensen station (figs. 15–17, 19, 20). Thus, bed-sand fining at the Green-Jensen station during or immediately following Yampa River floods would indicate the likely arrival of a sand wave from the Yampa River. In addition, bed-sand fining at the Green-Ouray station that is uncorrelated with increases in Q would indicate the arrival of a sand wave from upstream.

For the analysis in figure 25, we used the β values calculated from the EWI measurements made at the highest Q during the last week of May through the first week in June. Though these measurements were not necessarily made at peak Q during the annual flood, they were typically made within a week of peak Q. Though no natural annual flood exists on the upper Green River downstream from Flaming Gorge Dam, the EWI measurements made during the typically short-duration artificial floods released from the dam to advantage native fish (U.S. Fish and Wildlife Service, 1992; Bureau of Reclamation, 2005, 2006; Bestgen and others, 2011; LaGory and others, 2012) were used to calculate high-flow β at the Green-Lodore station. Even though most of these EWI measurements were not made at peak Q, we chose the EWI measurements over the calibrated-pump or acoustical measurements made at peak Q because of the much greater accuracy of the EWI measurements. Thus, the greater accuracy of the high-flow β values calculated using these EWI measurements was given preference over the possible change in β between the time of the EWI measurements and peak Q that may not be accurately reflected by the β values calculated from the less accurate calibrated-pump or acoustical measurements. When two EWI measurements were made at similar Q within 24 hours, we averaged the β values calculated among these two measurements. To easily compare the high-flow β time series between the stations, we normalized the β values using the mean β of those calculated among all high-flow EWI measurements at a given station. Although the much-shorter period of record at the Green-Ouray station caused β to be normalized over a much-shorter period (2017–2021) than at the Green-Jensen station (2013–2021), this difference in record length did not introduce much error in this analysis because the mean of the normalized high-flow β values at Green-Jensen during 2017–2021 differed from that at Green-Ouray by only 1.5 percent.

We use two metrics to describe the annual flood in the analysis in figure 25 and in the subsequent analyses in this report: peak Q, and the March–July median Q. This approach is similar to that used by Dean and others (2020) on the lower Green River and the Colorado River upstream from Canyonlands National Park. The March–July period encompasses the entire annual snowmelt flood; thus, the March–July median Q serves as a reasonable proxy for the duration of the higher Q within the annual flood. Although peak Q is commonly used as a key flood measure in geomorphic analyses, it is not necessarily the best metric to use in analyses of sediment transport and associated geomorphic change in the case where (1) the “slope” of the Q—sediment-concentration point clouds are relatively low (meaning that a substantial amount of sediment transport occurs at Q lower than peak), and (2) the hydrograph shape is not well-correlated with the peak Q during the annual flood. Both aspects of this case occur in our study area. Because Q increases much faster than $u_{\ast }$ at all the stations in our study area, the slopes of the Q—C_SAND point clouds in figures 9–14 are relatively low. In addition, the correlations between peak Q and the March–July median Q are only significant (p < 0.05) and very strong (r ≥ 0.8) at two stations: Yampa-Maybell and Yampa-Deerlodge (fig. 26A). Finally, the construction and operation of Flaming Gorge Dam has eliminated the annual snowmelt flood on the upper Green River in our study area. Although artificial floods are released from this dam to advantage native fish or disadvantage nonnative fish (U.S. Fish and Wildlife Service, 1992; Bureau of Reclamation, 2005, 2006; Bestgen and others, 2011; LaGory and others, 2012, 2019), the peak Q of these artificial floods is limited by the dam such that the correlation between peak Q and the March–July median Q at the Green-Lodore station is insignificant and weak (p = 0.44, r = 0.3; fig 26A). Thus, the March–July median Q is a more universal metric than the peak Q in evaluating the sediment effects of the annual flood in our study area.

