Physics-guided deep learning for rainfall-runoff modeling by considering extreme events and monotonic relationships

Deep learning methods have recently shown a broad application prospect in rainfall-runoff modeling. However, the lack of physical mechanism becomes a major limitation in using machine learning methods that rely on the available labeled observations. To address this issue, the study proposes that synthetic samples are added to train the deep learning network by using three previously undiscussed physical mechanisms as follows: (1) extreme heavy rainfalls when the soil water is saturated, (2) long-duration rainless events when soil water is exhausted, and (3) the monotonic relationship between rainfall and runoff. A physics-guided Long Short-Term Memory (LSTM) network, shortly named PHY-LSTM, is then formulated. PHY-LSTM network is trained on 531 basins of the Catchment Attributes and Meteorology for Large-sample Studies (CAMELS) dataset, indicating that the performance is significantly improved compared to conventional LSTM. Specifically, the mean Nash-Sutcliffe Efficiency (NSE) improves from 0.52 to 0.61 from the daily simulations during the testing period in local models. It is demonstrated that synthetic samples can effectively improve the simulation of flood peaks and reduce the number of negative streamflow, and strong monotonicity is still maintained even if a slight disturbance is involved in the training dataset. The proposed PHY-LSTM shows that physical mechanisms are very useful to improve efficiencies of the data-driven rainfall-runoff model.