A Novel Optimal Layout Method for Rain Gauge Network Based on Mutual Information Entropy and Deep Learning Model

Rain gauge networks are the core infrastructure for hydrological and water resource monitoring, flood control and disaster mitigation early warning, and water resource planning and regulation. The rationality of their layout directly determines the accuracy, representativeness, and economy of regional precipitation data acquisition. Considering that information entropy can accurately characterize the spatial distribution law and information complexity of rainfall, and spatiotemporal deep learning models have strong capabilities in fitting spatiotemporal features, this paper couples mutual information entropy with a spatiotemporal deep learning model and proposes a novel optimal layout method for rain gauge networks. Daily observed rainfall data from 50 ground-based rain gauges in the upper reaches of the Tuojiang River during 2015-2024, as well as the PERSIANN-CCS remote sensing precipitation product for the same period, were used in the study. A CNN-LSTM spatiotemporal deep learning model integrating spatial features and temporal dependence was constructed, coupled with the mutual information entropy index, and the GA-PSO hybrid optimization algorithm was applied for solution. The superiority of the proposed method was verified by comparison with the calculation results of the traditional mutual information entropy-based greedy optimization algorithm. The results show that the hybrid optimization algorithm driven by the spatiotemporal deep learning model coupled with mutual information entropy is significantly superior to the comparison algorithm in terms of the rationality of the station network structure, the ability to characterize spatial rainfall distribution, the control of average relative error, and the improvement of total information entropy. After optimization, the number of rain gauges in the upper reaches of the Tuojiang River can be reduced from 50 to 25. While greatly reducing the number of stations, the optimized network can still relatively accurately reflect the spatiotemporal characteristics of rainfall in the basin, which can provide a theoretical basis and technical support for the optimal layout of basin rain gauge networks and water resource management.