A New Wavelet Based Approach to Assess Hydrological Models

In this study, a new wavelet based multi-scale performance measure (Multiscale Nash Sutcliffe Criteria, and Multiscale Normalized Root Mean Square Error) for hydrological model comparison was developed and tested. The new measure provides a quantitative measure of model performance across different timescales. Model and observed time series are decomposed using the a trous wavelet transform, and performance measures of the model are obtained at each time scale. The usefulness of the new measure was tested using real as well as synthetic case studies. The real case studies included simulation results from the Soil Water Assessment Tool (SWAT), as well as statistical models (the Coupled Wavelet-Volterra (WVC), Artificial Neural Network (ANN), and Auto Regressive Moving Average (ARMA) methods). Data from India and Canada were used. The synthetic case studies included different kinds of errors (e.g., timing error, as well as under and over prediction of high and low flows) in outputs from a hydrologic model. It was found that the proposed wavelet based performance measures (i.e., MNSC and MNRMSE) are a more reliable measure than traditional performance measures such as the Nash Sutcliffe Criteria, Root Mean Square Error, and Normalized Root Mean Square Error. It was shown that the new measure can be used to compare different hydrological models, as well as help in model calibration.