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 article, 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.由不同数值模式模拟生成的集合预报数据集，可为气象学者提供降水云团等即将发生天气过程的丰富研判信息。一类核心预报形式会呈现由多个集合成员生成的云图。从这些云图中提取的共性特征常被用作整个集合预报的一致性预测结果，而云图间的差异则反映了预报的不确定性。然而，云图数量庞大且彼此间可能存在极高的异质性，给决策研判带来了认知层面的挑战。本文针对云图表征的集合预报，开发了全新的汇总方法，并将其统一命名为几何敏感集合平均（Geometry-Sensitive Ensemble Mean, GEM）工具包。传统的逐像素平均或基于特征的平均方法，要么会丢失有价值的几何信息，要么仅局限于针对预先选定的待预报云团特征进行处理。在GEM工具包中，我们采用高斯混合模型（Gaussian Mixture Model, GMM）对云团模拟结果进行表征，可在无需施加额外特殊假设的前提下，有效捕捉云团的形态特征。此外，借助当前前沿的优化算法，我们针对一组概率分布实体计算瓦瑟斯坦重心（Wasserstein barycenter），该重心可被视为瓦瑟斯坦度量（Wasserstein metric）下的一致性均值或质心。本文给出了针对两组集合模拟云图的实验结果。本文的补充材料可在线获取。