A Comparison between the Hoskins-Bretherton Model of Frontogenesis and the Analysis of an Intense Surface Frontal Zone

Abstract

The Hoskins-Bretherton model of frontogenesis employed here represents the counterpart of the two-dimensional Eady problem expressed in geostrophic coordinate space. The fundamental characteristics of the model solution are shown to be derivable from the properties of the nonlinear one-dimensional advection equation and the linearized Eady problem. Detailed comparisons are made between the predictions of this model and the analysis of an intense frontal zone presented by Sanders. Qualitative agreement is found in details of the horizontal wind field and potential temperature distributions. The major discrepancy occurs in the vertical velocity field: the most intense vertical velocities occur at midlevel in the model and are significantly smaller in magnitude than the rising narrow jet above the analyzed zone of maximum cyclonic relative vorticity. The presence of this jet is responsible for the most significant frontogenetical properties of the front associated with vertical tilting of potential isotherms and isopleths of the horizontal velocity component parallel to the frontal zone. In contrast, ageostrophic convergence and horizontal distortion of potential isotherms make the largest contribution to frontogenesis in the model. Ekman-layer pumping is introduced into the model to simulate the vertical velocity jet. Yet this feature is not sufficient to increase the contribution of vertical tilting to frontogenesis because the vertical gradients of potential temperature and geostrophic velocity are weaker in this case. Trajectories of the air motion tend to show the pattern of upgliding warm air ahead of the frontal zone with relatively stagnant cold air to the rear. In general, the model is able to provide qualitative agreement with gross features of this frontal situation. Discrepancies seem to be associated with the absence of a realistic boundary layer formulation and mesoscale mixing processes in the model.