Geoscience Reference
In-Depth Information
For a so-called grey body, the emissivity is equal for all wavelengths (
ε
λ
=
ε
), and
hence Eq. (
A.5
) becomes:
∞
ε
4
MM
=
b
d
λ εσ
=
T
(A.6)
0
Kirchhoff's law states that, under equilibrium conditions, the monochromatic emis-
sivity and monochromatic absorbtivity (
α
λ
) are equal:
αε
λ
=
(A.7)
λ
A.2 Solar Radiation: Instantaneous
The amount of solar radiation at Earth's surface is determined by the amount of
radiation at the top of the atmosphere and by the composition of the interfering
atmosphere. The radiation at the top of the atmosphere is given by:
2
↓
=
d
d
()
Sun
,
0
K
I
cos θ
(A.8)
0
0
z
Sun
where
I
0
is the solar constant (lux density of solar radiation at the mean distance
from Sun to Earth). This value varies with period of 11 years and an amplitude of
about 1 W m
-2
. Here we use a value of 1365 W m
-2
for the solar constant, though re-
cent research suggests a value of 1361 W m
-2
(Kopp and Lean,
2011
). Furthermore
d
Sun,0
is the
mean
(over a year) distance between the Sun and Earth,
d
Sun
is the
actual
distance between the Sun and Earth (depending on the date) and
θ
z
is the solar zenith
angle (angle between solar beam and the normal to Earth's surface) which depends
on the location, date and time.
The eccentricity correction factor can be approximated as:
2
d
d
Sun,0
=
1 000110
.
+
0 034221
.
cos
Γ
+
0 001280
.
sin
Γ
(A.9)
Sun
+
0 000
.
719
cos
20000077
Γ
+
.
sin
2
Γ
( )
with Γ=
π d
n
/ , where
d
n
is the day number of the year (January 1 equals 1).
Γ is sometimes called the day angle.
The expression for the solar zenith angle is:
2
1
365
cos
θ
z
=
sin sin os
δ φ δ φω
+
coscos
(A.10)
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