Determining this coefficient required the well-known dependence Rrsλ~bbλaλ+bbλ

( Gordon & Morel 1983) and formula  (7) (derived in this work) describing the relationship between the light absorption coefficient a and the reflectance Rrs to be taken into consideration. It was additionally assumed that the scattering coefficient b is associated with the backscattering coefficient bb and the SPM concentration, the latter being highly correlated with ca Rrs(800 nm) (see Ficek et al. 2011). The relationship selleck chemicals llc obtained is shown in Figure 9 and expressed by formula (8): equation(8) b440nm=15.59×Rrs800nm0.282×100.554logx2−1.380logx+0.161, where x = Rrs(490 nm)/Rrs(665 nm). Having established the empirical relationships between the absorption and scattering of light of particular wavelengths, we can determine approximate values of these selected inherent optical properties of Type I and III lake waters for any wavelength from the PAR range from measurements of remote reflectance spectra Rrs  (λ). We obtain the spectrum of the coefficient of light absorption by SPM by first determining the value of this coefficient for λ = 440 nm from equation (6)

and then using equation (3) and Table 3 to determine its value for other wavelengths. The spectrum of light absorption by CDOM is also determined in two stages. In the first stage we determine a  CDOM(440 nm) from equation (5); CX-5461 supplier then, using the relationship a  CDOM(λ) = a  CDOM(440 nm) exp[−S¯(λ−440nm)] we obtain the value of this coefficient very for waves of different lengths. The parameter S¯ appearing in this equation varies from 0.015 to 0.018 nm−1 and depends on the type of lake (see the caption to Figure 2). We obtain the total absorption spectrum by summing the coefficients of absorption by SPM ap(λ), dissolved substances aCDOM(λ) and the water itself aw(λ). Values of the last-mentioned component can be found in e.g. Woźniak & Dera (2007). We obtain the spectrum of the light scattering coefficient by first determining this factor for light of wavelength 440 nm,

and then its values for other wavelengths using equation (4). In these calculations we could also take the values for water molecules into account. But since scattering by water is negligible compared to that by SPM (see e.g. Haltrin 2006), it makes no significant difference to the final result of the calculations. The great complexity of the results presented in this work precludes the precise definition of the errors of measurements and analyses, even though we took the greatest care with the measurement procedures stated in the Introduction. These procedures and the measuring apparatus they require govern the accuracy of these studies, in which we estimated the measurement errors of different magnitudes to be from 3 to 10% and more, e.g. with respect to the remote sensing reflectance Rrs and the scattering coefficients.