An Approach to Improve Land–Water Salt Flux Modeling in the San Francisco Estuary

Abstract

In this case study, we used the Delta Simulation Model II (DSM2) to study the salt balance at the land–water interface in the river delta of California’s San Francisco Estuary. Drainage, a source of water and salt for adjacent channels in the study area, is affected by channel salinity. The DSM2 approach has been adopted by several hydrodynamic models of the estuary to enforce water volume balance between diversions, evapotranspiration and drainage at the land–water interface, but does not explicitly enforce salt balance. We found deviations from salt balance to be quite large, albeit variable in magnitude due to the heterogeneity of hydrodynamic and salinity conditions across the study area. We implemented a procedure that approximately enforces salt balance through iterative updates of the baseline drain salinity boundary conditions (termed loose coupling). We found a reasonable comparison with field measurements of drainage salinity. In particular, the adjusted boundary conditions appear to capture the range of observed interannual variability better than the baseline periodic estimates. The effect of the iterative adjustment procedure on channel salinity showed substantial spatial variability: locations dominated by large flows were minimally impacted, and in lower flow channels, deviations between baseline and adjusted channel salinity series were notable, particularly during the irrigation season. This approach, which has the potential to enhance the simulation of extreme salinity intrusion events (when high channel salinity significantly impacts drainage salinity), is essential for robustly modeling hydrodynamic conditions that pre-date contemporary water management infrastructure. We discuss limitations associated with this approach and recommend that—for this case study—further improvements could best be accomplished through code modification rather than coupling of transport and island water balance models.

1. Introduction

Estuarine salt transport is affected by oceanic and land-side salt and water fluxes. Salinity predictions using hydrodynamic and salt transport models are commonly used for restoration and planning activities, particularly in estuaries with a strong anthropogenic influence. This work explores refinements in salinity modeling related to land-side salt fluxes in one such estuary, the San Francisco Estuary in California (Figure 1). In this work, we utilize a widely used hydrodynamic water quality model, the Delta Simulation Model II or DSM2 model [1]. As shown in Figure 1, a key feature of the Estuary is a network of channels and leveed islands formed at the confluence of the Sacramento and San Joaquin Rivers. Developing a better understanding of the magnitude and variations in land-side salt fluxes in DSM2 is valuable for effective salinity modeling, particularly during extreme events, such as droughts, and in the face of continuing climate change in the form of changing inflows and sea levels.

Because of the sparsity of salt flux data from the islands to the channels, modeling in the estuary relies heavily on assumptions to characterize these interactions. Besides DSM2, several 2-D and 3-D numerical models have been developed, maintained and utilized to study hydrodynamics and salt transport in the Delta [2,3,4,5]. These models represent the study area’s land–water interface through a common integrated modeling approach; a key element of this common approach is the specification of Delta island drain volume and water quality as internal boundary conditions, with drainage water quality being independent of channel water quality. Although this approach enforces water volume balance between island diversions, evapotranspiration and returns, it does not explicitly enforce salt balance. To our knowledge, this deviation from salt balance has not been explored as part of the development process of any of the numerical models identified above. A field investigation [6] suggests that, rather than being a net source of salt, Delta islands “…act as a salt reservoir by first storing some of the salts that enter the islands during the summer and then by releasing those salts during the winter through leaching and/or drainage of precipitation.”

In this case study, we first evaluate deviations from mass balance (between the amount of salt entering and leaving Delta islands) associated with the DSM2 model [1]. We then present results from a procedure that seeks to improve on the existing modeling approach by enforcing mass balance through iterative updates of the DSM2 drain salinity boundary conditions and compare the land-side concentrations obtained in this manner to the repeating values used in the current DSM2 calibration. In the literature on modeling integration (e.g., [7]), this procedure would be termed a loose integration of models, as compared to approaches that incorporate a tighter coupling of processes through model codes. Building on this work, we discuss the benefits and limitations of the loose integration approach on the salinity problem in San Francisco Estuary and identify opportunities for further enhancing modeling of the variable land-side boundary input.

