MECHANISM OF PRESSURE CHANGE 
effect of the deviations from the gradient wind upon 
the surface pressure field. It seems evident that only 
limited conclusions concerning the pressure-change 
process can be drawn from an analysis which specifies 
a particular type of wind field. Nevertheless this type 
of approach gives valuable information on the impor- 
tance of the various parts of the wind field and, there- 
fore, aids in establishing an internally consistent picture 
of the field of motion with a field of pressure change. 
Vorticity Studies 
The density changes which lead to a change in mass 
in an atmospheric column invariably involve the wind 
field as illustrated by equation (2). A transformation 
of the horizontal equations of motion leads, with a few 
simplifying assumptions, to a vorticity equation 
1 d 
sig et, (6) 
where V, ¢, and ) are the horizontal velocity vector, 
the vertical component of vorticity, and the Coriolis 
parameter, respectively. Although equation (6) does not 
directly refer to pressure change, it plays an important 
role in pressure-change research because it expresses 
certain relationships which must be satisfied by the 
wind field. For example, if a hypothesis specifies hori- 
zontal divergence in the upper troposphere, then vor- 
ticity changes consistent with equation (6) should occur 
in this region. 
Consequently, such a vorticity equation and the pres- 
sure tendency equations together provide a means for 
testing the validity of a theory of pressure change. 
However, like the pressure tendency equations, equa- 
tion (6) does not lead directly to an explanation of the 
mechanism of pressure change. 
An ever-present difficulty in all wind studies is the 
lack of a dense network of reliable wind observations, 
particularly above 10,000 ft. Consequently, most studies 
of vorticity change have been based upon some assumed 
wind field such as a geostrophic wind field [28]. In all 
likelihood, the vorticity of the geostrophic wind differs 
from the vorticity of the actual wind and this difference 
may well be large in a region of active pressure change. 
Since equation (6) is a powerful tool for testing pressure 
change theories it seems desirable that additional re- 
search be conducted on the vorticity field and its 
changes. 
div. V = —_— 
Thermal Theory of Pressure Change 
Several aspects of a thermal explanation of pressure 
change will now be considered. This elaboration of a 
thermal approach is undertaken because the theory has 
the advantage of a simple physical picture and because 
it appears to be as well developed as other theories of 
pressure change. 
Nonadiabatic Temperature Changes. The significant 
aspects of the thermal theory of pressure change may 
pe demonstrated by means of a simple model. Consider 
a mass of air above the earth’s surface, BCNM in Fig. 
la, and let the air be heated uniformly from 1000 mb 
to 600 mb. As a consequence of the heating all the pres- 
sure surfaces above BC are raised. This expansion is not 
633 
accompanied by adiabatic temperature changes insofar 
as there is no change in pressure on individual air par- 
ticles. The heating then creates a pressure gradient to 
accelerate air out of the column above BC. The vertical 
displacement of each pressure surface is given by 
oZ _ oT 
Tihsarta le, 
where Z is height of the surface and 7 is the mean 
temperature from the earth’s surface to the level Z. It 
follows that 6Z increases from 0 for the 1000-mb surface 
to a maximum at 600 mb and that all pressure surfaces 
above 600 mb are raised by the same amount as the 
600-mb surface. The new horizontal pressure field then 
creates a maximum mass outflow about 600 mb. In 
response to this outflow the pressure falls near the base 
of the column BC and upward accelerations are created 
(7) 
-600 
PRESSURE IN MB 
1000 
i=} (a) Cc B (b) c 
Fig. 1—Two atmospheric models with (a) heating and (6) 
cooling in the region BCMN. The arrows indicate the fields 
of horizontal divergence and vertical motion. 
within BCN M. As a consequence of these pressure falls 
there are inward horizontal accelerations near the base 
of the column. Even though this analysis has treated 
the problem in a stepwise manner, it is recognized that 
the process is a continuous one. 
The heating then produces a pressure fall at BC and 
a pressure rise in the environment. One modifying in- 
fluence is the adiabatic temperature changes which 
accompany the vertical displacements after the estab- 
lishment of the accelerational field. These adiabatic 
changes modify the original temperature difference be- 
tween the heated column and its environment, and the 
pressure difference at any given time depends upon the 
net contribution of the heating and cooling processes 
to the establishment of a temperature difference be- 
tween the column BC and its environment. The wind 
field at the same time may be determined from the 
accelerational field created by the heating, from the 
Coriolis acceleration, and from the effect of friction. 
The well-known low-level convergence and high-level 
divergence in the vicinity of centers of pressure fall are 
readily deduced. 
Similar reasoning could be applied to the converse 
problem of the effect of local cooling. It is apparent 
from the previous discussion that cooling gives a pres- 
sure rise at BC, a pressure fall in the environment, and 
a divergence field like that of Fig. 1b. 
