The primary purpose of this study is to provide volumetric estimates of sand exiting the Delta to Suisun Bay from WY 2001 to WY 2020. A secondary purpose is to identify potential sources of error in the estimates of sand load that might be improved with additional data collection or analysis.

The estimates include bedload at the Sacramento River at Rio Vista, California (DWR station SRV; California Department of Water Resources, 2023; USGS Station 11455420), and the San Joaquin River at Jersey Point, California (DWR station SJJ; California Department of Water Resources, 2023; USGS Station 11337190; U.S. Geological Survey, 2023). In this report, the Sacramento River at Rio Vista streamgage is abbreviated as SRV, and the San Joaquin River at Jersey Point streamgage is abbreviated as SJJ (fig. 1). The estimates also include suspended-sediment load at MAL and an adjustment of bedload for sediment removal through dredging and mining between SRV, SJJ, and MAL. These findings can be used to help inform management decisions related to sand supply to San Francisco Bay via Suisun Bay.

Water and sediment from the Central Valley pass through the Delta to Suisun Bay and eventually San Francisco Bay (fig. 1). For this study, Mallard Island was used as the downstream boundary of the Delta (fig. 1). At this location, DWR and USGS have operated the MAL monitoring station from 1994 to present (2024). Turbidity measurements at MAL were used as a surrogate for suspended-sediment concentration (SSC) (Rasmussen and others, 2009). Turbidity measurements were collected at a 15-minute sampling interval at two positions in the water column at the monitoring station (an upper sensor 1 meter [m] below water surface and a lower sensor 1.5 m above bed [for a detailed description, see Buchanan and Morgan, 2014]). In addition, DWR estimated daily (tidally-averaged) streamflow from the Delta to San Francisco Bay at this location using the Dayflow model (California Department of Water Resources, 2019, 2021).

In this study, suspended-sediment load entering San Francisco Bay at Mallard Island was estimated using methods developed by McKee and others (2006). Due to the tidal nature of this location, the method includes both the advective and dispersive load. McKee and others (2006) determined that the upper sensor was most representative of advective load and that the SSC point samples at the MAL streamgage were generally representative of average SSC of the channel cross section.

Between WY 2015 and WY 2020, suspended-sediment samples were collected at the MAL streamgage and analyzed for SSC and particle-size distribution. This dataset included 103 discrete SSC point samples (Haught, 2023), 22 of which had particle-size distribution data. All suspended-sediment data are in the National Water Information System (NWIS; https://waterdata.usgs.gov/nwis; U.S. Geological Survey, 2023). Samples were collected following standard sediment sampling procedures in Edwards and Glysson (1999) and analyzed at a USGS sediment laboratory following the methods described in Guy (1969).

In addition, two acoustic Doppler current profiler (ADCP) cross-section measurements were collected during a high-outflow event (280,000 cubic feet per second; ft³/s) in the Delta in 2019 (Hart and others, 2021). The ADCP measurements were collected using a boat-mounted RiverPro 600 kilohertz (kHz) ADCP instrument (Teledyne Marine, 2020) and were processed using WinRiver II software (Teledyne RD Instruments, 2001). Acoustic backscatter (ABS) data of the two ADCP measurements were used as a qualitative surrogate for SSC.

The two ADCP measurements were collected on February 26, 2019, approximately 140 m upstream (to the east) from the pier at the MAL streamgage (fig. 2) at the start of flood tide during a period of high outflow from the Delta. The ADCP measurements were collected 86 minutes apart. In addition, two discharge-weighted vertical suspended-sediment samples were collected between the ADCP measurements using a D-96 depth-integrated suspended sediment sampler (Federal Interagency Sedimentation Project, 2001).

The ABS data derived from the ADCP transects were used to qualitatively observe the cross-sectional variability of ABS, which is often used as a surrogate for SSC, and to qualitatively assess if the point measurements of SSC at the pier where the Mallard Island streamgage (MAL) is located would be a suitable proxy for SSC in the cross section. The discrete SSC samples were used to determine the percentage of sand in suspension and if SSC and streamflow were correlated.

