Simulation of Flow and Salinity in a Large Seasonally Managed Wetland Complex

: Seasonally managed wetlands in the San Joaquin River (SJR) watershed in California provide important benefits to wildlife and humans but are threatened through anthropogenic activity. Wetlands in the SJR are subject to salinity regulation, which poses challenges for wetland management. Salinity management in the SJR basin is supported by a process-based model, the Watershed Analysis Risk Management Framework (WARMF). Wetlands are simulated with a “bathtub” analog where water levels are assumed to be the same over one model compartment and the storage volume depends on depth. The complexity and extent of hydrological features pose challenges for input data acquisition. Two approaches to estimating inflow and pond depth and determining water sources were assessed. Approach 1 used mostly monitored data, while Approach 2 used wetland manager knowledge. Approach 2 predicted outflow and salinity better than Approach 1, and an important benefit was the simulation of water reuse within the wetland complex, which was previously not implemented. Approach 1 is generally suited for estimating pond depth when a model compartment represents one wetland, while Approach 2 is suited for wetlands with large spatial extent, many hydrological features, and managed flows. The improved model will support wetland management.


Introduction
Wetlands provide important ecosystem functions, such as serving as habitats for waterfowl, storing carbon, and improving water security and water quality [1].Wetlands store a disproportionately high amount of carbon compared to other ecosystems due to their high productivity and slower rates of organic matter decomposition [2].Although wetlands currently cover only around 6% of the global land area, they contain 12% of the terrestrial global carbon pool [3].In addition, they can be important regulators of water quality throughout an entire watershed by retaining nutrients and sediments [4].However, wetlands could become carbon sources due to global warming or if constructed wetlands are not managed properly [2].Over 80% of natural wetlands have been lost globally, while there has been an increase in artificial wetlands for food production [5].In addition to disturbances of hydrological and ecological conditions within a wetland, the biggest threat to wetlands comes from upstream anthropogenic activities such as water diversion for agriculture [6].The conservation and restoration of wetlands have been recognized as important nature-based climate solutions, in addition to providing flood control and improved water quality [7,8].However, a better understanding of carbon dynamics after restoration is needed to ensure optimal carbon storage in restored wetlands [9].
In this study, we focused on seasonally managed wetlands within the Grasslands Ecological Area (GEA) in the San Joaquin River (SJR) watershed (CA, USA), which is threatened by salinization.The GEA is composed of a mixture of state, federal, and private wetland and refuge areas encompassing ~140,000 acres in central California interspersed within a region of intense agricultural use (Figure 1).Salinization is a threat to ecosystems in arid and semi-arid climates [10], and is a particular concern in the SJR watershed.Salinity increases naturally in seasonal wetlands.During the flooded season, evapotranspiration, groundwater discharge, and dissolution of salt residues on soils cause increased salinity in wetland water, which is released in spring.Salt residues build up when the soil dries.In addition, salinity is exacerbated in the SJR watershed because of altered hydrology (caused by diversion and unintentional reuse), the import of water with degraded quality from the Sacramento-San Joaquin Delta, and the use of groundwater that is naturally high in salts [11].Higher salinity decreases primary productivity through decreased metabolic efficiency, and causes plant stress [12] and plant death [13].The SJR basin is a leading region for agricultural production that generates 50% of California's agricultural output [14], resulting in more than USD 5 billion in crop revenue per year [15].Salinity mitigation in the SJR watershed is challenging due to the diverse interests of stakeholders.A particular challenge is that salt export from seasonally managed wetlands coincides with the germination of salt-sensitive irrigated crops on agricultural lands that are located downstream.To protect irrigated crops and avoid salt buildup on wetland soils, salt export can be coordinated with tributary inflows that are low in salinity [16].To mitigate salinization, salinity regulation was developed in the early 2000s with a phased compliance schedule that will be fully implemented in 2026.This regulation has spurred important developments towards sustainable salinity management in the SJR [17], including the deployment of an extensive real-time monitoring system, and the development of the Watershed Analysis Risk Management Framework (WARMF) as a decision support tool [18][19][20].The WARMF model is currently the only model that simulates the hydrology and water quality of the GEA wetland complex.
Simulation of hydrology and water quality for large complex systems such as the seasonally managed wetlands in the GEA is inherently difficult because (1) the management of flows prevents use of elevation models; (2) small differences in elevation complicate prediction of groundwater interaction; (3) the large number of small canals and ponds requires aggregation of modeled hydrological features to keep the model manageable, thereby requiring alternative data acquisition strategies; and (4) some processes might not be incorporated into the model because it is unfeasible to acquire sufficient monitored data or because these processes have been overlooked.A recent paper [21] proposed a global model for wetlands to simulate ecosystem services-all benefits that humans gain from ecosystems [22].However, the study recommended an elevation model that is not suitable for wetlands with managed flows [21].We argue that the WARMF hydrological model discussed in this study is better suited for managed wetlands.The WARMF model mimics managed flows by simulating changes in water storage volume with prescribed input time series.Therefore, the model is appropriate for all wetlands with managed water flows, e.g., rice fields.However, appropriate selection and optimization of time series input parameters are critical for accurate forward-modeling simulations, particularly for salinity (or salt load), which is challenging to forecast in hydrologically complex managed systems.
Here, we present two different approaches to estimate model input time series for inflow, initial EC, and pond depth for seasonally managed GEA wetlands.Approach 1 employed predominantly monitored data, which refers to data that is automatically and continuously collected for a certain period.Approach 1 shows how monitored pond depth data can be transformed for application to a bathtub analog, which is relevant for a range of wetland types that have seasonally fluctuating water levels.Approach 2 employs wetland manager knowledge for data acquisition of pond depth, water sources, and inflow.Using wetland manager knowledge provides the opportunity to consider processes that are inherently difficult to monitor or unfeasible to monitor; however, stakeholder involvement can lead to differences in model outcome [23] and introduces an additional layer of uncertainty [24].We show that employing wetland manager knowledge as well as selecting monitored data that match the spatial scale of the model is beneficial for the simulation of hydrology and water quality in large and complex managed wetland systems.Simulation of hydrology and water quality for large complex systems such as the seasonally managed wetlands in the GEA is inherently difficult because (1) the management of flows prevents use of elevation models; (2) small differences in elevation complicate prediction of groundwater interaction; (3) the large number of small canals and ponds requires aggregation of modeled hydrological features to keep the model manageable, thereby requiring alternative data acquisition strategies; and (4) some processes might not be incorporated into the model because it is unfeasible to acquire sufficient monitored data or because these processes have been overlooked.A recent paper [21] proposed a global model for wetlands to simulate ecosystem services-all benefits that humans gain from ecosystems [22].However, the study recommended an elevation model that is not suitable for wetlands with managed flows [21].We argue that the WARMF hydrological model discussed in this study is better suited for managed wetlands.The WARMF model mimics managed flows by simulating changes in water storage volume with prescribed input time series.Therefore, the model is appropriate for all wetlands with managed water flows, e.g., rice fields.However, appropriate selection and optimization of time series input parameters are critical for accurate forward-modeling simulations, particularly for salinity (or salt load), which is challenging to forecast in hydrologically complex managed systems.
Here, we present two different approaches to estimate model input time series for inflow, initial EC, and pond depth for seasonally managed GEA wetlands.Approach 1 employed predominantly monitored data, which refers to data that is automatically and continuously collected for a certain period.Approach 1 shows how monitored pond depth data can be transformed for application to a bathtub analog, which is relevant for a range of wetland types that have seasonally fluctuating water levels.Approach 2 employs

