Geoscience Reference
In-Depth Information
that the Earth moves on an ellipse around the Sun, but as noted above the eccentricity of
this ellipse is small. The declination is usually determined as a function of day of the year
(see Paltridge and Platt, 1976; Liou, 2002). Figure 2.23 gives an idea of the variability of
the daily totals of solar radiation
Q
se
; the Earth is closest to the Sun in the month of January,
so that the curves are somewhat asymmetric between North and South, with the maximal
radiation occurring in the South.
Surface albedo
This is the ratio of the global short-wave reflected radiative flux and the flux of the
corresponding incident radiation; in contrast to the term reflectivity, the albedo also
includes the diffuse portion of the radiation. In energy budget studies the albedo usually
refers to an integral value over all wave lengths; however, sometimes, to distinguish it
from the spectral albedo, it is called the integral albedo. In the case of an ideal rough
surface, the albedo should be independent of the direction of the primary beam. For
most natural surfaces the fraction of directly and diffusely reflected radiation depends
on the direction of the incoming beam. Therefore, on days with sunshine, the albedo
of most surfaces depends on the altitude of the Sun, but this dependence decreases
with increasing cloudiness. For example, for water surfaces it appears that the albedo
can be represented well by a power function of the solar altitude (see Anderson, 1954;
Payne, 1972). The albedos of other surfaces obey similar relationships. However, for
daily totals it is common practice to use a mean value of the albedo. Table 2.7 presents
a brief summary of mean albedo values for various surfaces obtained from summaries
of available data (see Van Wijk and Scholte-Ubing, 1963; Kondratyev, 1969; List, 1971;
Budyko, 1974)
Long-wave or terrestrial radiation
Also sometimes called nocturnal radiation, this is the radiant flux resulting from the
emission of the atmospheric gases and the land and water surfaces of the Earth. All
materials on Earth and around it have a much lower temperature than the Sun, so that
the radiation they emit has much longer wavelengths than the global radiation. There
is practically no overlap, since most of the radiation emitted by the Earth is contained
in the range from 4 to 100
m. Long-wave radiation can be measured, but the needed
measurements for a particular area of interest are rarely available, so that it must often
be calculated from other measurements. It is convenient to consider two components of
the terrestrial radiation at the Earth's surface separately, namely a component of upward
radiation from the surface
R
lu
, and that of downward radiation from the atmosphere
R
ld
.
The upward component is usually obtained by assuming that the ground, the canopy
or the water surface under consideration is equivalent with an infinitely deep grey body of
uniform temperature and emissivity
μ
ε
s
which is close to unity. This allows the following
formulation
T
s
R
lu
=
ε
s
σ
(2.79)
10
−
8
Wm
−
2
K
−
4
in terms of the (absolute) surface temperature
T
s
;
σ
(
=
5.6697
×
=
10
−
12
cal cm
−
2
s
−
1
K
−
4
) is the Stefan-Boltzmann constant. Table 2.8
1.354
×
