A two-phase copula entropy-based multiobjective optimization approach to hydrometeorological gauge network design

Abstract Hydrometeorologicaldata are needed for obtaining point and areal mean, quantifying the spatial variability of hydrometeorologicalvariables, and calibration and verification of hydrometeorologicalmodels. Hydrometeorologicalnetworks are utilized to collect such data. Since data collection is expensive, it is essential to design an optimal network based on the minimal number of hydrometeorologicalstations in order to reduce costs. This study proposes a two-phase copula entropy- based multiobjective optimization approach that includes: (1) copula entropy-based directional information transfer(CDIT) for clustering the potential hydrometeorologicalgauges into several groups, and (2) multiobjective method for selecting the optimal combination of gauges for regionalized groups. Although entropy theory has been employed for network design before, the joint histogram method used for mutual informationestimation has several limitations. The copula entropy-based mutual information(MI) estimation method is shown to be more effective for quantifying the uncertainty of redundant information than the joint histogram ( JH) method. The effectiveness of this approach is verified by applying to one type of hydrometeorologicalgauge network, with the use of three model evaluation measures, including Nash–Sutcliffe Coefficient (NSC), arithmetic meanof the negative copula entropy (MNCE), and MNCE/NSC. Results indicate that the two-phase copula entropy-based multiobjective technique is capable of evaluating the performance of regional hydrometeorologicalnetworks and can enable decision makers to develop strategies for water resources management.