Wavelet‐based multiscale performance analysis: An approach to assess and improve hydrological models

Abstract

The temporal dynamics of hydrological processes are spread across different time scales and, as such, the performance of hydrological models cannot be estimated reliably from global performance measures that assign a single number to the fit of a simulated time series to an observed reference series. Accordingly, it is important to analyze model performance at different time scales. Wavelets have been used extensively in the area of hydrological modeling for multiscale analysis, and have been shown to be very reliable and useful in understanding dynamics across time scales and as these evolve in time. In this paper, a wavelet-based multiscale performance measure for hydrological models is proposed and tested (i.e., Multiscale Nash-Sutcliffe Criteria and Multiscale Normalized Root Mean Square Error). The main advantage of this method is that it provides a quantitative measure of model performance across different time scales. In the proposed approach, model and observed time series are decomposed using the Discrete Wavelet Transform (known as the a trous wavelet transform), and performance measures of the model are obtained at each time scale. The applicability of the proposed method was explored using various case studies--both real as well as synthetic. The synthetic case studies included various kinds of errors (e.g., timing error, under and over prediction of high and low flows) in outputs from a hydrologic model. The real time case studies investigated in this study included simulation results of both the process-based Soil Water Assessment Tool (SWAT) model, as well as statistical models, namely the Coupled Wavelet-Volterra (WVC), Artificial Neural Network (ANN), and Auto Regressive Moving Average (ARMA) methods. For the SWAT model, data from Wainganga and Sind Basin (India) were used, while for the Wavelet Volterra, ANN and ARMA models, data from the Cauvery River Basin (India) and Fraser River (Canada) were used. The study also explored the effect of the choice of the wavelets in multiscale model evaluation. It was found that the proposed wavelet-based performance measures, namely the MNSC (Multiscale Nash-Sutcliffe Criteria) and MNRMSE (Multiscale Normalized Root Mean Square Error), are a more reliable measure than traditional performance measures such as the Nash-Sutcliffe Criteria (NSC), Root Mean Square Error (RMSE), and Normalized Root Mean Square Error (NRMSE). Further, the proposed methodology can be used to: i) compare different hydrological models (both physical and statistical models), and ii) help in model calibration.

Multi-scale event synchronization analysis for unravelling climate processes: a wavelet-based approach

“…Yan and Gao (2007) mother wavelets which could be used for wavelet decomposition; however, it has been demonstrated that the choice of the mother wavelets does not affect the results to a great extent for rainfall (Rathinasamy et al, 2014). In case I(a) the noise-signal ratio is quite high in the range of 2.7-3 (Table 1), such that the effect of the noise is felt up to scale 7 (Fig.…”

“…Following the approach of Rathinasamy et al (2014), Yan and Gao (2007), and Hu and Si (2016), we test MSES using a set of case studies including stationary and non-stationary synthetic data. The details of the case studies and the wavelet power spectra are given in Table 1 and Fig.…”

“…However, climate-related processes typically show variability at a range of scales. Synchronization and interaction can occur at different temporal scales, as localized features, and can even change with time (Rathinasamy et al, 2014;Herlau et al, 2012;Steinhaeuser et al, 2012;Tsui et al, 2015). Features at a certain timescale might be hidden while examining the process at a different scale.…”

“…In addition, single-scale measures, such as correlation and ES, are valid and meaningful only for stationary systems. For non-stationary systems, they may underestimate or overestimate the strength of the relationship (Rathinasamy et al, 2014).…”

“…The wavelet transform can potentially convert a nonstationary time series into stationary components (Rathinasamy et al, 2014), and this can help in analysing nonstationary time series using the proposed method.…”