Geoscience Reference
In-Depth Information
value estimated by the same equation for clear sky conditions. Two empirical
formulae are used to calculate
f
, one applicable in humid conditions and one in
arid conditions. In
humid
conditions:
⎛
⎞
⎡
anNb
+
(
)
⎤
S
d
a
+−
(1
c b
)
s
s
f
=
i.e.,
s
s
; or
(5.24)
⎢
⎥
⎜
⎟
S
d
ab
+
ab
+
⎝
⎠
⎣
⎦
clear
s
s
s
s
but in
arid
conditions:
⎛
⎞
anNb
+
(
)
d
⎡
a
+−
(1
c b
)
⎤
S
(5.25)
s
s
f
=
1.35
−
0.35
i.e., 1.35
s
s
−
0.35 ; or, 1.35
−
0.35
⎢
⎥
⎜
⎟
d
S
ab
+
ab
+
⎝
⎠
⎣
⎦
s
s
s
s
clear
Net radiation at the surface
As described in Chapter 2, the all
day average net radiation at the surface is the
sum of the downward and reflected solar radiation and the net longwave radia-
tion as illustrated in Figure 4.2, and the daily average net radiation flux,
R
n
d
, is
given by:
−
d
d
d
RS L
=+
(5.26)
n
n
n
Equation (5.26) is written in terms of daily total values but it is of course possible
to write equations describing the instantaneous radiation balance, as follows:
RS
=+ + +
(
S LL
)
(
)
(5.27)
n
r
d
u
or:
RSaL
=−+
(1
)
(5.28)
n
n
The value of
R
n
varies greatly through the day. Net longwave radiation is negative
and usually fairly constant through the day, with the net solar radiation provid-
ing a positive input during the daylight hours. The typical diurnal cycle of net
radiation therefore has a temperature dependent negative offset, upon which is
superimposed a positive diurnal input of solar radiation whose magnitude
depends on the latitude of the site, the day of the year, fractional cloud cover on
that day, and, not least, time of day. The resulting diurnal pattern of net radiation
may therefore have a strong seasonal dependence at high latitude as illustrated
in the case of the radiation balance for Bergen, Norway at 60°N, which is shown
in Fig. 5.11.
