Spatial Verification Using Wavelet Transforms: A Review

TL;DR

This review discusses how wavelet transforms can improve spatial verification of weather forecasts by analyzing data at multiple scales, highlighting recent advances and potential for cross-disciplinary applications.

Contribution

The paper provides a comprehensive review of wavelet-based spatial verification techniques and explores their potential beyond meteorology, including texture analysis and data clustering.

Findings

Wavelet transforms effectively decompose spatial data into multiple scales.

Recent applications show improved forecast skill assessment.

Potential exists for cross-disciplinary use in image and feature analysis.

Abstract

Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet transforms offer an effective framework to decompose spatial data into separate (and possibly orthogonal) scales and directions. Most wavelet based spatial verification techniques have been developed or refined in the last decade and concentrate on assessing forecast performance (i.e. forecast skill or forecast error) on distinct physical scales. Particularly during the last five years, a significant growth in meteorological applications could be observed. However, a comparison with other scientific fields such as feature detection, image fusion, texture analysis, or facial and biometric recognition, shows that there is still a considerable, currently unused potential to derive useful diagnostic information. In order to tab the full potential of wavelet analysis, we revise the state-of-the art in one- and two-dimensional wavelet analysis and its application with emphasis on spatial verification. We further use a technique developed for texture analysis in the context of high-resolution quantitative precipitation forecasts, which is able to assess structural characteristics of the precipitation fields and allows efficient clustering of ensemble data.