Bokhove, O, Cantarello, L orcid.org/0000-0002-1005-8463 and Tobias, S (2022) An Idealized 1½-Layer Isentropic Model with Convection and Precipitation for Satellite Data Assimilation Research. Part II: Model Derivation. Journal of the Atmospheric Sciences, 79 (3). pp. 875-886. ISSN 0022-4928
Abstract
In this Part II paper we present a fully consistent analytical derivation of the “dry” isentropic 1½-layer shallow-water model described and used in Part I of this study, with no convection and precipitation. The mathematical derivation presented here is based on a combined asymptotic and slaved Hamiltonian analysis, which is used to resolve an apparent inconsistency arising from the application of a rigid-lid approximation to an isentropic two-layer shallow-water model. Real observations based on radiosonde data are used to justify the scaling assumptions used throughout the paper, as well as in Part I. Eventually, a fully consistent isentropic 1½-layer model emerges from imposing fluid at rest (v₁ = 0) and zero Montgomery potential (M₁ = 0) in the upper layer of an isentropic two-layer model.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 American Meteorological Society. See https://www.ametsoc.org/PUBSReuseLicenses for further information. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Data assimilation; Nonlinear models; Primitive equations model; Shallow-water equations; Idealized models |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Dec 2021 12:51 |
Last Modified: | 25 Jun 2023 22:50 |
Status: | Published |
Publisher: | American Meteorological Society |
Identification Number: | 10.1175/JAS-D-21-0023.1 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:181182 |