2. Background

2.1. Study Area

San Francisco Estuary, the largest estuary on the Pacific Coast of the Americas, consists of several water bodies including the open waters of San Francisco Bay and the delta formed by the Sacramento and San Joaquin Rivers (hereafter Delta). The study area is an example of an estuary that provides vital ecological services and supports one of the largest urban regions in the world through water supply, transportation infrastructure, storm and flood buffering, and wastewater conveyance [8,9]. Through out-of-basin water exports, the estuary supports much of California by providing freshwater resources for agricultural and municipal use [10]. Salt transport within the estuary is influenced by saline inflows from the Pacific Ocean at Golden Gate through the action of tides, by freshwater inflows from the contributing watersheds, (which exhibit great seasonal and interannual variability), and by surface water and groundwater interactions with coastal lands peripheral to the estuary and the large number of islands within the Delta. Most of these islands, originally part of a tidal wetland landscape, have been leveed and converted to agricultural use [11]. Many of these Delta islands have subsided below sea level through intensive farming activities and exchange water, salt and other land-derived constituents with the surrounding Delta channels through diversions, seepage and discharge. Island return flow and salt discharge, while relatively minor contributors to overall system balance on an annual and estuary-wide basis, can be significant in some parts of the Delta, particularly during low-flow summer months and drought periods [12,13]. Because humic substances are leached from Delta peat soils because of farming activities, return flow tends to be highly concentrated with organic disinfection by-product precursors and can present challenges for drinking water treatment [14,15]. Delta island return flow water quality has been monitored by the California Department of Water Resources (CDWR) as part of its Municipal Water Quality Investigations (MWQI) Program [16]; however, spatial and temporal data coverage remains sparse.

2.2. DSM2 Model and Island Salt Flux Representation

We focus in this case study on DSM2 (Version 8.2.0), CDWR’s 1-D hydrodynamic and salt transport model for the San Francisco Estuary upstream of the Carquinez Strait near Martinez [1]. DSM2 is integrated with CDWR’s Delta Channel Depletion (DCD) model [17], a water balance model for estimating Delta island diversion and return flows, to represent land–water interfaces in the estuary. DSM2 represents Delta waterways as a network of one-dimensional channels meeting at model nodes (see Figure 1 inset for interconnected nodes representing the Delta channels). It simulates network hydrodynamics and salt transport with a discretized solution to the governing differential equations. Flow and salt transport within the channels are fully determined by the evolution of these differential equations, but other processes such as surface runoff, diversions for agricultural and municipal use, and drainage from islands are all treated as internal boundary conditions that are specified as time series inputs to the model. The water volume portion of these boundary conditions is derived from the DCD model. While the salinity of water leaving the DSM2 network through internal diversion boundary conditions is based on the dynamic channel salinity in the timestep at which the diversion occurs, the salinity of water re-entering the DSM2 network through internal drainage boundary conditions is not calculated dynamically but is specified by spatially and temporally coarse time series input [18]. Thus, DSM2’s integrated approach for modeling land–water interface does not explicitly enforce mass balance between the amount of salt entering and leaving the islands. This gap in the mechanistic representation of a key process—in DSM2 as well as other numerical models of Delta salinity—is of particular importance during periods of high salinity intrusion in Delta channels, as might occur during very low flows and during extreme droughts.

3. Methods

3.1. Model Subregion Delineation

Five subregions were delineated to compare salt balance at the land–water interface within the integrated modeling approach. The subregions, located in Figure 1 and described in

Table 1. Model subregions.

Model Subregion	Acronym	General Description
Freshwater Boundary	SAC	main stem of the Sacramento River upstream of the confluence with the San Joaquin River
Seaward Boundary	SEA	confluence of the Sacramento and San Joaquin Rivers
Old-Middle River Export Corridor	OMR	a region uniquely influenced by hydrodynamic patterns driven by State Water Project and Central Valley Project diversions from the Delta
San Joaquin River Corridor	SJR	main stem of the San Joaquin River downstream of Vernalis
South Delta	SDELTA	a region uniquely influenced by salt loads that enter the Delta at Vernalis, the placement of seasonal in-channel rock barriers, and local sources of salinity (including agricultural drainage and groundwater)

, approximately follow geographic boundaries and nomenclature as defined in [19] to evaluate spatial variability in the ionic makeup of Delta waters.

3.2. Observed Drainage Salinity Data

We used grab sample data collected by CDWR’s MWQI Program to evaluate the reasonableness of drainage salinity adjustments resulting from the iterative modeling approach presented here. The MWQI program and predecessor programs have conducted discrete water quality monitoring in the Delta since the early 1980s. The spatial and temporal extent of this monitoring has varied in response to program needs and system understanding [16]. Here, we use data from five monitoring sites located in Figure 1. Details on these data are provided in

Table 2. Observed drainage salinity at five MWQI monitoring locations, including the range of dates and number of data points.

