Evaluation of Mathematical Models with Utility Index: A Case Study from Hydrology

Abstract

Conventional error-based statistical parameters like the Nash–Sutcliffe efficiency index are popular among hydrologists to check the accuracy of hydrological models and to compare the relative performance of alternative models in a particular modelling scenario. A major drawback of those traditional indices is that they are based on only one modelling attribute, i.e. the modelling error. This study has identified an overall model utility index as an effective error-sensitivity-uncertainty procedure which could serve as a useful quality indicator of data-based modelling. This study has also made an attempt to answer the question—should the increasing complexity of the existing model add any benefit to the model users? The study evaluates the utility of some popular and widely used data-based models in hydrological modelling such as local linear regression, artificial neural networks (ANNs), Adaptive neuro fuzzy inference system (ANFIS) and support vector machines (SVMs) along with relatively complex wavelet hybrid forms of ANN, ANFIS and SVM in the context of daily rainfall–runoff modelling. The study has used traditional error-based statistical indices to confirm capabilities of model utility index values in identifying better model for rainfall–runoff modelling. The implication of this study is that a modeller may use utility values to select the best model instead of using both calibration and validation processes in the case of data scarcity. The study comprehensively analysed the modelling capabilities of SVM and its waveform in the context of rainfall–runoff modelling.