Frontogenesis in the Presence of Small Stability to Slantwise Convection

It is often observed that, despite the existence of near neutrality to slantwise convection, rainbands and snowbands can persist for long periods with narrow intense updrafts producing large quantities of precipitation in many cases. This is probably due to the presence of active frontogenesis which, as shown here, maintains such structures. In order to investigate this process, we use two-dimensional semigeostrophic theory to solve the deformation-forced frontogenesis problem for a circumstance in which the stability to moist slantwise convection is small but positive. In this case, numerical simulation is necessary to determine the evolution of the front. Several previous studies have described the role of diabatic forcing in modifying the cross-frontal circulation by use of the Sawyer-Eliassen equation. In particular, analytic solutions of that equation for the case of small moist symmetric stability show that a narrow updraft should occur ahead of the maximum geostrophic frontogenesis. Numerical solutions to the time-dependent problem are described in this paper it is apparent that the latent heat release produces significant sources and sinks of potential vorticity which lead to a sharp increase in the rate of surface frontogenesis. As shown by previous diagnostic solutions, the scale of the ascent is considerably reduced and there is descent at midlevels in the frontal region where ascent would occur in the absence of condensation. However, the surface maxima of vorticity and ageostrophic convergence are only slightly displaced toward the warm air. Due to the increased rate of frontogenesis and the local variations in potential vorticity, the geostrophic flow is weakly modified. The variations in potential vorticity along isentropes produced by the slantwise convection could lead to the growth of a (secondary) internal baroclinic/barotropic instability, which may explain the tendency for frontal precipitation bands to become wavelike in the “along-front” direction. Such an instability cannot be described in the present two-dimensional numerical model but should be investigated further using a more appropriate model. It is also shown that the growth of the baroclinic wave in which such frontogenesis is assumed to occur is increased by the presence of the diabatic forcing. This is done by solving the Eady problem assuming small stability to slantwise convection. In addition to an increased growth rate, the wave of maximum growth has a smaller horizontal scale.