A New Method for Postprocessing Numerical Weather Predictions Using Quantile Mapping in the Frequency Domain

Abstract

Abstract Improving lead time for forecasting floods is important to minimize property damage and ensure the safety of the public and emergency services during flood events. Numerical weather prediction (NWP) models are important components of flood forecasting systems and have been vital in extending forecasting lead time under complex weather and terrain conditions. However, NWP forecasts still have significant uncertainty associated with the precipitation fields that are the main inputs of the hydrologic models and thus the resulting flood forecasts. An issue often overlooked is the importance of correctly representing variability over a range of different temporal scales. To address this gap, here a new wavelet-based method for postprocessing NWP precipitation forecasts is proposed. First, precipitation forecasts are decomposed into the frequency domain using a wavelet transform, providing estimates of the amplitudes and phases of the time series at different frequencies. Quantile mapping is then used to correct bias in the amplitudes of each frequency. Randomized phases are used to generate an ensemble of realizations of the precipitation forecasts. The postprocessed precipitation forecasts are reconstructed by taking the inverse of adjusted time-frequency decompositions with the corrected amplitudes and randomized phases. The proposed method was used to postprocess NWP precipitation forecasts in the Sydney region of Australia. There is a significant improvement in postprocessed precipitation forecasts across multiple time scales in terms of bias and temporal and spatial correlation structures. The postprocessed precipitation fields can be used for the modeling of fully distributed hydrologic systems, improving runoff stimulation, flood depth estimation, and flood early warning. Significance Statement A new method accounting for the timing and spatial errors of NWP precipitation forecasts is proposed, and it can improve the skill of forecasts across multiple time scales, especially at short lead times. The proposed method provides a practical and effective way to correct these errors by incorporating spatiotemporal neighborhood information through the frequency domain using sophisticated wavelet transforms. With systematic timing and spatial errors removed, precipitation forecasts will be more skillful, and hydrological modeling using the postprocessed forecasts can provide higher accuracy of streamflow estimation.