Because both bed-sand and suspended-sand grain size are inversely related to Q at the stations on the Little Snake and Yampa Rivers (fig. 1), larger Yampa River floods generate finer sand waves, as evidenced by the smallest values of β at the Yampa-Maybell, LS-Lily, and Yampa-Deerlodge stations generally aligning with the larger peaks in both peak Q and March–July median Q at the Yampa-Deerlodge station (fig. 25). For simplicity, the values of peak Q and March–July median Q at the Yampa-Maybell and LS-Lily stations are not shown in figure 25 because they are respectively very strongly correlated with the values of peak Q (r = 0.95, 0.81, respectively) and March–July median Q (r = 0.99, 0.90, respectively) at the Yampa-Deerlodge station. Similarly, the values of peak Q and March–July median Q at the Green-Ouray station are not shown in figure 25 because they are almost identical to the values of peak Q at the Green-Jensen station. Though barely insignificant at the Yampa-Deerlodge station (p = 0.063), the negative correlations between Q at the time of the EWI measurement used to calculate β and normalized β are significant at the Yampa-Maybell and LS-Lily stations, and strong to very strong at the Yampa-Maybell (r = −0.8), LS-Lily (r = −0.7), and Yampa-Deerlodge (r = −0.6) stations (fig. 26B). This result indicates that the signal detected in the β values calculated from only the high-flow EWI measurements is generally consistent with the inverse relation between Q and β indicated by all EWI measurements at these stations (figs. 15F, 16F, 19). Thus, by accessing finer bed sand at higher Q, larger values of peak Q or March–July median Q at the Yampa-Deerlodge station are associated with the generation of finer sand waves.

The annual sand waves introduced to the middle Green River during the annual flood of the Yampa River migrate downstream past the Green-Jensen station within the same flood and arrive at the Green-Ouray station the following year (fig. 25B, C). This result is indicated by the general alignment of the peaks and troughs in the high-flow β time series among the Yampa-Maybell, LS-Lily, Yampa-Deerlodge, and Green-Jensen stations (fig. 25B), and the 1-year lag between the peaks and troughs between the high-flow β time series at the Green-Jensen and Green-Ouray stations (fig. 25C). The similar magnitudes of the peaks and troughs in the high-flow β time series among the Yampa-Maybell, LS-Lily, Yampa-Deerlodge, and Green-Jensen stations indicate that finer annual sand waves in the Yampa River cause greater bed-sand fining in the middle Green River at the Green-Jensen station. No relation exists between Q at the time of the EWI measurement and normalized β at either the Green-Jensen or Green-Ouray station (fig. 26B), thus confirming that the pattern in high-flow β at these stations (fig. 25) arises from the downstream migration of annual sand waves and not from changes in Q.

Given that the Yampa River supplies most of the sand at the confluence of the Yampa and Green Rivers, sand waves generated in the upper Green River likely have only minimal influence on the bed-sand grain size in the middle Green River at the Green-Jensen station. Thus, even though the peaks and troughs in the high-flow β time series are also somewhat aligned between the Green-Lodore and Green-Jensen stations, the influence of the high-flow β time series at the Green-Lodore station on the high-flow β time series at the Green-Jensen station is likely restricted to years like 2017 (figs. 25A, 26A). Sustained large releases from Flaming Gorge Dam in 2017 resulted in elevated March–July median Q values at both the Green-Lodore and Green-Jensen stations (figs. 25A, 26A), likely causing the coarsest value of normalized β (from extended bed-sand winnowing) at the Green-Lodore station (fig. 25B). Importantly, even though high-flow β was at its coarsest value at the Green-Lodore station in 2017, this major bed-sand coarsening event had, at most, minimal downstream influence on β at the Green-Jensen station.

Effects of Sand-Wave Migration on Sand Transport at the Green-Jensen and Green-Ouray Stations Leading to Changes in Sand Mass in the Uinta Basin Segment of the Middle Green River

Changes in sand mass (that is, net deposition or erosion) in the Uinta Basin segment of the middle Green River are controlled by Q-independent shifts in sand transport at the Green-Jensen and Green-Ouray stations associated with the downstream migration of sand waves generated during a sequence of annual floods on the Yampa River. We refer to the first large flood in a sequence of annual Yampa River floods as the “year-1 flood,” the second flood in this sequence as the “year-2 flood,” and collectively to all floods in this sequence after the year-1 flood as “out-year floods.” The Q-independent shifts in sand transport at the Green-Jensen and Green-Ouray stations result from the changes in bed-sand grain size associated with the longitudinal positions of the Yampa-generated sand waves.

