Continuous Spectral Transformation for Forecasting Hydroclimatic Extremes

Accurate hydrological forecasting at local scales is often constrained by the limited ability to effectively translate large-scale climate predictors into reliable local predictions. To improve this translation, wavelet-based predictor refinement methods operating in the discrete domain, such as Wavelet System Prediction (WASP), have been applied; however, these approaches are constrained by limitations inherent to the Discrete Wavelet Transform (DWT), including limited scale resolution. More importantly, it primarily adjusts predictor amplitude in the time-frequency domain and does not address spectral mismatches arising from phase and amplitude misalignment between predictors and responses, leading to reduced predictive reliability.

Here, we introduce Continuous Spectral Transformation (CST), a framework that leverages continuous wavelets to simultaneously adjust variance structure and phase misalignment by exploiting their high-resolution continuous scales in the frequency domain. CST enables precise redistribution of predictor variance across continuous frequency bands while simultaneously correcting phase alignment. The performance of CST is evaluated through a rigorous validation scheme spanning synthetic experiments, including chaotic systems, and a real-world drought forecasting application.

Results from the real-world application demonstrate the clear superiority of CST, with correlation improvements of 40–61% relative to models using raw and WASP-transformed predictors, effectively transforming marginally skilful forecasts into operationally reliable predictions. CST establishes a robust and physically interpretable framework for predictor refinement in hydroclimatic forecasting and offers strong potential for enhancing decadal-scale projections of hydrological extremes and other climate-driven extreme events.

Keywords: Hydroclimatic extremes, Wavelet analysis, Continuous Spectral Transformation