Geoscience Reference
In-Depth Information
Under these simple assumptions,
T
E
for the earth can be calculated if the rate
at which energy is absorbed by the system is known, since in a state of radiative
equilibrium the energy emitted is equal to the energy absorbed. If
S
ABS
denotes
the rate at which solar radiation is absorbed by a unit surface area of the black
spherical earth model, then
J
S
N
14
/
ABS
4
σ
TS T
=
=
K
O
.
(4.6)
&
E
ABS
E
σ
L
P
To calculate an expression for
S
ABS
we first consider the average rate at
which solar energy is incident on a unit surface area of the earth,
S
INC
. The rate
at which solar energy is incident on a unit area perpendicular to the solar beam
at the earth-sun distance (drawn in
Fig. 4.1a)
is known as the
solar constant
,
S
0
. (The inconstancy of the solar “constant” is discussed below.) It is equal to
the total energy output of the sun, or the solar luminosity,
L
S
, divided by the
area over which that energy is distributed:
L
3.9
#
10
26
W
m
2
S
S
== =
^
1380 W,
(4.7)
0
2
2
4
π
r
41.5
π
#
10
11
m
h
where
r
is the average earth-sun distance. This simple calculation yields a value
for the solar constant that is a little high, since reduction of the solar beam by
interactions with interplanetary dust is not taken into account. A more repre-
sentative value is 1368 W/m
2
, although
S
0
varies by a few W/m
2
(see the follow-
ing section).
S
0
is greater than
S
INC
because the only location that receives insolation at
the value of
S
0
is the subsolar point. In calculating
S
INC
we need to account for
(a)
(b)
Unit area
perpendicular to
the solar beam
Earth intercepts solar
energy across a
surface area π
R
2
perpendicular to the
solar beam
Solar rays assumed
to be parallel
r
R
Sun
Earth's orbit
R
= radius of Earth = 6371 km
Figure 4.1 Calculation of the average solar radiation incident on a unit surface area
of the earth.
