Surface Frontogenesis in Isentropic Coordinates

Abstract

The semigeostrophic equations take a particularly simple form when isentropic and geostrophic coordinates are used simultaneously: the horizontal ageostrophic velocities are entirely implicit, and the entire dynamics reduces to a predictive equation for the potential pseudodensity (inverse Ertel potential vorticity) and an invertibility relation. However, a perceived disadvantage of isentropic coordinates is the difficulty of treating a lower boundary that is not an isentropic surface. Here we present the massless layer method, which allows isentropic surfaces to intersect the lowerboundary, and show that this extends the applicability of potential vorticity modeling in isentropic/geostrophic coordinates. When applied to the classic problem of surface frontogenesis by a vertically independent deformation field, the model produces realistic fronts with a surface discontinuity in finite time and tropopause folding, without the need for special treatment of the lower boundary.