Amplified Impact of Climate Change on Fine-Sediment Delivery to a Subsiding Coast, Humboldt Bay, California

In Humboldt Bay, tectonic subsidence exacerbates sea-level rise (SLR). To build surface elevations and to keep pace with SLR, the sediment demand created by subsidence and SLR must be balanced by an adequate sediment supply. This study used an ensemble of plausible future scenarios to predict potential climate change impacts on suspended-sediment discharge (Qss) from fluvial sources. Streamflow was simulated using a deterministic water-balance model, and Qss was computed using statistical sediment-transport models. Changes relative to a baseline period (1981–2010) were used to assess climate impacts. For local basins that discharge directly to the bay, the ensemble means projected increases in Qss of 27% for the mid-century (2040–2069) and 58% for the end-of-century (2070–2099). For the Eel River, a regional sediment source that discharges sediment-laden plumes to the coastal margin, the ensemble means projected increases in Qss of 53% for the mid-century and 99% for the end-of-century. Climate projections of increased precipitation and streamflow produced amplified increases in the regional sediment supply that may partially or wholly mitigate sediment demand caused by the combined effects of subsidence and SLR. This finding has important implications for coastal resiliency. Coastal regions with an increasing sediment supply may be more resilient to SLR. In a broader context, an increasing sediment supply from fluvial sources has global relevance for communities threatened by SLR that are increasingly building resiliency to SLR using sediment-based solutions that include regional sediment management, beneficial reuse strategies, and marsh restoration.


Introduction
In Humboldt Bay, California, sea-level rise (SLR) includes the combined effect of global SLR and vertical land motion caused by local tectonic subsidence (Clarke and Carver 1992;Valentine et al. 2012). In places like Humboldt Bay, where relative SLR (4.7±1.5 mm/yr) is higher than regional averages due to tectonic subsidence (Russell and Griggs 2012;Montillet et al. 2018), an adequate sediment supply is vital for maintaining surface elevations and keeping pace with SLR.
Although sediment has long been considered a resource (Owens et al. 2008), accelerated rates of sea-level rise (SLR) produced a transition in thinking (Goodrich and Warrick 2015). Maintaining an adequate sediment supply is now considered to be a fundamental strategy for adapting to SLR (Nicholls 2018). Historically, grey infrastructure was used for shoreline protection, but sediment-based solutions (Ganju 2019), which include regional sediment management (Rosati et al. 2004) and beneficial reuse through marsh restoration (Hill 2011;CA-CSMW 2012), are now widely accepted adaptation strategies for building resiliency in coastal ecosystems threatened by SLR (Powell et al. 2019).
The impact of climate change on sediment yield from fluvial sources is well documented (Langbein and Schumm 1958;Walling and Webb 1996;Coulthard et al. 2012;Li and Fang 2017;Dunn et al. 2019), but evaluating the sustainability of sediment-based solutions within the context of regional sediment budgets (Rosati 2005) represents a critical knowledge gap (Ganju 2019). The conservation of mass principle requires that sediment influx, efflux, and changes in stored sediment must balance across an ecosystem boundary. Without an adequate sediment supply, an increase in sediment demand caused by subsidence, SLR, and tidal prism expansion can produce morphological and ecological responses (Friedrichs and Perry 2001;Ganju and Schoellhamer 2010;Mariotti and Carr 2014;Kirwan et al. 2016;Hopkinson et al. 2018).
In coastal communities threatened by SLR, there is an ongoing need to provide local projections of sediment supply under future climate conditions to guide the implementation of sustainable adaptation strategies to mitigate SLR impacts. Saltmarsh restoration, and associated blue carbon sequestration, is an adaptation strategy that is particularly well-suited for building shoreline protection and resiliency to SLR, while mitigating the impact of extreme events through wave attenuation, shoreline stabilization, and floodwater retention (Shepard et al. 2011;Leonardi et al. 2016;Nicholls 2018). Resiliency in this context is defined as the capacity of salt marshes to accrete sediment, gain elevation, and keep pace with SLR while providing coastal protection and maintaining critical ecological services (Barbier et al. 2011).
We hypothesized that documented declines in the regional sediment supply (Warrick et al. 2013) may be offset under future climates by increases in suspended-sediment discharge (Q ss ) produced by increases in the magnitude and frequency of extreme precipitation events (Trenberth 1999;Dettinger 2016). To test this hypothesis, we investigated the impact of climate change on Q ss using an integrated modeling approach. Implications were explored by assessing the availability of sediment for natural marsh accretion, a sediment-based solution for building resiliency to SLR. The impact of climate change on marine processes (tidal exchange and wave events) was outside the study scope, but the influx of fine sediment from the coastal margin was assessed on the basis of previous investigations of coastal river plume dynamics.

