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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
The derivative of the in-band reflectance R; with respect to
water depth (Figure 4) can be used as an indicator of the depth
sensitivity of each spectral band. Figure 4 indicates that the
Green band (Band 3) has the highest depth sensitivity for the
typical turbid coastal water with a dark seabed. For this type of
sea water, the peak reflectance is about 0.04 sr. Suppose that
the noise level is one percent of the peak value, and that a depth
resolution of 0.25 m is desired, then the depth derivative of
reflectance must have a value greater than about 0.0016 sr’! m!
in order. Figure 4 shows that the Green Band meets this
requirement for water depth up to 5.3 m. The Green Band is the
most penetrative and the depth sensitivity (and hence the
penetration depth) decreases towards the blue end of the
spectrum as the absorption coefficient is high in this part of the
spectrum due to absorption by CDOM. The depth sensitivity
also decreases towards the red end of the spectrum due to the
high absorption by water itself.
0.04 4
0.035 3
0.03 3
0.025 À
0.02 3
0.015 3
0.01 À
0.005 3
Oll cu E
400 600 800 1000
Wavelength (nm)
Ris (sr)
Figure 2. A typical reflectance spectrum of coastal sea water
with a bright sandy bottom and 2 m water depth. The solid blue
line is the computed spectrum while the red dots are the in-band
effective reflectance of WorldView-2 plotted at their respective
effective wavelengths.
0.045 -:
0.04 - rem
0.035 -
003 .
0.025 -
0.02 -
0.015 -
0.01
0.005
Reflectance (sr?)
Water Depth (m)
Figure 3. Variation of reflectance with water depth for the first
6 spectral bands of WorldView-2 for coastal sea water with a
dark seabed.
0.02
E i.
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4
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s 5 "^2
i9 Eu SUMI OHI- EREQUUI ONSE ae B3
a
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8 | ci Mee e des >
9 0 — B6
=
c 2
-0.005 reprenne dns
0 2 4 6 8 10
Water Depth (m).
Figure 4. Derivative of reflectance with respect to water depth
for the first 6 spectral bands of WorldView-2 for coastal sea
water with a dark seabed.
0.002
-0.002
E
5
o
E
=
s
= -0004 :
o
à i
9 i
$ -0.006
© :
5 i
= -0.008
u i
= 1 i f
-0.01 Eh cá i ; ed
0 2 4 6 8 10
Water Depth (m)
Figure 5. Derivative of reflectance with respect to water depth
for the first 6 spectral bands of WorldView-2 for coastal sea
water with a bright sandy seabed.
Figure 5 shows the depth derivative of reflectance for the
typical sea water with a bright sandy seabed. The derivative
mostly has negative values because now the reflectance
generally decreases with increasing water depth. The depth
sensitivity of each spectral band is indicated by the absolute
value of the derivative. For coastal sea water with a bright sandy
sea bed, the Red and Yellow bands have the best depth
sensitivity. They are capable of probing water depth up to 2.4
m. All other bands are not sensitive to a change in water depth
beyond about | m. Table 2 lists the maximum depth for each
spectral band where the absolute value of the depth derivative
of reflectance exceeds the threshold value of 0.0016 sr! m'!.
Bad Band Name NN MT
! dark seabed bright seabed
1 “Coastal” 1.8 1:3
2 Blue 3.6 1.1
3 Green 5:3 0.8
4 Yellow 3.0 2.3
5 Red 2.0 244
6 “Red Edge” 0.6 1.4
Table 2. Maximum depth where the absolute value of depth
derivative of reflectance exceeds 0.0016 sr" m™ for the first six
spectral bands of WorldView-2, for typical coastal sea waters
with dark and bright seabed.
