705 
700 800 
ity of the 
scale, of 
ons in The 
:ed at 440 nm. 
el, with d = 
:pth measurement 
ata. Reflection 
is with 
lured at a water 
i reflected flux 
if extinctions 
mus. This 
ring of the 
i bottom depth 
m at two 
nm. Other 
istant and known 
500 nm and 630 
, and the ratio 
avelengths. Two 
sured 
n figure 1 and 
el, with 
epth 
a parameter 
ction at 500 nm 
; the measured 
unction, and 
al function was 
ential humus 
depth 
i reflection 
on values and 
nction, for the 
the humus is 
at 500 nm. 
column. 
r 
The calculated depth using the ratio of measured 
humus extinction corresponds well with the depth of 
.345 m. The calculated depth based on the exponential 
absorption is systematically higher than the real 
depth. The relative error increases with the humus 
concentration. 
The choice of the two wavelengths was arbitrary. A 
pair of wavelengths that introduce a smaller relative 
depth error is possible. The shape of the humus 
extinction spectrum determines the wavelength range 
where the exponential can be used. This range is 
different for humus from an other place, as can be 
seen in figure 2. 
The variability of the absorption spectrum of humus 
from different locations in the Netherlands is shown 
in figure 2. The spectra are normalized at 440 nm. 
The extinction at 440 nm varied from 1.06-9.33 m 1 . 
The dashed line is the humus spectrum according the 
exponential function, with d = -.014 nm 1 and 
Ao = 440 nm. 
It turns out that the differences among the samples 
are even greater than the deviation from the 
exponential model in the example shown before. 
4 DISCUSSION 
The results, obtained with spectrophotometric 
measurements, demonstate that the shape of the humus 
absorption spectrum cannot be described by an 
exponential function. It also appears that the 
variability of the humus absorption spectrum is 
considerable. The simplified depth experiment 
illustrates that substantial errors are made, when 
the exponential function, with a fixed value for d, 
is used. 
Considerable improvement in the accuracy of the 
interpretation of airborne reflection measurements 
may be expected when actually measured absorption 
spectra of aquatic humus (part of the optical 
seatruth) are used as input for the deconvolution 
algorithm. 
Futher progress in the mathematical description of 
the absorption spectrum of humus can only be made by 
the introduction of models more complicated than an 
exponential curve. As a first attempt we applied 
conventional factor analysis to the data-set (figure 
2). Preliminary results indicate that four components 
are sufficient to cover the observed variability of 
shape (Krijgsman and Buiteveld, unpublished results). 
It will likely be possible to obtain more accurate 
correlation between optical and chemical data of 
humus than was possible with the exponential model. 
In further studies factor analysis will be applied 
to introduce error calculation and noise-analysis in 
our experimental procedures and in the analysis of 
reflection spectra of more complicated and realistic 
situations, e.g. by the introduction of silt and 
algae in the system. 
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Bricaud, A, A. Morel and L. Prieur 1981. Absorption 
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Kalle, K. 1966. The problem of Gelbstoff in the sea. 
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Prieur, L. and S. Sathyendranath 1981, An optical 
classification of coastal and oceanic waters based 
on the specific absorption curves of phytoplankton 
pigments, dissolved organic matter and other 
particulate materials. Limnol. Oceanogr. 
26:671-689. 
Smith, R.C. and K.S. Baker 1981. Optical properties 
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Applied Optics 20:177-184. 
Zepp, R.G. and P.F. Schlotzhauer 1981. Comparison of 
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