Light attenuation model for waters: Linear and nonlinear dependencies on suspended sediment

Diffuse optical sensors estimate attenuation of natural light (solar irradiance) by measuring its vertical distribution in the water column, and the sensors are useful for estimating both suspended sediment concentration and light availability for organisms in rivers, lakes, and estuaries. However, currently there is a lack of reliable light attenuation models that account for particle size and density, have widely applicable dimensionless form, and show usefulness for coupling with sensors. To overcome these deficiencies, the authors revisit earlier dimensional analysis and relax a number of assumptions to provide a more robust and applicable dimensionless number for light attenuation by sediments. Second, the authors formulate an analytical light attenuation model that is found to be in general agreement with the dimensionless model and provides a theoretical description of the controlling dimensionless number. Third, the authors perform a meta-analysis for a wide range of data sets in diverse waters to test the model across a range of particle sizes and sediment concentrations from 9 to 90 μm and 0 to 670 mg L^-1 respectively. The dimensionless light attenuation number clearly divides the light attenuation data into two categories: one linear and one with nonlinear dependence on suspended sediment concentration, both of which collapse the respective data sets. About 90% of the data displays linear properties, and the linear empirical coefficient found for the dimensionless model agrees almost exactly with the equation derived with the analytical model. Results that exhibit nonlinearity when scaled with the dimensionless number suggest the influence of secondary processes upon attenuation that most likely arise from the measurement methods for sediment and light properties. The authors recommend ways to avoid nonlinearity, when it can be avoided, that may be followed in future research to enhance the usefulness of sensors and sensor networks.