Study Area
The Humboldt Bay-Eel River study region (Fig. 1) is located in northwestern California. The climate is Mediterranean with dry summers and wet winters. The average annual precipitation is 1585 mm/yr with only 3% occurring between June and September. The strong orographic effects of the Coast Range create a west to east precipitation gradient. Annual precipitation along the coastal margin is greater than 2000 mm/yr but less than 1300 mm/yr in the upper basin of the Eel River. Peak runoff events are typically rainfall driven with snowmelt discharge playing a less significant role. Extreme precipitation events, referred to as atmospheric rivers (Dettinger et al. 2011), produced the largest historic floods (Brown and Ritter 1971;Waananen et al. 1971).
The mountainous rivers that drain the study region have sediment yields that are higher than global averages (Milliman and Syvitski 1992;Milliman and Farnsworth 2011). High yields are caused by the cumulative effects of regional tectonic uplift, erodible lithologies, steep uplands, extreme precipitation, and land use (Brown and Ritter 1971;Kelsey 1980;Nolan and Janda 1995;Milliman and Farnsworth 2011;Warrick et al. 2013). Historically, the upland forests were extensively logged (Leithold et al. 2005;Klein et al. 2012), and low-lying areas adjacent to the bay were diked and disconnected from bay circulation (Schlosser and Eicher 2012).
Humboldt Bay is a tidally forced coastal lagoon (Costa 1982) with rates of relative SLR (Rovere et al. 2016) that are exacerbated by localized tectonic subsidence. The bay is composed of three sub-embayments with limited freshwater inputs during most of the year. The three sub-embayments (North Bay, Entrance Bay, and South Bay) are connected by navigation channels and an entrance channel connects the bay to the open coast. Protected by barrier spits, the bay experiences energetic conditions driven by storm, wave, and wind events. The bay is relatively shallow, with 39 km 2 of mudflats exposed at mean lower low water (MLLW). The mean tide encompasses 73 km 2 and the tidal exchange is approximately 114 Mm 3 /day (NHE 2015).
The conceptual sediment budget for Humboldt Bay (Barnhart et al. 1992) includes local and regional sources of fluvial sediment. Local basins that discharge directly to the bay have a combined contributing area of 442 km 2 . The Eel River discharges to the coastal margin and has a contributing area of 9415 km 2 .
The coastal sediment budget is dominated by the Eel River (Wheatcroft et al. 1997;Wheatcroft and Borgeld 2000;Warrick 2014). Remarkably, the Eel River is the largest fluvial source of fine-sediment along the coast of California (Farnsworth and Warrick 2007). In December of 1964, a massive regional flood generated the peak of record (21,240 m 3 /s). Flooding was accompanied by extensive channel aggradation and unprecedented sediment loads (Brown and Ritter 1971;Waananen et al. 1971;Gray et al. 2016), which remained high for several decades before declining (Warrick et al. 2013).
Coastal-river plumes (Horner-Devine et al. 2015) are the primary mechanism for dispersing fine-sediment from fluvial sources along the coastal margin . The winter runoff season generally coincides with seasonal downwelling winds that produce northerly coastal currents (Kniskern et al. 2011). The northerly currents transport buoyant plumes of fine sediment from the Eel River along the coastal margin where near-shore turbulence and downwelling lead to retention of fine sediment within the plume (Hill et al. 2007). Plume dynamics enable fine sediment to remain in suspension for multiple days, which allows for northward conveyance and transport into Humboldt Bay during flood tides Hill et al. 2000).
The regular occurrence of coastal-river plumes, along with the large tidal exchange and tidal asymmetry, suggests that the bay may function as a sink for fine sediment in the regional Fig. 1 Map of Humboldt Bay-Eel River (HBER) modeling domain in northwestern California, showing gaged basins with streamflow and suspended-sediment measurements. Basin identifiers for the streamflow gages correspond to descriptions in Table 1, and acronyms for the sediment gages correspond to basin identifiers in Table 3 sediment budget. There are no physical data to directly investigate this assertion; however, there is a depositional center of fine sediment located directly offshore from the entrance of Humboldt Bay (Leithold 1989;Wheatcroft et al. 1997;Wheatcroft and Borgeld 2000), which strongly supports the assertion that the bay is a repository for Q ss from the Eel River.

Methods
A combination of empirical and statistical models was used to assess the impacts of climate change on the delivery of finesediment from fluvial sources. A deterministic water-balance model, which models the hydrologic response to climate, was used to simulate a daily time series of streamflow for each basin within the modeling domain (Fig. 1). Sedimenttransport models, which describe the statistical relationship between mean daily streamflow and Q ss , were used to compute a daily time series of Q ss for each basin.
The water-balance model was calibrated using daily streamflow measured at twelve unimpaired streamflow gages, and the sediment-transport models were fit using daily values of simulated streamflow and Q ss computed for five sediment gages (Fig. 1). Hereafter, sediment reporting basins that discharge directly to Humboldt Bay (Jacoby Creek, Freshwater Creek, Elk River, and Salmon Creek) are collectively referred to as the bay basins, and the Eel River sediment reporting basin is referred to as the Eel River basin.

