Estimation of radiance reflectance and the concentrations of optically active substances in Lake M¨alaren, Sweden, based on direct and inverse solutions of a simple model

A semi-analytical model which predicts radiance reflectance just below the water surface ŽLu Ed 0 . has been developed and used to predict the spectral variability of radiance reflectance in Lake M¨alaren, Sweden. Radiance reflectance is predicted as a function of the optically active substances in the water, which include the concentrations of chlorophyll-a phaeophytin-a, suspended particular inorganic material ŽSPIM., suspended particulate organic material ŽSPOM., and dissolved yellow substances. These substances are linked to the absorption and backscattering coefficients through a series of empirical relationships, and ultimately radiance reflectance is estimated as a function of the ratio of backscattering to absorption. Parameterization of the model, i.e. the development of the empirical relationships linking the optically active substances to the inherent optical properties ŽIOPs., is based on both in situ measurements and laboratory analyses. We have collected data that allowed us to examine the potential variability in radiance reflectance, as predicted by our model, due to both variations in the optically active substances, and in the model parameterization. Simulations based on a data set collected during the fall of 1997 from 12 sites, which span a large range in water quality Žsecchi depth 0.8 5.0 m., suggest that, with the proper parameterization, the model can accurately predict the spectra of radiance reflectance as a function of the concentration of optically active substances. Variations in the concentrations of optically active substances accounted for a large portion of the total simulated variability in radiance reflectance Ži.e. that resulting from variations in parameterization and in the concentrations of optically active substances.. However, the measured variability in parameterization could account for up to 50% of the total variability in simulated radiance reflectance. This suggests that variability in the model parameterization, arising from both real variability and experimental error, will limit the use of this model for interpreting remote sensing data. Nevertheless, inverse solutions of the model are able to estimate the concentra-tions of chlorophyll, suspended inorganic material ŽSPIM. and the absorption of yellow substances from measured radiance reflectance spectra The average error for the 12 sites was a 0.07 for chlorophyll, 0.15 for dissolved yellow substances Žmeasured as the absorption at 400 nm. and 0.07 for SPIM, even though individual errors could be as great as 50%