Geoscience Reference
In-Depth Information
Consequently, the energy reaching the top of the atmosphere as solar radiation
normal to the solar beam is calculated by:
S dS
=
(5.6)
top
r
o
D
is the day of the year (sometimes inaccurately called the
Julian day
), with
D
=
1
on 1 January and
D
=
365 on 31 December.
Maximum solar radiation at the ground
The starting point for calculating how much solar energy reaches the ground is to
calculate the energy that would reach the surface if there were no intervening
atmosphere. The amount of solar radiation which would be received per unit area
over a specified time interval
t
1
to
t
2
on a horizontal surface on Earth were there no
intervening atmosphere is called the
insolation, I,
which is calculated from:
t
1
∫
I Sd t
=
cos(
q
).
(5.7)
or
t
2
where
q
is the
solar zenith angle,
i.e., the apparent angle of the Sun relative to the
normal angle to the surface at the specific location.
The need is, therefore, to calculate the solar zenith angle. Doing this is complex,
because the solar zenith angle depends not only on the latitude of the site for
which the calculation is made (because the Sun is on average closer to overhead
nearer the equator), and the time of day (because the Earth rotates each day), but
also because it depends on the
solar declination
,
d
. The solar declination is the
angle between the rays of the Sun and the plane of the Earth's equator. The axis of
rotation of the Earth is at an angle of
23.5° with respect to the plane in which the
Earth moves around the Sun, see Fig. 5.7. Consequently, the solar declination
changes with time of year. It is zero at the vernal and autumnal equinox, and
around 23.5° and -23.5° at the summer and winter solstice, respectively. The value
of
∼
δ
can be calculated (in radians) for each day of the year,
D
y
, from:
2
p
⎛
⎞
D
(5.8)
d
=
0.4093sin
−
1.405
⎜
⎟
⎝
⎠
365
For a site at latitude
f
(positive in the northern hemisphere; negative in the southern
hemisphere), the cosine of the solar zenith angle required in Equation (5.7) to
calculate the insolation is given by:
cos
q
=
sin
f
sin
d
+
cos
f
cos
d
cos
ω
(5.9)
