Geography Reference
In-Depth Information
pure water
a
w
(
) and thus exhibits a strong increase with
wavelength through the red and near-infrared. There-
fore, as depth increases, the radiance
L
T
(
λ
2
)measured
in a longer-wavelength band experiencing greater atten-
uation decreases more rapidly than the radiance
L
T
(
λ
1
)
in the band with weaker attenuation. Consequently, the
band ratio
L
T
(
λ
1
)
/
L
T
(
λ
2
) increases as depth increases
and is not strongly influenced by changes in bottom
reflectance. The ratio calculation also accounts for varia-
tions in the irradiance incident upon sloping streambeds
because these topographic effects influence the numerator
anddenominator bands in the sameway. In addition, both
bands are affected to a similar degree by reflectance from
the water surface, which is spectrally flat and thus cancels
in the ratio. Taking the natural logarithmof the band ratio
to account for the exponential attenuation of light with
distance traveled through the water column thus pro-
vides an image-derived quantity useful for bathymetric
mapping (Legleiter et al., 2009). Importantly, however,
this simple algorithm requires ground-based measure-
ments to calibrate the relationship between the band
ratio and water depth. More recent, radiative transfer-
based techniques do not require such tuning and have
largely replaced band ratios for remote sensing of shal-
low marine environments (e.g., Lee et al., 2001; Mobley
et al., 2005). Similarly, in the context of rivers, new
methods based on hydraulic (Fonstad and Marcus, 2005)
and photogrammetric (Lane et al., 2010) principles can
now be used to calibrate image-derived depth estimates
without requiring simultaneous field data. Development
of robust, flexible bathymetric calibration procedures
remains an area of active research.
λ
quantify river attributes such as bathymetry and bottom
type, which are directly related only to
L
B
(
). A scaling
analysis of this kindwas conducted by Legleiter et al. 2009,
who supported their arguments by performing radiative
transfer simulations, collecting ground-based reflectance
measurements, and producing bathymetric maps from
hyperspectral image data. This study indicated that the
bottom-reflected radiance is the dominant component of
L
T
(
λ
) in shallow, clear-flowing rivers with depths on the
order of tens of cm, water columns dominated by pure
water absorption rather than scattering by suspended sed-
iment, and highly reflective substrates, provided that the
illumination and viewing geometry are favourable (small
L
S
(
λ
)) and that atmospheric effects do not overwhelm
the aquatic signal of interest (small
L
P
(
λ
λ
)). Under these
circumstances, the other radiance components can be
considered negligible - that is,
L
B
(
λ
)
L
C
(
λ
)
+
L
S
(
λ
)
+
L
P
(
λ
)
.
More specifically, the radiance contribution from the
bottom will exceed that from the water column by
an increasing amount as depth decreases, as bottom
reflectance increases, and as absorption within the water
column predominates over scattering. Where, when, and
in which wavelengths these conditions are met, water
depth
d
is linearly related to the image-derived quantity
X
given by
X
=
ln
L
T
(
≈
ln
L
B
(
λ
1
)
λ
1
)
L
T
(
λ
2
)
L
B
(
λ
2
)
=
[
K
(
λ
2
)
−
K
(
λ
1
)]
d
(3.16)
ln
R
B
(
λ
1
)
−
R
C
(
λ
1
)
+
+
A
3.4.2 Relativemagnitudesof thecomponents
of theat-sensor radiancesignal
R
B
(
λ
2
)
−
R
C
(
λ
2
)
In this expression subscripts denote the two spectral
bands used to compute the ratio,
K
(
λ
) is the effective
Equation (3.14) indicates that the radiance measured by
a remote detector is the sum of four components: 1)
L
B
(
attenuation coefficient,
R
B
(
λ
) is the irradiance reflectance
λ
of the streambed,
R
C
(
) is the volume reflectance of
the water column, and
A
is a constant that accounts
for the downwelling irradiance incident upon the river,
transmission and reflection at the air-water interface, and
transmission losses within the atmosphere. This equation
describes a straight line with a slope given by the difference
in the effective attenuation coefficient between the two
bands, and
X
increases with
d
if
K
(
λ
), the bottom-reflected radiance of primary inter-
est for depth retrieval or substrate mapping; 2)
L
C
(
λ
),
radiance scattered within the water column before reach-
ing the bed; 3)
L
S
(
λ
), radiance reflected from the water
surface before interacting with the water column or sub-
strate; and 4)
L
P
(
), radiance scattered within the Earth's
atmosphere. Considering the relative magnitudes of these
four components can provide some insight as to the con-
ditions under which remotely sensed data can be used to
λ
λ
1
). The
intercept of the line accounts for the bottom contrast
λ
2
)
>
K
(
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