A well?designed hydrologic network can reflect the spatial?temporal variability of hydrologic variables adequately at catchment scale and reveal the hydrologic regularities systematically and precisely.Hydrologic network optimization requires a minimum number of sites to gather abundant and accurate information.In this study，an entropy based multi?objective optimization model for hydrologic networks was established.Firstly，based on the information entropy theory，the sites were sorted under the principle of the minimum mutual information.Then different number of sites composed several combinations of sites.Secondly，in order to evaluate the information carrying capacity of these combinations，an objective function composed of joint entropy percentage，average mutual information and Nash?Sutcliffe Efficiency Coefficient(NSC)was constructed，which is the core of the network optimization model.Finally，based on the multi?objective decision?making method，a Pareto solution set was determined and an optimum solution was chosen through the ideal point method.Taking the monthly runoff data of the Yiluo River—a tributary of the Yellow River—as a sample，the paper analyzed the hydrologic network of the Yiluo River Basin.Results showed that the network of the Yiluo River can be optimized.After removing some redundant sites，the new hydrologic network still provides sufficient information，meanwhile the cost of network construction and maintenance is reduced.As a result，the network’s utility is maximized.The model proposed in this study takes 3 targets into account and integrates the multi?objective optimization method.The targets include the total information，the overlapped information and the residual of the data.This model meets the requirement of quantitative analysis of information as well as getting a network optimization solution under multiple targets.The model is proved effective and rational and will play an important role in water resources management and policy?making.
Li Heshu，Wang Dong*，Wang Yuankun.
Entropy based multi?objective optimization for hydrologic networks[J]. Journal of Nanjing University(Natural Sciences), 2017, 53(2): 326
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