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https://doi.org/10.13140/RG.2.2.36204.37768
https://doi.org/10.13140/RG.2.2.36204.37768
28 Nov 2024
 | 28 Nov 2024
Status: this preprint is open for discussion.

Alignment of geophysical fields: a differential geometry perspective

Yicun Zhen, Valentin Resseguier, and Bertrand Chapron

Abstract. To estimate the displacements of physical state variables, the physics principles that govern the state variables must be considered. Technically, for a certain class of state variables, each state variable is associated to a tensor field. Ways displacement maps act on different state variables will then differ according to their associated different tensor field definitions. Displacement procedures can then explicitly ensure the conservation of certain physical quantities (total mass, total vorticity, total kinetic energy, etc.), and a differential-geometry-based optimisation formulated. Morphing with the correct physics, it is reasonable to apply the estimated displacement map to unobserved state variables, as long as the displacement maps are strongly correlated. This leads to a new nudging strategy using all-available observations to infer displacements of both observed and unobserved state variables. Using the proposed nudging method before applying ensemble data assimilation, numerical results show improved preservation of the intrinsic structure of underline physical processes.

Yicun Zhen, Valentin Resseguier, and Bertrand Chapron

Status: open (until 23 Jan 2025)

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Yicun Zhen, Valentin Resseguier, and Bertrand Chapron
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron

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Short summary
In a previous paper we made the conclusion that two different stochastic perturbation schemes can be derived under the same framework. The key is to associate each state variable a differential form. The perturbation of the state variables are thus consequences of the differential forms perturbed by a random map. A natural followup question is how to find the realizations of those random perturbations of identity map. An optimisation problem is proposed and further used for a nudging algorithm.