论文标题
在瓦斯坦的空间上的集合利曼数据同化
Ensemble Riemannian Data Assimilation over the Wasserstein Space
论文作者
论文摘要
在本文中，我们在配备了Wasserstein度量的Riemannian歧管上提出了一个集合数据同化范式。与欧几里得空间中的欧拉（Eulerian）对误差的惩罚不同，Wasserstein指标可以捕获背景状态的正方形概率分布和观察值的平方综合概率分布之间的翻译和差异，从而使状态空间中具有非高斯分布的状态空间中的地球物理偏见正式惩罚。与经典的变化和过滤数据同化方法相比，新方法应用于耗散和混乱的进化动力学及其潜在的优势和局限性。
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.