As inferred from β (fig. 25A, B), large Yampa River floods (that is, year-1 floods) generate sand waves with fine fronts that emanate into the Green River and migrate into the Uinta Basin segment past the Green-Jensen station but may not reach the Green-Ouray station (fig. 27). This longitudinal position of the year-1 sand wave is associated with bed-sand fining at the Green-Jensen station (fig. 25B). Because the Green-Ouray station is downstream from the front of the year-1 sand wave, the Green-Ouray station is in the coarser tail of an out-year sand wave from a preceding flood sequence (fig. 27A). In addition, because this tail of the preceding out-year sand wave is winnowed as this sand wave migrates downstream during the year-1 flood, this longitudinal position of the year-1 sand wave, with its front located between the Green-Jensen and Green-Ouray stations, is associated with bed-sand coarsening at the Green-Ouray station (fig. 25B). Consequently, increased sand transport occurs at the Green-Jensen station while decreased sand transport occurs at the Green-Ouray station during the year-1 flood. As described below in the “Influence of Flood Magnitude and Source on Sediment Budgets During Annual Floods” section of this report, sand deposition in the Uinta Basin segment thus occurs during the year-1 flood owing to a downstream decrease in sand transport associated with downstream bed-sand coarsening between the Green-Jensen and Green-Ouray stations.

The downstream migration of the year-1 sand wave during out-year Yampa River floods in combination with the generation of out-year sand waves results in either no substantial net downstream change in bed-sand grain size between the Green-Jensen and Green-Ouray stations or downstream fining between these stations (fig. 27B, C). During the year-2 flood, the front of the year-1 sand wave migrates downstream past the Green-Ouray station causing bed-sand fining at this station (figs. 25C, 27B, C). Depending on the magnitudes of the year-2 and other out-year floods, however, the bed-sand grain size at the Green-Jensen station will either not change substantially or will coarsen during these floods. The tail of the year-1 sand wave will be winnowed as it migrates downstream, thereby causing bed-sand coarsening. The degree of this coarsening at the Green-Jensen station may be offset depending on the magnitudes of the out-year floods. As inferred from β (fig. 25A, B), a series of similar-magnitude Yampa River floods will likely generate a succession of similar-sized sand waves of similar grain size in the Uinta Basin segment. Under this scenario, the resupply of sand during each flood could offset the bed-sand coarsening at the Green-Jensen station caused by the downstream migration of the year-1 sand wave, thereby leading to no substantial downstream change in bed-sand grain size between the Green-Jensen and Green-Ouray stations (fig. 27B). Moreover, a series of declining Yampa River floods will likely generate a succession of smaller, coarser sand waves in the Uinta Basin segment. Under this scenario, the bed sand at the Green-Jensen station would progressively coarsen mostly from the winnowing of the tail(s) of the year-1 or amalgamated preceding sand wave(s) and possibly also from the addition of coarser sand during these smaller out-year floods, thereby leading to downstream fining between the Green-Jensen and Green-Ouray stations (fig. 27C).

Successive floods in a sequence of annual Yampa River floods of equal or declining Q thus generate annual sand waves in the middle Green River of roughly similar or coarsening grain size, as inferred from the normalized high-flow β values in figure 25. Consequently, the continued downstream migration of sand waves in the middle Green River during out-year floods can result in either no net downstream change in bed-sand grain size or downstream fining in the Uinta Basin segment. Thus, out-year floods will typically be associated with sand conveyance through (fig. 27B) or sand erosion in (fig. 27C) the Uinta Basin segment. Because the upper Green River supplies far less sand to the middle Green River than does the Yampa River, sustained large releases from Flaming Gorge Dam are likely to limit bed-sand fining at Green-Jensen and increase bed-sand coarsening at Green-Ouray and thereby modify the downstream migration of the sand waves generated by Yampa River floods (fig. 27C).

