Hyperspectral synthetic image generation of shallow waters using a coupled Monte-Carlo optical model with water surface slopes

A hyperspectral optical Monte Carlo model coupled with realistic water surface wave slopes has been developed for shallow aquatic systems. The coupled model simulates the propagation of visible radiant energy (light) in a homogeneous or stratified water column that may be optically deep or shallow. Individual photons are tracked in a three-dimensional reference frame. This improved Monte Carlo model is composed of several characteristics that make the model unique. The medium is assumed to have non-homogeneous optical characteristics from the top of a parallel plane or random sea surface to a bottom boundary and photons are tracked as a function of parallel planes at any specified depth. Thus, the model is a non-homogeneous three-dimensional model that is sampled as a "layered" system of parallel heterogeneous planes. The model allows for vertically heterogeneous distributions of inherent optical properties (i.e. absorption and scattering coefficients), however, the scattering phase function (SPF) and the refractive index do not change as a function of depth. The latter simplification is a result of a lack of available data for depth dependent SPF and refractive indices. The air-water interface is either flat or with realistic water waves and slopes. The flat surface is modeled to allow for a comparison between this model and other models. The bottom boundary may have varying bottom reflectance as a function of wavelength. The light source (above the air-water interface) may be a direct source (sun), a diffuse source (skylight) or a combination of both. Note that there is no internal source of light (i.e. no fluorescence). The photons within the medium travel from one pixel to another making the model fully three-dimensional. All scattering events are elastic in nature (i.e. when a photon is scattered, its wavenumber does not change). Photons enter the water body pixel at a single centered location "or" at random locations within the pixel. This model is compared with previous Monte Carlo models, quasi-analytical and stochastic models and gives nearly identical results. However this coupled Monte Carlo model assumes the water is not a flat surface but utilizes output of a Monte Carlo driven statistical wave model to estimate the wave facet slopes. The coupled model output is used to simulate hyperspectral passive remote sensing signatures. The model can also be used to generate hyperspectral synthetic images (as seen from airborne or spaceborne remote sensing platforms) of various water types. Compared to other Monte Carlo models, the relative error of this model ranged from 0.06 to 0.2 percent for downwelling irradiance estimates. For successive order scattering (SOS) model comparisons, the relative error between models ranged from 0.02 to 0.15 percent. In all the comparisons made during this research, model differences were nearly always less than 0.5 percent from other previous models. These results demonstrate that the model performs nearly identical to previous models with no water wave effects included. When water waves are simulated in the coupled model, the results clearly show that shape factors for downwelling diffuse light can change from 60 to 80 percent due to the presence of capillary and small gravity waves. Model results for upwelling irradiance shape factors can change up to 90 percent due to the influence of these water surface waves. These results demonstrate the value of the coupled model to estimate shape factors since no previous model as well as in-situ instrumentation is readily available for estimating shape factor under the influence of capillary and small gravity waves.