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Advances in machine-learning techniques can serve practical water management needs such as salinity level estimation. This study explores machine learning, particularly deep-learning techniques in developing computer emulators for a commonly used process model, the Delta Simulation Model II (DSM2), used for salinity estimation in California’s Sacramento-San Joaquin Delta (Delta). We apply historical daily input data to DSM2 and corresponding salinity simulations at 28 study locations from 1990 to 2019 to train two machine-learning models: a multi-layer perceptron (MLP) and Long-Short-Term Memory (LSTM) networks in a multi-task learning framework. We assess sensitivity of both networks to the amount of antecedent input information (memory) and training data to determine appropriate memory size and training data length. We evaluate network performance according to several statistical metrics as well as visual inspection. The study further investigates two additional networks, the Gated Recurrent Unit (GRU) and Residual Network (ResNet) in salinity modeling, and compares their efficacy against MLP and LSTM. Our results demonstrate strong performance of the four neural network models over the study period, achieving absolute bias below 4%, plus near-perfect correlation coefficients and Nash–Sutcliffe efficiency coefficients. The high complexity LSTM shows slight performance edge. We further show that deeper and wider versions of MLP and LSTM yield only marginal benefit over their baseline counterparts. We also examined issues related to potential overfitting by the proposed models, training data selection strategies, and analytical and practical implications. Overall, this new study indicates that machine-learning-based emulators can efficiently emulate DSM2 in salinity simulation. They exhibit strong potential to supplement DSM2 in salinity modeling and help guide water resource planning and management practices for the Delta region.

Salinity management in estuarine systems is crucial for developing effective water-management strategies to maintain compliance and understand the impact of salt intrusion on water quality and availability. Understanding the temporal and spatial variations of salinity is a keystone of salinity-management practices. Process-based numerical models have been traditionally used to estimate the variations in salinity in estuarine environments. Advances in data-driven models (e.g., deep learning models) make them effective and efficient alternatives to process-based models. However, a discernible research gap exists in applying these advanced techniques to salinity modeling. The current study seeks to address this gap by exploring the innovative use of deep learning with data augmentation and transfer learning in salinity modeling, exemplified at 23 key salinity locations in the Sacramento–San Joaquin Delta which is the hub of the water-supply system of California. Historical, simulated (via a hydrodynamics and water quality model), and perturbed (to create a range of hydroclimatic and operational scenarios for data-augmentation purposes) flow, and salinity data are used to train a baseline multi-layer perceptron (MLP) and a deep learning Residual Long-Short-Term Memory (Res-LSTM) network. Four other deep learning models including LSTM, Residual Network (ResNet), Gated Recurrent Unit (GRU), and Residual GRU (Res-GRU) are also examined. Results indicate that models pre-trained using augmented data demonstrate improved performance over models trained from scratch using only historical data (e.g., median Nash–Sutcliffe efficiency increased from around 0.5 to above 0.9). Moreover, the five deep learning models further boost the salinity estimation performance in comparison with the baseline MLP model, though the performance of the latter is acceptable. The models trained using augmented data are then (a) used to develop a web-based Salinity Dashboard (Dashboard) tool that allows the users (including those with no machine learning background) to quickly screen multiple management scenarios by altering inputs and visualizing the resulting salinity simulations interactively, and (b) transferred and adapted to estimate observed salinity. The study shows that transfer learning results more accurately replicate the observations compared to their counterparts from models trained from scratch without knowledge learned and transferred from augmented data (e.g., median Nash–Sutcliffe efficiency increased from around 0.4 to above 0.9). Overall, the study illustrates that deep learning models, particularly when pre-trained using augmented data, are promising supplements to existing process-based models in estuarine salinity modeling, while the Dashboard enables user engagement with those pre-trained models to inform decision-making efficiently and effectively.

Salinity in estuarine environments has been traditionally simulated using process-based models. More recently, data-driven models including artificial neural networks (ANNs) have been developed for simulating salinity. Compared to process-based models, ANNs yield faster salinity simulations with comparable accuracy. However, ANNs are often purely data-driven and not constrained by physical laws, making it difficult to interpret the causality between input and output data. Physics-informed neural networks (PINNs) are emerging machine-learning models to integrate the benefits of both process-based models and data-driven ANNs. PINNs can embed the knowledge of physical laws in terms of the partial differential equations (PDE) that govern the dynamics of salinity transport into the training of the neural networks. This study explores the application of PINNs in salinity modeling by incorporating the one-dimensional advection–dispersion salinity transport equation into the neural networks. Two PINN models are explored in this study, namely PINNs and FoNets. PINNs are multilayer perceptrons (MLPs) that incorporate the advection–dispersion equation, while FoNets are an extension of PINNs with an additional encoding layer. The exploration is exemplified at four study locations in the Sacramento–San Joaquin Delta of California: Pittsburg, Chipps Island, Port Chicago, and Martinez. Both PINN models and benchmark ANNs are trained and tested using simulated daily salinity from 1991 to 2015 at study locations. Results indicate that PINNs and FoNets outperform the benchmark ANNs in simulating salinity at the study locations. Specifically, PINNs and FoNets have lower absolute biases and higher correlation coefficients and Nash–Sutcliffe efficiency values than ANNs. In addition, PINN models overcome some limitations of purely data-driven ANNs (e.g., neuron saturation) and generate more realistic salinity simulations. Overall, this study demonstrates the potential of PINNs to supplement existing process-based and ANN models in providing accurate and timely salinity estimation.