The pressure tendency at the bottom of an air column that extends from the level where the pressure is 850 mb to the tropopause where the pressure is 250 mb is given as
where the Pressure Tendency Equation has been simplified by the boundary condition w2 = 0 at the tropopause.
Equation (1) states that the change in pressure observed at the bottom of a slab of air of thickness dp is due to the net horizontal divergence in/out of the slab modified by the amount of mass being brought in through the bottom of the slab. In this case, the top of the slab is the top of the troposphere and the bottom is at the surface, at which level the pressure is 850 mb. See Fig. 1.
Figure 1: Conceptual setup of problem
Fig 2: Observed 3 h pressure tendencies, 12 UTC 22 October 2004