An idealized 1½-layer isentropic model with convection and precipitation for satellite data assimilation research. Part II: model derivation

Abstract

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.