Physically Constrained Covariance Inflation from Location Uncertainty

Yicun Zhen; Valentin Resseguier; Bertrand Chapron

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arXiv · 2211.04207

Physically Constrained Covariance Inflation from Location Uncertainty

Yicun Zhen·Valentin Resseguier·Bertrand Chapron

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Abstract

Motivated by the concept of ``location uncertainty", initially introduced in \cite{Memin2013FluidFD}, a scheme is sought to perturb the ``location" of a state variable at every forecast time step. Further considering Brenier's theorem \cite{Brenier1991}, asserting that the difference of two positive density fields on the same domain can be represented by a transportation map, perturbations are demonstrated to consistently define a SPDE from the original PDE. It ensues that certain quantities, up to the user, are conserved at every time step. Remarkably, derivations following both the SALT \cite{Holm2015VariationalPF} and LU \cite{Memin2013FluidFD, Resseguier2016GeophysicalFU} settings, can be recovered from this perturbation scheme. Still, it opens broader applicability since it does not explicitly rely on Lagrangian mechanics or Newton's laws of force. For illustration, a stochastic version of the thermal shallow water equation is presented.

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Yicun Zhen, Valentin Resseguier, Bertrand Chapron. 2022-11-08. Physically Constrained Covariance Inflation from Location Uncertainty. https://arxiv.org/abs/2211.04207

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