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

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.

Journal article(s) based on this preprint

29 Jun 2023
Physically constrained covariance inflation from location uncertainty
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron
Nonlin. Processes Geophys., 30, 237–251, https://doi.org/10.5194/npg-30-237-2023,https://doi.org/10.5194/npg-30-237-2023, 2023
Short summary
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-416', Daniel Goodair, 09 Apr 2023
  • RC2: 'Comment on egusphere-2023-416', Baylor Fox-Kemper, 21 Apr 2023
  • AC1: 'Comment on egusphere-2023-416', Yicun Zhen, 13 May 2023
  • AC2: 'Comment on egusphere-2023-416', Yicun Zhen, 13 May 2023

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-416', Daniel Goodair, 09 Apr 2023
  • RC2: 'Comment on egusphere-2023-416', Baylor Fox-Kemper, 21 Apr 2023
  • AC1: 'Comment on egusphere-2023-416', Yicun Zhen, 13 May 2023
  • AC2: 'Comment on egusphere-2023-416', Yicun Zhen, 13 May 2023

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload
AR by Yicun Zhen on behalf of the Authors (13 May 2023)  Author's response   Author's tracked changes   Manuscript 
ED: Publish as is (23 May 2023) by Jinqiao Duan
AR by Yicun Zhen on behalf of the Authors (25 May 2023)

Journal article(s) based on this preprint

29 Jun 2023
Physically constrained covariance inflation from location uncertainty
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron
Nonlin. Processes Geophys., 30, 237–251, https://doi.org/10.5194/npg-30-237-2023,https://doi.org/10.5194/npg-30-237-2023, 2023
Short summary
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron

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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.