The observed shifts in the Q—C_SAND point clouds at the Green-Jensen and Green-Ouray stations are consistent with the above-described changes in bed-sand grain size associated with the downstream migration of sand waves generated during the annual flood of the Yampa River (fig. 28). In figure 28, the Q—C_SAND point clouds at Green-Jensen and Green-Ouray are plotted for all measurement types during the March–July annual-flood period in each year. Because the sand bedload during March–July at Green-Ouray is a much larger percentage of the sand total load (that is, sand bedload plus suspended-sand load) than at Green-Jensen, and because C_SAND does not include bedload, large overlap of the Q—C_SAND point clouds at these two stations indicates sand erosion in the Uinta Basin segment. Among the 2017–2021 March–July annual-flood periods, the sand bedload at Green Jensen ranged from 4 to 12 percent of the sand total load, whereas the sand bedload at Green-Ouray ranged from 20 to 34 percent of the sand total load (appendix 1). To place the positions of the Q—C_SAND point clouds each year in context, the March–July median Q at the Yampa-Deerlodge and Green-Lodore stations are reported, the normalized high-flow β and measured bed-sand area (A_B) associated with the high-flow EWI measurements are indicated, and the “C_SAND slopes” are indicated. The “C_SAND slope” is simply the slope of the least-squares linear regression of C_SAND on Q, forced through the origin, and is used as a metric for the steepness of a Q—C_SAND point cloud; all C_SAND measurement types are included in this regression (EWI, calibrated pump, and acoustical). For example, an increase in the C_SAND slope indicates an upward shift in C_SAND at any given Q and thereby an increase in sand transport, whereas a decrease in the C_SAND slope indicates a downward shift in C_SAND at any given Q and thereby a decrease in sand transport.

For direct comparison of the results in figure 28 to those presented in the next section of this report, the geomorphic implication of the March–July change in sand mass from the continuous mass-balance sand budgets for the Uinta Basin segment (from the “Influence of Flood Magnitude and Source on Sediment Budgets During Annual Floods” section below) is also indicated for each year. This implication is given in each figure panel in terms of sand erosion, likely sand erosion, sand conveyance, or sand deposition (no years fell into the likely sand deposition category). The uncertainty thresholds used to determine whether sediment budgets are indeterminate or indicate erosion, likely erosion, deposition, or likely deposition are the same as in Topping and others (2018) and were reviewed in the “Sediment Budgets” subsection in the “Analytical Methods” section. Although indeterminate sand budgets typically arise from erosion offsetting deposition in a river segment, and not necessarily from sand being transported through a segment with zero local erosion and deposition, we neglect this complexity to be consistent with the conceptual model in figure 17 and simply use the term “sand conveyance” for cases with indeterminate sand budgets.

Influence of Flood Magnitude and Source on Sediment Budgets During Annual Floods

Larger Yampa River floods cause erosion in the Deerlodge Park and Dinosaur sediment-budget areas but tend to cause deposition farther downstream in the Uinta Basin segment of the Green River (figs. 29–31). Conversely, although longer duration large releases from Flaming Gorge Dam cause no detectable change in sand mass in the Dinosaur sediment-budget area (fig. 30B), these releases may cause erosion in the Uinta Basin segment (fig. 31B). Though small in magnitude, unequivocal erosion of sediment from the Uinta Basin segment has only been observed during low-flow years with small Yampa River floods (fig. 31). These results are consistent with the earlier results of Topping and others (2018) for the Deerlodge Park and Dinosaur sediment-budget areas. In addition, these results are those expected for the Dinosaur and Uinta Basin sediment budgets given the bed-sand grain-size changes (fig. 25), and associated shifts in sand transport (fig. 28), caused by the downstream migration of the sand waves generated during annual floods of the Yampa River (fig. 27).

The Deerlodge Park sediment-budget area has been a likely source of sand for the lower Yampa River for many years. Although minor overlap of the error bars with the line of zero change exists for a few cases, net sand erosion has occurred from this part of the Yampa River basin during all annual floods where the peak Q and the March–July median Q, respectively, exceed ~7,800 and ~1,500 ft³/s at the Yampa-Maybell station (fig. 29A, B), ~2,800 and ~360 ft³/s at the LS-Lily station (fig. 29C, D), and ~10,300 and ~1,800 ft³/s at the Yampa-Deerlodge station (fig. 29E, F). The negative correlations between these annual-flood metrics (peak Q and March–July median Q) and the change in sand mass in this sediment-budget area during the March–July annual-flood period is moderate to strong (with r ranging from 0.4 to 0.6). On average, ~70,000±62,000 metric tons of sand were eroded from the Deerlodge Park area each year during the March–July annual-flood period between 2013 and 2021. Given the uncertainties in the loads at the Yampa-Maybell and LS-Lily stations, this amount was equal to between 5 and 130 percent of the average amount of sand supplied to the Deerlodge Park area by the upper Yampa and Little Snake Rivers during the annual flood. Thus, a considerable amount of sand supplied to the middle Green River during the annual floods of the Yampa River during 2013–2021 could have been eroded from the Deerlodge Park sediment-budget area.

