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This work presents a simplified approach for estimating ionic concentrations from specific electrical conductance (EC) data in the San Francisco Estuary. Monitoring the EC of water through electrodes is simple and inexpensive. As a result, a wealth of high-resolution time-series data is available to indirectly estimate salinity concentrations and, by extension, seawater intrusion throughout the study domain. However, scientists and managers are also interested in quantifying ionic (e.g., bromide, chloride) and total dissolved solids (TDS) concentrations to meet water-quality regulations, protect beneficial uses, support environmental analyses, and track source-water dominance. These constituent concentrations, reported with lower spatial and temporal resolution than EC, are typically measured in the laboratory from discrete (grab) water samples. We divided the study domain into four unique regions to estimate concentrations of major ions and TDS as mathematical functions of measured or model-simulated EC. Salinity relationships in three of the four regions—regions that represent Sacramento-San Joaquin Delta (Delta) inflow and seawater-dominated boundaries—reflect ionic make-ups that are either independent of or weakly dependent on season and hydrologic condition, and are highly correlated with EC. The fourth region—represented by the interior Delta—exhibits salinity characteristics associated with complex-boundary source-water mixing that varies by season and hydrologic condition. We introduce a novel method to estimate ionic and dissolved solids concentrations within this fourth region, given month, water year type, and (optionally) X2 isohaline position, which allows for more accurate EC-based estimates than previously available. The resulting approach, while not a substitute for hydrodynamic modeling, can provide useful information under constrained schedules and budgets.

The deviation of specific electrical conductance (EC) from conservative mixing behavior is well-established in the scientific literature. This principle is based on the observation that, as salt concentration in a water sample increases, the mobility of individual ions in the sample decreases, and thus their ability to conduct electricity decreases. Despite this fact, some commonly used models for salinity transport in the San Francisco Estuary (estuary) utilize EC as a primary simulation constituent, treating it as a conservative quantity. Such a modeling approach has likely been followed to exploit the wide availability of EC data for model calibration and validation, and to obviate the need to translate between EC and salinity in a domain characterized by multiple source waters with varying ionic make-ups. Arguably, this approach provides a reasonable trade-off between data translation error and model simulation error. In this paper, we critically evaluate this approach, employing an extensive salinity data set that includes measurements of EC and major ion concentrations in the estuary. We demonstrate and quantify EC deviation from steady-state, conservative mixing behavior; review the conservative mixing behavior of three bulk salinity measures (practical salinity, ionic strength, and limiting equivalent conductance); and evaluate their source-dependent correlations with EC in the estuary. We find limiting equivalent conductance—a value that assumes uninhibited mobility among individual ions in a water sample—to be an attractive alternative for salinity transport in the estuary. In addition to being a conservative quantity, it is consistently correlated with EC in the estuary’s dominant source waters, and thus addresses concerns related to data-translation error. We conclude this paper discussing pros and cons of adopting various salinity-transport model constituents.

Accurate estimates of freshwater flow to the San Francisco Estuary are important in successfully regulating this water body, in protecting its beneficial uses, and in accurately modeling its hydrodynamic and water-quality transport regime. For regulatory purposes, freshwater flow to the estuary is not directly measured; rather, it is estimated from a daily balance of upstream Delta inflows, exports, and in-Delta water use termed the net Delta outflow index (NDOI). Field research in the 1960s indicated that NDOI estimates are biased low in summer–fall and biased high in winter–spring as a result of conflating Delta island evapotranspiration estimates with the sum of ungauged hydrologic interactions between channels and islands referred to as net channel depletions. In this work, we employed a 50-year observed salinity record along with gauged tidal flows and an ensemble of five empirical flow-salinity (X2) models to test whether a seasonal bias in Delta outflow estimates could be inferred. We accomplished this objective by conducting statistical analyses and evaluating whether model skill could be improved through seasonal NDOI flow adjustments. Assuming that model residuals are associated with channel depletion uncertainty, our findings corroborate the 1960s research and suggest that channel depletions are biased low in winter months (i.e., NDOI is biased high) and biased high in late summer and early fall months (i.e., NDOI is biased low). The magnitude of seasonal bias, which can reach 1,000 cfs, is a small percentage of typical winter outflow but represents a significant percentage of typical summer outflow. Our findings were derived from five independently developed models, and are consistent with the physical understanding of water exchanges on the islands. This work provides motivation for improved characterization of these exchanges to improve Delta outflow estimates, particularly during drought periods when water supplies are scarce and must be carefully managed.

This work surveys the performance of several empirical models, all recalibrated to a common data set, that were developed over the past 25 years to relate freshwater flow and salinity in the San Francisco Estuary (estuary). The estuary’s salinity regime—broadly regulated to meet urban, agricultural, and ecosystem beneficial uses—is managed in spring and certain fall months to meet ecosystem objectives by controlling the 2 parts per thousand bottom salinity isohaline position (referred to as X2). We tested five empirical models for accuracy, mean, and transient behavior. We included a sixth model, employing a machine learning framework and variables other than outflow, in this survey to compare fitting skill, but did not subject it to the full suite of tests applied to the other five empirical models. Model performance was observed to vary with hydrology, year, and season, and in some cases exhibited unique limitations as a result of mathematical formulation. However, no single model formulation was found to be consistently superior across a wide range of tests and applications. One test revealed that the models performed equally well when recalibrated to a uniformly perturbed input time-series. Thus, while the models may be used to identify anomalies or seasonal biases (the latter being the subject of a companion paper), their use as inverse models to infer freshwater outflow to the estuary from salinity observations is not expected to improve upon the absolute accuracy of existing outflow estimates. This survey suggests that, for analyses that span a long hydrologic record, an ensemble approach—rather than the use of any individual model on its own—may be preferable to exploit the strengths of individual models.

We evaluated two historically important data sets to characterize the San Francisco Estuary’s salinity regime before the State of California began systematic data collection in the early 1920s. One set documents barge travel along the Sacramento and San Joaquin rivers to obtain water of adequate quality for local industry; a second set documents Delta inflow used to compute antecedent outflow. The barge travel distance reported over 2 decades (1908–1929) was well explained by flow–salinity modeling, indicating internal consistency in these measurements. However, absolute salinity intrusion estimated through the barge travel data is systematically lower than suggested by contemporaneous water-quality measurements available since 1921. Through integration of these data sets, our work showed substantial similarities between 1908–1921 and the subsequent period before construction of Shasta Dam (1922–1944). Our analysis reveals an apparent shift in the estuary’s salinity regime, with lesser salinity intrusion occurring in pre-1919 summer and fall months as a result of higher summer Delta outflow; this shift may be related to lower storage and irrigation diversions as well as a preponderance of wet years with higher summer runoff in the pre–1919 period. We found seasonal patterns of wet year salinity intrusion to be comparable over the full study period (1908–1944), indicating that the relative effect of upstream water management is minimal when flows are high, consistent with findings reported in later periods. The barge and flow data provide qualitative insights on early 20th century conditions, when limited data are available. Post–1920 hydrology and salinity data are preferable for quantitative analyses because of better documentation associated with collection and analysis, and sustained reporting over several decades. This work provides a foundation for future efforts to characterize the hydrologic and hydrodynamic changes that occurred in the system between the 1850s (i.e., natural or pre-development conditions) and the 1920s.