Preprints
https://doi.org/10.13140/RG.2.2.18433.53603
https://doi.org/10.13140/RG.2.2.18433.53603
09 Mar 2023
 | 09 Mar 2023
Status: this preprint is open for discussion.

Physically Constrained Covariance Inflation from Location Uncertainty

Yicun Zhen, Valentin Resseguier, and Bertrand Chapron

Abstract. Motivated by the concept of "location uncertainty", initially introduced in Mémin (2014), a scheme is sought to perturb the "location" of a state variable at every forecast time step. Further considering Brenier's theorem Brenier (1991), 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 Holm (2015) and LU Mémin (2014); 5 Resseguier et al. (2016) 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.

Yicun Zhen et al.

Status: open (until 04 May 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Yicun Zhen et al.

Yicun Zhen et al.

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Short summary
This manuscript provides with the perspective that the displacement vector field of physical state fields should be determined by the tensor fields associated to the physical fields. The advantage of this perspective is that certain physical quantities can be conserved while applying a displacement vector field to transfer the original physical field. A direct application90of this perspective is the physically constrained covariance inflation scheme proposed in this manuscript.