Analysis of aerial lidar (light detection and ranging) surveys indicates that ~50,000±130,000 (±95-percent-confidence-level uncertainty) cubic meters (m³) of sediment were eroded from the downstream ~3.7 km of the Yampa River in Deerlodge Park between 2011 and 2015 (Leonard, 2022; volume of sediment erosion and uncertainty revised by C. Leonard, National Park Service, written commun., May 7–8, 2024). The river segment in which this erosion was measured encompassed the lower ~3.1 km of the Deerlodge Park sediment-budget area and extended ~0.6 km downstream from the Yampa-Deerlodge station. This erosion resulted from a combination of slight net channel-bed scour (−0.07±0.24 m) and the lateral migration of the Yampa River, which caused the erosion of higher cut banks on the outsides of meanders and the deposition of lower banks on the insides of meanders (Leonard, 2022; value of net channel-bed scour and 95-percent-confidence-level uncertainty revised by C. Leonard, National Park Service, written commun., May 6, 2024). Conversion of this volume of sediment erosion to mass yields 80,000±210,000 metric tons of erosion between 2011 and 2015, assuming 40 percent porosity (after Curry and others, 2004) and a quartz density of 2,650 kilograms per cubic meter (kg/m³). This magnitude of likely predominantly sand erosion equates to a mean-annual erosion rate of ~20,000 metric tons, an erosion rate in agreement with that determined for the 2013–2021 annual-flood period from the continuous mass-balance sediment budget calculated for the longer river segments that comprise the entire Deerlodge Park sediment-budget area. Moreover, repeat surveys of cross sections suggest that erosion of sand from the Deerlodge Park area has been ongoing since at least 1983, with a 1997–2017 mean-annual sand erosion rate of ~37,000 metric tons (Griffiths and others, 2024), an erosion rate also in agreement with that for the 2013–2021 annual-flood period determined from our continuous mass-balance sediment budget. Therefore, it is likely that sand has been eroded from the Deerlodge Park sediment-budget area during the annual flood of the Yampa River for quite some time. Although this long-term erosion may be a legacy of the bed-sand coarsening associated with the downstream migration of the tail(s) of the sand wave(s) generated by the 1956–1966 Sand Creek floods, as suggested by Topping and others (2018), this erosion likely also owes to the natural lateral migration of the river (Leonard, 2022).

In contrast to the sediment-budgeting results for sand, no net change in the amount of silt and clay stored in the Deerlodge Park sediment-budget area has occurred during the annual floods of 2013–2021, although large changes in the stored amount of silt and clay did occur during some years. The mean change in March–July silt and clay mass in the Deerlodge Park area among the 2013–2021 annual floods was +35,000±77,000 metric tons. Following Topping and others (2018), we conclude that sediment budgets are indeterminate when the uncertainty is ≥2 times the absolute value of the zero-bias value, demonstrably positive or negative when the uncertainty is less than the zero-bias value, and either likely positive or negative when the uncertainty falls between these bounds. In this case, the uncertainty is 2.2 times the zero-bias value of 35,000 metric tons, and therefore no net change in silt and clay mass can be demonstrated among the 2013–2021 annual floods. The only annual-flood metric possibly related to changes in silt and clay mass in the Deerlodge Park sediment-budget area is the peak Q of the Little Snake River flood (fig. 29C); the correlation between peak Q at the LS-Lily station and deposition of silt and clay in the Deerlodge Park area during the annual flood is moderate (r = 0.4).

Sand eroded from the Dinosaur sediment-budget area during larger Yampa River floods can be deposited farther downstream in the Uinta Basin segment of the middle Green River (figs. 30–31). The strong tendency toward erosion of sand from the Dinosaur sediment-budget area during large Yampa River floods is indicated by the strong negative correlation between the peak Q of the annual flood at the Yampa-Deerlodge station and sand mass balance in the Dinosaur sediment-budget area (r = −0.7, fig. 30C), and the very strong negative correlation between the March–July median Q at Yampa-Deerlodge and sand mass balance in the Dinosaur sediment-budget area (r = −0.9, fig. 30D). It is not simply the magnitude of the annual flood that causes erosion in the Dinosaur sediment-budget area, otherwise the very strong negative correlation between the March–July median Q at Yampa-Deerlodge and the sand mass balance in the Dinosaur sediment-budget area would be reflected in a similar negative correlation at the Green-Jensen station, where this correlation is, in fact, only weak (r = −0.3, fig. 30F). The annual floods that cause the greatest amount of erosion in the Dinosaur sediment-budget area are thus the large Yampa River floods that also supply the largest amounts of sand to the Dinosaur sediment-budget area.

