Estimation of the hydrological model parameters, known as model calibration, is an important step in application of these models for various water resources problems. In the auto-calibration approach, the match between the simulated and observed variables is assessed using the statistical performance measures, which are used as objective functions. Earlier studies show that the use of traditional single-objective functions alone cannot capture all the features of the hydrographs, motivating the utilization of multi-objective calibration. Further, wavelet-based approaches can capture features that occur at different time scales. In this study, Wavelet Transforms are employed to formulate a Wavelet based Multi-Scale Multi-Objective Performance Evaluation (WMMPE) metric that combines multiple standard metrics at multiple time scales. The performance of WMMPE along with other objective functions such as Nash Sutcliffe Efficiency (NSE), Kling Gupta Efficiency (KGE)), Euclidean distance based Multi Objective Calibration Function and wavelet based Multi-Scale NSE in calibrating two conceptual hydrologic models were tested on 53 watersheds. The performance of the five calibrated models were evaluated for their efficacy in simulating different characteristics of hydrograph such as, low and high flows, water balance components, frequency domain characteristics and average error magnitude. The results show that WMMPE calibrated models are performing well in matching all the flow segments of hydrograph in >22 basins for the two conceptual models. Further, results of the analysis suggested that the presence of outliers have minimum impact on the simulation of WMMPE calibrated models in the validation period.

中文翻译：

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用于改进水文模型校准的基于小波的多尺度多目标性能评估 (WMMPE) 度量的制定

水文模型参数的估计，称为模型校准，是将这些模型应用于各种水资源问题的重要步骤。在自动校准方法中，模拟变量和观察变量之间的匹配是使用统计性能测量来评估的，这些测量被用作目标函数。早期的研究表明，单独使用传统的单目标函数不能捕捉水位线的所有特征，从而激发了多目标校准的使用。此外，基于小波的方法可以捕获在不同时间尺度上出现的特征。在这项研究中，小波变换用于制定基于小波的多尺度多目标性能评估 (WMMPE) 度量，该度量在多个时间尺度上结合了多个标准度量。WMMPE 与其他目标函数（例如 Nash Sutcliffe 效率 (NSE)、Kling Gupta 效率 (KGE)）、基于欧几里德距离的多目标校准函数和基于小波的多尺度 NSE 在校准两个概念水文模型时的性能在 53 上进行了测试分水岭。对五个校准模型的性能进行了评估，以评估它们在模拟低流量和高流量、水平衡分量、频域特性和平均误差幅度等水文过程线的不同特征方面的功效。结果表明，对于两个概念模型，WMMPE 校准模型在匹配 >22 个流域的所有水文流段方面表现良好。更远，