On the Deformation Term in the Quasigeostrophic Omega Equation

Abstract

It is a common diagnostic, synoptic practice to consider the Trenberth–Sutcliffe approximation to the quasigeostrophic (QG) omega equation, which relates upward vertical motion to regions of cyclonic vorticity advection by the thermal wind. Use of this approximate form of the QG omega equation requires the neglect of the so-called deformation term, which is often described as important only in frontal regions. Here, an alternative expression for the deformation term is derived that clearly illustrates its relationship to the mathematical forcing function in the Q-vector form of the QG omega equation. The magnitude of the deformation term in the middle troposphere is traced throughout the life cycle of a typical midlatitude cyclone. It is found that this term is generally small at midlevels in the early stages of the cyclone life cycle. As the cyclone approaches and passes its mature stage, however, the deformation term exerts a comparable, locally predominant influence on the total QG forcing for vertical motion. Particularly interesting is the large magnitude this term acquires in the axis of high potential temperature, characteristic of a post–mature stage cyclone’s horizontal thermal structure. The large magnitude of the deformation term in such regions demonstrates that there are nonfrontal, midtropospheric regions within cyclones in which the deformation term may not be small.