Location	Dates	# Data Points
Twitchell Island Drain	19 July 1989–6 August 2001	127
Jersey Island Drain	20 June 1994–2 September 1997	34
Palm Tract Drain	31 July 1991–18 July 1994	32
Bacon Island Drain	23 January 1990–3 July 2001	78
Lower Jones Tract Drain	19 July 1989–19 July 1994	36

.

3.3. Modeling Approach

An iterative approach was used to adjust DSM2 boundary conditions associated with the land–water interface. First, a baseline DSM2 simulation was conducted assuming historical hydrology and water management operations for the period spanning Water Years 1990–2021 (October 1989–September 2021). Running totals of baseline-simulated salt fluxes–both inflows (drainage) and outflows (diversion)–were tracked for each of the model subregions by multiplying boundary flows and boundary salinity concentrations. DSM2 flows are reported in units of cubic feet per second (cfs) and DSM2 salinity concentrations are reported as specific conductance in units of micro-Siemens per centimeter (μS/cm). Therefore, by directly using model output, the salt flux for a given timestep (Δt) is nominally computed in units of cfs × μS/cm × Δt. We assumed a conversion factor of 1 μS/cm = 0.6 mg/L total dissolved solids to report salt flux in more convenient and interpretable mass units. It is also worth noting that at the lower salinity values present in the interior Delta region being examined here, 1 ppm ≈ 1 mg/L. This assumption is based on broad natural water characteristics reported in [20] and local conditions reported in [21]. Salt flux results were ultimately reported in units of tons.

Baseline inflow and outflow salt fluxes were then compared for each model subregion. If the inflow salt flux was higher than the outflow salt flux, then the net baseline salt flux was away from the land side and the drainage salinity boundary conditions were adjusted downwards in the subsequent iteration. Conversely, if the inflow salt flux was lower than the outflow salt flux, then the net baseline salt flux was toward the land side and the drainage salinity boundary conditions were adjusted upwards in the subsequent iteration. For purposes of computing the salt balance deficit (i.e., comparing inflow and outflow salt fluxes) for each model iteration, Δt was set to be equal to six months. The subregion-specific salt balance deficit was distributed evenly among the relevant DSM2 model nodes and multiplied by a subregion-specific heuristic factor (SAC = 1.3, SEA = 0.95, OMR = 1.1, SJR = 1.0, SDELTA = 1.0) to speed convergence and reduce overshooting of the mass correction. That is, each model run is computationally costly, and the imprecise spatial representation of drains and pumps within the model mean that the first-order estimate of just adjusting the boundary conditions by the exact amount of the deficit. The heuristic factors applied are relatively small (less than 30% off from the nominal deficit), and an iteration without them would trend toward similar final values, just over a much larger number of computationally expensive iterations. Five DSM2 model simulations were conducted: one baseline simulation plus four iteration simulations guided by the salt flux comparison described above. Four iterations achieved approximate salt balance across the land side boundary in the model subregions. This procedure is summarized in tabular form in

Table 3. Summary of mass flux computation procedure.

Step	Step Title	Step Description
1	Run hydrodynamic model	Run DSM2 HYDRO module
2	Run salinity transport model	Run DSM2 QUAL module
3	Compute subregional salt mass fluxes	For each node in a given subregion, add up the inflowing and outflowing salt masses
4	Convert EC to mg/L	Based on broad natural water characteristics reported in [20] and local conditions reported in [21] assume 1 μS/cm = 0.6 mg/L
5	Convert to tons of salt mass	1 ac × ft of water with 1 mg/L salinity = 0.000815808 t
6	Compute mass balance deficit	Over 6-month time windows, compute the difference between inflows and outflow salt masses
7	Adjust deficit by heuristic factors	Multiply a subregion-specific heuristic factor (SAC = 1.3, SEA = 0.95, OMR = 1.1, SJR = 1.0, SDELTA = 1.0) to each salt balance deficit
8	Update boundary conditions	Distributed the adjusted mass deficit offset uniformly over the 6-month time window
9	Iterate until approximate convergence	Return to step 2, repeat as necessary until estimates no longer substantially change (4 repetitions were necessary in this case)

. Based on results from the final DSM2 iteration, the adjusted drainage boundary conditions were compared with observed data at several locations. Additionally, adjusted and baseline salinities were compared at several channel locations.

