Translation of Balanced Air Mass Models of Fronts and Associated Surface Pressure Changes

The problem of explaining the surface pressure rise in simple balanced models of fronts, discussed at length by Sutcliffe, is reexamined. It is shown that air mass models for steadily translating fronts (including the Margules' front) are dynamically consistent, except along a vertical line above the surface front, only if there is vertical motion (subsidence for a cold front, ascent for a warm front) in the warm air that overlies the cold air. In this case, the local post-frontal pressure rise in a model cold front and the pre-frontal pressure fall in a model warm front can be attributed to advection. However, the presence of the vertical motion is a limiting factor in the applicability of such models. The analysis resolves an apparent inconsistency between the surface pressure changes computed in Boussinesq models and the prediction of a theorem of Brunt. Irrespective of the Boussinesq approximation, it is shown that, in the model, the surface pressure change at any fixed location bears no relation to the variation of surface pressure normal to the front at any given instant. This would imply that it is inappropriate to infer space cross-sections of pressure from observed time series at a single station, even for a steadily translating front. The result highlights a further limitation of balanced air mass models when applied to fronts in the atmosphere.