Streamflow Simulated Using a Water-Balance Model
Daily streamflow, under historical and future climates, was simulated using the Basin Characterization Model (BCM; Flint et al. 2013). The BCM is a fine-scale (270 m) regional water-balance model that mechanistically simulates the hydrologic response to climate using spatially-gridded data. The BCM data inputs include climate (precipitation and air temperatures) and landscape attributes (topography, soils, and bedrock geology). Energy balance equations are used to partition available water into estimates of local runoff and recharge (Fig. 2). Daily runoff values in each 270-m grid cell are then summed to determine daily streamflow values for each basin. A detailed explanation of the BCM input parameters is provided in ESM 1, and a model archive for the Humboldt Bay-Eel River BCM was published separately (Stern et al. 2020).
For the historical model runs (1960 to 2017), gridded climate data were derived from 94 climate stations distributed across the study region. Historical climate observations were downloaded from the National Weather Service Cooperative Observer Program (COOP, www.ncdc.noaa.gov/), the Remote Automated Weather Stations (RAWS, www.raws. dri.edu/), and the California Irrigation Management Information System (CIMIS, www.cimis.water.ca.gov/). Climate observations were reviewed, and poor-quality data were identified and removed using a jack-knifing statistical method (Efron and Stein 1981).
Daily climate grids for the historical model were spatially interpolated from the measured observations using Gradient and Inverse Distance Squared (GIDS; Nalder and Wein 1998) weighting. At scales from tens of meters to kilometers, the GIDS method adjusts for local gradients caused by lapse rates, inversions, or rain shadows. This method produces accurate climate grids with sparse data, and data requirements are far less than the requirements for techniques such as kriging (Hughes and Lettenmaier 1981). The daily GIDS grids were then scaled to monthly climate grids downloaded from the PRISM Climate Group (PRISM; http://prism.oregonstate. edu; Daly et al. 2008) as a check to ensure that the sum of the daily precipitation and the average of daily air temperatures match the monthly PRISM grids.
The historical model was calibrated (2009 to 2016) and validated (2000 to 2008) using daily streamflow measured at twelve unimpaired streamflow gages ( Table 1). The most recent period was selected for calibration to best represent current hydrologic conditions. During calibration, model parameters were iteratively adjusted to match simulated and measured streamflow values and to optimize goodness-of-fit statistics. Because the study objective was to assess the impact of climate change on Q ss , optimization of high flows was prioritized over baseflows during model calibration. The BCM post-processing and calibration procedures are described in ESM 1.
California's climate is uniquely variable in both space and time (Dettinger 2016). To capture this variability, a probabilistic framework of climate projections was developed using a multi-model ensemble of five global climate models (GCMs; Table 2) and two projections for greenhouse gas (GHG) emissions. The five GCMs were selected, from the full ensemble of models used in the Intergovernmental Panel on Climate Change (IPCC) Coupled Model Inter-comparison Project Phase 5 (CMIP5), on the basis of historical performance and the ability to best represent California-specific climate features (CADWR-CCTAG, 2015). The multi-model ensemble captured a range of potential future climate conditions (wetter/ drier, warmer/hotter), and the two Representative Concentration Pathways (RCPs) captured mitigated (RCP4.5) and business-as-usual (RCP8.5) GHG atmospheric emissions. The ten climate projections provide a robust framework of plausible future climate change scenarios and capture variability and potential future climate trends that may influence the Q ss projections.
For the future model runs (1960 to 2099), we used the CMIP5 daily climate grids, which were statistically downscaled and bias-corrected (Pierce et al. 2014) to match historical climate statistics (Livneh et al. 2013) using Localized Constructed Analogs (LOCA). The bias-corrected climate grids provided improved precipitation estimates for extreme events, reduced the common downscaling problem of too many light-precipitation days, and greenhouse-gas (GHG) forcings were imposed beginning in 2006. Hereafter, the bias-corrected projections are referred to as the LOCA projections. The LOCA projections were downloaded from Cal-Adapt (http://cal-adapt.org/data/loca/) and downscaled to 270 m across the modeling domain for this study using a GIDS method described by Flint and Flint (2012).
As explained above, the historical and future model runs used two different climate datasets to simulate streamflow for the historical period. The historical model used climate grids spatially interpolated from observations within the study region; whereas, the future models used the LOCA projections, which were bias-corrected to observations across California.
Streamflow simulated using the historical model was used to calibrate BCM parameters to local conditions across the modeling domain. Model parameters, calibrated using results from the historical model run, were used to simulate streamflow with the future models. Changes in streamflow and Q ss between the baseline (1981-2010), mid-century (2040-2069), and end-of-century (2070-2099) periods were assessed using the LOCA projections.