Study Area
The GEA is a wetland complex covering 140,000 acres with thousands of single wetland ponds [25] (Figure 1).As a result of large-scale hydrologic engineering and land reclamation beginning in the 1850s, the GEA is a highly managed network of wetlands, ponds, and water conveyance structures in the floodplains and low-lying areas of the upper SJR basin.The wetlands are part of the Pacific Flyway and are managed to provide food for migrating and overwintering waterfowl [11].Management of wetland ponds to mimic seasonal changes involves (1) flooding between August and December-with most of the ponds being flooded in October; (2) maintenance flows for improved water quality during winter; (3) drawdown in spring to allow germination of moist-soil plants; and (4) additional irrigation after drawdown if needed.This hydrology is different from the original undisturbed hydrology where flooding occurred in spring and summer due to snowmelt.
The Grassland Water District (GWD), the agency responsible for delivering water to GEA wetlands, operates multiple monitoring stations within the GEA.Flow and EC are measured in 15 min intervals.Quality control involves manual measurement of flows and calibration of EC against standards.Aggregated daily values and accompanying quality control data were obtained from GWD.Four monitoring stations provided data that were used in the simulations: SFC at 152, SL1, Mud Slough at Gun Club Road (GCR), and Fremont at GCR (Figure S1).The first three stations typically had sufficient water levels to cover the sondes that monitor flow and EC, resulting in excellent or good data according to U.S. Geological Survey data quality control guidelines [26].However, the Fremont Canal at GCR generally experiences highly variable flow, which often means that the channel stage is insufficient to cover the acoustic Doppler sensor.Between July 2018 and June 2019, the flow data at Fremont had many missing values that were estimated with linear interpolation.The accuracy of EC data at Fremont Canal at GCR was only fair or poor (defined as a deviation in the calibrated and measured values of more than 10 and 15%).
Within the GEA, two model compartments were selected for this study based on how well monitoring stations represented inflow and outflow at each model compartment.Assessment of adequate representation of inflow and outflow was based on a comparison of flood-up and drainage maps from the U.S. Bureau of Reclamation with the delineation of WARMF model compartments.The two selected model compartments roughly correspond to drainage areas serviced by the monitoring stations Mud Slough (MS) at GCR and Fremont Canal (FC) at GCR (Figure S2).These two drainage canals account for more than 80% of the total wetland drainage from the GWD.The two model compartments are located next to each other within the North GWD.The MS compartment (11,667 acres) receives most of its water supply from the Santa Fe Canal (SFC), a major water supply and drainage conveyance that connects the southern and northern divisions of the district.The SFC conveys water from the Delta Mendota Canal, with wetland return flows that are diverted and returned to the SFC along its length.In addition, the MS receives water via a recirculation system that began operation in 2019.The FC compartment represents a much smaller wetland area (1876 acres) and receives water mostly from the San Luis Canal, which receives water from the DMC and minor volumes of local drainage.
Model simulations were performed for two years: July 2018 to June 2019, and July 2019 to June 2020.This time frame was chosen because the wetland flood-up starts in late August.California typically has a rainy season during winter and early spring and a dry season from approximately May to October.For California, the 2019 water year was classified as wet with a water year index of 10.3, precipitation at 190% of average for the SJR, and streamflow at 171% of average in the SJR [27].The 2020 water year was classified as dry with a water year index of 6.1, precipitation at 67% of average precipitation statewide, and streamflow at 58% of average in the SJR [28].The average water year index is 8.0.

