An Analytic Five-Layer Quasigeostrophic Model for Initial-Value Problems

Abstract

A five-layer analytic model of quasigeostrophic flow is developed. The model provides exact analytic solutions to the nonlinear quasigeostrophic omega and vorticity equations for various atmospheric temperature and geopotential structures. These solutions yield instantaneous three-dimensional fields of vertical motion and geopotential tendency given some finite-amplitude flow. Hence, unlike traditional eigenvalue analyses that provide time-dependent solutions for simple linearized flows, the five-layer model yields nonlinear diagnostic solutions to initial-value problems. It is demonstrated that the five-layer model can reproduce many of the disturbance characteristics that are deduced from more traditional analyses of baroclinic instability. It is also shown that, because of its flexible vertical temperature structure specification, it can simulate complex temperature and geopotential structures in the atmosphere. The flexible specification of the total temperature and geopotential structure makes the five-layer model an attractive means for comparing theory with observations. Additionally, the versatility and simplicity of the five-layer model make it a potentially useful research and pedagogical tool.