Although more sediment-transport data at the stations bracketing the Uinta Basin segment during larger Yampa River floods would help solidify this relation, an equally strong tendency toward deposition of sand in the Uinta Basin segment during large Yampa River floods is strongly suggested by the strong positive correlation between the peak Q of the annual flood at Yampa-Deerlodge and the sand mass balance in the Uinta Basin segment (r = 0.7, fig. 31C), and the very strong positive correlation between the March–July median Q at Yampa-Deerlodge and the sand mass balance in the Uinta Basin segment (r = 0.8, fig. 31D). Sand is eroded from the Uinta Basin segment during the annual-flood period in years with smaller Yampa River floods (fig. 31C, D), and possibly also eroded during years with larger sustained Flaming Gorge Dam releases (r = −0.5, fig. 31B). Sand deposition occurs in the Dinosaur sediment-budget area during smaller Yampa River floods (fig. 30C, D), and in the lower Q periods during the months of the year outside the March–July annual-flood period.

Larger peak Q of Flaming Gorge Dam releases (r = −0.5, fig. 30A) or larger March–July median Q in the Yampa River (r = −0.4, fig. 30D) provide the most likely mechanisms for erosion of silt and clay from the Dinosaur sediment-budget area. As with the sand, much of the net deposition of silt and clay in the Dinosaur sediment-budget area occurs during the months of the year outside the March–July annual-flood period shown in figure 30. Flows during the annual flood have little effect on the amount of silt and clay stored in the Uinta Basin segment of the middle Green River, although larger sustained Flaming Gorge Dam releases may erode silt and clay from this segment (r = −0.7, fig. 31B).

Over longer sequences of floods in both the Dinosaur sediment-budget area and Uinta Basin segment, the change in sand mass has been negligible whereas slight silt and clay erosion may have occurred. Among the 2013–2021 annual floods in the Dinosaur sediment-budget area, the change in March–July sand mass was −19,000±88,000 metric tons (indeterminate change) and the change in March–July silt and clay mass was −90,000±95,000 (likely negative but small change). Similarly, among the 2017–2021 annual floods in the Uinta Basin segment, the change in March–July sand mass was 2,600±82,000 metric tons (indeterminate change) and the change in March–July silt and clay mass was −52,000±86,000 metric tons (likely negative but small change). Because tributaries, which likely supply much more silt and clay than sand, are not included in these sediment-budget calculations (as described in the “Analytical Methods” section), it remains possible, however, that these “likely negative” results for silt and clay are artifacts of the exclusion of tributaries. If the silt-and-clay loads of tributaries were measured and then included in the sediment-budget calculations, the changes in silt and clay mass, like the changes in sand mass, could also be indeterminate when integrated over many annual floods.

Given that most of the demonstrable changes in sediment mass in the Dinosaur sediment-budget area during the annual-flood period involve Yampa River flows, it is most likely that these changes in sediment mass occur within the lower Yampa and alluvial reaches of the middle Green River and not within the upper Green River in the Canyon of Lodore. The geographic scope of where most of the changes in sand mass are likely located can be further refined based on the stations where the largest shifts in the Q—C_SAND point clouds occur as a function of changes in bed-sand grain size. The large Yampa River floods that cause substantial upward shifts in the Q—C_SAND point clouds at the Green-Jensen station cause relatively little change in the Q—C_SAND point clouds at the Yampa-Deerlodge station (for example, the large 2019 flood). Thus, the location of the net erosion of sand from the Dinosaur sediment-budget area associated with the bed-sand fining and increase in sand transport at Green-Jensen was likely much closer to the Green-Jensen station than the Yampa-Deerlodge station. Thus, as suggested by Topping and others (2018), it is likely that most of the changes in sediment mass occur in the shorter alluvial reaches with the greatest sediment accommodation space, for example, Echo, Island, and Rainbow Parks (fig. 1B), all of which are along the middle Green River, much closer to the Green-Jensen station than the Yampa-Deerlodge station.

