An analytical exericise to elucidate quasi-geostrophic frontogenesis

Abstract

Frontogenesis is frequently described by theQ-vector (Hoskins et al., 1978), a term being composed of several derivatives of basic meteorological parameters and their products. Its distribution and especially the ∇ H ·Q-fields are highly important to estimate frontogenesis and cross frontal circulation. Although theQ-vector (Hoskins et al., 1978) allows an easier assessment of the vertical wind forcing than the original omega equation of the quasi-geostrophic theory, it is still difficul to imagine the three-dimensional (3-d) spatial distribution ofQ and ∇ H ·Q even for standard atmospheric fields. Thus there is a need to shed more light in theQ and ∇ H ·Q-fields for special synoptic situations. This is done here by constructing analytical 3-d geostrophically balanced wind-and temperature fields, for which theQ-forcing (Qformed with the geostrophic wind) can easily be computed and presented. Three examples (see Sections 3 to 5) are discussed yielding typical and realistic (compared to known pattern) 3-d forcing distributions ofQ and ∇ H ·Q. Within the simple analytical scheme used here their origin can casily be understood. These fields of a 2000×2000 km2 horizontal domain ranging up to 250 hPa are: A modified Bergeron deformation field containing a cold front (case I a) and a warm front (case I b); an upper tropospheric jet including a jet-parallel transition zone between warm and cold air (case II); and a circular low pressure circulation pattern with two fronts (case III). The paper presents these 3-d fields with the advantage that the analytical method is not affected by any kind of limited numerical resolution. It also shows how these fields degenerate with decreasing resolution if the analytical data are used in descrete form. This simulates working with discrete numerical data and demonstrates how narrow frontal zones of structure elements ofQ and ∇ H ·Q considerably smooth out with increasing grid distances.