Two hybrid data-driven models for modeling water-air temperature relationship in rivers.

River water temperature (RWT) forecasting is important for the management of stream ecology. In this paper, a new method based on coupling of wavelet transformation (WT) and artificial intelligence (AI) techniques, including multilayer perceptron neural network (MLPNN) and adaptive neural-fuzzy inference system (ANFIS) for RWT prediction is proposed. The performances of the hybrid models are compared with regular MLPNN and ANFIS models and multiple linear regression (MLR) models for RWT forecasting in two river stations in the Drava River, Croatia. Model performance was evaluated using the coefficient of correlation (R), the Willmott index of agreement (d), the root mean squared error (RMSE), and the mean absolute error (MAE). Results indicate that the combination of WT and AI models (WTMLPNN and WTANFIS) yield better models than the conventional forecasting models for RWT simulation for both regular periods and heatwave events. The MLPNN and ANFIS models outperform the MLR models for RWT simulation for the studied river stations. RMSE values of WTMLPNN2 and WTANFIS2 models range from 1.127 to 1.286 °C, and 1.216 to 1.491 °C for the Botovo and Donji Miholjac stations respectively. Additionally, modeling results further confirm the importance of the day of year (DOY) on the thermal dynamics of the river. The results of this study indicate the potential of coupling of WT and MLPNN, ANFIS models in forecasting RWT.