Application of the Beer–Lambert Model to Attenuation of Photosynthetically Active Radiation in a Shallow, Eutrophic Lake

Abstract

Models of primary production in aquatic systems must include a means to estimate subsurface light. Such models often use the Beer–Lambert law, assuming exponential attenuation of light with depth. It is further assumed that the diffuse attenuation coefficient may be estimated as a summation of scattering/absorbing constituent concentrations multiplied by their respective specific attenuation coefficients. While theoretical deviations from these assumptions have been documented, it is useful to consider the empirical performance of this common approach. Photosynthetically active radiation (PAR) levels and water quality conditions were recorded weekly from six to eight monitoring stations in western Lake Erie between 2012 and 2016. Exponential PAR extinction models yielded a mean attenuation coefficient of 1.55 m (interquartile range = 0.74–1.90 m). While more complex light attenuation models are available, analysis of residuals indicated that the simple Beer–Lambert model is adequate for shallow, eutrophic waters similar to western Lake Erie (R2 > 0.9 for 96% of samples). Three groups of water quality variables were predictive of PAR attenuation: total and nonvolatile suspended particles, dissolved organic substances (dissolved organic carbon and chromophoric dissolved organic matter), and organic solids (volatile suspended solids and chlorophyll). Multiple regression models using these variables predicted 3–90% of the variability in PAR attenuation, with a median adjusted R2 = 0.86. Explanatory variables within these groups may substitute for each other while maintaining similar model performance, indicating that various combinations of water quality variables may be useful to predict PAR attenuation, depending on availability within a model framework or monitoring program.