*Article* **Comparison of Deterministic and Statistical Models for Water Quality Compliance Forecasting in the San Joaquin River Basin, California**

**Nigel W. T. Quinn 1,2,3,\*, Michael K. Tansey <sup>2</sup> and James Lu <sup>2</sup>**


**\*** Correspondence: nwquinn@lbl.gov; Tel.: +1-510-612-8802

**Abstract:** Model selection for water quality forecasting depends on many factors including analyst expertise and cost, stakeholder involvement and expected performance. Water quality forecasting in arid river basins is especially challenging given the importance of protecting beneficial uses in these environments and the livelihood of agricultural communities. In the agriculture-dominated San Joaquin River Basin of California, real-time salinity management (RTSM) is a state-sanctioned program that helps to maximize allowable salt export while protecting existing basin beneficial uses of water supply. The RTSM strategy supplants the federal total maximum daily load (TMDL) approach that could impose fines associated with exceedances of monthly and annual salt load allocations of up to \$1 million per year based on average year hydrology and salt load export limits. The essential components of the current program include the establishment of telemetered sensor networks, a webbased information system for sharing data, a basin-scale salt load assimilative capacity forecasting model and institutional entities tasked with performing weekly forecasts of river salt assimilative capacity and scheduling west-side drainage export of salt loads. Web-based information portals have been developed to share model input data and salt assimilative capacity forecasts together with increasing stakeholder awareness and involvement in water quality resource management activities in the river basin. Two modeling approaches have been developed simultaneously. The first relies on a statistical analysis of the relationship between flow and salt concentration at three compliance monitoring sites and the use of these regression relationships for forecasting. The second salt load forecasting approach is a customized application of the Watershed Analysis Risk Management Framework (WARMF), a watershed water quality simulation model that has been configured to estimate daily river salt assimilative capacity and to provide decision support for real-time salinity management at the watershed level. Analysis of the results from both model-based forecasting approaches over a period of five years shows that the regression-based forecasting model, run daily Monday to Friday each week, provided marginally better performance. However, the regression-based forecasting model assumes the same general relationship between flow and salinity which breaks down during extreme weather events such as droughts when water allocation cutbacks among stakeholders are not evenly distributed across the basin. A recent test case shows the utility of both models in dealing with an exceedance event at one compliance monitoring site recently introduced in 2020.

**Keywords:** water quality forecasting; decision support; WARMF; regression model; salinity; irrigated agriculture; stakeholder involvement
