Geometry-Sensitive Ensemble Mean based on Wasserstein Barycenters: Proof-of-Concept on Cloud Simulations

An ensemble of forecasts generated by different model simulations provides rich information for meteorologists about impending weather such as precipitating clouds. One major form of forecasts presents cloud images created by multiple ensemble members. Common features identified from these images are often used as the consensus prediction of the entire ensemble, while the variation among the images indicates forecast uncertainty. However, the large number of images and the possibly tremendous extent of dissimilarity between them pose cognitive challenges for decision making. In this paper, we develop novel methods for summarizing an ensemble of forecasts represented by cloud images and call them collectively the <i>Geometry-Sensitive Ensemble Mean</i> (GEM) toolkit. Conventional pixel-wise or feature-based averaging either loses interesting geometry information or focuses narrowly on some pre-chosen characteristics of the clouds to be forecasted. In GEM, we represent a cloud simulation by a Gaussian mixture model, which captures cloud shapes effectively without making special assumptions. Furthermore, using a state-of-the-art optimization algorithm, we compute the Wasserstein barycenter for a set of distributional entities, which can be considered as the consensus mean or centroid under the Wasserstein metric. Experimental results on two sets of ensemble simulated images are provided. Supplemental materials for the article are available online.