SAD: Verifying the scale, anisotropy and direction of precipitation forecasts

Abstract

One important attribute of meteorological forecasts is their representation of spatial structures. While several existing verification methods explicitly measure a structure error, they mostly produce a single value with no simple interpretation. Extending a recently developed wavelet‐based verification method, this study separately evaluates the predicted spatial scale, orientation and degree of anisotropy. The scale component has been rigorously tested in previous work and is known to assess the quality of a forecast similar to other, established methods. However, directional aspects of spatial structure are less frequently considered in the verification literature. Since important weather phenomena related to fronts, coastlines and orography have distinctly anisotropic signatures, their representation in meteorological models is clearly of interest. The ability of the new wavelet approach to accurately evaluate directional properties is demonstrated using idealized and realistic test cases from the MesoVICT project. A comparison of precipitation forecasts from several forecasting systems reveals that errors in scale and direction can occur independently and should be treated as separate aspects of forecast quality. In a final step, we use the inverse wavelet transform to define a simple post‐processing algorithm that corrects the structural errors. The procedure improves visual similarity with the observations, as well as the objective scores.

Verification of Near Surface Wind Patterns in Germany using Clear Air Radar Echoes

“…The idea of this study is to compare the correlation structures of the radar reflectivities and divergence fields, summarized in terms of scale, anisotropy and direction. To extract these properties from divergence and reflectivity images, we use the SAD methodology of Buschow and Friederichs (2021): The image to be analyzed is convolved with a series of localized 2D…”

“…The dual-tree complex wavelet transform (Selesnick et al, 2005) used in this study provides daughter wavelets with six orientations and up to J scales for an image of size 2 J × 2 J . Following Buschow and Friederichs (2021), the largest three scales are removed because their support is larger than the image, rendering their interpretation ambiguous. After spatial averaging, a radar image with 128 × 128 pixels is thus summarized by 4 × 6 values, the so-called wavelet spectrum.…”

“…For a detailed description of the calculation of these properties, as well as the details of the wavelet transform itself, we refer to Buschow and Friederichs (2021) and references therein. The software for this analysis is freely available in the open source dualtrees R-package (Buschow et al, 2020).…”

“…For a fair, quantitative validation of the model, the spatial patterns must be analyzed objectively. Here, we rely on the wavelet-based SAD verification methodology of Buschow and Friederichs (2021) which applies a series of directed filters to objectively determine the dominant spatial Scale, Anisotropy and Direction in an image. A closely related approach was used to define a wavelet-based index of convective organization in radar and satellite images by Brune et al (2021).…”

Verification of boundary layer wind patterns in COSMO-REA2 using clear-air radar echoes

“…For a fair, quantitative validation of the model, the spatial patterns must be analyzed objectively. Here, we rely on the wavelet-based scale, anisotropy, and direction (SAD) verification methodology of Buschow and Friederichs (2021), which applies a series of directed filters to objectively determine the dominant spatial scale, anisotropy, and direction in an image. A closely related approach was used to define a wavelet-based index of convective organization in radar and satellite images by Brune et al (2021).…”