Toward a more efficient Calibration Schema for HBV rainfall-runoff model

Summary The aim of this study is to improve the efficiency of the global optimisation method SCE - UA applied to the calibration of HBV rainfall–runoff model. Three efficiency-improving techniques are adopted and combined together: (i) estimation of the objective function by KNN approach applied to some parts of the optimisation process (ii) parameter space transformation, (iii) SCE - UA algorithm modification. Firstly a hybrid optimisation algorithm using KNN technique to estimate the objective function is developed on the basis of several test functions. The objective function is calculated by an interpolation using nearest neighbours in the normalised parameter space with Euclidean distance. This is only performed for some situations selected according to discrimination of the new generated point in relation to its neighbours objective function values and the distance that separates it from its nearest neighbours. The distinctive contribution of the study consists in dynamically tuning and updating the algorithmic parameters of the KNN . The implementation of the KNN technique for the case of test functions shows an improvement of the efficiency from 25% to 50% compared to the initial SCE - UA . Then, the enhanced optimisation algorithm using the three techniques is applied to the case of calibration of HBV model under synthetic data. Evaluation of the model performance is achieved through the objective function RV  =  Nash–ω|RD| , where Nash is Nash–Sutcliffe coefficient related to discharges, ω weight and | RD | absolute relative bias. The effectiveness of the SCE - UA remains at its normal level. We noticed that the Logarithmic transformation of the HBV recession coefficients leads to 20% improvement of the convergence speed. The modification of the SCE - UA algorithm is performed by enhancement of the Simplex Evolutionary Algorithm through an additional shifting step of the reflected or contracted point to the best point. This modification makes an improvement of the convergence speed of about 30%. Finally, the combination of the three enhancement techniques gives an optimisation algorithm tow to three times faster than the initial SCE - UA which brings out very substantial improvements in performance. The enhanced algorithm is further applied to real world cases of several catchments with different climatic conditions: the Rottweil in Germany and the Tessa, Barbra, and Sejnene in Tunisia. This results in improvements in performance which could reach 89%.

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