Calculating Irradiance Penetration into Water Bodies from the Measured Beam Attenuation Coefficient

The relationships between the numerical values and spectral distributions of the downward irradiance attenuation coefficient, Kd,λ, and the beam attenuation coefficient, cλ, were investigated. Using experimental data for the Baltic Sea with Secchi disk transparency of 1.5-6 m, we obtained formulae allowing us to determine the spectra of the scattering coefficient in the range of 400-700 nm from data for the beam attenuation coefficient at 580-nm wavelength. Formulae connecting the values of the downward irradiance attenuation coefficient, the absorption coefficient, and the scattering coefficient for different illumination conditions were then used to determine the spectra of Kd,λ from measured cλspectra. A preliminary test of this method was carried out based on experimental data from three Estonian and two Finnish lakes. The correlation coefficient between the measured and the computed (through cλ) values of Kd,λ is 0.97 and standard deviation is 0.23 m-1. This method may be useful in conditions where in situ measuring of the underwater solar radiation spectra cannot be performed because of weather conditions. Because characterization of the underwater radiation field is often a complicated and expensive procedure, our numerical method (which needs only water samples and the recording of the spectra of incident irradiance) may be useful for estimating spatial-temporal variations of the underwater solar radiation.