Geoscience Reference
In-Depth Information
36
32
28
24
20
16
12
8
4
Figure 2.2 The average
relationship between atmospheric
pressure and altitude.
0
200
400 600
Pressure (hPa)
800
1000
In the figures that follow, atmospheric variables are presented on surfaces of
constant pressure, or
isobars
, instead of surfaces of uniform elevation.
Figure
2.2
can be used to estimate the altitude of any pressure surface. Where topog-
raphy extends up into the atmosphere, certain pressure levels may not exist.
For example, since the surface pressure over Antarctica is 700 hPa or lower
(see
Fig. 2.1)
, there is no 900 hPa surface.
Such regions may be specified as hav-
ing missing data, or the data may be extrapolated to fill in the missing values.
When pressure is substituted for height as an
independent
variable, then
the height of the pressure level becomes a
dependent
variable. (Recall that in-
dependent variables are the coordinate axes, and dependent variables describe
the system. For the atmosphere, temperature and wind speeds are examples of
dependent variables.) It is common to use
geopotential height
,
Z
, as the inde-
pendent variable instead of height,
z
, where
z
1
#
Z
/
gdz
.
(2.2)
g
0
0
In Eq. 2.2,
g
0
is the acceleration due to gravity at the surface of the earth.
Because the gravitational attraction between two bodies depends on the dis-
tance between them, the acceleration due to gravity decreases with increas-
ing height—or decreasing pressure—in the atmosphere. At the earth's surface,
g
g
0
9.81 m/s
2
.
At 10 km elevation,
g
9.77 m/s
2
. This 0.4% reduction in
g
within the lower atmosphere is relatively small, so
g
can be taken as constant
in Eq. 2.2. With this assumption, geopotential height,
Z
, can be interpreted as
the elevation,
z
, of a pressure level.
Geopotential height is closely related to the gravitational potential energy,
, given by
z
Φ=
#
(
z
gdz
.
(2.3)
0
