Entropy-MIMR-LSTM framework for rain gauge network optimization in mountainous small watersheds: A case study of Fuhuxi Watershed, China

Global climate change has intensified the frequency and severity of extreme rainfall events, thereby exacerbating flood disasters. To mitigate such risks, timely and accurate rainfall measurements are essential, yet cost-effectiveness must also be considered. However, many river basins—particularly mountainous small watersheds—suffer from poorly designed rain gauge networks, limiting real-time data acquisition. Existing optimization methods are largely developed for large river basins or plains and are not directly applicable to mountainous small watersheds, where rainfall exhibits strong spatial heterogeneity and gauge networks are sparse. To address this gap, this study takes the Fuhuxi Watershed of Mount Emei in Sichuan Province, Southwest China, as a case study and develops a collaborative optimization framework integrating information entropy, the Maximum Information Minimum Redundancy (MIMR) criterion, and Long Short-Term Memory (LSTM) networks. Specifically, we quantified the information entropy matrix of seven existing rain gauge stations and applied the MIMR criterion, resulting in the retention of five key stations. The optimized network preserves 99% of the effective rainfall information from the original seven stations while significantly reducing operational and maintenance costs. Using data from nine rainfall-induced flood events between 2018 and 2023, we developed an LSTM-based runoff simulation model. The optimized network, which removes stations with low information content and high redundancy, achieved excellent flood simulation accuracy. The study demonstrates that: (1) information entropy theory effectively interprets the spatial correlation and information redundancy of rain gauge stations in mountainous small watersheds; and (2) the LSTM model validates the feasibility of using an optimized rain gauge network to support high-precision flood simulations. Finally, we propose suggestions for future research, particularly regarding the optimization of rain gauge networks to improve the understanding of optimal network design and thereby enhance the accuracy of rainfall-runoff simulations.