Enhancing runoff simulation precision in the critical zone through spatiotemporal interpolation of areal rainfall with matrix decomposition

Modelling hydrological process in the critical zone not only contributes to a better understanding of interactions across different Earth surface spheres but also holds significant practical implications for water resource management and disaster prevention. Rainfall-runoff simulation in critical zones is particularly challenging due to the amalgamation of temporal and spatial complexity, rainfall variability, and data limitations. As a pivotal input variable of hydrological models, accurate estimation of areal rainfall is critical to successful runoff simulation. However, most estimation methods ignore temporal information, thereby increasing uncertainty in rainfall estimation and constraining the precision of rainfall-runoff simulation. In this study, the matrix decomposition-based estimation method (F-SVD), which considers the spatial and temporal correlation of the rainfall process is employed to estimate areal rainfall. The superiority of the method in producing two-dimensional rainfall information is evaluated through its application in runoff simulation with the Xin'anjiang model. The simulation results of selected flood events in the Jianxi basin in southeast China, spanning from 2009 to 2019, are compared with those of two widely used rainfall estimation methods, namely Arithmetical Mean (AM) and Thiessen Polygons (TP). The results show that (1) F-SVD not only produces the highest Pearson correlation coefficient between rainfall and runoff series but also reduces the number of flood events with abnormal rainfall-runoff relationships; (2) the Xin'anjiang model based on F-SVD achieves the highest Nash-Sutcliffe efficiency and lowest Relative Error, and performs best in simulating peak flow and its occurrence time as compared to AM and TP. This study contributes to a finer characterization of watershed rainfall distribution, enhancing the accuracy and sharpness of runoff simulation. It provides reliable data support for critical zone research and offers a scientific foundation for rationally allocating and managing water resources. A spatiotemporal rainfall estimation method based on Funk-SVD is applied to rainfall-runoff simulation to explore whether considering the spatiotemporal information of the rainfall process can more truly express the physical relationship between rainfall and runoff, and improve the accuracy of the runoff simulation in the critical zone.image