Geoscience Reference
In-Depth Information
Fig. 2.25 Comparison between
measured long-wave
radiation
R
lds
under
various sky conditions
and radiation
R
ld
estimated by means of
Equations (2.80) and
(2.82) with
a
=
0
.
0496
and
b
=
2
.
45 and with
cloudiness values from
visual sky inspection.
(From Sugita and
Brutsaert, 1993.)
R
ld
(W m
−
2
)
the Great Plains by expressing
a
as an empirical sinusoidal function of month of the
year.
The downward long-wave radiation is affected by cloudiness. Several empirical
methods of incorporating this effect (see Bolz, 1949; Budyko, 1974) can be expressed
in the form
R
ldc
1
am
c
R
ld
=
+
(2.82)
where
m
c
is the fractional cloudiness and
a
and
b
are (different) constants. On the
basis of measurements in Germany, Bolz (1949) obtained
b
=
2 and different values
of
a
depending on cloud type, with an average of
a
0.22. More recently, with visual
cloudiness observations in the Great Plains, Sugita and Brutsaert (1993) derived values
a
=
=
=
2.45, without consideration of cloud type, and different values of
a
and
b
for different cloud types. Their analysis also showed that the standard error
of prediction with Equation (2.80) was of the order of 10-15 W m
−
2
for clear sky
conditions and of the order of 20-25 W m
−
2
for various sky (including cloudy) conditions
without cloudiness correction; incorporation of a cloudiness correction with (2.82) and
these constants improved the
R
ld
estimate with (2.80), i.e. reduced the standard error,
by roughly5Wm
−
2
on average (see Figure 2.25), and by an additional amount of
roughly the same magnitude when also information was included on the type of cloud.
Deardorff (1978) proposed a simple weighting parameterization, namely an atmospheric
emissivity for cloudy sky given by
0.0496 and
b
ε
a
=
[
m
c
+
(1
−
m
c
)
ε
ac
]; this is equivalent to (2.82)
with
a
=
[(1
/ε
ac
)
−
1] and
b
=
1.