Suspended-Sediment Discharge Computed Using Sediment-Transport Models
Sediment-transport models, for each of the five sediment reporting basins (Fig. 1), were defined statistically using simple linear regression and monitoring data with variable periods of record (Table 3). In the bay basins, data collection followed Fig. 2 Schematic describing the inputs, outputs, and water balance components of the basin characterization model (BCM), which mechanistically simulates daily streamflow using spatially gridded data. Flint et al. (2013) provide a description of the complete workflow, and a description of the post-processing and calibration procedure is provided in ESM 1 procedures described by Lewis and Eads (2009). In the Eel River basin, data collection followed procedures described by Edwards et al. (1999) and Turnipseed and Sauer (2010). Monitoring data collected at three of the sediment gages (HHB, KRW, SFM) were previously published by Lewis (2013). Data collected at the Eel River gage (USGS 11477000; U.S. Geological Survey 2021) are publicly available at https://waterdata.usgs.gov/nwis. Unpublished monitoring data collected at the JBW gage, along with additional datasets used to compute Q ss for the five sediment reporting basins, are available in the Electronic Supplemental Material (ESM). Hereafter, we use the following terminology, sediment-rating curves were used to compute SSC from continuous measurements of turbidity (bay basins) or streamflow (Eel River). Sediment-transport models were used to compute Q ss from streamflow simulated by the historical and future model runs.
For the bay basin gages, continuous turbidity values were used as a surrogate measurement to compute 10-min SSC values. ESM 1 contains a detailed explanation of the monitoring data and the methods used to convert turbidity to SSC using sediment-rating curves. Sediment-rating curves were previously published for HHB, KRW, and SFM (Lewis 2013). Synchronous measurements (stage and streamflow, turbidity, and SSC) for the JBW gage and the regression analyses used to compute 10-min values of streamflow and SSC are provided in ESM 2. The suspended-sediment load in the bay basins is predominantly composed of fine-grained sediment (diameter <63 μm), the channels are relatively small, and SSC is well-mixed at the cross-sections where sediment is measured. The influence of grain size on the statistical relationship between turbidity and SSC for the bay basins was previously assessed (Lewis 2013). For the bay basins, no corrections to adjust SSC values for grain size were applied and the 10-min values of streamflow and SSC (ESM 3) were averaged to compute the mean daily values (ESM 4) of Q ss for the period of record for each basin (Table 3).
For the Eel River gage, continuous streamflow values were used as a surrogate measurement to compute 15-min SSC   (Warrick 2014). Data collected before the baseline historical period  were excluded from the regression analysis to mitigate the impact of timedependent trends and SSC values were corrected for the percentage of fine-sediment (<63 μm) to exclude the sand-sized fraction. The 15-min values of streamflow and SSC (ESM 3) were averaged to compute mean daily values (ESM 4) of Q ss for the period of record (Table 3). Sediment-transport models for each of the five sediment reporting basins were defined using linear regression and log-transformed variables where Q ss is suspended-sediment discharge (metric tons/day), Q w is streamflow (m 3 /s), and a and b are regression coefficients. The sediment-transport models (Eq. 1) were fit using daily values of Q ss (ESM 4) paired with streamflow values simulated using the calibrated historical model (ESM 5). Estimates of Q ss for the Eel River were corrected for fines, but the estimates of Q ss for the bay basins did not require a correction. A group-average method (Glysson 1987;Curtis et al. 2006) was used to define low and high flow regression models for each of the five sediment reporting basins. The group average method is appropriate when a large number of low to moderate data values create a sampling bias that strongly influences the slope of the regression models and is useful for improving the sediment-transport predictions for high flows. This is an extremely important consideration because slight errors in the slope of a regression model can generate large errors in predicted transport. Daily values of simulated streamflow and Q ss from 1981 to 2017 were log 10 -transformed, binned, and group-averages determined. Streamflow bin sizes, which ranged from 0.07 to 0.11 in log 10 units, were scaled to basin size.
Curvature and retransformation bias are two common problems associated with regression models that are fit to logtransformed data (Helsel and Hirsch, 2002). Separate regression models were defined for low flows and high flows to mitigate curvature. Thresholds used to separate low and high flows were determined iteratively by optimizing regression statistics and testing for linearity and equal variance in the residuals. Retransformation bias causes underprediction of sediment transport and was corrected for using a nonparametric "smearing estimator" (Duan 1983), which is insensitive to non-normality in the regression residuals.
Sediment-transport models, defined using historical data, were used to predict changes in Q ss on the basis of streamflow simulated for future climates. To mitigate the problem of nonstationarity (Milly et al. 2008), we followed the approach of Warrick (2014). The computational period, for estimating Q ss under historical conditions, began in 1981 after the lingering effects of the massive 1964 flood had declined. Although we addressed non-stationarity in the development of the sediment-transport models, we assumed no time-dependent trends in the statistical relationship between streamflow and Q ss under future climates. The sediment-transport models are stationary, and the impact of climate change assessed solely on the basis of streamflow response.
Accuracy and prediction errors for simulated historical streamflow were assessed for each calibration basin by comparing measured and simulated streamflow using standard statistical metrics (Legates and McCabe 1999). Goodness-of-fit was assessed using the coefficient of determination (r 2 ) and the Nash-Sutcliffe efficiency metric (NSE, Nash and Sutcliffe 1970). Values of r 2 describe the proportion of total variance in the measured data described by the simulated data and can range from 0 to 1. NSE is less sensitive to the differences in the mean and the variance in the measured and simulated data. The NSE, which can range from negative infinity to 1, is calculated as the ratio of one minus the mean square error divided by the variance. Larger r 2 and NSE values indicate better agreement between measured and simulated streamflow.
