Physically Constrained Covariance Inflation from Location Uncertainty
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.
Cite
@article{arxiv.2211.04207,
title = {Physically Constrained Covariance Inflation from Location Uncertainty},
author = {Yicun Zhen and Valentin Resseguier and Bertrand Chapron},
journal= {arXiv preprint arXiv:2211.04207},
year = {2023}
}