4. Results

Return flow from Delta islands is a relatively minor contributor to overall system water balance on an annual and estuary-wide basis; however, it can be a significant fraction of flow volume in some parts of the Delta, particularly during low-flow summer months and drought periods. Figure 2, which shows the time series of nominal drainage volume (as a percent of total channel volume) at representative locations within three model subregions, illustrates the spatial and temporal variability associated with drainage volume impacts. The influence of drainage volume is particularly noticeable in the SDELTA subregion (reaching approximately 40 percent of total channel volume in some months), where total channel flow volumes tend to be relatively small. This result suggests that deviations from salt balance in the SDELTA subregion may have important implications for model performance in this area.

The top panels of Figure 3 show the cumulative salt fluxes for inflows (drainage) and outflows (diversion) by model subregion for the baseline DSM2 simulation. The scale of the absolute difference varies widely among the subregions, as expected by the heterogeneity of hydrodynamic and salinity conditions throughout the Delta. Differences between the inflow and outflow fluxes quantify deviations from mass balance in the baseline simulation. The bottom panels of Figure 3, which show the updated salt fluxes after the final model iteration, suggest that the iteration approach reasonably converges to mass balance. In terms of an overall comparison across all five subregions, before iteration inflowing and outflowing salt fluxes have a correlation coefficient of 0.69, while after iteration the correlation coefficient becomes 0.9995. The good match is unsurprising, given this was the target of the iteration procedure. While the high correlation does not imply a perfect calibration of mass balance, it does suggest that four iterations were sufficient for achieving approximate mass balance.

Deviations from mass balance in the baseline simulation can be quite large and, except for the SEA region, cumulative salt fluxes entering Delta channels (from land drainage) are consistently larger than those leaving Delta channels. Cumulative deficits (by the end of the baseline simulation) for the SAC and OMR model subregions are 25% and 22%, respectively, of the annual flux past the model boundary at Vernalis (approximately 760,000 t).

Figure 4 compares baseline and adjusted drainage salinity with field observations at five locations in the Delta. Salinity is reported as specific conductance in units of µS/cm. Precise coordinates of the observation stations were not readily available. Furthermore, given the approximate representation of drain locations in DSM2, modeled drainage coordinates must also be taken as approximate. The baseline drain salinity values are periodic and generally either fall in the middle range of observed drain salinities (Jersey Island, Palm Tract) or are towards the upper end of observed drain salinities (Bacon Island, Lower Jones Tract, Twitchell Island). In contrast, the adjusted drain salinities show some interannual variation from the adjustment procedure. In some cases (Bacon Island, Lower Jones Tract, Palm Tract), the adjusted drain salinity appears to follow the observed data variation more closely than the periodic baseline data. In the other cases (Jersey Island, Twitchell Island), the adjustment appears to have pushed the adjusted data away from the observed data. Despite the inherent level of approximation introduced by these uncertainties, some level of agreement between observed and simulated drain salinity is apparent in the figure.

Figure 5 and Figure 6 compare baseline and adjusted in-channel salinity (again reported as specific conductance in units of µS/cm) at standard DSM2 output locations nearby model subregion. In general, differences between baseline and adjusted in-channel salinity are quite limited at the monthly or greater timescale at which the adjustments were made (Figure 5). Nevertheless, a few periods demonstrate moderate to significant differences, particularly in the SDELTA subregion where channels are relatively small and return flows are a greater percentage of total channel flow (Figure 6).

5. Discussion

A widely used model for delta hydrodynamics and water quality in the San Francisco Estuary (DSM2) was employed to test a methodology for improving land–water salt flux modeling in the study area. We found a detectable imbalance between the salt flux from Delta channels (i.e., entering Delta islands through diversions and seepage) and the salt flux from Delta islands (i.e., entering Delta channels through island drainage) in a baseline DSM2 simulation of historical hydrology and water management operations. An iterative adjustment procedure—in which the cumulative salt fluxes were tracked, and an offsetting amount of salt was added or removed from the internal drainage boundary conditions—enforced an approximate salt balance throughout the model domain. The approximate salt balance produced by the adjustment procedure resulted in drainage salinity boundary conditions that were much more variable from year to year compared to the baseline inputs which assumed consistent periodic salt flux, regardless of hydrology. Mass imbalances of up to 25% percent were corrected in the subregions adjusted, and the overall correlation of cumulative mass influxes and outfluxes across all subregions improved from 0.69 to 0.9995. The adjusted drainage time series do not perfectly match salinity observations; however, they appear to capture the range of observed interannual variability better than the baseline periodic estimates in the extent of the observed drain dataset. The procedure could be used in transport models that rely on uncertain boundary conditions, as long as the models’ calibrations are sufficiently resilient to having those boundary conditions modified.

