Geology Reference
In-Depth Information
Lambertian surface—isotropic
Non-Lambertian surface—anisotropic
Figure 7.20
Schematic diagram showing the difference of reflectance pattern between an idealized Lambertian
(isotropic) surface and an actual anisotropic (non‐Lamberian) surface.
behavior of surface scattering for a given illumination
geometry as a function of the viewing angle of the sen-
sor. If
R
and
E
are the reflected and incident energy,
respectively, then
the Southern Ocean. They found that FY ice exhibited
stronger surface anisotropy than the MYI because the
latter had a smoother surface. Moreover, the BRDF pattern
of the FY ice had a minimum in the backward direction
where the pattern of MY ice had a peak. The authors
attributed the peak to the reflectance from the fore slopes
of MY ice surface undulation.
Heygster et al.
[2012]
asserted the importance of determining the BRDF for
snow‐covered sea ice since it is an essential input to the
retrieval of the reflectance.
The knowledge of surface BRDF is crucial for estimating
the albedo using observations from optical remote sensing.
Albedo is defined as the weighted angular integration of
the BRDF. It varies between zero and one; zero means
fully absorbing medium and one means fully reflective.
Although the above‐mentioned definition is widely recog-
nized, the term is loosely used in the literature. Its usage is
confused with the reflectance. It is worth reiterating that
reflectance is an angular dependent measurement while
albedo is a characteristic of the surface integrated over
the hemisphere and presented as an integrated flux over
a portion of the visible/NIR spectrum. Unless the surface
is Lambertian, albedo depends on the direction of the
incoming radiation because this is a major factor in deter-
mining the directional distribution of the reflected radia-
tion. Albedo is the most commonly used surface property
derived from space‐borne optical sensors. In the absence
of an accurate estimate of the BRDF and if the surface
is not an isotropic reflector, the estimated albedo from
satellite measurements may not be accurate.
Lindsay and
Rothrock
[1994] estimated the total narrowband albedo of
sea ice from reflectance measured by AVHRR augmented
by the BRDF. Surface albedo is a regular product from
MODIS, calculated accurately on a 16 day cycle basis
[
MODIS
, 1999]. The method is summarized in
Luo et al.
[2005]. Its main application in sea ice is in discrimination
of ice from the surrounding open water. It is also used in
the energy balance at snow‐covered ice surface and there-
fore in climate models.
R
(
,,,,
,,
)
(
BRDF ,,,
) (
)
i
i oo
(7.42)
i
i oo
E
i
i
where
λ
is the wavelength of the observed radiation;
θ
i
and
ϕ
i
are angles of the illuminating (incoming) radiation
in spherical coordinates (zenith and azimuth);
θ
o
and
ϕ
o
are viewing angles of the outgoing (reflected) radiation
in the same coordinates. The BRDF characterizes the
scattering properties of the surface. It simply describes
the familiar observation when an object looks different
when illuminated and viewed from different directions. It
assumes that the light striking the surface at some point
will be reflected from that same point. In other words, it
ignores subsurface scattering and the contribution of the
neighboring pixels (i.e., leakage) to the illumination of
the given pixel (section 7.7.1).
The BRDF can be estimated from a set of reflectance
measurements at various incidence and viewing angles
using either ground measurements or satellite observa-
tions. When using a satellite, measurements have to be
obtained from multidate and multiorbit satellite observa-
tions. They can then be used as input into a numerical
model to produce the BRDF. Various investigators have
proposed theoretical and empirical models [e.g.
Wanner
et al.
, 1997].
Rösel
[2013] verified the assumption (against
a common notion) that the ice surface can be a Lambertian
reflector, and therefore the BRDF is not crucial for cal-
culations of sea ice reflectance or albedo from optical
sensor. Only a few studies of BRDF for sea ice have been
accomplished.
Li and Zhou
[2002] determined the BRDF
of FY and MY sea ice from 512 spectra channels of
wavelength between 350 and 1050 nm. Data were obtained
during two austral summer cruises in 1999 and 2000 in
