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Paul A. Hirschberg
and
J. Michael Fritsch

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.

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Paul A. Hirschberg
and
J. Michael Fritsch

Abstract

A new five-layer, quasigeostrophic model of baroclinic development is utilized to examine the initial-value problem sensitivity of extratropical cyclogenesis to the variation of stratospheric thermal and geopotential configurations associated with tropopause undulations. Previous studies have suggested that such undulations or potential vorticity anomalies can influence both the structure and evolution of lower-tropospheric cyclones. A series of experiments with the five-layer model are performed to evaluate the sensitivity of the model height, vertical motion, and height tendency patterns to various stratospheric temperature and geopotential distributions. It is found that idealized tropospheric baroclinic systems do not show typically observed characteristics unless certain stratospheric temperature, geopotential, and wind anomaly configurations associated with tropopause undulations are present. Furthermore, for given tropospheric patterns, there are particular lower-stratospheric configurations that optimize the development of model lower-tropospheric cyclones. These stratospheric configurations are functions of 1) the value of the lower-stratospheric temperature anomaly, 2) the amplitude of the tropopause undulation, and 3) the horizontal location of the undulation relative to the tropospheric temperature anomalies. Finally, both the rate of cyclogenesis and the amplification of the tropopause undulation increase if tropospheric static stability is reduced.

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