A novel optimized model based on NARX networks for predicting thermal anomalies in Polish lakes during heatwaves, with special reference to the 2018 heatwave

In 2018, Europe experienced one of the most severe heatwaves ever recorded. This extreme event's impact on lake surface water temperature (LSWT) in Polish lakes has largely remained unknown. In this study, the impact of the 2018 European heatwave on LSWT in 24 Polish lakes was investigated based on a long-term observed dataset (1987-2020). To capture the LSWT dynamics during the heatwave period and reproduce lake heatwaves, a novel BO-NARX-BR model was developed and evaluated. This model combines the capabilities of the Nonlinear Autoregressive network with Exogenous Inputs (NARX) neural network, the 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. The results showed that from April to October 2018, the mean and maximum LSWTs were 2.35 and 3.38 °C warmer than the base-period average (1987-2010) due to the impact of the extreme heatwave. The NARX-based model outperformed another widely used model called air2water in calibration and validation periods. The results also revealed that the BO-NARX-BR model produced significantly better results in capturing lake heatwaves, with computed duration and intensity of lake heatwaves close to the in-situ data. Additionally, LSWT anomaly significantly impacted the duration and intensity of heatwaves that occurred in lakes. Extreme climatic events are gaining increasing importance for the functioning of various elements of the hydrosphere. Such a situation encourages the search for more accurate methods and tools for their prediction. The model applied in the paper corresponds with these assumptions, and its good performance allows for its adaptation to lakes in other regions.