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1
Chapter 5
Radiative Properties
of Natural Surfaces
2
Chapter 5. Radiative Properties of Natural Surfaces
Absorptivity
(a, unitless): Fraction of incident radiation that is absorbed.
Reflectivity
(r, unitless): Fraction of incident radiation that is reflected.
Since these depend on wavelength, refer to them as a
λ
and r
λ
.
Since they depend on angle of incident radiation, write them as fn(
θ
,
Φ
).
For opaque surface (no transmission):
a
λ
(
θ
,
Φ
) + r
λ
(
θ
,
Φ
) = 1
If the reflection is isotropic
(independent of
θ
and
Φ
) then the reflected
monochromatic (spectral) irradiance can be written as:
F
λ
,r
= r
λ
F
λ
,o
[W m
2
nm
1
]
(F
λ
,o
= incident, F
λ
,r
= reflected)
And the absorbed irradiance is:
F
λ
,a
=
F
λ
,o
F
λ
,r
= F
λ
,o
r
λ
F
λ
,o
= (1 – r
λ
) F
λ
,o
=
a
λ
F
λ
,o
[W m
2
nm
1
]
Petty 5.1
Petty 5.2
Petty 5.3
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Petty Figure 5.2.
Shortwave
reflectance spectra
of various natural
surface types.
Where, in the visible, does
chlorophyll absorb?
www.arborsci.com/CoolStuff/cool22.htm
4
Graybody Approximation
Approximate the reflectivity of a surface as independent of wavelength, so the
surface appears “gray”.
The effective graybody reflectivity, r_bar (unitless), and absorptivity, a_bar (unitless),
are defined as (Petty 5.4):
r
a
F
F
r
i
r
−
=
≡
1
Here F
r
is the total reflected irradiance (flux)
in some broad wavelength interval (W m
2
).
F
i
is the total incident irradiance (flux) over
this interval (W m
2
).
The graybody approximation is commonly used in problems dealing with the
Earth’s radiation budget.
Slightly more complex – Divide the reflectivity and absorptivity into shortwave
and longwave:
lw
i
lw
r
lw
lw
sw
i
sw
r
sw
sw
a
F
F
r
a
F
F
r
−
=
=
−
=
=
1
1
,
,
,
,
r =
“albedo”
. For most terrestrial surfaces, r
lw
~ 0, but r
sw
is variable.
Average shortwave albedo ~ 0.1 for the Earth’s surface, and 0.3 for the Earth
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This note was uploaded on 01/19/2011 for the course ATOC 5235 taught by Professor Randell during the Fall '10 term at Colorado.
 Fall '10
 Randell

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