Ensemble Riemannian Data Assimilation over the Wasserstein Space

TL;DR

This paper introduces an ensemble data assimilation method on a Riemannian manifold using the Wasserstein metric, effectively capturing shape differences in probability distributions for improved geophysical state estimation.

Contribution

It proposes a novel Wasserstein-based data assimilation framework on Riemannian manifolds, addressing non-Gaussian distribution biases in geophysical models.

Findings

Effective in dissipative and chaotic dynamics

Captures shape differences in probability distributions

Compared favorably to classic methods

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.