Errors in streamflow, simulated using the historical model, were assessed using the mean percent error (MPE), and an overall mean absolute error (MAE) was defined for the study region. The MPE, calculated as the sum of the differences between the measured and simulated values divided by the total number of values, is negative when simulated streamflow is underestimated and positive when simulated streamflow is overestimated. The overall MAE was calculated as the absolute value of the MPE values averaged across the calibration basins.
The accuracy of the Q ss estimates, computed from streamflow simulated with the historical model, was assessed by comparison with Q ss computed from measured streamflow. Table 3 Summary of continuous turbidity and streamflow measurements and discrete suspended-sediment concentration (SSC) samples used to develop sediment-transport models (Eq. 1) for five sediment gages in the Humboldt Bay-Eel River study region. Discrete SSC samples and streamflow (15-min) data for the Eel River gage are available at https://waterdata.usgs.gov/nwis. Turbidity and streamflow (10-min) data for the bay basin gages are provided in ESM 3. See Fig. 1  For the bay basins, Q ss results were validated against turbidityderived Q ss (ESM 4). For the Eel River, the Q ss results for the baseline historical period  were validated against previously published estimates for a 90-yr period (1911-2000Warrick 2014). Prediction errors for the turbidity-derived Q ss were assumed to be equal to the sum of individual errors reported by Wright and Schoellhamer (2005). Four sources of error were considered by Wright and Schoellhamer (2005): error of the relation between turbidity and SSC (26%), laboratory error of SSC (8.8%), error of measured and actual SSC (15.2%), and error of the streamflow estimates (1.4%). Wright and Schoellhamer (2005) combined the errors with quadrature, a standard method for propagating random measurement errors, to define a mean error of 31.5%. In this study, we assumed a mean error of 31.5% for the turbidity-derived Q ss for the bay basins.
Prediction errors for Q ss , computed using the sedimenttransport models (eq.1), were computed using the standard error of the prediction (RMSE%), which captures error due to uncertainty in the regression coefficients. The RMSE%, calculated as the square root of the sum of the squared differences divided by the number of values used to fit the regression, considers variance and mean error with smaller values indicating higher accuracy. This method only accounts for errors associated with fitting the regression models and does not account for systematic errors associated with measurements of SSC or streamflow.
The "sum of the individual errors" is commonly used in sediment budget studies to provide some information about the error associated with Q ss , but there is no standardized method and no way to translate these errors with certainty to the future climate results. A 30-year window was used to assess climate change impacts across the ten climate scenarios, which has been proposed as the shortest time period necessary to capture climate variability (Schindler et al. 2015). Changes were determined as the relative percent difference between ensemble means calculated for the historical baseline (1981-2010), mid-century (2040-2069), and end-of-century (2070-2099) periods. Uncertainty was determined using the standard deviation of the 30-year means across the ten climate scenarios.

Water-Balance Model Performance
Calibration and validation results for the 12 calibration basins showed good agreement between simulated streamflow and measured streamflow (Table 4). During the calibration period, the r 2 and NSE values for daily streamflow were ≥ 0.65 for 11 out of 12 basins. During the validation period, the r 2 values were ≥ 0.65 for 11 basins, and the NSE values were ≥ 0.65 for 8 basins. The mean percent errors showed that simulated mean daily streamflow was overestimated during the calibration period and underestimated during the validation period, and the mean absolute error for the calibration period was higher than for the validation period.
The majority of fine-sediment transport occurs during peak flows in the mountainous basins that drain the study region, and for this reason, peak flow results are of particular interest. A comparison of simulated and measured streamflow for the Eel River gage (USGS 11477000, Fig. 3) showed that peak flow magnitudes were underestimated during the validation period. The implications associated with underestimating peak flows will be revisited in the discussion.

Sediment-Transport Model Performance
The regression statistics for the five sediment-transport models (Table 5) showed that variance in the data was wellfit by the regression models (Fig. 4). Fitting separate low-flow and high-flow models using the group-average method improved the statistical fit and resulted in r 2 values that were all greater than 0.81. The prediction errors (RMSE%) for the high-flow models were 25% less than for the low-flow model errors, which is a positive result. Again, the majority of finesediment transport occurs during higher flows, and lower prediction errors for the high-flow models improved the Q ss projections.
Validation of the Q ss results (Table 6) showed that the sediment-transport models underestimated Q ss by up to 47 %. Because Q ss is often not in phase with streamflow, and statistical models that use streamflow as a predictor variable commonly underestimate Q ss (Horowitz 2003). Although high flows were prioritized over low flows during the calibration of the historical model, underestimation of peak magnitudes (Fig. 3) contributed to the underprediction of Q ss .

