Abstract
Abstract. 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.
Highlights
Extending the forecast skill of Earth system models (ESMs) relies on advancing the science of data assimilation (DA) (Tsuyuki and Miyoshi, 2007; Carrassi et al, 2018)
Apart from particle filters (Spiller et al, 2008; Van Leeuwen, 2010), which are intrinsically designed for state space with a non-Gaussian distribution, numerous modifications to the variational DA (VDA) and ensemblebased filtering methods have been made to tackle the non-Gaussianity of geophysical processes (Pires et al, 1996; Han and Li, 2008; Mandel and Beezley, 2009; Anderson, 2010)
We introduced an ensemble data assimilation (DA) methodology over a Riemannian manifold, namely ensemble Riemannian DA (EnRDA), and illustrated its performance in comparison with other ensemble-based DA techniques for dissipative and chaotic dynamics
Summary
Extending the forecast skill of Earth system models (ESMs) relies on advancing the science of data assimilation (DA) (Tsuyuki and Miyoshi, 2007; Carrassi et al, 2018). Non-Gaussian statistical models often form geometrical manifolds, which is a topological space that is locally Euclidean. Inspired by the theories of optimal mass transport (Villani, 2003), this paper presents the ensemble Riemannian data assimilation (EnRDA) framework using the Wasserstein metric or distance, which is a distance function defined between probability distributions, as explained in detail in Sect. Feyeux et al (2018) suggested a novel approach employing the Wasserstein distance in lieu of the Euclidean distance to penalize the position error between state and observations. (c) The paper studies the advantages and limitations of DA over the Wasserstein space for dissipative advection–diffusion dynamics and a nonlinear chaotic Lorenz-63 model in comparison with the well-known ensemble-based methodologies.
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