At the time of this writing (2024), bedload is not measured at any place in the Delta, and physical bedload samples have not been collected as part of any previous studies in the Delta. Given the absence of bedload measurements, bedload was estimated by applying the van Rijn equations (1984a, equations 1, 2, 17, 18, 22; 1984b, equation 20) at two upstream sites (SRV and SJJ, each about 25 kilometers (km) upstream from Mallard Island; fig. 1). The bedload transport formulae developed by van Rijn (1984a, 1984b) were chosen because of their ability to incorporate changes in hydraulic roughness due to bedforms and the performance of predicted values against large sets of available bedload data. These two sites were used because of the long-term availability of stage, streamflow, and velocity records, which are required for most bedload transport equations. The streamgage at MAL does not have streamflow or velocity records. One limitation of using the van Rijn equations to estimate bedload is that they assume transport-limited conditions.

The input requirements for the van Rijn (1984a, 1984b) equations include time series of stage, cross-sectional area, and mean channel velocity, and discrete values of 50th percentile (median) particle size diameter (D₅₀), 90th percentile particle size (D₉₀), and bedform (dunes) dimensions (average length and height).

Stage and velocity at SRV and SJJ were recorded at 15-minute intervals at the USGS streamgages, and data were accessed from NWIS (U.S. Geological Survey, 2023). Cross-sectional area time series were computed using stage and measurements of channel cross sections and were made available by Ely and Marineau (2023).

Bed-material particle size was determined from samples previously collected between 2010 and 2013 and published in Marineau and Wright (2017). Average bedform dimensions were measured in 2012 from several 100–130-m longitudinal depth profiles. Bedform dimensions are used to estimate surface roughness in the van Rijn equations (van Rijn, 1984b).

The sand portions of the bedload (the material in transport) at SRV and SJJ were assumed to be the same as the sand portion of the bed-material sediment samples collected at those sites. The sand portion was averaged from all bed-material samples collected at each respective site between 2010 and 2013 (Marineau and Wright, 2017).

Bed-material particle sizes at each site did not change substantially from year to year, and channel cross-sectional area generally did not change in the Delta. However, bedforms were only measured one time, and their dimensions were assumed static for the period of study (WY 2001–20). However, bedforms in fluvial environments can often change with increasing or decreasing streamflow (Julien and Klaassen, 1995; Dinehart, 2002). In the Dinehart (2002) study in the Sacramento River, bedforms washed out during high flow conditions and transitioned to a plane-bed condition. A plane-bed condition occurs when stream velocity is high enough to wash out bedforms, resulting in a smooth bed without bedform roughness. Particle-size and bedform dimensions are used to calculate hydraulic roughness (van Rijn, 1984b), which can have a large effect on the bedload transport estimates. For this study, two estimates are made: a low and high estimate. The low estimate assumes plane-bed conditions and only uses particle size to compute a hydraulic roughness (van Rijn, 1984a), which is used for all time steps in the bedload estimate calculations. The high estimate uses particle size and bedform dimension to compute hydraulic roughness (van Rijn, 1984b).

As discussed in the “Introduction” section, the Delta traps about two-thirds of the sediment inflow, and much of the bedload and sand is likely mined and dredged (Marineau and Wright, 2014). Therefore, mined and dredged sand-size material was removed from upstream estimates of bedload to produce a total estimate of sand being transported out of the Delta through the Mallard Island cross section.

Estimates of bedload in this report were computed in volume of sediment. Bedload volumes were then converted to mass using the Lara and Pemberton (1963) empirical equation (eq. 1) for type IV (riverbed sediments):γ = W_cρ_c + W_mρ_m + W_sρ_s(1)where

Descriptions of sediment classes (clay, silt, sand, gravel) in this report are based on the Wentworth (1922) scale. Clay was defined as sediment particles smaller than 0.004 millimeters (mm), silt was greater than or equal to 0.004 mm but smaller than 0.0625 mm, sand was greater than or equal to 0.0625 mm but smaller than 2 mm, and gravel was larger than 2 mm. The terms “fine sediment” or “fines” refer to the combination of clay and silt sizes and include all particles less than 0.0625 mm.

The values for the coefficients W_c, W_m, and W_s, assuming a type IV reservoir operation (riverbed sediment; Lara and Pemberton [1963]), are 60, 73, and 97, respectively, which provide a bulk density result in English units of pounds per cubic foot (lb/ft³). The percentages of clay, silt, and sand (including coarse sand and gravel) were determined by averaging bed-material samples for each site collected between 2010 and 2013 (Marineau and Wright, 2017). At SJJ, the composition measured was 3-percent clay, 11-percent silt, and 86-percent sand (which included 8-percent gravel). At SRV, the composition measured was 1-percent clay, 2-percent silt, and 97-percent sand (less than one-half of a percent of the material was larger than 2 mm). The average for the two sites is 2-percent clay, 6.5-percent silt, and 91.5-percent sand (which includes 4-percent gravel).

