Research on Optimizing Rainfall Interpolation Methods for Distributed Hydrological Models in Sparsely Networked Rainfall Stations of Watershed

Rainfall stations in small and medium-sized river basins in China are sparsely distributed and unevenly spaced, resulting in insufficient spatial representativeness of precipitation data and posing challenges to the accuracy of flood forecasting. Spatial interpolation methods for rainfall data are a key tool for bridging the gap between discrete rainfall station data and continuous surface rainfall data; however, their applicability in flood forecasting for small and medium-sized river basins with sparse rainfall stations requires further investigation. Taking the Hezikou basin as the study area and focusing on the Liuxihe model, this study analyzes the distribution characteristics of the seven rainfall stations in the basin and the interpolation effectiveness of the original Thiessen Polygon Interpolation (THI) method in the model. It compares and discusses the applicability of the THI, the Inverse Distance Weighting (IDW) method, and the Trend Surface Interpolation (TSI) method in flood forecasting for this basin. Different rainfall station distribution scenarios (full coverage, upstream only, downstream only, single rainfall station) were set up to study the performance differences in each method under extremely sparse conditions. The results indicate that, under the sparse condition of only 0.0068 rainfall stations per square kilometer in the Hezikou basin, IDW interpolation yields the best flood forecasting results, with model Nash–Sutcliffe Efficiency (NSE) values all above 0.85, Kling–Gupta Efficiency (KGE) values exceeded 0.78, and the Peak Relative Error (PRE) was controlled within 0.09, significantly outperforming THI and TSI. Additionally, as rainfall station sparsity increased, IDW exhibited the smallest decline in performance, showing a weak negative correlation (p ≤ 0.05) between prediction performance and rainfall station sparsity, demonstrating stronger adaptability to sparse scenarios. When station information is extremely limited, IDW performs more stably than THI and TSI in terms of certainty coefficients (NSE, KGE) and flood peak error control. The Inverse Distance Weighting method (IDW) can provide reliable rainfall spatial interpolation results for flood forecasting in small and medium-sized basins with sparse rainfall stations.