Analytic model for the direct and diffuse components of downwelling spectral irradiance in water

The direct and diffuse components of downwelling irradiance have in general different path lengths in water, and hence they decrease differently with sensor depth. Furthermore, the ever-changing geometry of a wind-roughened and wave-modulated water surface induces uncorrelated intensity changes to these components. To cope with both effects, an analytic model of the downwelling irradiance in water was developed that calculates the direct and diffuse components separately. By assigning weights f(dd) and f(ds) to the intensities of the two components, measurements performed at arbitrary surface conditions can be analyzed by treating f(dd) and f(ds) as fit parameters. The model was validated against HydroLight and implemented into the public-domain software WASI. It was applied to data from three German lakes to determine the statistics of f(dd) and ff(ds), to derive the sensor depth of each measurement and to estimate the concentrations of water constituents.