New model for subsurface irradiance reflectance in clear and turbid waters

Modeling of subsurface irradiance reflectance fields especially in turbid coastal, harbor and lagoon waters has important applications in ecology, engineering and optical remote sensing. The present study aims at exploring many possible causes of variation in the proportionality factor f and analyzing its effect on the subsurface irradiance reflectance in different waters. A new model is then developed to estimate this optical property as a function of the absorption coefficient (a), backscattering coefficient (bb), incident illumination condition, and other wavelength-depth dependent factors. Implementation of this new model is examined for five types of waters with varying turbidity and chlorophyll. Model results are verified with in situ measurements data and compared with the results from existing models. Formulas already proposed for estimating R in the previous studies and generally expressed by R = 0.33(bb/(a + bb)) or R = f (bb/(a + bb)) where f = 0.975-0.629 μ(0) (μ(0) is the incident photons just below the sea surface) work fairly well in clear oceanic waters, but yield large errors in turbid coastal and lagoon waters due to the use of a constant value ~0.33 or the dimensionless parameter f which does not account for certain processes in the model (e.g., multiple scattering, depth-dependent changes in the diffuse components of solar radiation, and spectral variation in f). By contrast, the new model estimates the reflectances having good agreement with in situ data from just below the water surface and throughout the water column. The improved performance of the present model is because it includes a parameterization of the proportionality factor f which varies with wavelength and depends on the sun angle, inherent optical properties, and diffuse attenuation coefficients. Knowledge related to interrelationships between inherent optical properties and apparent optical properties can be used to study the variability of the subsurface reflectance in homogeneous and stratified coastal waters with respect to many possible causes of its variations.