g where we have used hydrostatic balance, Eq. 3-3. So the mass of an elemental fixed volume in pressure coordinates cannot change! In effect, comparing the top and bottom line of the previous equation, the equivalent of "density" in pressure coordinates—the mass per unit "volume"—is 1/g, a constant. Hence, in the pressure-coordinate version of the continuity equation, there is no term representing rate of change of density; it is simply

Vp ■ up =—+—+—= 0, (6-12) H F dx dy dp where the subscript p reminds us that we are in pressure coordinates. The greater simplicity of this form of the continuity equation, as compared to Eqs. 6-9 or 6-10, is one of the reasons why pressure coordinates are favored in meteorology.

is conserved. Written in terms of 0, Eq. 6-13 becomes

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