776 
where r(A) is the bottom reflectance, determines 
the solution of the radiative transfer equation. 
The supernatant waterlayer is assumed to be verti 
cally homogeneous, i.e. the absorption and scatter 
ing coefficients are then depth independent. 
For natural waters where the absorption dominates 
the scattering, solution for the near surface re 
flectance R can be approximated as 
b (A) 
R o (X) = a (A) + a^(X) 
u 
... -(a (A) + a (A))h 
+r(A) eu d 
The first term of the above equation is depth in 
dependent and represents the deep-water reflectance. 
The radiance L detected by the remote sensing 
instruments can be calculated from an integral of 
the R q multiplied by spectral sensitivity of each 
channel of the scanner. 
Since the reflectance of the natural water is 
very low at the longer wavelengths, calculations 
can be limited to 700 nm and thus only the response 
in the first two (MSS, HRV) or three (TM) bands of 
the optical scanners can be further considered. 
No substantial differences were found when using 
in the algorithms computations MSS band 4 (500- 
600 nm), TM band 2 (520-600 nm) or HRV band 1 (500- 
590 nm); and analogously MSS band 5(600-700 nm), TM 
band 3 (630-690 nm), HRV band 2 (610-680 nm) or 
AVHRR band 1 (580-680 nm). 
Seawater absorption, scattering and bottom 
reflectance coefficients, either measured in our 
laboratory of tabulated previously (Prieur and 
Sathyendranath, 1981; Lyzenga, 1978), were used in 
the computations. Three bottom types: sandy, mud 
and vegetation were considered. 
The applicability of the computed algorithms is 
limited by radiometric sensitivity (noise 
equivalent reflectance) of the instruments 0.5-0.8% 
(Robinson 1985). 
3 RESULTS 
Figures 1,2,3 show examples of the computed 
reflectance spectra for the sand, mud and vegetation 
bottom types respectively. 
wavelength (nm) 
Figure 1. Reflectance spectra of natural water 
with sandy bottom. Depth in metres are indicated. 
The line at zero depth represents the bottom 
reflectance. 
wavelength (nm) 
Figure 2. Reflectance spectra of natural water 
with muddy bottom. Depths are indicated. 
wavelength (nm) 
Figure 3. Reflectance spectra of natural water with 
vegetation-type bottom. Depths are indicated. 
Algorithms for the bottom depth and for the 
bottom composition assessment were further in 
vestigated. Requirements for the applicability of 
each type of the algorithm differ. An optimal 
bottom depth algorithm should be insensitive to the 
variation of the bottom and watercolumn composition, 
while a bottom composition algorithm should be 
insensitive to the watercolumn structure including 
the depth. Logarithmic transformation of the 
differences between the shallow-water and the deep 
water reflectances (or radiances) appears to be 
advantageous due to the exponential depth dependence 
of the irradiance (Lyzenga, 1978). 
Several suitable algorithms can be proposed from 
the model calculations. 
Generally the algorithms can be expressed as 
A = £ k.ln (L. - L. ) 
IX 1 1W 
where L. is the integrated radiance in the channel i, 
is the 
L. 
iw . . 
negative cc 
signatures 
knowledge c 
of the wate 
accuracy of 
Examples 
the bottom 
and turbid 
5. 
A Z 2 
(rel.uniti 
I0i 
N 
Figure 4. 
the bottom 
(dashed lir 
) bott 
Longer line 
shorter lir 
of the dete 
l b3 
(rel.units) 
I0i 
0.1 
Figure 5. E 
of the bott 
bottom type 
S = 1 for p 
représentât 
as indicate 
turbid wate 
Final tur 
seatruth de 
mapped. A c 
using Lands