Semi-analytical modeling and parameterization of particulates-in-water phase function for forward angles

A model based on Mie theory is described for predicting scattering phase functions at forward angles (0.1°-90°) with particle size distribution (PSD) slope and bulk refractive index as input parameters. The PSD slope 'ξ ' is calculated from the hyperbolic slope of the particle attenuation spectrum measured in different waters. The bulk refractive index 'n' is evaluated by an inversion model, using measured backscattering ratio (Bp) and PSD slope values. For predicting the desired phase function in a certain water type, in situ measurements of the coefficients of particulate backscattering, scattering and beam attenuation are needed. These parameters are easily measurable using commercially available instruments which provide data with high sampling rates. Thus numerical calculation of the volume scattering function is carried out extensively by varying the optical characteristics of particulates in water. The entire range of forward scattering angles (0.1°-90°) is divided into two subsets, i.e., 0.1° to 5° and 5° to 90°. The particulates-in-water phase function is then modeled for both the ranges. Results of the present model are evaluated based on the well-established Petzold average particle phase function and by comparison with those predicted by other phase function models. For validation, the backscattering ratio is modeled as a function of the bulk refractive index and PSD slope, which is subsequently inverted to give a methodology to estimate the bulk refractive index from easily measurable optical parameters. The new phase function model which is based on the exact numerical solution obtained through Mie theory is mathematically less complex and predicts forward scattering phase functions within the desired accuracy.