Using the percentages of clay, silt, and sand in the equation above results in a bulk density estimate of 94.7 lb/ft³, which is equivalent to 1.517 metric tons per cubic meter (t/m³). This bulk density estimate was used in this report to convert volumetric bedload transport estimates to mass.

The objective of this study was to determine the annual volume and mass of sediment (and sand portion of that sediment) that exits the Delta at MAL (fig. 1). Bedload transport was estimated at the next two upstream streamgages (SJJ and SRV; fig. 1), which are about 25–28 km upstream from MAL. In the study reach between these streamgages, sediment is removed by dredging and sand-mining operations. The estimate of bedload transport reaching MAL from SJJ and SRV is adjusted by subtracting the amount of dredged and mined sediment in that section between MAL and the upstream streamgages (SJJ and SRV).

Annual sediment dredging quantities for the Sacramento River Deep Water Ship Channel and the Stockton Deep Water Channel were provided by the U.S. Army Corps of Engineers; dredged sediment particle-size data were also provided by the U.S. Army Corps of Engineers and were used to estimate the sand portion of the dredged material (Charity Meakes and Nancy Lam, U.S. Army Corps of Engineers, Sacramento Branch, written commun., 2022).

Annual sand-mining volumes for the Suisun Associates 7781 lease area (most of which is upstream from the MAL streamgage cross section) were obtained from Brenda Goeden (BCDC, written commun., 2022) for the WY 2001–20 period. Particle-size information for a subset of those years (2017–20) was provided by Lind Marine (Bill Butler, Vice President of Programs and Compliance at Lind Marine, written commun., 2021).

Results are presented regarding suspended-sediment variation in the MAL streamgage cross section. Then, variation in the percent sand in suspension at this cross section relative to streamflow is shown. Finally, total suspended-sediment load and suspended-sand load results are presented.

Seaward bedload transport was estimated at the two upstream streamgages (SRV and SJJ) for the WY 2011–20 period. Annual results for the WY 2001–10 period were published previously (Schoellhamer and others, 2018) and are also provided (app. 1, table 1.1). For the WY 2011–20 period, two estimates were made (a “low” estimate and a “high” estimate), as described in the “Data Collection and Analysis” section of this report. The estimates were calculated using a 15-minute time step and then averaged over the water year to determine the net (seaward) transport. The average annual volume of bedload moving seaward at the upstream streamgages (SRV and SJJ) for the WY 2011–20 study period was estimated to be between 0.038 million cubic meters per year (Mm³/yr; low estimate) and 0.202 Mm³/yr (high estimate). The high and low estimates represent an average of 0.182 Mm³/yr with a standard deviation of 0.125 Mm³/yr. The annual results are provided in table 1.1 of appendix 1. Low and high estimates were not calculated for WY 2001–10 because of limited source data. For the entire study period (WY 2001–20), the average annual volume of bedload moving seaward at streamgages SRV and SJJ was 0.128 Mm³/yr. Full time series of bedload estimates at SRV and SJJ for the WY 2011–20 period are available from Ely and Marineau (2023). Using a dry bulk density conversion factor of 1.517 t/m³ (see “Data Collection and Analysis” section for details on the conversion assumptions), the mean annual mass of bedload for the WY 2010–20 study period was 0.057 million metric tons per year (Mt/yr; low estimate) to 0.307 Mt/yr (high estimate), or 0.128 Mt/yr for the entire study period (WY 2001–20). Figure 7 shows annual estimates of bedload for SRV, SJJ, and combined (SRV+SJJ) for the study period.

Total bedload estimates varied from year to year, but the greatest estimated bedload transport rates happened in WY 2017. Water year 2017 had major storm events with substantial outflow from the Central Valley. The total seaward bedload for WY 2017 (at SJJ+SRV) was estimated to be 0.689 Mm³/yr (1.039 Mt/yr, assuming a conversion rate of 1.517 t/m³). The average annual bedload rate for all other years was estimated at 0.113 Mm³/yr. The estimated WY 2017 bedload at SRV and SJJ was about 6 times the average annual rate for the other years in the WY 2001–20 study period. On average, during the WY 2001–20 period, the sand portion of bedload that was transported seaward at SRV and SJJ was estimated to be about 88 percent of the total bedload, or about 0.067±0.099 Mm³/yr, which is equivalent to 0.151 Mt/yr (assuming a bulk density of 1.517 t/m³).

