Refining Predictor Spectral Representation Using Wavelet Theory for Improved Natural System Modeling

Abstract Predicting future surpluses or shortages of water is a long‐standing problem having considerable ramifications to water management across the world. Any prediction model for a natural system such as one that estimates water surpluses or shortages requires a two‐step approach. These are the following: first, identify and select meaningful predictor variables from a large number of potential predictors and second, formulate an accurate, efficient, and robust predictive model between selected predictors and the response. Recognizing that the timescales at which a response may operate is usually different from that of the predictors being identified, we introduce here a wavelet‐based unique variance transformation to each of the multiple predictor variables in the system which ensures an improved regression relationship to the modeled response. All existing methods assume no change in predictors even if they characterize variability at markedly different timescales, a deficiency that is addressed using the variance‐transformed predictor which can explain maximal information in an associated response. Using this unique variance transformation, additional predictor variables can be selected by assessing their ability to characterize residual information in the response that accounts for the effect of preidentified predictors. We demonstrate the utility of the wavelet‐based method using synthetically generated data sets from known linear and nonlinear systems with parametric and nonparametric predictive models. Applications to a dynamic system and a real‐world example to downscale a drought indicator over the Sydney region confirm its utility in an applied setting.