Hydrological Model WARMF
The Watershed Analysis Risk Management Framework (WARMF) is used for shortterm forecasting of salinity and salt load assimilative capacity in the SJR by the U.S. Bureau of Reclamation.WARMF is a distributed, physically based watershed model that has utility for total maximum daily load (TMDL) analysis considering point and nonpoint sources [29].The model was derived from the storm water management model (SWMM) [30] and the integrated lake-watershed acidification study (ILWAS) model [31,32].The WARMF model simulates a range of hydrological and water quality processes.Simulated hydrological processes are canopy interception, snowpack accumulation, snow melt, infiltration into soil, evapotranspiration from soil, ex-filtration of groundwater to stream segments, groundwater pumping, and kinematic wave routing of stream flows.WARMF performs flow routing and mass balance with a series of connected continuously stirred tank reactors (CSTR), which represent canopy, snowpack, wetland ponds, and five soil layers.Surface runoff and groundwater exfiltration are routed to stream compartments.A range of water quality parameters can be empirically simulated, e.g., alkalinity, pH, dissolved oxygen, and biochemical oxygen demand.In 2006, WARMF was enhanced to simulate mercury cycling [33].

Wetland Hydrology in WARMF
Hydrological wetland processes represented in WARMF are shown in Figure 2. In WARMF, many wetland ponds are aggregated into one model compartment with eleven compartments in total (Figure 2).The wetland compartment receives water through inflow from canals and precipitation.Water leaves the wetland via evapotranspiration, infiltration into the soil, and surface runoff.
performs flow routing and mass balance with a series of connected continuously stirred tank reactors (CSTR), which represent canopy, snowpack, wetland ponds, and five soil layers.Surface runoff and groundwater exfiltration are routed to stream compartments.A range of water quality parameters can be empirically simulated, e.g., alkalinity, pH, dissolved oxygen, and biochemical oxygen demand.In 2006, WARMF was enhanced to simulate mercury cycling [33].

