Baroclinic Instability in an Environment of Small Stability to Slantwise Moist Convection. Part I: Two-Dimensional Models

In the semigeostrophic system, the growth rate of baroclinic waves varies with the inverse square root of the potential vorticity, which acts as the effective static stability. Recent observations in the ascent regions of middle latitude cyclones show that the effective potential vorticity for saturated air is very near zero. In this paper we examine the structure and rate of growth of baroclinic cyclones when the effective potential vorticity is small for upward (saturated) displacements but large in regions of descent. Analytic solutions for two-dimensional disturbances in a two-layer semigeostrophic model and numerical simulations using a multilevel semigeostrophic model show that when the effective potential vorticity is small in regions of upward motion, growth rates are modestly increased and the region of ascent intensifies and collapses onto a thin ascending sheet. In the limit of zero moist potential vorticity the fastest growing wave has a finite growth rate which is about 2.5 times the dry value while the horizontal scale is reduced by a factor of about 0.6 compared to the dry modes. The asymmetry associated with condensation heating leads to frontal collapse first at the surface, rather than at both boundaries as in the dry case. In contrast to the analytic model, the numerical simulations allow the effect of (dry) potential vorticity evolution due to the latent heat release to be included. The anomalies of potential vorticity are advected horizontally through the wave, enhancing the low-level and diminishing the upper-level cyclonic vorticity and static stability in both the saturated and unsaturated regions of the flow.