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 (BP) 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.