Wetland Hydrology in WARMF
Hydrological wetland processes represented in WARMF are shown in Figure 2. In WARMF, many wetland ponds are aggregated into one model compartment with eleven compartments in total (Figure 2).The wetland compartment receives water through inflow from canals and precipitation.Water leaves the wetland via evapotranspiration, infiltration into the soil, and surface runoff.In 2015, the simulation of water retention was updated to a "bathtub" analog that better represents flooding and draining of seasonally managed wetlands [34].The analog makes the following assumptions: (1) water levels are the same in each CSTR; (2) water depth as a function of time is prescribed (in the following called "pond depth profile"); and (3) water in excess of the available water storage is subject to overland routing according to Manning's equation.
Water storage is calculated as: where V W is water stored in one wetland compartment (cm 3 ), A W is the wetland compartment area (cm 2 ), and d W is the prescribed pond depth at time t (cm).This approach allows a rapid change in retained water that mimics the actual management of seasonally managed wetlands.To determine how much water is available as outflow, the water depth at time step t is calculated as: where d t−1 is the water depth at the previous time step (cm), and d I is the inflow depth (cm).When d t < d w , all water is retained.When d t > d W , water above d w is subject to Manning's overland flow as follows: where Q S is the runoff (cm), n is Manning's roughness coefficient (day/[cm 1/3 ]), W is the width of the compartment parallel to the receiving stream (cm), S is the slope of the hydraulic grade line (cm/cm), and d M is the water depth above the prescribed pond depth: If Manning's n > 0, some water will be retained, and the final depth will be added to the prescribed depth.

Model Parameterization
WARMF requires a range of model input data and model parameters, including land use, soil characteristics, meteorology, managed flows (inflow to wetland), and pond depth profiles.We will only focus on a small set of input times series in this study.Input time series, which have been established as reliable in previous research, e.g., daily precipitation, and previously calibrated model parameters that apply to the entire watershed or multiple model catchments, are not further discussed and can be found elsewhere [35].Table 1 provides an overview of the WARMF model simulations that were performed with two distinct sets of input time series for inflow, prescribed pond depth, and EC that were developed with two different approaches.The first approach uses mostly monitored data, while the second approach uses wetland manager knowledge to revise flow routing and pond depth profiles.Approach 1 has the advantage that it reduces the need to make assumptions and reduces the time needed for data analysis; however, the approach might not be suitable for large wetland complexes or if data gaps exist.Approach 2 provides the opportunity to describe known processes that cannot be easily monitored but the approach requires a range of assumptions based on in-depth knowledge and poses the risk of overlooking important processes.Some assumptions were considered essential to both approaches.Approach 1: Input time series following Approach 1 were previously developed and are described in the following [34].The inflow was based on U.S. Bureau of Reclamation Water Management Plans, and data from the Water Acquisition Program and the Central Valley Operations Office.A data limitation was that water sources were not reported, and inflow values were monthly instead of daily values that are needed for the model.The data limitations resulted in a need to make some assumptions about the inflow and water sources.Because the water for the entire wetland complex is delivered from the Delta Mendota Canal (DMC) and the Mendota Pool (MP), it was assumed that EC monitored at DMC and MP is representative of the initial EC.Pond depth profiles were based on a State Water Resources Control Board (SWRCB) monitoring campaign.The campaign monitored pond depth at twelve individual pond outlets (Figure 3).Data from seven of the monitored outlets were chosen because they had no data gaps and showed a similar temporal pattern as the fall flood-up cycle.It is notable that the pond depth at an outlet is typically considerably deeper than the average pond depth.To account for this discrepancy, the data were normalized to an estimated maximum pond depth of 1 feet.Averaging the normalized data resulted in a maximum pond depth of 0.75 feet.An additional adjustment accounted for a difference in pond bed shapes between model and reality.The model has an idealized shape with vertical walls resulting in a constant increase in depth with volume.
In the field, a pond bed has varying depths resulting in varying increases in average depth per added volume, particularly at the beginning of flood-up.The pond depth adjustment was based on observed volume-elevation data [36].Finally, the data were smoothed by a 30-day running average.Approach 2: Knowledge about wetland management from decades-long involvement in salinity management of GEA wetlands provided the basis for this approach.In this approach, the nearest major canal was set to be the water source, which means considerable changes in the distribution of water compared to Approach 1. Water would flow sequentially through multiple wetland compartments if this approach were to be fully implemented.This simulates reuse within the system, which was not previously imple- Approach 2: Knowledge about wetland management from decades-long involvement in salinity management of GEA wetlands provided the basis for this approach.In this approach, the nearest major canal was set to be the water source, which means considerable changes in the distribution of water compared to Approach 1. Water would flow sequentially through multiple wetland compartments if this approach were to be fully implemented.This simulates reuse within the system, which was not previously implemented in the model.The nearest major canal was determined by comparing flood-up maps from the U.S. Bureau of Reclamation with the model compartment delineation.For the MS model compartment, it was assumed that a monitoring station in the Santa Fe Canal captured nearly all flow available for diversion.For the FC compartment, it was assumed that a monitoring station in the San Luis Canal captured all flow available for diversion.It was assumed that during flood-up, nearly all available flow is diverted to the compartments.It was assumed that the inflow during winter and spring was similar to the assumed inflow in Approach 1 because the approach provided a good simulation of hydrology after flood-up.The initial EC was set based on the EC monitored at the two stations.Pond depth profiles were based on flood-up schedules.This approach considered that many single wetland ponds are aggregated into one wetland model compartment.The flood-up map that is shown in Figure 3 is for a different wetland model compartment but was considered representative because it covers a similar spatial extent as the larger simulated compartment.The maximum depth was assumed to be 0.75 feet as in Approach 1.There was no map available for the drawdown; however, Approach 1 resulted in good predictions of outflow during the drawdown.

