Geoscience Reference
In-Depth Information
Vernal equinox
20
−
21 March
δ
= 0
1 astronomical unit
Summer solstice
20
−
21 June
δ
= +23.5
Winter solstice
20
−
21 December
δ
= -23.5
1.017 astronomical unit
0.983 astronomical unit
1 astronomical unit
Autumnal equinox
22/23 October
δ
= 0
Figure 5.7
The elliptic orbit of the Earth with the Sun as one focus illustrating the change in distance between the Sun and
the Earth and declination of the Earth with season.
amount of radiation emitted by the Sun fluctuates by a few tenths of a percent during
the 11 year sunspot cycle and is also believed to have changed more gradually at
much longer timescales with implications for the Earth's climate. However, for
many purposes it is possible to assume the solar constant is constant with the value
1367 W m
−2
. The spectrum of solar radiation reaching the Earth is close to being
a pure blackbody spectrum, but it is not perfectly so. In part this is because there
are variations in temperature across the surface of the Sun. However, by integrat-
ing the energy in the observed solar spectrum at the top of the atmosphere and
equating this to that from a blackbody, the effective blackbody solar temperature
has been calculated to be 5777 K.
Because Earth is in an elliptical orbit with the Sun as one focus, see Fig. 5.7, the
distance between the Sun and the Earth changes with time of year around its mean
value of 1.496
10
8
km (i.e., one 'astronomical unit, AU). Because of this, and
because radiation density follows an inverse square law with distance from the
radiation source, the maximum radiant energy reaching the top of the atmosphere
also changes seasonally. However, the seasonal change in Sun-Earth distance is
only about 3% so it is possible to adequately parameterize the yearly cycle in solar
radiation reaching the Earth using a simple, sinusoidal multiplicative factor which
is called the e
ccentricity factor, d
r
, and which is given for each day of the year,
D
y
, by:
×
⎛
2
p
⎞
d
=+
1
0.033cos
D
(5.5)
⎜
⎟
r
⎝
y
⎠
365
