Rainfall, as the main driving force of natural disasters such as floods and droughts, has strong non-linear and abrupt characteristics, which makes it difficult to predict. As extreme weather events occur frequently in the Yellow River Basin, it is especially critical to reveal the physical mechanism of rainfall in the basin and integrate monthly scale meteorological data to achieve monthly rainfall prediction. In this paper, we propose a rainfall prediction model coupled with a physical mechanism and a temporal convolutional network (TCN) to achieve the prediction of monthly rainfall in the basin, aiming to reveal the physical mechanism between rainfall factors in the basin based on the transfer entropy and the multidimensional Copula function and based on the physical mechanism which is embedded into the TCN to construct a dual-driven prediction model with both physical knowledge and data, while the SHAP is used to analyze the interpretability of the prediction model. The results are as follows: (1) Temperature, relative humidity, and evaporation are key characteristic factors driving rainfall. (2) The physical mechanism features between temperature, relative humidity, and evaporation can be described by the three-dimensional Gumbel–Hougaard Copula function, with a more concentrated data distribution of their joint distribution probability. (3) The PHY-TCN model can accurately fit the extremes of the rainfall series, improving the model accuracy in the training set by 3.82%, 1.39%, and 9.82% compared to TCN, CNN, and LSTM, respectively, and in the test set by 6.04%, 2.55%, and 8.91%, respectively. (4) Embedding physical mechanisms enhances the contribution of individual feature variables in the PHY-TCN model and increases the persuasiveness of the model. This study provides a new research framework for rainfall prediction in the YRB and analyzes the physical relationship between the input data and output results of the deep learning model. It has important practical significance and strategic value for guiding the optimal scheduling of water resources, improving the risk management level of the basin, and promoting the ecological protection and high-quality development of the YRB.
Ma et al. (Mon,) studied this question.