Developing an entropy-based model of spatial information estimation and its application in the design of precipitation gauge networks

•An improved information theory-based method for hydrometric networks is proposed.•Spatial information is estimated by 2D T–D model and multivariate approximation.•Temporal and spatial patterns of information content were analyzed. This study proposed a spatial information estimation model for the analysis of precipitation gauge networks, to improve on previous methods based on information theory. The proposed model employs a two-dimensional transinformation–distance (T–D) relationship in conjunction with multivariate information approximation to estimate transinformation to ungauged locations from existing stations, while taking into consideration the influence of multiple stations and anisotropy. The proposed model is used to evaluate the spatial distribution of precipitation data and the characteristics of information transfer, which are then applied in a spatial optimization algorithm for the selection of additional station locations. This framework was implemented to investigate temporal and spatial patterns in information content in the Shihmen Reservoir watershed. The results demonstrate obvious anisotropy associated with the delivery of information. By comparing different cases, it was determined that the efficiency of information delivery dominates the spatial distribution of the information content, such that eccentricity is merely supplemental. Efficiency in information delivery is also heavily influenced by temporal scale. For data covering long intervals (monthly and annual), efficiency in the delivery of information is relatively high, while the uncertainty or heterogeneity of hourly or daily time series produces low spatial correlations due to the inefficient delivery of information. The proposed spatial optimization algorithm confirmed that the optimal location for new stations lies close to the center of low information zones. Additional stations could improve information content considerably; however, the margin of improvement decreases with the number of stations.