**1. Introduction**

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. Model selection for water quality forecasting depends on many factors including analyst expertise and cost, stakeholder involvement and expected performance.

**Citation:** Quinn, N.W.T.; Tansey, M.K.; Lu, J. Comparison of Deterministic and Statistical Models for Water Quality Compliance Forecasting in the San Joaquin River Basin, California. *Water* **2021**, *13*, 2661. https://doi.org/10.3390/w13192661

Academic Editors: Francesco De Paola and Thomas Meixner

Received: 10 June 2021 Accepted: 22 September 2021 Published: 27 September 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

An American Society of Civil Engineers (ASCE) Task Committee was convened within the Environmental Water Research Institute (ASCE, 2021) to document the state of the practice in the use of water quality models that addresses selection, data collection and organization, calibration, and independent testing to define uncertainty and to envisage both the state of the art and future development. This paper draws on this effort focusing specifically on two distinctly different approaches to involving stakeholders in salinity management in a highly regulated river basin in California, dominated by agricultural and managed wetland return flows.

Management of salinity in the United States and around the world is typically performed through environmental regulation. In the United States, the federal Environmental Protection Agency (USEPA) uses the concept of a total maximum daily load (TMDL) to establish safe and sustainable pollutant concentrations in receiving waters and pollutant load assimilative capacity to help guide stakeholders in determining pollutant load reduction strategies. The TMDL goal for salt loading to impaired waterbody [1,2] can be defined as:

$$TMDL = \sum WLA + \sum LA + MOS + RC \tag{1}$$

where *WLA* is the waste load allocation for each point source of salt load, *LA* is the salt load allocation for non-point sources and *MOS* is the margin of safety selected that accounts for measurement and analytical uncertainty. The *RC* is a reserve capacity that is seldom used in California applications but that could be used to account for future anticipated loading from both point sources and non-point sources. Possible examples are future climate change, population growth, land use and land cover changes, sea-level rise and environmental policy initiatives.

Models are commonly used in the development of TMDLs and to assess their impact under a range of environmental conditions [2–8]. Models can range in complexity from simple salinity mass balances, that may use simple regression equations to relate salinity to flow and other water quality parameters, to comprehensive, physically-based hydrologic and water quality models [3,9] that attempt to simulate important processes. These models may be used at various phases of TMDL development and implementation including (a) the assessment of the level of impairment and the impacts of existing best management practices on the water quality; (b) the evaluation and comparison of load reduction strategies; (c) the computation of TMDL uncertainty and margin of safety [10]; (d) as decision support tools [11–13]; and (e) for real-time or near-real-time forecasting after implementing a TMDL [14–16]. This paper compares the performance of two modeling techniques used in near-real-time forecasting of compliance with salinity objectives in the San Joaquin River Basin in California.
