An idealized 1.5-layer isentropic model with convection and precipitation for satellite data assimilation research. Part II: model derivation

In this part II paper we present the analytical derivation of the isentropic 1.5-layer shallow water model described and used in part I of this study. The mathematical derivation presented here is based on a combined asymptotic and slaved Hamiltonian analysis. The scaling assumptions throughout the paper are supported by real observations based on radiosonde data. Eventually, a fully consistent isentropic 1.5-layer model emerges from imposing fluid at rest and zero Montgomery potential in the upper layer of an isentropic two-layer model.