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 second component is related to the seabed reflectance 
pp O-) modelled by, 
PppA) = AP), (4) 
where Q(A) is the reflectance spectrum of a typical sandy bed 
normalized such that p(555nm)=1 and 4 is the seabed albedo 
at 555 nm. 
  
   
  
   
  
    
  
  
  
  
  
  
  
  
  
  
  
  
  
3 n Fh "Coastal" 
3 A i 
o 0.9 : — Blue 
g 0.8 3 PO Green 
a 0 3 2 a Yellow 
gi — Red 
= 05 € 
3 os J wenn "Red Edge" 
9 e m —NIR1 
^ 94 : ——NIR2 
> 03 
= N 
202 - 
e 0.1 s = | | 
dre écran ++ 
350 450 -550 650 750 850 950 1050: 1150 
Wavelength (nm) 
  
  
Figure 1. The relative spectral response curves of the 8 
multispecral bands of the World View-2 satellite sensor. 
  
  
  
  
  
  
  
  
  
Bae Band Name en Bandwidth 
(nm) (nm) 
1 “Coastal” 429.3 47.3 
2 Blue 478.8 54.3 
3 Green 547.5 63.0 
4 Yellow 607.8 37.4 
5 Red 658.5 37.3 
6 “Red Edge” 723.5 39.3 
7 NIR 1 825.0 98.9 
8 NIR2 919.4 99.6 
  
  
  
  
  
  
Table 1. Effective wavelengths and bandwidths of the 
WorldView-2 spectral bands. 
The other parameters common to both components in the 
equation (1) are the water depth H, effective attenuation 
coefficient K 
K(X) 2 a(4) * by.) , (5) 
and the geometric path length factor M, 
M =1/cos0, +1/cos6,, (6) 
where 0, .0, are respective the in-water sensor view angle and 
solar zenith angle. 
The absorption and backscattering coefficients of water is a 
linear combination of various optically active constituents. 
by 0.) - bp) - bp 0) 
aA) =a, (MN) + ag (X) aq (X) 
(7) 
(8) 
where the subscripts w, g, p and ¢ refer to water, coloured 
dissolved organic matter (CDOM) and phytoplankton 
respectively. The absorption and backscattering coefficients of 
each component are computed according to the commonly used 
bio-optical models (Lee et al., 1999), with the following water 
quality parameters: G (CDOM absorption coefficient at 440 
nm), X (particulate matter backscattering coefficient at 550 nm), 
and P (phytoplankton absorption coefficient at 440 nm). 
The above water reflectance can then be calculated according to 
(Lee et al., 2002), 
0.52550) 
Rs (A) = 9 
A 1-1.755 (4) 9 
The in-band effective reflectance of each WorldView-2 spectral 
band is computed by aggregating the above-water spectral 
reflectance R,;(A) using the respective relative spectral 
response function S;(A) and the solar flux density F(A), 
J SjQQFQ)R, Q.) à 
cad 
R (10) 
Ay 
[$;Q)FQ.) dA 
^ 
where the subscript / is the band number. The lower and upper 
wavelength limits of integration are, respectively, A; =380nm 
and À, =1100nm. 
4 RESULTS 
The in-band effective reflectance of coastal sea water was 
calculated for each of the first six WorldView-2 spectral bands 
using equations described in the previous section. The values of 
the water quality parameters were set to G=04 mi. 
1 
Xz0.1m . Phytoplankton is assumed to be absent, i.e. 
P -0m'!. These are the typical values for coastal waters in the 
Singapore Strait southwest of the Singapore main island. The 
path length parameter was set at M =2.1 and the reflectance 
was calculated for water depth varying from 0.1 m to 10 m. Two 
values of the seabed albedo, 4-0 and A=0.2 were used, 
representing cases with a dark (muddy) and bright (sandy) sea 
bottom respectively. 
Figure 2 shows the typical reflectance spectrum of coastal sea 
water with a bright sandy sea bottom and water depth H — 2 m. 
The solid line is the computed reflectance spectrum (equation 9) 
while the red circles are the in-band effective reflectance of the 
eight WorldView-2 spectral bands (equation 10) plotted at their 
respective effective wavelength (Table 1). 
The in-band reflectance values of coastal sea water with a dark 
seabed for the first 6 spectral bands of WorldView-2 are plotted 
as functions of the water depth in Figure 3. The reflectance 
generally increases monotonically with water depth for all the 
spectral bands plotted. The Green band (Band 3) has the highest 
reflectance and the reflectance values fall off at shorter and 
longer wavelengths. The reflectance seems to saturate (i.e. does 
not change with increasing water depth) after a certain threshold 
depth. This threshold depth is a function of the spectral band.