Runoff prediction in gauged and ungauged basins using Transformer-XAJ model

In hydrology, regional runoff forecasting and prediction in ungauged basins (PUB) are two challenging tasks, which are important to water resources management and flood prevention. In recent years, deep learning based models, especially long short-term memory (LSTM) based and Transformer based ones, have promoted the development of handling those two tasks. However, there is still considerable room for improvement, e.g., the prediction accuracy and the interpretability. Integrating a deep learning model and a traditionally hydrological model for exploring both excellently nonlinear ability and the process information is beneficial for the above desirable improvement. In this paper, we integrate a Transformer and a differentiable Xinanjiang (XAJ) model, and name it Transformer-XAJ model, which has an end-to-end structure and is learnable. The Transformer part is data-driven and provides dynamic parameters for the XAJ part; and the XAJ part explores the process information and gives the Transformer part necessary constrains. We apply the Transformer-XAJ model for regional runoff forecasting and PUB in humid and semi-humid regions. The results in catchment attributes and meteorology for large-sample studies – Switzerland (CAMELS-CH) show that the Transformer-XAJ model performs better than popular deep learning models in those two tasks.