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An implementation of Hasselmann's paradigm for stochastic climate modelling based on stochastic Lie transport *

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Title: An implementation of Hasselmann's paradigm for stochastic climate modelling based on stochastic Lie transport *
Authors: Crisan, D
Holm, DD
Korn, P
Item Type: Journal Article
Abstract: A generic approach to stochastic climate modelling is developed for the example of an idealised Atmosphere-Ocean model that rests upon Hasselmann's paradigm for stochastic climate models. Namely, stochasticity is incorporated into the fast moving atmospheric component of an idealised coupled model by means of stochastic Lie transport, while the slow moving ocean model remains deterministic. More specifically the stochastic model stochastic advection by Lie transport (SALT) is constructed by introducing stochastic transport into the material loop in Kelvin's circulation theorem. The resulting stochastic model preserves circulation, as does the underlying deterministic climate model. A variant of SALT called Lagrangian-averaged (LA)-SALT is introduced in this paper. In LA-SALT, we replace the drift velocity of the stochastic vector field by its expected value. The remarkable property of LA-SALT is that the evolution of its higher moments are governed by deterministic equations. Our modelling approach is substantiated by establishing local existence results, first, for the deterministic climate model that couples compressible atmospheric equations to incompressible ocean equation, and second, for the two stochastic SALT and LA-SALT models.
Issue Date: Sep-2023
Date of Acceptance: 26-Jun-2023
URI: http://hdl.handle.net/10044/1/109006
DOI: 10.1088/1361-6544/ace1ce
ISSN: 0951-7715
Publisher: IOP Publishing
Start Page: 4862
End Page: 4903
Journal / Book Title: Nonlinearity
Volume: 36
Issue: 9
Copyright Statement: © 2023 IOP Publishing Ltd & London Mathematical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Publication Status: Published
Online Publication Date: 2023-08-03
Appears in Collections:Pure Mathematics
Applied Mathematics and Mathematical Physics
Mathematics



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