Scattering phase function for particulates-in-water: modeling and validation

Abstract

Scattering phase function plays a crucial role in studies and calculations based on radiative transfer theory in water as well as atmosphere. A model based on Mie theory is developed for estimating the particulates-in-water scattering phase function for forward angles (0.1° - 90°). Particle size distribution (PSD) slope ( ξ ) and bulk refractive index ( n ) are chosen as key inputs for this proposed model. The PSD slope can be estimated from the attenuation spectrum measured directly in-situ and the bulk refractive index can be calculated by an inversion model using measured backscattering ratio ( B P ) and PSD slope. The attenuation spectrum and backscattering ratio can be easily measured in-situ using commercially available instruments in real time. The entire range of forward angles is divided into two ranges and phase function is modeled separately in the ranges 0.1° - 5° and 5° - 90°, from numerically calculated Volume Scattering Function (VSF) using Mie theory. The division boundary is decided owing to the fact that the scattering phase functions, for different oceanic conditions, exhibit a change in slope at approximately 5°. Performance of the present model is evaluated by comparing with existing empirical and analytical models as well as measured phase functions. The proposed phase function model shows a considerable improvement upon existing models, and will have important applications in remote sensing applications and underwater studies.