imple two types 
apparent beam 
ired the light in 
(5) 
mtration of the 
) %. The results 
wo assumptions 
the ratio bjb f 
ach water type, 
0.6 to 25 m' 1 , 
ves for humus, 
ort wavelengths 
son for the low 
e increases cor- 
total absorption 
in co 4 and R(O-) 
lectra per water 
lade. The most 
amples. This is 
in these waters, 
¡suits of Petzold 
( 6 ) 
) 800 
canal 
However, additional measurements of volume scattering functions of particulate material from a variety of inland water 
types are required to test the validity of Eq. ( 6 ). The B' for each of the four water types is given in Table 2. Fig. 2a 
shows the calculated backscattering albedo co 4 . 
3.2. Determination of R( 0-) 
The underwater irradiance reflectance is defined as the ratio of the subsurface upwelling irradiance £„ to the subsurface 
downwelling irradiance E wd : 
E 
R( 0-) = (7) 
E \vd 
For remotely sensed data the reflectance was obtained from radiance measurements above the surface which were 
converted to irradiance and corrected for the air-water interface (a value of 9.08: see Dekker, 1993). was calculated 
from the upwelling radiance LJfi) in nadir direction above the air-water interface corrected for the specular reflection 
(= 0 . 021 ) of the downwelling skylight L 0 ( 0 ) in zenith direction 
E wu = 9.08 {L au (*) - 0.021L 0 (0)} ( 8 a) 
where L o (0) was measured in situ using a Spectron SE590 field spectrophotometer and a halon Lambertian reflectance 
panel. In case of in situ measurements a more reliable determination of E m is available by measuring the subsurface 
upwelling radiance LJ0) and by converting it to by multiplying with the angular distribution factor Q: Q L w {0). 
Often the value of Q is assumed to have the value 5, however, there is some discrepancy in results presented in 
literature (Dekker, 1993). Next, the downwelling E wd was calculated from L 0 , which was separated into a direct sunlight 
component £^(0,,) and a diffuse component £ dif corrected for surface reflection (1 - 0.066 = 0.934). Furthermore, the 
downward reflection (0.48) of the underwater upwelling light against the air-water interface was taken into account 
E wd = (1 -'-(e 0 ) > xL sun <V + 0.934xL di/ +0.48E wu (8b) 
where rfQg) is the Fresnel coefficient. Fig 2.b shows the measured R(O-). Comparison with Fig. 2.a shows that R(O-) 
and to,, have a similar spectral signature. 
4. RESULTS 
A regression analysis of the relationship given in Eq. 4 was performed for the linear case n=0,1. Assuming that r 0 and 
r \ are independent of wavelength they can be estimated for each sample separately. The results are given in Table 2 
along with an optical characterization by co 0 , b 5 and cu 4 integrated over 400 - 700 nm, and the illumination conditions 
at the time of the R(O-) measurements. The values of r, ranged from 0.12 to 0.56 with an average of 0.29, with a relati 
ve error of 1 % to 5 %. The variation in r, between the water bodies was large. This suggests that the conclusions of 
Whiüock et al. (1981) and Kirk (1991), that the coefficient(s) change with changing water type are confirmed. A change 
of the coefficients with solar zenith angle and sky conditions cannot be deduced from the results. This may be caused 
by a masking effect of the change of the coefficients with water type. Whitlock et al. (1981) did not present the values 
for the coefficients of the polynomial. The only relationship that can be deduced from the values of r, and optical 
characterization is a general increase in error with increasing b } and co 0 . 
In 15 cases the estimated r 0 was smaller than its standard error, S y , which suggests that Eq. 4 can be 
approximated by R(O-) =r,ci) 4 . This may not hold for the turbid, but algae-poor samples of River Vecht and Amsterdam- 
Rijn Kanaal, which deviated markedly from the lake samples. 
Figs. 3.a-d show the spectral nature of the relationship between measured R(O-) and co 4 for the four water 
types. The figures confirms the linear dependence of R(O-) on co 4 . From the comparison with Table 2 it may be deduced 
that a low correlation is caused by a spectral dependency of r,, most markedly for the eutrophic lakes.