The SRV and SJJ streamgages are approximately 17 km from the confluence of the Sacramento and San Joaquin Rivers (the western most extent of the Delta) and 25 km upstream from the MAL streamgage (fig. 1). In the 25 km between SRV/SJJ and MAL, bedload transport volumes were reduced by sand-mining operations and maintenance dredging for ship navigation.

During the WY 2001–20 study period, a total of 1.050 Mm³ of sediment was removed through dredging operations to support shipping and navigation in the reaches between MAL and SRV/SJJ. The average annual volume removed was 0.053 Mm³/yr, of which approximately 76 percent (0.040 Mm³) was sand. The total annual volume of sediment mined on the Sacramento River upstream from MAL during WY 2001–20 was approximately 1.518 Mm³, or an average annual volume of 0.076 Mm³/yr. Figure 8 shows a time series of annual quantities of sediment removed through mining or dredging operations.

Particle-size analysis data were only available for WY 2017–20 and indicated that the sediment mined was predominantly sand: 97 percent of the sediment was between 0.07 mm and 2.4 mm, which generally corresponds to sand sizes on the Wentworth classification scale (Wentworth, 1922). About 0.9 percent was larger than 2.4 mm (fine gravels), and 1.6 percent was smaller than 0.07 mm (silts and clay). There was no discernible trend in particle size within years over the 4-year period; therefore, we assumed that the particle-size distribution for the WY 2017–20 period was representative of the past 20 years and that the sand portion of the mined sediment was approximately 97 percent of the total sediment.

The total estimated volume of material removed through dredging and mining (between MAL and SRV/SJJ) during the 20-year study period exceeded the estimated seaward bedload fluxes. During that period, 2.211 Mm³ of material was removed, and seaward bedload was estimated to be 2.033 Mm³. The volume of material removed through dredging exceeds the seaward estimate of bedload, which results in a deficit of bedload entering Suisun Bay at Mallard Island of 0.009 Mm³/yr (or 0.013 Mt/yr, assuming a conversion rate of 1.517 t/m³). This deficit might be interpreted as a landward flux; however, we assume the uncertainty in these estimates is large even though we could not quantify the uncertainty (app. 1, table 1.2).

Total suspended sediment was in the seaward direction and was larger in magnitude than the (landward) deficit of bedload. Therefore, the net sediment flux from the Delta to Suisun Bay through the MAL streamgage cross section was estimated to be 0.47 Mt/yr in the seaward direction (app. 1, table 1.2). On average, the results indicated a net flux of sand out of the Delta (at MAL) of 0.003 Mt/yr (app. 1, table 1.2).

Suspended-sediment particle-size data were not sufficient to derive a tidally or streamflow-dependent dynamic suspended-sediment load model but did expose areas of SSC variation unaccounted for in the regression model (shown in fig. 6). McKee and others (2006) analyzed error of computed suspended-sediment load at MAL using the upper sensor of the MAL streamgage to calculate sediment flux, which resulted in an error of ±32 percent that accounted for total errors in tidal variation, Dayflow data, laboratory analysis, turbidity-SSC regression models, and vertical and cross-sectional variabilities. More recent data (Hart and others, 2021) indicate that the previous estimate of cross-sectional variability in suspended sediment was underestimated at higher discharge values. Data collected during the high-outflow event (280,000 ft³/s) from the Delta indicated cross-sectionally average SSC varying from 28 to 50 percent of SSC from the MAL pier based on discharge-weighted vertical samples and ABS. SSC samples, including sand percentage taken after the McKee and others (2006) study, indicated a root mean squared error of 1.8 percent in the 3 percent sand fraction model assumption. Accounting for the cross-sectional variation measured in the 2019 high-outflow event, the total computed error for sand fraction calculations increases from ±32 to ±52 percent, with the predominant source of error being cross-sectional heterogeneity.

Bedload was not measured at any point during the study period at any of the study sites. Estimates of bedload were calculated using sediment particle-size data from bed-material samples, which were collected only a few times during the study period, and bedform dimension data were collected only once. Bedform dimensions and types are known to change with different flow conditions and sediment supply (Julien and Klaassen, 1995; Dinehart, 2002). Bedload estimates may include uncertainty caused by assuming static bedform dimensions and particle sizes as inputs in the bedload transport formulae, particularly with regard to changing bedform conditions. Bedforms have “washed out” during high flows, in which the bed transitions from well-formed dunes to a plane bed (Dinehart, 2002). In this study, four different time series were computed. For each of the two sites (SRV and SJJ), one time series was produced assuming plane-bed conditions for the entire study period, and one time series was produced by applying the 2012 measured bedform dimensions to the entire study period.

