A hybrid model for river water temperature as a function of air temperature and discharge

Water temperature controls many biochemical and ecological processes in rivers, and theoretically depends on multiple factors. Here we formulate a model to predict daily averaged river water temperature as a function of air temperature and discharge, with the latter variable being more relevant in some specific cases (e.g., snowmelt-fed rivers, rivers impacted by hydropower production). The model uses a hybrid formulation characterized by a physically based structure associated with a stochastic calibration of the parameters. The interpretation of the parameter values allows for better understanding of river thermal dynamics and the identification of the most relevant factors affecting it. The satisfactory agreement of different versions of the model with measurements in three different rivers (root mean square error smaller than 1oC, at a daily timescale) suggests that the proposed model can represent a useful tool to synthetically describe medium- and long-term behavior, and capture the changes induced by varying external conditions.