Geoscience Reference
In-Depth Information
space and they also absorb solar energy. Thick clouds will reflect as much as 70%
of solar radiation and absorb a further 20%, while transmitting just 10%. As a
result, the proportion of solar radiation absorbed, which is typically just 25% in
cloudless conditions, is about 75% for overcast skies.
Actual solar radiation at the ground
The complex scattering and absorbing properties of the atmosphere can and often
are represented explicitly in meteorological models. Commonly in hydrology,
however, atmospheric loss of solar radiation is parameterized more simply either
in terms of an estimate of the fractional cloud cover,
c
, on a particular day, or the
number of hours with bright sunshine,
n
, in a day lasting
N
hours. In terms of
fractional cloud cover, the actual daily total solar radiation,
S
d
, is given by:
S
d
a
c b S
d
=+−
[
(1)
]
(5.16)
s
s
0
And in terms of bright sunshine hours by:
⎡
n
⎤
⎛⎞
=+
S
d
a
b
S
d
(5.17)
⎢
⎥
⎜
⎝⎠
s
s
0
N
⎣
⎦
Ideally, empirical values of
a
s
and
b
s
would be derived locally by comparing
estimates from Equation (5.16) with measurements of
S
d
on overcast days to give
a
s
and on days with continuous bright sunshine to give (
a
s
+
b
s
). Typical values
derived in this way are
a
s
0.25 and
b
s
0.5, corresponding to a 25% and 75% loss
of energy in clear sky and overcast conditions, respectively. These values of
a
s
and
b
s
are often assumed in the absence of any locally calibrated values.
As already discussed, once the solar radiation reaches the Earth's surface, a
proportion is reflected, depending on the albedo of the surface. Consequently, the
net daily solar radiation,
S
n
d
,
is less than
S
d
and is given by:
=
=
S
d
=−
(1
a S
)
d
(5.18)
n
where
a
is the daily average value of albedo described earlier.
Longwave radiation
The terrestrial surface emits thermal radiation following the Stefan
Boltzman
Law, with the surface temperature
T
s
in Equation (5.3) being
T
surface
, the effective
temperature of the land surface, and an appropriate value for the surface emissiv-
ity,
e
surface
, see Table 5.2. Thus, there is an upward flux of radiant energy in the
longwave waveband,
L
u
, which is given by:
−
L
=
-e s
T
4
(5.19)
u
surface
surface
