Modeling The Bidirectional Reflectance Distribution Function (BRDF) Of Water Based On Monte Carlo Simulation

Bi-directional Reflectance Distribution Function (BRDF) of water is one of the most important factors to describe the optical characteristics of ocean, It also plays important roles in the research of remote sensing modelling and inversion. Study of this BRDF of water is meaningful to the quantitative remote sensing and the development of remote sensing technology, which need to be solved for monitoring the quality and temperature of water and assess the ocean productivity.BRDF is the most basic macroeconomic phenomenon in nature. The directional distribution of light field on water surface carry the important information of water properties such as the composed of water, concentration of component, minerals, the distribution of particle size and surface roughness. It can bring some errors if we ignoring its direction. However, early applications of remote sensing are usually assumed that the object surface is a Lambert. It is uniformly distributed in all directions and the intensity of reflected radiation, reflection direction are nothing to do with the direction of incident radiance. With the continuous development of quantitative remote sensing technology, it's urgent to obtain the more accurately information.Now, The BRDF is widely implemented in land remote sensing, especially for quality assessment of vegetation and soil. However, it has only been occasionally applied in marine optics to date. This is mainly because many factors affect the marine spectrum and it is not easy to simulate accurately; It is very difficult to measure BRDF in situ. Sea waves, shadows, sky conditions can lead to large errors on the results. The Monte Carlo model by constructing simulation of radiation transfer model can solve these problems well. Thus, building the mathematical model and validate the models will become the hot and difficult point in ocean color remote sensing.This research was based on certain assumptions, by using Monte Carlo method to track a large number of photon collisions in the water. We use random number to select the location of the collision and the scattering angle of photons by the knowledge of scattering phase function, single scattering albedo, and attenuation coefficient. The Monte Carlo model was built to treat those problems such as highly absorbing and highly scattering waters, scattering by molecules and by particulates, incident sun-zenith, sky light. Based on this, the result was through statistical a large number of the photon which formed the light field using quad-averaged techniques, and present in three-dimensional coordinate.Through analysis of the results of the model, both single scattering albedo, solar incident angle, the ratio between sky light and whole light and scattering phase function have an impact on shape and quantity of BRDF. The results are as follows:(1) Solar incident angle, especially zenith angle can change the shape of BRDF. When the major scattering particle of water was suspended particles, most of the power was concentrated and the maximum appear near the direction of light incidence (backscattering light).(2) The results showed that the ratio of sky to total radiance can also change the shape of BRDF. The peak of BRDF decreased with increasing ratio and the shape tend to be axial symmetrical, the axial of symmetry was identical to the line perpendicular to the horizontal plane. The backward hot spot was gradually disappearing.(3) The single scattering albedo has an impact on the BRDF quantity, the number of BRDF increased with the raise of single scattering albedo at the same conditions. On the contrary, BRDF became smaller.(4) Scattering phase function was a dominant factor to affect the shape of the BRDF. When the major scattering material was water molecules, a Rayleigh phase function was used to describe the angular scattering properties of the water. The distribution of photon was not concentrated and nothing to do with the incident zenith angle. But for water which major scattering material of water was suspended particles was used to describe the angular scattering properties use Petzold phase function. The Petzold phase function was characterized by a intense forward scattering. So most of photon seldom escaped the water. The picture of BRDF also showed that the most power was concentrated in the backword hot spot.