Geoscience Reference
In-Depth Information
What does the temperature profile displayed in
Figure 2.8
imply about the
heat sources for the atmosphere? Because we expect temperature to be high-
est near these heat sources,
Figure 2.8
suggests that the earth's surface and the
stratopause are regions of heat input to the atmosphere. The troposphere is
heated primarily from below. As discussed in
chapter 4,
much of the incoming
solar radiation passes through the atmosphere and warms the surface. Heat
from the surface is then delivered to the atmosphere.
The only region where the incoming solar radiation is strongly absorbed is in
the stratosphere, where ozone absorbs ultraviolet wavelengths. The stratopause
marks the level of maximum absorption of solar radiation by ozone, but it is not
the location of the greatest ozone concentrations. Ozone concentrations gener-
ally peak at an altitude of about 25 km, but much of the ultraviolet radiation
has been removed from the solar beam at that level by the ozone above.
The regions of the atmosphere are distinguished by the sign of the
lapse
rate
,
, defined as the negative of the vertical temperature derivative
1
2
=−
T
Γ
.
(2.4)
2
z
The lapse rate is positive in the troposphere and mesosphere, where tempera-
ture decreases with increasing height (decreasing pressure), and negative in the
stratosphere and thermosphere.
Figure 2.8
can be used to estimate the magnitude of the lapse rate between
two levels (
z
1
and
z
2
) using a inite-differenced form of Eq. (2.4):
TT
−
_
i
1
2
Γ=−
.
(2.5)
zz
−
_
i
1
2
Moving from the one-dimensional depiction of atmospheric temperature
profiles in
Figure 2.8
,
Figure 2.9
depicts atmospheric temperature as a func-
tion of latitude and pressure. Averaging in longitude completely around the
globe generates the
zonal mean
plots of atmospheric temperature shown in
Figure 2.9.
The vertical scale is stretched relative to the horizontal scale in the
figure to make the temperature structures discernible. Because the radius of
the earth is 6371 km, the distance across the surface from the South Pole to
the North Pole is about 20,000 km (half the circumference). The height of the
troposphere and lower stratosphere is about 20 km (see
Fig. 2.8)
. Therefore, if
Figure 2.9
were drawn to scale, keeping the width of the figure the same, the
height of the figure would be about 0.005 in. In other words, the horizontal
scale of the atmosphere is much greater than its vertical scale. In this sense, the
atmosphere is thin.
Figure 2.9
provides an opportunity for quantifying meridional variations in
temperature. In spherical coordinates, and using finite differencing, the zonal
mean meridional temperature gradient is
2
1
[]
1
T
(
TT
−
)
1 2
"
φ φφ
,
(2.6)
a
2
a
(
−
)
1
2
1
Note that the partial derivative, /
z
, is used instead of the total derivative,
d
/
dz
, because
temperature depends on other independent variables (e.g., latitude and longitude) as well as on
z
.
