Applications of the Geometry-Sensitive Ensemble Mean for Lake-Effect Snowbands and Other Weather Phenomena

Ensembles of predictions are critical to modern weather forecasting. However, visualizing ensembles and their means in a useful way remains challenging. Existing methods of creating ensemble means do not recognize the physical structures that humans could identify within the ensemble members; therefore, visualizations for variables such as reflectivity lose important information and are difficult for human forecasters to interpret. In response, the authors create an improved ensemble mean that retains more structural information. The authors examine and expand upon the object-based Geometry-Sensitive Ensemble Mean (GEM) defined by Li and Zhang from a meteorological perspective. The authors apply low-intensity thresholding to WRF-simulated radar reflectivity images of lake-effect snowbands, tropical cyclones, and severe thunderstorms and then process them with the GEM system. Gaussian mixture model-based signatures retain the geometric structure of these phenomena and are used to compute a Wasserstein barycenter as the centroid for the ensemble; D2 clustering is employed to examine different scenarios among the ensemble members. Three types of ensemble mean image are created from the centroid of the ensemble or cluster, which each improve upon the traditional pixel-wise average in different ways, successfully capture aspects of the ensemble members' structure, and have potential applications for future forecasting efforts. The adjusted best member is a better representative member, the Bayesian posterior mean is an improved structure-based weighted average, and the mixture density mean is an outline of the key structures in the ensemble. Each is shown to improve upon a simple arithmetic mean via quantitative comparison with observations.