Spatial Verification with Wavelets

Abstract

Modern numerical weather prediction models can simulate atmospheric processes at a resolution of single kilometers. With growing complexity, the realism of these simulations becomes increasingly difficult to quantify. Simply put, more details also leave more room for diverse kinds of errors, especially in the hardly predictable locations of small-scaled features. Traditional scores that compare forecast and observation grid-point by grid-point tend to prefer smoother, less detailed predictions and fail to appraise the realism of the simulated spatial structure. This thesis explores novel verification methods based on image filters, which isolate components at individual spatial scales and locations. These so-called textit{wavelets} are widely used in image processing and computer vision. In the context of meteorological forecast verification, wavelets were previously employed to remove noise, or split up the overall error into small- and large-scale contributions. Pursuing a different direction, this study demonstrates how wavelets can extract specific information about the scale-structure, directedness and preferred orientation of the fields to be compared. The result is a series of scores which translate the abstract information resulting from the wavelet transform into robust, easily interpretable statements about the realism of the simulated correlation structure. Directional aspects in particular -- predicted features being too linear, too round or oriented at the wrong angle -- are not explicitly treated by most existing verification tools. In addition, it is shown how the wavelets' localized nature can be exploited to visualize the local correlation structure on a map, quantify spatially varying displacements, or correct structural errors in a simple post-processing algorithm. Unlike other popular approaches in the literature, the new techniques are not limited to the special case of precipitation verification. Provided that observations on a regular grid exist, wavelet-based scores can, in principle, be applied to any meteorological field of interest.