__Problem
1__

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

* ** *(1)

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