Variable transformations in the spectral domain – Implications for hydrologic forecasting

Abstract

Forecasting of hydrologic extremes across a range of timescales is critical for minimizing the socio-economic costs of these events. Regression-based prediction is commonly adopted even in operational forecasting systems, often necessitating the use of distributional transformations to improve model specifications. One of the issues in such predictions, however, is the marked differences that distinguish the frequency spectrum of the hydrologic response from the predictor variables used. This raises the question of whether there exists an optimal predictor variable transformation that can mimic the frequency spectrum embedded in the observed response variable series. The present paper discusses the need to transform predictor variables to improve hydrologic forecasts, and specifically focuses on the frequency domain of the variables involved. A number of alternatives using wavelet-based approaches are presented as a means of transforming the variance associated with different frequency bands in each predictor variable. The limitations and advantages of these transformations are summarized and demonstrated using synthetic examples. A stepwise variance transformation framework is further proposed that facilitates transformations of the residual error from a given predictor variable conditioned on existing (or pre-identified) predictor variables. Results of the stepwise framework demonstrate that the response is better characterized using both synthetic case studies and when applied to forecasting the El Niño–Southern Oscillation (ENSO) over long lead times.