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.