Multiobjective Optimization of Rain Gauge Network Design in the Huaihe River Basin Based on Information Theory

Abstract Against the backdrop of increasingly complex spatiotemporal patterns of precipitation, the scientific design of rainfall gauge networks has become essential for improving hydrological monitoring efficiency and regional flood control capacity. To address the long-standing uncertainties in discretization and the neglect of climatic nonstationarity, this study developed an entropy-based multiobjective optimization framework for rainfall gauge networks. The proposed method integrates Shannon entropy with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="epsilon" display="inline" overflow="scroll"> <mml:mi>ε</mml:mi> </mml:math> -dominance hierarchical Bayesian optimization algorithm ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="epsilon" display="inline" overflow="scroll"> <mml:mi>ε</mml:mi> </mml:math> -hBOA) and establishes a multiobjective optimization system centered on informational representativeness: maximizing joint entropy to ensure overall information content, minimizing total correlation to reduce information redundancy, and maximizing mutual information to strengthen spatial representativeness. Three discretization approaches—the floor function method, Scott’s method, and Sturges’ method—were evaluated systematically to determine the optimal discretization scheme. Furthermore, a sliding window approach was adopted to quantify the time-varying impacts of trend-induced nonstationarity on network stability. Applications in the Huaihe River Basin show that the spatial layout of the network is characterized by boundary stations forming its core backbone, and internal stations present obvious information redundancy. In addition, significant fluctuations in station selection frequencies were observed across different sliding windows. Accordingly, future network updates should adapt to climate change through regular iterative optimization, so that the monitoring network remains consistent with the dynamically evolving hydrological regime.