A physics-informed method for dynamic warning of debris flows in remote areas

A reliable precipitation estimation in mountainous areas plays a critical role in issuing timely warnings for debris flows. However, the scarcity of rainfall gauge stations and the coarse resolution of satellite products pose challenges in developing an effective warning model. To generate precipitation with fine resolution, we need to assess some descriptors of the spatial variability of precipitation called the regional environmental variables (REVs). Physical equations were therefore designed to decide REVs, such as the normalised difference vegetation index (NDVI), normalised difference water index (NDWI), modified soil-adjust vegetation index (MSAVI2), the difference of land surface temperature between daytime and night-time (\(\Delta \text{LST}\)), and the surface soil moisture (SSM). Then, a deep learning model was developed to establish the relationship between REVs and Global Precipitation Measurement (GPM) daily product, enabling the downscaling of GPM to daily precipitation at a spatial resolution of 1 km. The rain gauge observations were used to calibrate the downscaled results using the geographical differential analysis (GDA) method relying on data from a transition zone between the Tibetan Plateau and Sichuan Basin, China, spanning the year of 2010. After that, event rainfall–duration (E-D) equations were developed using the calibrated rainfall data and then utilised the relationships to improve debris-flow susceptibility to propose a debris-flow warning model in the Luding earthquake-affected area. The results show that: (1) REVs based on a physical equation can effectively reproduce the spatial distribution of precipitation; (2) the calibrated GPM exhibits a substantial improvement, with an average 48.6% reduction in mean absolute error (MAE), a 51.5% decrease in root mean square error (RMSE), and a remarkable 63.9% reduction in mean bias (MB) when compared to original GPM; (3) the newly developed warning model exhibits a better performance than susceptibility map in forecasting debris-flow occurrence. Overall, this model can provide accurate regional-scale alerts for debris flows by overcoming the limitations of susceptibility maps, which are inherently static products.