Prediction of daily river water temperatures using an optimized model based on NARX networks

Water temperature is an important physical indicator of rivers because it impacts many other physical and biogeochemical processes and controls the metabolism of aquatic species in rivers. Having a good knowledge of river thermal dynamics is of great importance. In this study, an advanced machine learning based model that is fast, accurate and easy to use, namely the nonlinear autoregressive network with exogenous inputs (NARX) neural network, was coupled with Bayesian Optimization (BO) algorithm for optimizing the number of NARX hidden nodes and lagged input/target values and the Bayesian Regularization (BR) backpropagation algorithm for the NARX training, to forecast daily river water temperatures (RWT). Long-term observed data from 18 rivers of the Vistula River Basin, one of the largest rivers in Europe, were used for model testing, and model performance was compared with the air2stream model. The results showed that the NARX-based model performs significantly better than the air2stream model in the calibration and validation stages, and can better capture the seasonal pattern and peak values of RWT. Input combinations impact the performance of the NARX-based model in RWT modeling, and air temperature and the day of the year (DOY) are the major inputs, while streamflow and rainfall play a minor role on modeling RWT at the Vistula River Basin. Considering that future times series of air temperatures are easily accessible from climate models and DOY is easy to be considered in the model, the NARX-based model can serve as a promising tool to investigate the impact of climate change on river thermal dynamics.