Model Evaluation
Evaluation of the input times series data was based on a visual comparison and statistical evaluation of observed and simulated flow, EC, and salt load at the outlet.To compare observed and simulated data mean absolute percent error (MAPE), mean squared error (MSE) and root mean squared error (RMSE) were calculated: where n is the number of observations, y t,obs is the observed value at time point t, and y t,pred is the predicted value at the same time point.Statistical measures were applied to observed data that were provided by the monitoring agency, not interpolated values.

Pond Depth Profiles
The pond depth profiles from the two approaches differ considerably during fall flood-up and slightly during spring.They are the same during winter and summer because the same maximum depth was assumed in winter, and there is no water in the seasonal wetlands in the summer.Approach 1 leads to a fast increase within a few days in the fall (Figure 3), while Approach 2 leads to a slow increase over several months (Figure 4), which is because many single wetland ponds are aggregated into one model compartment.

Approach 1
For the MS compartment, the simulated outflow aligned well with the observed outflow in the winter, spring, and summer of 2019 (Figure 4).However, the EC was underestimated during most of the simulated time (Figure 5).There were instances when the simulated flow was nearly zero, and at the same time, the simulated EC was unrealistically high EC (>3000 µmho/cm).This combination of simulation results occurs when the simulated outflow is derived completely from subsurface flow, as can be seen when inspecting WARMF output for each soil layer.The simulated and observed salt load aligned well during the winter and spring of 2019, although there was some underestimation (Figure 6).

Approach 1
For the MS compartment, the simulated outflow aligned well with the observed outflow in the winter, spring, and summer of 2019 (Figure 4).However, the EC was underestimated during most of the simulated time (Figure 5).There were instances when the simulated flow was nearly zero, and at the same time, the simulated EC was unrealistically high EC (>3000 µmho/cm).This combination of simulation results occurs when the simulated outflow is derived completely from subsurface flow, as can be seen when inspecting WARMF output for each soil layer.The simulated and observed salt load aligned well during the winter and spring of 2019, although there was some underestimation (Figure 6).For the simulation from July 2019 to June 2020, the agreement between the simulated and observed data mirrored that of the previous simulated year.For the FC compartment, the simulated flow, EC, and salt load aligned well with observed data in the winter, spring, and summer of all simulated years.Trends in the simulation of the FC compartment were similar to trends in the MS compartment.

Approach 2
In the MS compartment, the simulated and observed outflow aligned well over the entire simulated time from July 2018 to June 2019 (Figure 4).Compared to Approach 1, the simulated outflow started around 80 days earlier.The flow was overestimated following precipitation events.
The simulated EC aligned well with the observed EC during fall 2018 and April 2019 for the MS compartment (Figure 5).During winter 2019, the simulated EC was around 500 µmho/cm higher than with Approach 1 but was still underestimated.Simulated EC generally following rain events.However, these short-term simulated trends were not visible in the observed EC.
The simulated and observed salt load aligned well between July 2018 and June 2019 (Figure 6, Table 2).For the FC compartment, the salt load prediction was good during fall, winter, and spring, but there was some overprediction during the summer months when drainage flow was minimal.The discrepancy in the EC during summer holds minimal significance because it adds little to the total salt load.* MAPE = mean absolute percent error (Equation ( 5)).† MSE = mean squared error (Equation ( 6)).‡ RMSE = root mean squared error (Equation ( 7)).
The inclusion of water input from a recirculation system that started operation in 2019 improved the prediction of EC for the MS compartment during 2019/20 (Table S1).When recirculated water constituted 12% of the inflow, the simulated drainage EC was on average 100-200 µmho/cm higher.The simulated EC in the drainage was 200-300 µmho/cm higher when nearly all drainage was recirculated and constituted 23% of the inflow.The recirculated water constituted the largest percent of inflow in January and February, and the effect of increased EC was most pronounced at the end of February and the start of March.Statistical measures are provided in Tables 2 and S1-S3.