Climate Change Impacts
The future climate projections for the study region showed a high probability of a warmer and more variable climate with increased annual precipitation (Fig. 5). For both the midcentury and end-of-century, the CanESM2 RCP8.5 scenario projected the greatest warming. The CNRM-CM5 is a warmer-wetter GCM, and the CNRM-CM5 RCP8.5 scenario projected the largest increase in precipitation for both the midcentury and end-of-century. In comparison, the HadGEM2-ES is a hotter-drier GCM, which projected potential declines in precipitation for the mid-century (RCP4.5 and RCP8.5) and end-of-century (RCP4.5). Six scenarios projected increases in mean precipitation for the mid-century, but nine scenarios projected increases in precipitation for the end-of-century. The climate change results showed that mean annual precipitation and the magnitude and frequency of extremes, interpreted as precipitation variability, are likely to increase under future climates.
One of the study objectives was to explore the availability of sediment for natural marsh accretion, a sediment-based solution for building resiliency to SLR. Hereafter, we focus on comparing study results for the historical baseline and midcentury periods, because this comparison period represents a realistic time frame for implementing adaptation strategies. A complete summary of climate change impacts on streamflow and Q ss is provided in ESM 1.
Mid-century increases in precipitation were translated into increased streamflow. For the bay basins, seven scenarios projected increases in mean annual streamflow, peak flows, and the number of peak flow days. For the Eel River, seven scenarios projected increases in mean annual streamflow, eight scenarios projected increases in peak flows, and nine scenarios projected increases in the number of peak flow days. The streamflow results showed that mean annual flows and the magnitude and frequency of peak flows are likely to increase under future climates.
The timing of peak flow days is relevant to changes in the seasonality of Q ss (Fig. 6). The RCP4.5 scenarios projected the largest increase in the number of peak flow days in January, and the RCP8.5 scenarios projected the largest increases in peak flow days in December. The RCP8.5 scenario for the hotter-drier HadGEM2-ES model projected a shift in the occurrence of peak flows to February. The MIROC5 model projected a warmer climate with relatively small changes in precipitation and a shift in peak flow days to March.
A shift in the winter runoff season could impact the delivery of fine-sediment to Humboldt Bay. Coastal-river plumes discharged from the Eel River must coincide with winter upwelling events. These upwelling events produce the northerly currents that convey sediment northward along the coastal margin allowing flood tides to transport sediment entrained within the plumes into the bay. The occurrence of peak runoff events during periods dominated by southerly coastal currents would decrease the delivery of fine sediment to the bay.
Increases in mid-century streamflow produced amplified increases in Q ss . The warmer-wetter CNRM-CM5 RCP8.5 scenario projected the largest increase in Q ss for both the bay basins and the Eel River (Table 7). The hotter-drier MIROC5 RCP4.5 scenario projected the largest decline in Q ss for the bay basins, and the HadGEM2-ES 8.5 scenario projected the largest decline for the Eel River. Six scenarios projected increases in Q ss for the bay basins and seven scenarios projected increases for the Eel River. A comparison of exceedance curves for the Eel River for the baseline and mid-century periods (Fig. 7) showed climate impacts across the complete probability distribution. For the ten mid-century scenarios, Q ss is consistently higher than the baseline period over the full range distribution with the one exception being the hotterdrier HadGEM2-ES RCP8.5 scenario. The Q ss results showed Table 4 Daily and monthly statistical metrics, for twelve gaged basins in the Humboldt Bay -Eel River study region, used to calibrate and validate streamflow simulated using the Basin Characterization Model (Flint et al. 2013). See Fig. 1 Table 4 for the goodness-of-fit statistics that the regional fine-sediment supply is likely to increase under future climates. Results for the end-of-century showed larger climate change impacts on streamflow and Q ss (ESM 1) are likely to occur. For the bay basins, nine scenarios projected increases in mean annual streamflow and the number of peak flow days, ten scenarios projected increases in peak flows, and nine scenarios project increases in Q ss . For the Eel River, eight scenarios projected increases in mean annual streamflow and peak flows, ten scenarios projected increases in the number of peak flow days, and ten scenarios projected increases for the Eel River.
The study region is underlain by erodible lithologies and basins that discharge to the coastal margin have sediment yields that are higher than global averages. In these high yield basins, the wetter climate scenarios produced amplified increases in Q ss . As envisioned by Coulthard et al. (2012), these high yield basins act as "geomorphic multipliers." When the signal of increased precipitation is translated to runoff, streamflow, and Q ss , the climate change impacts are amplified. For the bay basins, the ensemble means projected changes in Q ss of 27% for the mid-century (Table 7) and 58% for the endof-century (ESM 1). For the Eel River, the ensemble means projected changes in Q ss of 53% (Table 7), and 99% for the end-of-century (ESM 1).

Discussion
Quantifying the impacts of climate change on finesediment delivery involves considerable uncertainty. The largest uncertainties are associated with the climate projections, emissions scenarios, and downscaling methods, and smaller uncertainties are related to the water-balance model, sediment transport models, and observational data (Vetter et al. 2017).
