Diagnostic Equations in Isobaric Coordinates

Abstract

Diagnostic studies of the general circulation are conducted, almost exclusively, using data and equations where pressure is the vertical coordinate. The complexity of the lower boundary condition in these isobaric coordinates may lead to some ambiguity in the manner of calculating and displaying the pertinent diagnostic statistics and budget terms. A formalism is developed using the unit and delta functions which permits an unambiguous calculation of the appropriate diagnostic terms. Using this formalism, budget equations are derived which display a number of unfamiliar boundary terms. The more familiar budget equations are seen to be approximations to these more complete equations. Examples of some basic general circulation statistics involving temperature are used to illustrate the application of the formalism.