*3.2. ANN-Based Statistical Models*

The USBR developed a statistical approach as an alternative to the physically-based SJR WARMF model for flow and salinity forecasting in the SJR. This approach was limited to the Vernalis, Crows Landing and Maze Road Bridge compliance monitoring stations (Figure 1) [29]. Two Artificial Neural Networks (ANN) based models a Recurrent ANN and an Autoregressive ANN were identified as potential alternatives [30]. The most salient features of these ANN alternatives were that the underlying basis should be easy to understand and independent of having a deep understanding of basin hydrology [29,30]. ANN and regression-based approaches have the advantage of ready automation and have the advantage that daily flow forecasts are available online from the National Oceanic and Atmospheric Administration (NOAA) California River Forecast Center (RFC) providing the basis for river EC forecasts at the compliance monitoring stations. The significance of

this work is that daily bulletins from dam operators along the three major tributaries to the SJR are recognized in these forecasts.

Under normal basin hydrologic conditions, there is sufficient salt load assimilative capacity in the river when defined as the 30 day running average EC. Only in rare circumstances such as a prolonged drought is action required to limit salt loading during certain months to the SJR. During these periods, the more comprehensive WARMF model could be called upon to assist stakeholder management entities to determine appropriate salt loading reduction by subarea within the basin to avoid fines.

Recurrent ANN models are statistical learning models that are used in machine learning, inspired by biological neural networks such as in the human brain [30]. A number of ANN and recurrent neural network architectures with both short- and long-term memory were developed and applied to the Vernalis compliance monitoring station using existing flow and salinity data resources. None of the ANN architectures or network hyperparameters performed sufficiently well due to time series water quality data limitations and the impact of random anthropogenic factors that can affect reservoir operations [29]. In conducting the analysis, less than 5000 observations were available, whereas most applications of this method typically require well over a million observations to be successful. An additional ANN-based model was investigated using the MATLAB machine learning toolbox using an embedded machine learning application called Autoregressive ANN that accommodated external inputs. Although the Autoregressive ANN approach performed better in salinity forecasts compared to the Recurrent ANN model, the model salinity forecast performance was unsatisfactory [29]. Future work in the application of neural networks to flow and EC time series forecasting on the SJR may find more success in the use of Bayesian neural networks for capturing water quality forecast uncertainty.