The limitations of simulating streamflow using the BCM are discussed at length by Flint et al. (2013). Errors were minimized through rigorous calibration of the historical model, but peak flows were underestimated during the validation period. Additional uncertainty was introduced by using model parameters, calibrated for the gaged basins, to simulate streamflow in the ungaged basins. Given the small range of values for the calibration parameters, this approach provided better estimates than a simple scaling approach, such as the ratio of ungaged to gaged areas.
The limitations of computing Q ss using statistical sedimenttransport models are well documented (Walling and Webb 1981;Rieger and Olive 1984;Glysson 1987;Asselman 2000;Lewis and Eads 2009;Warrick et al. 2013;Gray 2018). These models tend to underpredict sediment transport Table 5 Regression parameters, statistical metrics, and bias correction factors for sediment-transport models developed for five basins in the Humboldt Bay-Eel River study region. See Fig. 1  for high flows (Horowitz 2003). The accuracy of sediment transport predictions depends upon the range of values used to define the model, the statistical fit, whether conditions during the computational period are representative, and whether the variations in sediment transport are well explained by streamflow (Porterfield 1972;Gray and Simões 2008). The group-average method used to define the sedimenttransport models alleviated low-flow sampling biases, and Fig. 4 Separate low flow and high flow sediment-transport models (Eq. 1) fit using mean daily fine-sediment discharge paired with simulated streamflow for the five sediment reporting basins in the Humboldt Bay-Eel River study region. See ESM 4 and ESM 5 for raw data, Fig. 1 for gage locations, Table 3 for a summary of gage data, and Table 5 for model parameters and regression statistics the use of separate low-flow and high-flow models improved prediction errors. The validation results indicate that Q ss at the gaged locations may be underestimated by up to 47% (Table 6). Predictions errors (RMSE%) for the high flow models (Table 5) were 24 to 55%, which is similar to errors (30 to 50%) reported in previous studies (Meade et al. 1990;Glysson et al. 2001;Horowitz 2003;Farnsworth and Warrick 2007;Gray and Simões 2008;Gray 2018).
Although we recognize that Q ss is often out of phase with streamflow, we assumed that Q ss varied non-linearly with streamflow. Non-stationarity (Milly et al. 2008) and the influence of time-dependent trends (Warrick et al. 2013;Gray 2018) on the statistical relationship between streamflow and Q ss were minimized by excluding data collected before the historical baseline period . Although we addressed non-stationarity in the development of the sedimenttransport models, we assumed no time-dependent trends in the statistical relationship between streamflow and Q ss under future climates. The use of stationary sediment-transport models, fit to short-term historical data, added additional uncertainty.
Changes in land use or land cover were not investigated, although we recognize that the additive effect vegetation or land cover changes could substantially alter the magnitude and timing of streamflow and the statistical relationship between streamflow and Q ss . Dynamic sediment-transport models (Ahn and Steinschneider 2018), which allow regression parameters to change over time to account for persistent impacts such as large floods (Gray 2018) or changes in land use and land cover (Bussi et al. 2014), would be useful for further investigating time-dependent trends.
We did not address dynamic floodplain deposition, but we recognize low-lying areas at the bay interface as sinks for finesediment. Historically, former tidelands were diked, drained, and subsequently experienced local subsidence (Schlosser and Eicher 2012). Overbank flooding in these low-lying areas occurs during wet years and excessive floodplain sedimentation has been documented in the lower reaches of Freshwater Creek and Elk River (Lewis 2013). We assumed that fine sediment transported past the sediment gages was delivered to the tidal reaches at the bay interface.
Validation results showed that the water-balance model underestimated peak flows, and the statistical models underestimated Q ss . For these reasons, the Q ss estimates for historical and future climates are considered to be conservative. Poor model performance in simulating peak flow magnitudes is particularly important because the effective discharge for suspended-sediment transport in the study region is known to follow the small mountain-river paradigm (Milliman and Syvitski 1992). This paradigm, which states that Q ss in small mountain basins is strongly correlated to peak flows, has been confirmed by numerous studies (Tropeano 1991;Coppus and Imeson 2002;Grodek et al. 2012;Lewis 2013;Warrick et al. 2015).
Assessing uncertainty for the GCM outputs is challenging (Tebaldi and Knutti 2007), but ensemble averaging (Knutti et al. 2010) reduced uncertainty for the future climate projections. Selecting a subset of CMIP5 models that are most representative of California-specific climate features (CADWR-CCTAG 2015) further reduced uncertainty, and the use of multiple RCPs incorporated emissions uncertainty. A comparison of 30-year means among the different GCMs and RCPs for the historical, mid-century, and end-of-century periods showed the potential variability of streamflow and Q ss under future climates. Presentation of the results in terms of the percent change, relative to the historical baseline, provided the best metric for assessing differences among the scenarios and between different time periods. The ensemble means and standard deviations provided a single metric that captured multiple sources of variability and uncertainty.
