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In this paper, we present an ensemble data assimilation paradigm over aRiemannian manifold equipped with the Wasserstein metric. Unlike the Eulerianpenalization of error in the Euclidean space, the Wasserstein metric cancapture translation and difference between the shapes of square-integrableprobability distributions of the background state and observations -- enablingto formally penalize geophysical biases in state-space with non-Gaussiandistributions. The new approach is applied to dissipative and chaoticevolutionary dynamics and its potential advantages and limitations arehighlighted compared to the classic variational and filtering data assimilationapproaches under systematic and random errors.

Ensemble Riemannian Data Assimilation over the Wasserstein Space