Abstract. Small forecast ensemble sizes (< 100) are common in the ensemble data assimilation (EnsDA) component of geophysical forecast systems, thus limiting the error-constraining power of EnsDA. This study proposes an efficient and embarrassingly parallel method to generate additional ensemble members: the Probit-space Ensemble Size Expansion for Gaussian Copulas (PESE-GC; "peace gee see"). Such members are called "virtual members". PESE-GC utilizes the users' knowledge of the marginal distributions of forecast model variables. Virtual members can be generated from any (potentially non-Gaussian) multivariate forecast distribution that has a Gaussian copula. PESE-GC's impact on EnsDA is evaluated using the 40-variable Lorenz 1996 model, several EnsDA algorithms, several observation operators, a range of EnsDA cycling intervals and a range of forecast ensemble sizes. Significant improvements to EnsDA (p < 0.01) are observed when either 1) the forecast ensemble size is small (≤20 members), 2) the user selects marginal distributions that improves the forecast model variable statistics, and/or 3) the rank histogram filter is used with non-parametric priors in high forecast spread situations. These results motivate development and testing of PESE-GC for EnsDA with high-order geophysical models.

中文翻译：

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通过高斯 Copulas 的概率空间集合大小扩展 (PESE-GC) 改进集合数据同化

摘要。小预报集合规模（< 100）在地球物理预报系统的集合数据同化（EnsDA）组件中很常见，从而限制了 EnsDA 的误差约束能力。这项研究提出了一种高效且令人尴尬的并行方法来生成额外的集成成员：高斯 Copulas 的概率空间集成大小扩展（PESE-GC；“peace gee see”）。这样的成员被称为“虚拟成员”。PESE-GC 利用用户对预测模型变量边际分布的了解。虚拟成员可以从任何具有高斯联结函数的（可能是非高斯的）多元预测分布生成。PESE-GC 对 EnsDA 的影响是使用 40 变量 Lorenz 1996 模型、多种 EnsDA 算法、多种观测算子、一系列 EnsDA 循环间隔和一系列预测集合大小来评估的。当 1) 预测集合规模较小（≤20 个成员），2) 用户选择改进预测模型变量统计的边际分布，和/或 3) 排名直方图时，可以观察到 EnsDA 的显着改进 (p < 0.01 )在高预测传播情况下，滤波器与非参数先验一起使用。这些结果激励使用高阶地球物理模型为 EnsDA 开发和测试 PESE-GC。