Another primary source of error in the bedload estimates is due to relying solely on the van Rijn (1984a, 1984b) transport equations in the absence of physical bedload measurements that could be used to validate the estimates. In comparison to a compilation of published bedload datasets, the estimates produced from the van Rijn equations ranged from 0.33 to 3 times the measured (published) bedload values approximately 93 percent of the time (van Rijn, 1984a).

The flux of total suspended sediment was closely related to Delta outflow (fig. 9). Water year 2017 delivered 23 percent of the 20-year total suspended sediment. Overall, just 4 water years delivered 52 percent of the 20-year total suspended-sediment load to Suisun Bay. These results illustrate the importance of wet years for sediment transport and the importance of collecting data during a variety of conditions, including wet years. A comparison of bedload estimates with streamflow was not made because the equations use streamflow as one of the main input variables, and bedload was not measured.

The mean total suspended-sediment flux of 0.482 Mt reported here is less than previously reported values: 1.2 Mt (McKee and others, 2006), 0.89 Mt (McKee and others, 2013), and 0.73 Mt (Schoellhamer and others, 2018). Observed differences likely result from two factors: average streamflow during this study period was lower than previous studies, and an overall shift in SSC was observed starting in 1999, which was just before this study period began.

Streamflow during WY 2001–20 (the period of this study) averaged just 17.9×10⁹ m³/yr, which is drier than the recent 30-year mean (21.0×10⁹ m³/yr) and drier than the mean annual flow conditions discussed in the previous studies: 28.4×10⁹ m³/yr (WY 1995–04; McKee and others, 2006), 24.5×10⁹ m³/yr (WY 1995–10; McKee and others, 2013), and 21.5×10⁹ m³/yr (WY 1995–16; Schoellhamer and others, 2018). Because flow is strongly correlated with suspended-sediment mass flux (fig. 9), the climatic period during which the data are averaged has a large effect on mean suspended-sediment loads.

The data averaging period was entirely after 1999, the year that a statistically significant step decrease of 36-percent SSC was observed in San Francisco Bay based on a comparison of data from WY 1991–98 and WY 1999–07 (Schoellhamer, 2011). Schoellhamer (2011) presented a hypothesis that this phenomenon results from crossing a threshold from transport-limited conditions to supply-limited conditions because the erodible sediment pool from the gold mining era of the 19th century was finally depleted. Schoellhamer and others (2018) further explored this hypothesis using double mass plots and indicated that the data supported the hypothesis for an extended period through 2016. The wetter years of WY 2006 (51.3×10⁹ m³/yr) and WY 2011 (33.2×10⁹ m³/yr) did not indicate elevated SSC or any deviation from the 1999–2016 regression slope (Schoellhamer and others, 2018). The mean slope was 45.5 mg/L for 1995–98 and 25.2 mg/L for 1999–2016. Repeating this same analysis to include the data in this study (through WY 2020), the mean slope for 1999–2020 is 26.3 mg/L (fig. 10).

Additional measurements of bedload and suspended sediment (primarily cross-sectional sampling) in strategic locations could improve the accuracy of estimates of sand load exiting the Central Valley at the Delta. Analyzing samples for fine/sand split would facilitate the determination of the sand percentage in the sediment load.

Physical measurements of bedload were not collected at the sites used in this study during the study period (WY 2001–20). Cross-sectional measurements in the form of EDIs and equal-width increments (EWIs; Edwards and Glysson, 1999) of suspended sediment were collected periodically, but additional EDI/EWI measurements at a range of flow conditions would be needed to determine if point measurements at the MAL streamgage are representative of the channel cross section or if an adjustment coefficient is warranted (Edwards and Glysson, 1999; U.S. Geological Survey, 2006; U.S. Geological Survey, 2016).

Two improvements that could help increase the accuracy of suspended-sand flux estimates at MAL include improvements in understanding (1) the cross-sectional heterogeneity of suspended-sediment flux and (2) sand fraction with discharge. As noted previously, variability of SSC in the channel cross section may account for ±32 to ±52 percent of the uncertainties in current estimates. Also, streamflow velocity was not measured on site. Continuous streamflow velocity measurements at the MAL streamgage could reduce the variations observed.