Although it may seem counterintuitive for large Yampa River floods to erode sand from the middle Green River in the Dinosaur sediment-budget area because these floods supply the largest amount of sand to this river segment, the physical basis for this effect is well-established and arises from changes in bed-sand grain size. Einstein and Chien (1953) were perhaps the first to show that changes in bed-sand grain size have a much stronger effect on sand transport than changes in sand transport have on the bed-sand grain-size distribution (Rubin and Topping, 2001). Consequently, the bed-sand fining caused by the downstream migration of the front of a sand wave is associated with an immediate increase in C_SAND and thereby an immediate increase in sand transport. Thus, although the finest size classes of sand in a sand wave may migrate downstream quickly (Topping and others, 2000, 2021), the associated increase in C_SAND occurs even faster. Because of the nonlinear relation between bed-sand grain size and C_SAND (eq. 2A), small changes in bed-sand grain size thus cause large and immediate shifts in sand transport at constant $u_{\ast }$, and thereby at constant Q. Depending on the rate and depth of the mixing of the fine front of a sand wave with the antecedent coarser sand bed, these shifts in the Q—C_SAND point clouds may persist for long enough during the annual flood so that the bed-sand fining caused by a large Yampa River flood has a larger and longer effect on sand transport at Green-Jensen than does the actual amount of sand supplied during the Yampa River flood. In essence, the large reservoir of sand present on the bed buffers the rate at which the bed-sand grain-size distribution can change in response to a change in the upstream sand supply. This reservoir effect was observed in the laboratory by Einstein and Chien (1953) and formed the basis for their conclusion that changes in the bed-sand grain-size distribution had a “strong and immediate” effect on sand transport, whereas changes in sand transport had only a “weak and slow” effect on the bed-sand grain-size distribution. More extensive fining of the bed sand upstream from the Green-Jensen station during a larger Yampa River flood may therefore cause an increase in the sand export from the Dinosaur sediment-budget area that exceeds the amount of sand supplied to the Dinosaur sediment-budget area from both the Yampa and upper Green Rivers, as suggested by the increased sand erosion during progressively larger Yampa River floods (fig. 30C, D).

Sand deposition in the Uinta Basin segment of the middle Green River during a large year-1 annual flood on the Yampa River, and sand erosion from this segment during subsequent out-years also occur as the result of the longitudinal patterns in bed-sand grain size associated with the downstream migration of sand waves generated during Yampa River floods, as described in the previous section of this report. Consequently, large year-1 floods, like the 2019 Yampa River flood, can cause deposition in the Uinta Basin segment (fig. 31C, D). Because of the continued downstream migration of the year-1 sand wave and the addition of generally smaller and coarser sand waves during out-year Yampa River floods, the bed sand generally coarsens and sand transport decreases at the Green-Jensen station while the bed sand fines and sand transport increases at the Green-Ouray station during out-year floods (fig. 28D, E). As described in the previous section, the degree to which the bed sand coarsens at Green-Jensen during these out-year floods is of course limited or potentially offset by the magnitude of each out-year flood, thereby affecting whether sand will be eroded or deposited in the Uinta Basin segment. For example, it took 2 years for the bed sand to coarsen sufficiently at Green-Jensen and fine sufficiently at Green-Ouray for sand to be eroded from the Uinta Basin segment following the large (year-1) Yampa River flood of 2019 (fig. 31C, D). Over the first year following this large flood (year-2), the bed sand coarsened at Green-Jensen and fined at Green-Ouray only to the extent that sand was conveyed through this river segment during the 2020 annual flood. Differences between the sequencing of flows from the Yampa River and upper Green River increase the complexity of this problem. For example, sustained large releases from Flaming Gorge Dam may increase the degree of bed-sand coarsening at Green-Jensen (fig. 28A), and thereby increase the potential for sand erosion from the Uinta Basin segment (fig. 31B). Similarly, the degree to which the bed sand fines and sand transport increases at Green-Ouray during the years following a large year-1 flood on the Yampa River flood depends on magnitude of subsequent out-year floods.

Cross-Section Resurveys