We hypothesized that documented declines in the regional fine-sediment supply (Warrick et al. 2013) under current conditions might be offset under future climates by projected increases in Qss produced by increases in the magnitude and frequency of extreme precipitation events. Study results indicate that Q ss responded strongly to climate change. The ensemble means for the mid-century projected increases in Q ss Table 6 Validation of mean annual suspended-sediment discharge results. Q ss estimated using simulated streamflow from the historical waterbalance model are compared to Q ss estimated using measured streamflow for the bay basins (ESM 4) and the Eel River (Warrick 2014 of 27% for the bay basins and 53% for the Eel River (Table 7). These results contrast sharply with a recent study of sediment yield to the world's major deltas that determined climate change was responsible for increases in sediment yield of only 6 to 9% (Dunn et al. 2019). The strong contrast can be explained by mountainous physiography, highly erodible geology, a lack of flow regulation and reservoir entrapment, and the high sediment yields that characterize the study region. The ensemble of five GCMs and two RCPs provided a probabilistic framework for exploring the impacts of climate change on streamflow and Q ss . The ten scenarios used in this study captured plausible future climates (hotter-drier to warmer-wetter) and predicted a range of potential future sediment supply conditions. Despite large uncertainties, the study results provide useful projections to aid resource and land managers as they plan for future sediment supply scenarios, respond to potential vulnerabilities, and develop adaptation strategies for improving resiliency to SLR. The sediment supply projections can be used to guide adaptation strategies and to assess the availability of sediment for implementing sediment-based solutions to build resiliency to SLR.
Salt marshes, which respond dynamically to SLR and changes in sediment supply, provide shoreline protection and bolster resiliency to SLR. Recent work has shown that SLR impacts in salt marshes may be ameliorated by natural sedimentation events (Baustian and Mendelssohn 2018). In Humboldt Bay, the remaining salt marshes cover 3.6 km 2 . Direct measurements of marsh accretion indicate short-term accretion rates of 2.19±1.36 mm/yr (Curtis et al. 2019) and marsh cores indicate historical accretion rates of 3.5 to 5.7 mm/yr (Thorne et al. 2016). The annual supply of inorganic sediment required to balance rates of short-term accretion is 0.002 to 0.010 Mt/yr. This represents 4 to 19% of the Q ss (0.057±0.23 Mt/yr) computed for the bay basins using the historical model (Table 7). In comparison, the annual input Fig. 5 Summary of ten climate projections, shown as 30-year means, derived for the Humboldt Bay-Eel River study region from five global climate models (GCM) and two representative concentration pathways (RCP). Precipitation projections, shown as percent change, and air temperature projections, shown as change in degrees, were calculated as the difference between mean annual values for the historical baseline (1981-2010), mid-century (2040-2069), and end-of-century (2070-2099) periods. Standard deviation bars are used to show inter-annual variability Fig. 6 Number of peak flow days per decade ( > 95%-ile) during the historical baseline  and mid-century (2040-2069) periods for ten climate scenarios derived from five global climate models (Table 2) and two representative concentration pathways (RCP) of inorganic sediment required to balance historical marsh accretion rates is 0.010 to 0.016 Mt/yr, which represents 19 to 30% of the total annual Q ss computed for the bay basins.
Historically, sediment delivery from the local bay basins was sufficient to support natural marsh accretion, which increased surface elevations allowing the marshes to keep pace with SLR, and provided a remainder of additional sediment to fill subsided areas. The conceptual mass-balance calculations for the potential contribution of fluvial sediment for marsh accretion highlight the importance of understanding the balance between sediment supply and sediment demand. Under future climates, increased sediment demand, caused by the combined impacts of subsidence and SLR, may be partially or wholly balanced by projected increases in Q ss . In this case study for Humboldt Bay, fine-sediment delivery from fluvial sources was estimated but the internal sediment budget remains undefined. Studies of marsh accretion and sediment supply are continuing, and new marsh loss studies are underway.

Conclusions
This study presents a robust modeling approach and a probabilistic framework for assessing the impacts of climate change on the fine-sediment delivery from fluvial sources in a coastal region experiencing localized tectonic subsidence. In Humboldt Bay, sediment demand created by subsidence, SLR, and tidal prism expansion may be partially or wholly offset under future climates by projected increases in precipitation and streamflow that produce amplified increases in the regional sediment supply. Sediment demand caused by subsidence, SLR, and tidal prism expansion may be partially or wholly balanced under future climates by amplified increases in the regional sediment supply. Subsiding coastlines require a larger sediment supply to keep pace with SLR, and coastal regions with a higher sediment supply may be more resilient to SLR.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Fig. 7 Exceedance curves for the Eel River for a historical baseline  and ten mid-century (2040-2069) scenarios derived from five global climate models (Table 2) and two representative concentration pathways (RCP). Inset figure magnifies the upper portion of the curves and shows that suspended-sediment discharge (Q ss ) increased under all but one of the scenarios for the largest magnitude events