Constrained isentropic models of tropospheric dynamics

A two-layer isentropic model consisting of a tropospheric and a stratospheric layer is simplified using perturbation analysis while preserving the Hamiltonian structure. The first approximation applies when the thickness of the stratospheric layer is much larger than the tropospheric layer, such that the Froude number of the stratospheric layer is a small number. Using leading-order perturbation theory in the Hamiltonian formulation yields a conservative one-and-a-half isentropic layer model. Furthermore, when the Rossby number in this active lower layer is small, Hamiltonian theory either directly leads to (Salmon's) L1-dynamics using a geostrophic constraint, following a more concise derivation than shown before, or yields quasigeostrophic dynamics. The extension to multilayer isentropic balanced models for use in idealized climate forecasting is discussed.