Simulation of Hydrology and Salinity in Seasonal Managed Wetlands in the GEA
The simulations highlight the importance of the various input parameters for the simulation of wetlands in the GEA.The simulation results from the two approaches showed significant differences in the simulated outflow during fall and simulated EC during the entire time frame, which was caused by different assumptions about pond depth profiles and water sources.In Approach 1, the pond depth increased from 0 to 0.75 feet within a few days.In contrast, in Approach 2, the increase occurs over several months during the fall.There was a small difference between the two approaches in the assumed inflow to the wetlands, which might have also added partly to the difference in the simulated outflow.
The initial EC is integral to obtaining accurate simulation results.In Approach 2, water sources had an EC that was 500-2500 µmho/cm higher than in Approach 1.This resulted in a simulated EC that was around 500 µmho/cm higher than in Approach 1 during winter and spring.EC could not be compared during the fall because Approach 1 did not simulate outflow during the fall.Approach 2 considered degraded water quality due to unintentional reuse and intentional recirculation within the wetland complex.The remaining discrepancy between simulated and observed EC might be explained by rain events, as discussed below.
The simulations show how wetland manager knowledge can aid the simulation of complex wetland systems.From collaboration with wetland managers, it was known that reuse of water within the GEA wetland complex occurs, which has implications for inflow and water sources.Reuse occurs because many wetlands are connected through a complex network of canals.During flooding and maintenance, some water is returned to canals from which water is diverted to other wetlands.This means that estimates based on water acquisition will result in an underestimation of inflow to wetlands.Reuse will also result in increased EC.However, the difficulty is that this practice is not explicitly represented in current monitored data.Diverting water from the nearest major canal to a wetland compartment, as seen in Approach 2, will simulate reuse to some extent without requiring additional monitored data.

Recommended Revision to Simulate Retention of Precipitation
The remaining mismatch of simulated and observed data indicates a need to improve the simulation of rain events.Immediately after rain events, the simulated outflow peaks and EC drops (Figures 4C and 5B).This is expected because of the model formulation and the assumed input time series.At the end of fall, outflow is simulated even when no rain occurs, which means that d t > d W .At the same time, the prescribed pond depth reaches its maximum value and only decreases later, resulting in a corresponding decrease in storage volume according to Equation (1).The prescribed pond depth profile was set so that d t is always larger than d W , starting at the end of the flood-up period to simulate outflow resulting from maintenance flows.Additional water volume in the form of precipitation will add to the inflow depth at time step t according to Equation (2), leading to an additional increase in d t and all additional water above d W being subject to Manning's overland flow.Because all compartments are simulated as CSTRs, the simulated EC is expected to decrease during those rain events.However, the observed data indicates that some water from the precipitation events was either stored or infiltrated into the soil.Although the timing of some peaks in the outflow was predicted correctly, the monitored peak height was often only around half the magnitude of the predicted peak height.Moreover, observed EC in the outflow showed no distinct peaks related to rain events, which also supports the hypothesis that precipitation is partly retained.Instead, observed EC slowly increased over several weeks in January of 2019 and then decreased in February.It is notable that December 2018 had belowaverage precipitation, January had average precipitation, and February and March received precipitation that was almost twice the average precipitation (Figure S3).This timing of rain events could be an explanation for the observed patterns in EC.
A revised conceptual model should be implemented to test if retention of precipitation can improve the simulation of outflow and EC (Figure 2).A revised model would require a separate time series to simulate outflow that originates from maintenance flows, potentially defining a fixed additional outflow based on manager knowledge during the time between flood-up and drawdown.It would also require a new estimate of the pond depth time series during that time frame and with a focus on improved simulation of rain events instead of maintenance flows.No changes would be needed to simulate wetland behavior during flood-up and drawdown.

