In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the translation and difference between the shapes of square-integrable probability distributions of the background state and observations. This enables us 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 ensemble data assimilation approaches under systematic errors.

中文翻译：

---

Wasserstein 空间上的集合黎曼数据同化

在本文中，我们在配备了 Wasserstein 度量的黎曼流形上提出了一个集成数据同化范式。与经典数据同化方法中使用的欧几里德距离不同，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。这使我们能够以非高斯分布形式惩罚状态空间中的地球物理偏差。将新方法应用于耗散和混沌进化动力学，与系统误差下的经典集合数据同化方法相比，它的潜在优势和局限性得到了突出。