Ensemble Riemannian Data Assimilation over the Wasserstein Space

Abstract:

In this paper, we present a new ensemble data assimilation (DA) paradigm over Riemannian manifolds equipped with the Wasserstein metric – namely Ensemble Riemannian DA, whereby optimal mass transport theory promises to extend the geophysical forecast skills under non-Gaussian state-spaces and systematic errors. The Wasserstein metric is geodesic and thus enables assimilation in a space of sufficiently smooth probability distributions with finite second-order moments, leading to full recovery of non-Gaussian forecast probability distributions. Unlike Eulerian penalization of error in the Euclidean space, the Wasserstein metric can capture the translation of probability measures, enabling to formally penalize geophysical biases. The new approach is applied to dissipative and chaotic evolutionary dynamics with a wide range of applications in Earth system models. Its advantages over classic variational and particle filter techniques are documented under systematic errors and non-Gaussian state-spaces.