247 
■ophic), main 
vhyll a and 
malysed. See 
2. THEORY 
2.1. The inherent optical properties 
The underwater light field at a certain wavelength is specified by the absorption coefficient a(k) and the volume scatter 
ing function B(©,7) which describes the angular distribution of scattered flux resulting from the primary scattering 
process. Henceforth the wavelength is omitted from all expressions for notational convenience. For inland waters B(©) 
Diego Harbour is often used in optical models of the underwater light field. The optical model discussed in this paper 
is based on (back)scattering and absorption coefficients. The scattering coefficient is defined as 
Based on the angle over which the scattering is integrated two scattering coefficients are often used: the scattering 
coefficient b=b 0 and the backscattering coefficient b b =b 9 0 . Combinations of a, b and b h may also be used to 
characterize the underwater tight field. These are the beam attenuation coefficient c — a + b the single scattering 
albedo to 0 = b/c, the backscattering albedo co b =b b /( a+b ^ and the backscattering ratio B = p p lb (Krijgsman, 1993). 
These inherent optical properties are always within the range of 0 to 1. 
Direct field measurements of b are not yet feasible due to difficulties in measuring near-forward scattering. 
Instead an attenuation coefficient c' was measured using a spectrophotometer with a photomultiplier acceptance angle 
yielding the scattering coefficient b 5 (see § 3.1). Lack of knowledge about the near-forward scattering does not affect 
the relation between R(O-) and the IOP (see Eq. 4). 
2.2. The subsurface irradiance reflectance R(0-) as a function of the inherent optical properties 
Several authors have investigated the relation between R(O-) and IOP for ocean and river waters. Gordon et al. (1975) 
used Monte Carlo simulations to investigate R(O-) as function of the backscattering albedo a> b . They found that this 
function can be described by the series 
where the coefficients r„ depend on illumination conditions. Morel & Prieur (1977) and Kirk (1991) have evaluated Eq. 
(4) through Monte Carlo simulations for « = 1. They found that a) b could be approximated by b b /a. Kirk also found 
that r, was a function of both solar altitude and water type. Although no restrictions for co 0 were presented in either 
study, R(O-) was calculated for relatively clear oceanic waters and might not be valid for the turbid waters studied here. 
Whidock et al. (1981) investigated Eq. (4) using experimental data from turbid river waters, obtaining values 
of reflectance, absorption and backscattering for waters with co 0 ranging from 0.7 to 0.93. They concluded that R(O-) 
did not vary in a linear manner with b b / a but was correctly described by Eq. (4) for n=0,..,3. Moreover, they found 
that data from different water samples did not fit a single curve, in support of Kirks (1991) findings. 
Krijgsman (1993) found that the linear relationship R(0-)= 0.5 accurately fitted laboratory experiments with 
suspensions of scattering non-absorbing polystyrene particles and an absorbing dye, with (o b ranging from 0.15 to 1. 
It also appeared that this model was more accurate then two flow models. 
These results suggest that a linear model might be applicable to turbid inland waters. Hence, in this study 
Eq.(4) is evaluated for n =0,1. However, b h was not measured directly but instead we used the scattering coefficient 
b 5 (Eq. 2) and the backscattering ratio B'=b b lb s . Therefore, by substitution of b } and B' Eq. (4) was rewritten into the 
form that is still exact although near-forward scattering is not included 
is unknown and a particle-dominated normalized B(©) determined by Petzold (1972) for the turbid water of the San 
180 
( 1 ) 
e 
of 5°: 
c’ = a +b 5 , 
( 2 ) 
(3) 
(4)