The methodology presented here must contend with limited model spatial resolution and potential inaccuracy in the drain locations in the model representation. It is possible that these factors affect the few cases where the adjustment appeared to increase the degree of mismatch between drain salinity and observed data; Twitchell and Jersey Islands have different hydrodynamic behaviors but are subject to the same adjustments from being in the same subregion. The effect of the iterative adjustment procedure on channel salinity varied by location. In the study area subregions that tend to be dominated by large flows (i.e., the northern riverine SAC subregion and the western tidal SEA subregion), the channel salinity time series were minimally impacted by the adjustment procedure. In the remaining study area subregions (i.e., OMR, SJR and SDELTA), deviations between baseline and adjusted channel salinity series were notable, with the differences beginning to accumulate throughout the irrigation season of April-October.

In theory, adjustments to the internal DSM2 boundary conditions could invalidate the baseline model calibration and trigger the need for model recalibration. However, given that differences between baseline and adjusted in-channel salinity are generally limited at the monthly or greater timescale at which the adjustments were made, the integrity of the baseline model calibration will likely remain intact. Furthermore, the DSM2 dispersion factors indicate a somewhat coarse level of calibration, with little variance among the channels upstream of the SEA model subregion. The coarseness of the calibration suggests that our adjustments to the drain boundary conditions will likely have minimal impact on the calibration.

The assumption of mass balance at the land–water interface, as employed in this work, does not necessarily apply to all constituents of interest in the San Francisco Estuary. For example, mass balance constraints on total organic carbon loads would not be justified as island drainage is a well-established net source of total organic carbon in Delta channels [14]. Similarly, mass balance constraints on nonconservative water quality constituents (e.g., nutrients, temperature, dissolved oxygen) would not be justified due to transformations that may occur on the islands. Therefore, as a practical consideration, the iterative approach presented in this work is probably most appropriate for developing drainage time series for conservative mineral constituents such as bromide, chloride, and bulk salinity proxies such as practical salinity and specific conductance.

Baseline assumptions of salt flux at the Delta land–water interface, as well as the adjusted Delta island drainage time series developed here, are likely to poorly represent scenarios that are significantly different from contemporary conditions. Some scenarios of potential interest that are likely to fall into this category are pre-development conditions with a landscape characterized by tidal wetlands that were later “reclaimed” to leveed agricultural land use [22], pre-project drought conditions with extreme salinity intrusion (both temporal and spatial) that were not controlled by upstream and in-Delta water project operations [23,24], and dramatically modified future/hypothetical conditions (e.g., tidal wetland restoration) with salt loading boundary conditions substantially different than those that exist today. This lack of robustness points to the need for future work to enhance the general applicability of land–water interface modeling in San Francisco Bay hydrodynamic and constituent transport modeling.

Whether one is analyzing scenarios that represent larger departures from baseline conditions or is exploring the possibility of real-time calibration of the model parameters with enforced mass balance, real world application of the methodology presented here would likely require boundary condition adjustments at a finer spatial and temporal resolution, which might strain the computational time or accuracy limitations inherent to any offline method. Rather than making iterative offline adjustments to the drainage time series boundary conditions (as presented in this work), dynamic modeling approaches could be implemented in DSM2 and other existing models by modifying the source code to enforce an internal mass balance. Such model enhancements would likely lead to more accurate and refined results under a wider range of hydrologic conditions and would likely provide a better representation of feedback under extreme salinity intrusion conditions, where higher Delta channel salinity would ultimately result in higher island drain salinity. Such conditions occurred in much of the interior Delta during the historic 1928–1934 drought and were of consequence to the quality of irrigation water available to Delta agricultural prior to upstream and in-Delta operation of the Central Valley Project and State Water Project. Thus, this case study presents an example where further improvements to model integration could possibly be accomplished through code modification that enforces internal mass balance rather than the relatively loose model coupling presented here.