Recommendations for Application
There is currently no commonly used model to simulate seasonally managed wetlands and there is generally a lack of ecosystem service models for wetlands [21].Depending on the main drivers and the modeling purpose, different model approaches might be suitable to model wetlands.The bathtub analog has been used to simulate coastal wetlands and coastal inundation, although models that incorporate elevation and hydrodynamic attenuation due to plants provide better predictions for this type of wetland [37,38].The model DRAINMOD has been used to simulate wetland ditches that are managed to control the water table in adjacent agricultural fields, which requires explicit simulation of processes between those two model components [39].The SWAT model is like WARMF-a physically based model with spatially explicit parameterization.Differing approaches have been presented to simulate wetlands with SWAT [40][41][42].One study incorporated elevation data to simulate separate impoundments [40].This is not appropriate for the GEA wetlands because elevation differences are small, flows are managed, and there is a high density of small hydrological features.One study used SWAT in combination with prescribed water storage to design a small constructed wetland [41].A second study simulated rice paddy fields with an adapted SWAT model to simulate runoff from flooded rice paddy fields when the water level in the rice field exceeded a fixed depth [42].The study on rice fields explicitly accounted for precipitation events in their pond depth, which resulted in notably good model predictions during rain events.Flooded rice fields are similar to seasonal managed wetlands in that flows are managed and there can be a high density of small hydrological features.However, depending on the size of the open water to closed vegetation ratio, evapotranspiration can vary, and open water areas tend to be more prevalent in managed wetlands [43].Therefore, the presented bathtub analog as well as the two approaches for model parameterization can be useful to simulate rice fields but evapotranspiration would need adjustment.
Approach 1 is preferable if sufficient data is available.It has the advantage that fewer assumptions are necessary, making it less dependent on expert judgment and meaning that routine model runs are less time-consuming.With fewer assumptions, this approach might also be easier to communicate to stakeholders if stakeholders were not involved in the modeling effort.
Approach 2 can have advantages when important processes are difficult to monitor and when stakeholders are participating in the modeling effort.It has been recognized that stakeholders often hold more information than any other group involved in modeling efforts [24].That information could be quantitative but can also be anecdotal, and likely provides insight into processes that are relevant for the modeling effort.If a model leaves out processes that are considered essential by stakeholders, the modeling effort runs the risk of being perceived as inadequate, and the modeling success is threatened [44].Therefore, early stakeholder involvement and the use of stakeholder knowledge can aid the modeling effort.
Estimation of the pond depth profile with Approach 1 is preferable when one model compartment represents only a single pond or only a few ponds.In this case, the simplified model pond bed shape still requires the transformation of monitored data as outlined in Approach 1. Approach 2 is preferable if one model compartment represents more than a few single wetland ponds.In this case, the number of wetland ponds and the knowledge about the timing of flooding can be used to estimate the pond depth.
It should be noted that the input data that were evaluated in this study are only a subset of the data that were needed for the simulations.Model parameterization typically requires a combination of data and knowledge from model experts.Expert knowledge is needed to find and incorporate appropriate data for a particular model simulation and to find reasonable estimates if monitored data is not available or appropriate.In the shown simulations, land use, soil properties, and meteorological data were three types of input data that were the same for both approaches and were supplied from monitored data.The initial setup still required expert involvement to address uncertainties in the monitored data, e.g., soil properties are inherently heterogenous, and representative values were chosen for the simulations.Approach 2 is different in that it specifically uses knowledge from wetland managers.

Conclusions
The goal of this study was to improve the simulation of hydrology and salinity of seasonally managed wetlands in the SJR watershed.We employed two approaches that differ in the parameterization of inflow to a wetland, initial EC, and pond depth of the hydrological model.Approach 1 is predominantly based on monitored data and Approach 2 incorporates wetland manager knowledge.Simulation of outflow and EC was better with Approach 2, but it is notable that Approach 1 is applicable when one model compartment represents only one wetland pond.In this case, data transformations are necessary to apply monitored pond depth to a bathtub analog.Estimates for pond depth were improved with Approach 2 through the use of flood-up schedules for multiple wetland ponds.Approach 2 was also better suited for the simulation of a large wetland complex because it can include processes that are difficult to monitor but important.The most important process that was simulated with Approach 2 was the reuse of water within the wetland complex and the associated higher EC.In Approach 2, water was diverted from the closest major canal, which improved the simulation of the initial EC.Future research should adapt the conceptual model and input time series to better account for the retention of precipitation within wetlands.Simulation of hydrology and salinity is important for salinity management in the SJR and provides the basis for the simulation of other water quality parameters.The bathtub analog can be useful for other wetland types such as rice fields, and the parameterization proposed in Approach 2 can be useful for systems that are large and have complex hydrology features and extensively managed flows.

