Geology Reference
In-Depth Information
Albedo is usually presented as the summation of two
components: (1) black‐sky albedo (also called direct
albedo, resulting from directional hemispheric reflectance)
and (2) white‐sky albedo (also called diffuse albedo,
resulting from bihemispherical reflectance). The former
represents the reflection of the direct radiation that
strikes the surface while the later represents the reflection
of the diffuse radiation generated across the hemisphere
but gathered at the same point at the surface (Figure 7.38).
Albedo can be presented as either “spectral albedo” inte-
grated over a narrow band of the EM spectrum or “broad-
band climatological albedo” integrated across the entire
optical spectrum. Sometimes broadband albedo is sepa-
rated into two parts, one integrated over the visible
spectrum (0.4-0.7
μ
m) and the other integrated over
the near‐infrared spectrum (0.7-3.0
μ
m). When quoted
unqualified, it usually refers to the average reflection
across the visible spectrum.
Black‐sky albedo is calculated by integration of the
BRDF for particular illumination geometry. White‐sky
albedo is calculated by integration of the BRDF for the
entire viewing and solar hemisphere. MODIS‐derived
albedo products include both black‐sky and white‐sky
albedo; each one is provided in the form of spectral and
broadband [
Strahler et al.,
2003]. According to the
MODIS
[1999] document on albedo product the black‐
sky albedo
α
bs
and white‐sky albedo
α
ws
are given by the
equation
that a 20% decrease of albedo (i.e., more absorption of
sunlight) would cause the disappearance of perennial ice.
An important factor that determines surface albedo of
polar ice regimes is snow cover. Fresh snow reflects
most of the radiation in the optical spectrum [
Wiscombe
and Warren
, 1980;
Perovich
, 2001]. Therefore, even a
few millimeters of snow cover will decrease the penetra-
tion of solar radiation to the underlying ice significantly
[
Warren et al.,
1997;
Allison et al.,
1993]. Losing the snow
cover, on the other hand, will decrease the surface albedo
and contribute to higher temperatures of the ice. Data
on albedo from sea ice and its snow cover are presented
in section 8.3.
As pointed out before, if only a limited number of
reflectance measurements are available (for a few solar
incident and satellite viewing angles), some knowledge
(or assumptions) about the anisotropy of the surface
become necessary in order to estimate the albedo. Some
authors employ anisotropic reflectance factors (ARFs) to
convert a reflectance measurement to a channel albedo.
There are ARFs for various surface types and solar view-
ing geometries—some derived empirically and some from
BRDF models. Simple linear models also exist to further
extend channel albedo acquired via narrowband reflec-
tance measurements from sensors such as AVHRR to
broadband climatological albedo.
De Abreu
[1996] used
both approaches to derive albedo of Arctic sea ice from
AVHRR measurements.
In retrieving albedo from optical remote sensing obser-
vations, the data should be preprocessed to account for
atmospheric and cloud influences. Atmospheric correc-
tion aims at reconstructing the original radiance that
leaves the surface in the direction of the satellite sensor by
accounting for the major attenuating mechanisms along
the atmospheric path to the sensor [
De Abreu
, 1996].
Methods for atmospheric correction are mentioned in
section 7.7.1. An analytical expression to retrieve the ice
surface albedo from radiance measured at the TOA over
a Lambertian surface was developed by
Vermote et al.
[1997] and used in
De Abreu
[1996].
The radiance
L
TOA
recorded by the satellite sensor can be
decomposed into two components: radiation reflected from
the surface (
L
s
) and the perturbation contributed by atmos-
phere due to scattering (
L
a
) (known as path radiance):
(
,
)
f h
k
()()
(7.43)
bs
k
k
(7.44)
where
θ
is the zenith solar angle,
Λ
is the waveband,
f
k
is
the BRDF kernel
k
model parameter,
H
k
is the integral of
h
k
(
θ
) over
θ
, and
h
k
is the integral of BRDF model kernel
k
over the view zenith angle
ϑ
and the view‐Sun relative
azimuth angle
ø
;
h
k
(
θ
) and
H
k
are given by the equations
2
/
2
h
()
K
(
,,
) sin( )cos()
dd
(7.45)
k
k
0
0
and
/
2
)
(7.47)
L
(
,,,
)
L
(
, ,,
)
L
(
,,,
(7.46)
H
2
h
()sin( )cos()
d
TOA
i
i oo s
i
i oo
a
i
i oo
k
k
0
where
K
k
(
θ
,
ϑ
,
ϕ
) in the BRDF model kernel
k
and
H
k
is
the integral of
h
k
(
θ
) over
θ
. Kernel functions of sea ice are
presented in
Zhou
[2002].
Estimates of snow‐covered sea ice albedo in polar
regions has been presented in many studies. Model results
presented in
Maykut and Untersteiner
[1971] indicated
By assuming the surface to be a uniformly Lambertian
reflector, the surface reflection can be written as
(
,,,
)
ET
s
cos
(7.48)
L
s
i
i oo
TOA
s
1
(
,,,
)
s
i
i oo
