An optimized NARX-based model for predicting thermal dynamics and heatwaves in rivers

The thermal dynamics within river ecosystems represent critical areas of study due to their profound impact on overall aquatic health. With the rising prevalence of heatwaves in rivers, a consequence of climate change, it is imperative to deepen our understanding through comprehensive research efforts. Despite this urgency, there remains a noticeable dearth in studies aimed at refining modeling techniques to precisely characterize the duration and intensity of these events. In response to this gap, the present study endeavors to augment the NARX-based model (Nonlinear Autoregressive network with Exogenous Inputs) to enhance predictive capabilities regarding thermal dynamics and river heatwaves. The optimized NARX-based model included the Bayesian Optimization (BO) algorithm, which allows fine-tuning the number of NARX hidden nodes and lagged input/target values, and the Bayesian Regularization (BR) backpropagation algorithm to improve the NARX calibration process. A long-term dataset spanning from 1991 to 2021, encompassing 18 rivers across the expansive Vistula River Basin, one of Europe's largest river systems, was employed for this study. The performance of the BO-NARX-BR model was compared with that of the widely utilized air2stream model for modeling river water temperature (RWT). The results unequivocally demonstrated the superior performance of the NARX-based model across the calibration and validation periods, and four heatwave years. In the context of river heatwaves, the study revealed an escalating frequency and intensity within the Vistula River Basin. Furthermore, the NARX-based model exhibited superior proficiency in characterizing river heatwaves compared to the air2stream model. This study, as the inaugural examination of river heatwaves in Poland and one of the few globally, furnishes crucial reference points for subsequent research endeavors on this phenomenon.