Information theory‐based decision support system for integrated design of multivariable hydrometric networks

Abstract

Adequate and accurate hydrologic information from optimal hydrometric networks is an essential part of effective water resources management. Although the key hydrologic processes in the water cycle are interconnected, hydrometric networks (e.g., streamflow, precipitation, groundwater level) have been routinely designed individually. A decision support framework is proposed for integrated design of multivariable hydrometric networks. The proposed method is applied to design optimal precipitation and streamflow networks simultaneously. The epsilon‐dominance hierarchical Bayesian optimization algorithm was combined with Shannon entropy of information theory to design and evaluate hydrometric networks. Specifically, the joint entropy from the combined networks was maximized to provide the most information, and the total correlation was minimized to reduce redundant information. To further optimize the efficiency between the networks, they were designed by maximizing the conditional entropy of the streamflow network given the information of the precipitation network. Compared to the traditional individual variable design approach, the integrated multivariable design method was able to determine more efficient optimal networks by avoiding the redundant stations. Additionally, four quantization cases were compared to evaluate their effects on the entropy calculations and the determination of the optimal networks. The evaluation results indicate that the quantization methods should be selected after careful consideration for each design problem since the station rankings and the optimal networks can change accordingly.

Entropy Applications to Water Monitoring Network Design: A Review

“…For instance, if a noticeable amount of precipitation occurs, streamflow or groundwater level is likely increased; hence, the information content of a variable may affect that of other variables. Keum and Coulibaly [35] developed a multivariate network design method by taking conditional entropy as the measure of information that is independent to a given variable. In their study, the method designed precipitation and streamflow monitoring networks simultaneously.…”

“…Li et al [41] also investigated the changes of station rankings based on the maximum information minimum redundancy (MIMR) approach and obtained the similar conclusion. However, Fahle et al [31] and Keum and Coulibaly [35] drew the opposite opinion that station rankings can be affected by the binning method that defines the class intervals. The conflict comes from the selection of the binning methods compared.…”

“…They compared the performance of various regionalization methods including not only a conceptual hydrologic model, but also spatial proximity, physical similarity and their combinations with drainage area ratio. Based on the performance statistics by applying multiple basins, inverse distance weighting coupled with drainage area ratio performed the best, and this conclusion has been adopted in several studies [34,35,37,55].…”

“…Research has also shown that data length, catchment scale and ordering can influence the design of an optimal network [31,34,51]. Finally, when using discrete entropy, the binning method has been shown to influence the final network design [35]. The influence of binning on entropy calculation has received greater attention in other geophysical network design applications [83][84][85], and similar consideration should be given in the field of water resources, particularly owing to the unique and difficult nature of water variables (e.g., streamflow, precipitation) spatial and temporal distribution [30,60].…”

“…Coulibaly and Keum [66] and Samuel and Coulibaly [67] also used a multi-objective approach to add stations to snow monitoring networks in Canada. Their approach used a genetic algorithm to find networks that maximized the joint entropy and minimized the total correlation of the network to form a Pareto front of optimal network designs, some of which also included network cost in the optimization [35,67].…”