Geography Reference
In-Depth Information
surface remained small for incidence angles up to 65 ,
rays approaching the air-water interface frombelow expe-
rience greater Fresnel reflectance at smaller incidence
angles. In fact, because the index of refraction of air is less
than that of water ( n a <
characterize the BRDF, however, radiance measurements
must be made for a range of source and sensor orien-
tations. The difficulty of collecting such data, even in
terrestrial settings, dictates that BRDF's are only available
for a small number of materials (e.g., Zhang et al., 2003).
Typically, the substrate is assumed to behave as a Lam-
bertian surface (i.e., reflectance is the same for all view
directions); radiative transfer simulations performed by
Mobley et al. 2003 indicated that replacing a more com-
plex BRDF with a uniform, Lambertian BRDF with the
same irradiance reflectance entailed errors of less than
10%. In practice, then, R b (
n w ), a critical angle of incidence
exists for which the angle of refraction fromwater into air
is 90 , implying that the incident beam will be refracted
back into the water. For a typical n w of 1.333, this criti-
cal angle, determined from Snell's law (Equation 3.8), is
48
36 . Any upwelling photon with an in-water incidence
angle greater than 48
.
36 will not be transmitted through
the air-water interface; instead, total internal reflection
occurs. As a result, all of the radiance recorded by an air-
borne detector is derived from an underwater cone with
a half-angle of 48 . 36 . Moreover, because the radiant flux
contained within a given solid angle below the air-water
interface is spread into a larger solid angle above the
water surface (Figure 3.4b), the radiance from within the
stream channel is reduced by a factor of 1
.
) is the primary factor that
determines what fraction of the radiant flux reaching
the bed will begin propagating upward toward a remote
detector. This bottom reflectance ,or albedo , varies with
wavelength and depends on the characteristics of the
sand, gravel, vegetation, or other materials comprising
the streambed (Section 3.3.3).
Upon reflection from the streambed, photons embark
on a second traverse of thewater column, alongwhich they
are subject to the same absorption and scattering processes
that affect the downwelling light stream. Because the
substrate behaves, at least approximately, as a Lambertian
surface, the angular structure of the upwelling flux is
more uniform than that of the downwelling radiation
incident upon the bed. As a result, the upwelling flux will
be attenuated more rapidly as it propagates back toward
the air-water interface (Dierssen et al., 2003). Moreover,
these directional effects dictate that the attenuation of
upwelling photons reflected from the bed differs from the
attenuation of photons scattered upward within the water
column (Maritorena et al., 1994). These two factors give
rise to the distinction between K d (
λ
n w
563
upon entering the air (Bukata et al., 1995). These effects
can be summarised by saying that light can much more
easily get 'into the water' than 'out of the water' (Mobley,
1994). This is one of the main reasons why remote sens-
ing of rivers involves the measurement of relatively small
amounts of reflected solar energy.
In any case, for those photons that domanage to escape
the water column, the next link along the image chain
is a second trip through the atmosphere. These photons
experience additional absorption and scattering interac-
tions that modify the water-leaving radiance L w (
/
0
.
) en
route to the sensor. These effects are summarised in terms
of a path transmittance T (
λ
λ
λ
).
The former quantity, T ( λ ) < 1, is a multiplicative coef-
ficient that accounts for the losses that occur as radiance
is transmitted from the river channel to the sensor. The
latter quantity, L p (
)and path radiance L p (
, z ). Fully
accounting for these effects involves complex radiative
transfer modeling, and most applications have relied
upon an effective attenuation coefficient to summarise
the influence of the water column (e.g., Philpot, 1989).
This assumption over-simplifies the radiative transfer
process, however, and more rigorous approaches that
distinguish between the downwelling and upwelling light
streams have beendevelopedby the coastal remote sensing
community and could be applied to rivers as well.
Whether reflected from the bottom or scattered within
the water column, upwardlymobile photons approaching
the air-water interface from below are subject to the same
processes as the downwelling solar radiation approaching
the interface from above. The interaction of the upwelling
light streamwith the water surface differs in some impor-
tant ways, however, as illustrated in Figure 3.4b. Whereas
the Fresnel reflectance of air-incident rays from the water
λ
, z )and K u (
λ
), makes an additive contribution to
the radiance received by the sensor as light is scattered
into the detector's field of view by the atmosphere or
objects near the channel. Again, a full treatment of atmo-
spheric effects and their correction is beyond our scope,
and the interested reader is referred to remote sensing
texts (e.g., Schott, 1997). For our purposes here, a few key
points are worth noting. First, because water bodies have
such low reflectance, the energy signal associated with the
fluvial features of interest can be quite small relative to
extraneous sources of radiance, such as the atmosphere
or adjacent, typically much brighter terrestrial surfaces.
For these reasons, remotely sensed data acquired under
hazy conditions can be of limited value, and inmany cases
deriving useful river information from images will require
λ
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