Formulation of Wavelet Based Multi‐Scale Multi‐Objective Performance Evaluation (WMMPE) Metric for Improved Calibration of Hydrological Models

Abstract

Hydrological models are essential tools for assessing, analyzing and developing solutions for natural hydrologic systems (Mostafaie et al., 2018;Wagener et al., 2001). One of the steps in application of these models, is the estimation of their parameters, which is known as model calibration (Guinot et al., 2011;. Parameters of the hydrological models are estimated by comparing the simulated and observed variables of interest (usually streamflow) . The match between simulated and observed variables is expressed using statistical performance measures such as Nash Sutcliffe Efficiency (NSE)

A decomposition approach to evaluating the local performance of global streamflow reanalysis

“…This process is executed by controlling the scaling and shifting factors associated with a mother wavelet (Nalley et al, 2012). The DWT captures time series information at multiple scales in the time-frequency domain, with each scale corresponding to a specific period (Joo and Kim, 2015;Manikanta and Vema, 2022). Following Wei et al (2012), the Daubechies wavelet of order 5 is used to decompose the streamflow time series.…”

“…These components can be extracted by using some decomposition approaches (Nalley et al, 2012;Abebe et al, 2022;Xu et al, 2022). As one of the most important decomposition approaches, wavelet transform decomposes streamflow into time series of wavelet coefficients, of which each is linked to some frequencies (Manikanta and Vema, 2022). Owing to the time-frequency characterization, wavelet-based features of reanalysis and observed streamflow can be compared in order to zoom into detailed information for multiple time series segments (Manikanta and Vema, 2022).…”

“…As one of the most important decomposition approaches, wavelet transform decomposes streamflow into time series of wavelet coefficients, of which each is linked to some frequencies (Manikanta and Vema, 2022). Owing to the time-frequency characterization, wavelet-based features of reanalysis and observed streamflow can be compared in order to zoom into detailed information for multiple time series segments (Manikanta and Vema, 2022). If there are errors in the reanalysis at specific timescales or during specific periods, the sources of these errors can be identified by the technique of timefrequency characterization (Lane, 2007).…”

A Robust Strategy to Account for Data Sampling Variability in the Development of Hydrological Models

“…When applying a “ general ” hydrological model architecture to any specific location, it is important to adjust the model parameters so that the resulting “ calibrated ” model provides robust and credible simulations of the input‐state‐output behaviors of the system under a representative variety of conditions (Guinot et al., 2011; Vema & Sudheer, 2020). Ideally, the model residuals will have minimal variance and be unbiased (Evin et al., 2013; Manikanta & Vema, 2022), and their statistical properties will be consistent and predictable so that the prediction uncertainties are well understood and can be robustly accounted for when using the calibrated model for decision making (Pan et al., 2019; Reichert et al., 2021).…”

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When applying a "general" hydrological model architecture to any specific location, it is important to adjust the model parameters so that the resulting "calibrated" model provides robust and credible simulations of the input-state-output behaviors of the system under a representative variety of conditions (Guinot et al, 2011;Vema & Sudheer, 2020). Ideally, the model residuals will have minimal variance and be unbiased (Evin et al, 2013;Manikanta & Vema, 2022), and their statistical properties will be consistent and predictable so that the prediction uncertainties are well understood and can be robustly accounted for when using the calibrated model for decision making (Pan et al, 2019;Reichert et al, 2021).However, it can be remarkably challenging to ensure that the residuals of calibrated models have such properties (T. Smith et al, 2015). This can be due to a number of factors including: (a) observational noise/error, (b) model structural inadequacy (Gupta et al, 2012), and (c) data sampling variability (DSV) (Zheng et al, 2018).

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