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Spatial Verification of High-Resolution Ensemble Forecasts using Wavelet Transformation

Applicant Privatdozentin Dr. Petra Friederichs, since 3/2018
Subject Area Atmospheric Science
Term from 2017 to 2022
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 381875761
 
Final Report Year 2022

Final Report Abstract

Verification, i.e., the systematic comparison of forecasts against observed reference data, is integral to the science of weather forecasting. With increased resolution and fidelity of both observation systems and numerical weather prediction models, the task of comparing observed and simulated spatial fields has grown increasingly challenging due to the wide variety of potential error types and sources. In particular, displacement errors, for example in predicted rain features, tend to overshadow all other aspects of forecast quality, thereby rendering traditional point-wise verification approaches unsuitable. This observation has spurred the development of numerous new verification approaches in the emerging research field of spatial verification. Many of these techniques take inspiration form the world of computer vision and image processing. Wavelet transforms, which represent images as a superposition of localized waveforms, are a particularly useful tool for extracting concrete information from complicated and possibly noisy images. While some wavelets-based spatial verification techniques existed in the literature, their potential appeared greatly under-used compared to the plethora of applications in other scientific fields. In particular, none of the existing methods made full use of the fact that wavelets provide localized information on the spatial covariance structure. The aim of this project was to tap into that unused potential and develop new wavelet-based verification techniques for various types of weather forecasts. The first main outcome of this endeavor was the development of the SAD scores, which can analyze and verify the spatial scale, anisotropy and direction of any forecast field of interest. Using a variety of synthetic and realistic test cases, we have demonstrated that the scale component is qualitatively similar to existing “structure” scores but generally more robust and discriminative. The directional aspects measured by the A and D component are neglected by most existing scores but yield valuable information on meteorological features such as weather fronts which have strong preferred orientations. To achieve this, the classic discrete wavelet transforms used in the verification literature had to be abandoned in favor of dual-tree complex wavelets, which provide sufficiently good directional selectivity, as well as several other convenient advantages. Unlike many existing techniques, SAD can analyze local structural information at every grid-point and is applicable not only to precipitation but any spatial field of interest. Lastly, the existence of an inverse wavelet transform enables the correction of the detected structural errors, thereby paving the way for potential future applications in statistical post-processing. The structure scores are complemented by a newly developed location score — the first of its kind based on wavelets. Here, we exploit the complex nature of the chosen wavelet transform, which encodes spatial displacements in the phase of the coefficients. Unlike most existing measures of displacement errors, this approach requires no identification of discrete objects and is thus, in principle, applicable to fields like temperature and wind which may exhibit well defined location errors but no easily identifiable objects. This potential was demonstrated on a set of standardized test cases from the spatial verification community project MesoVICT. All of the results mentioned above have been shared with the research community in a series of open access publications and presented at a variety of international conferences. In addition, the software needed to apply our scores has been made publicly available via open source libraries written in the R programming language and uploaded to the official CRAN repository.

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