Geoscience Reference
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ation to the surface leads to a lower albedo of the canopy as a whole (e.g., dark soil) or
to a higher relectivity (e.g., snow; see Gryning et al.,
2001
).
Another aspect of the directional dependence of relectivity is its dependence on the
azimuth angle of the incoming radiation. An example where the directional depen-
dence is related to the azimuth angle (
ϕ
in
) is a row crop. If the radiation enters the
crop parallel to the rows, the radiation is relected both by the crop and by the soil
in-between (which may differ in relectivity). If, on the other hand, the radiation
falls on the crop perpendicular to the rows, the relection comes only from the crop
(unless the row spacing is very large, or the zenith angle of the incident radiation is
very small).
Apart from the dependence of relection on the direction of the
incident
radiation,
the
relected
radiation (for a given direction of incidence) may also have a directional
dependence (rather than being diffuse, equal in all directions). Here again, a water
surface is the clearest example: at low solar altitude the water acts as a mirror, but the
observer sees most of the relected light only if she looks in the direction towards the
Sun, and at a zenith angle equal to that of the Sun. Another example is a vegetated
surface. If the observer has the Sun at his back, he looks at the illuminated part of the
plants, whereas when he is facing the Sun he looks at the shadow side (which will
yield a lower amount of relected radiation).
Question 2.9:
Consider a row crop with dark bare soil in-between. The fraction of veg-
etation cover is 0.5 (i.e., 50% of the soil is covered by vegetation).
a) If the Sun shines in a direction parallel to the rows, what is the albedo of this com-
posite surface (see
Table 2.1
for representative values for simple surfaces).
b) As (a), but now a situation where the Sun shines in a direction perpendicular to the
rows (and where the direct radiation does not reach the soil). Neglect diffuse radia-
tion.
c) How large is the relative difference in net short wave radiation
K*
between the situ-
ation mentioned under (a), and (b) (take it relative to
K
* of question a).
Bidirectional Relectance Distribution Function
This complicated combination of the dependence of the relectivity (
r
) of a surface on
the directions of incident radiation, relected radiation (and wavelength) is summa-
rized in the bidirectional relectance distribution function (BRDF) of a surface:
r
= (, ,
λθϕθϕ
in
,
,
)
(2.20)
in
out
out
The combination of four angles (zenith and azimuth angle of incoming radiation,
and zenith and azimuth angle of the observer; see
Figure 2.8
) deines one point in the
BRDF. This implies that the determination of the BRDF of a natural surface is a very
laborious job, as radiative luxes have to be measured under many different incidence
angles and many different observing angles.
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