American Meteorological Society, Journal of the Atmospheric Sciences, 3(79), p. 875-886, 2022
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AbstractIn 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.