Abstract. In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Eulerian penalization of error in the Euclidean space, the Wasserstein metric can capture translation and difference between the shapes of square-integrable probability distributions of the background state and observations – enabling to formally penalize geophysical biases in state-space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics and its potential advantages and limitations are highlighted compared to the classic variational and filtering data assimilation approaches under systematic and random errors.

中文翻译：

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Wasserstein空间上的集合黎曼数据同化

摘要。在本文中，我们介绍了配备Wasserstein度量的黎曼流形上的整体数据同化范例。与欧氏空间误差的欧拉罚分法不同，Wasserstein度量可以捕获背景状态和观测值的平方可积概率分布的形状之间的平移和差异，从而能够以非高斯分布形式对状态空间中的地球物理偏差进行正式罚分。 。将该新方法应用于耗散和混沌的演化动力学，并与系统和随机误差下的经典变分和滤波数据同化方法相比，突出了其潜在的优势和局限性。