## Joint Centre for Mesoscale Meteorology (JCMM)

**JCMM Internal Report No.95:**

*The semigeostrophic diagnosis of vertical motion. Part II: Results for an idealised baroclinic wave life cycle*

by Alan J Thorpe and Mike A Pedder

In this paper we apply the method of solution of the semigeostrophic *(SG)* omega equation developed in Part I to data generated from a numerical simulation of an idealised dry adiabatic frictionless baroclinic wave life cycle. The aim is to compare quantitatively the quasigeostrophic *(QG)* and SG solutions for the vertical motion and to relate these to the model vertical motion field. This comparison allows an evaluation of how practical, and accurate, it would be to use such balance theories to estimate vertical motion from atmospheric data. It is found that the QG solution tends to overestimate both ascent and descent in the cyclone. This overestimation is due both to an overestimation of the forcing and to a poor treatment of the large horizontal gradients of static stability produced as the tropopause descends near the cyclone centre. As the SG theory more faithfully represents the Ertel-Rossby potential vorticity *(PV)*, the vertical motion which is implied by this distribution of PV is also quantitatively more similar to the model vertical motion than that produced by the QG theory. The PV distribution affects the vertical motion via the forcing and via explicit account of horizontal gradients of the local static stability distribution which appear in the differential operator in the omega equation. The residual between the vertical motion predicted by the SG, or any other balance, theory and that given by the model is produced partly by any intertia-gravity wave activity and partly by inaccuracies in the assumed balance condition.