Figure 1 .
Figure 1.(a) Map of remaining wetlands within the Grasslands Wildlife Area in the San Joaquin River basin in California in 2024 (source: USGS National Wetlands Inventory).Brown area in inset map indicates the location within California.(b) Graphical user interface of WARMF with wetland model compartments highlighted in dark grey.

Figure 1 .
Figure 1.(a) Map of remaining wetlands within the Grasslands Wildlife Area in the San Joaquin River basin in California in 2024 (source: USGS National Wetlands Inventory).Brown area in inset map indicates the location within California.(b) Graphical user interface of WARMF with wetland model compartments highlighted in dark grey.

Figure 2 .
Figure 2. Schematics showing fluxes simulated in a WARMF wetland compartment.P is precipitation, and ET is evapotranspiration.Recommended revision to WARMF's conceptual wetland model for future research: maintenance flow leaving the wetland should be simulated separately from surface runoff that occurs because of drawdown or rain.

Figure 4 .
Figure 4. Input time series for (A) pond depth, (B) assumed inflow, (C) precipitation, and (D) simulated outflow for Approach 1 and Approach 2 for the MS compartment.Observed data are shown as dotted line.Approaches 1 and 2 differ most notably in fall (grey area, days 110-160).

Figure 4 .
Figure 4. Input time series for (A) pond depth, (B) assumed inflow, (C) precipitation, and (D) simulated outflow for Approach 1 and Approach 2 for the MS compartment.Observed data are shown as dotted line.Approaches 1 and 2 differ most notably in fall (grey area, days 110-160).

Figure 5 .
Figure5.Electrical conductivity (EC) (A) assumed at the inlet and (B) simulated at the outlet of MS compartment with Approaches 1 and 2. Observed EC is shown as black dotted line.The occurrence of rain events larger than 0.02 mm is indicated with red marks.The grey area highlights an improved fit between observed EC and approach 2. The water source in Approach 2 has considerably higher EC than water sources 1 (DMC) and 2 (MP) assumed in Approach 1.At the outlet, extremely high simulated EC of around 4000 μmho/cm indicates that during those times simulated flow is close to zero and only originates from subsurface flow.

Figure 6 .
Figure 6.Salt load simulated with Approach 1 (green line) and 2 (blue line) at the outlet of the MS compartment.The observed salt load is shown as dotted line.Approach 1 and 2 differ most notably in fall (grey area).

Figure 5 . 17 Figure 5 .
Figure5.Electrical conductivity (EC) (A) assumed at the inlet and (B) simulated at the outlet of MS compartment with Approaches 1 and 2. Observed EC is shown as black dotted line.The occurrence of rain events larger than 0.02 mm is indicated with red marks.The grey area highlights an improved fit between observed EC and approach 2. The water source in Approach 2 has considerably higher EC than water sources 1 (DMC) and 2 (MP) assumed in Approach 1.At the outlet, extremely high simulated EC of around 4000 µmho/cm indicates that during those times simulated flow is close to zero and only originates from subsurface flow.

Figure 6 .
Figure 6.Salt load simulated with Approach 1 (green line) and 2 (blue line) at the outlet of the MS compartment.The observed salt load is shown as dotted line.Approach 1 and 2 differ most notably in fall (grey area).

Figure 6 .
Figure 6.Salt load simulated with Approach 1 (green line) and 2 (blue line) at the outlet of the MS compartment.The observed salt load is shown as dotted line.Approach 1 and 2 differ most notably in fall (grey area).

Author
Contributions: S.H.: conceptualization, methodology, formal analysis, visualization, and writing (original draft); N.W.T.Q.: conceptualization, methodology, data curation, writing (review and editing); M.W.B.: conceptualization, writing (review and editing); P.A.O.: conceptualization, methodology, funding acquisition and writing (review and editing).All authors have read and agreed to the published version of the manuscript.Funding: This research was funded by the Delta Science Program in partnership with the California Department of Fish and Wildlife (Contract #18208).

Table 1 .
Overview of assumptions for model input time series data.

Table 2 .
Statistical measures for MS compartment model simulations from July 2018 until June 2019.