A Coupled Rainfall–Runoff Hydrometric Network Design Method Based on Information Theory

Hydrometric data is needed for water resources management and decision making and are obtained from hydrometric networks. These networks should therefore be carefully designed and evaluated. Several methods are used for hydrometric network design and information theory-based methods have lately been receiving significant attention. This study focuses on individual and integrated designs of hydrometric network (rainfall and runoff). Mutual information (MI) is one of the important information measures and is used as a measure of information transmission or redundancy for network evaluation. The impact of estimation methods on rainfall and runoff network design was evaluated in this study. Here, we estimate mutual information using three different methods, including binning estimation, kernel density estimation (KDE) and k-nearest neighbor estimation (KNN), and compare them. A ranking method, based on total mutual information (TMI), is proposed and applied to the Wei River watershed in China. Results show that the MI estimation method exercises a great impact on relative entropy values of different stations and network evaluation. Further, results of evaluation of individual and integrated networks are found to be different for spatial distribution of stations but similar for specific stations. However, the augmentation of potential rainfall stations is not much affected by runoff stations, meaning that the information content in existing runoff stations does not much overlap with the information contained in potential rainfall stations in the study watershed. Generally, different evaluation results may stem from intrinsic statistical properties of rainfall or runoff data for different stations, which means that there still remains a difficult task for better integrated design of hydrometric networks. However, the augmentation of potential rainfall stations with or without considering runoff didn’t show much differences with binning estimators. Even maps from KDE estimators showed similar results, which means the incorporation of runoff may not have a significant impact on rainfall network augmentation.