Cun-Hai Wang

Monte Carlo simulation of spectral reflectance and BRDF of the bubble layer in the upper ocean.

The presence of bubbles can significantly change the radiative properties of seawater and these changes will affect remote sensing and underwater target detection. In this work, the spectral reflectance and bidirectional reflectance characteristics of the bubble layer in the upper ocean are investigated using the Monte Carlo method. The Hall-Novarini (HN) bubble population model, which considers the effect of wind speed and depth on the bubble size distribution, is used. The scattering coefficients and the scattering phase functions of bubbles in seawater are calculated using Mie theory, and the inherent optical properties of seawater for wavelengths between 300 nm and 800 nm are related to chlorophyll concentration (Chl). The effects of bubble coating, Chl, and bubble number density on the spectral reflectance of the bubble layer are studied. The bidirectional reflectance distribution function (BRDF) of the bubble layer for both normal and oblique incidence is also investigated. The results show that bubble populations in clear waters under high wind speed conditions significantly influence the reflection characteristics of the bubble layer. Furthermore, the contribution of bubble populations to the reflection characteristics is mainly due to the strong backscattering of bubbles that are coated with an organic film.

Transient radiative transfer in two-dimensional graded index medium by Monte Carlo method combined with the time shift and superposition principle

ABSTRACT Transient radiative transfer (TRT) in a two-dimensional scattering medium with graded refractive index distribution subjected to a collimated short-pulse irradiation is solved by a modified Monte Carlo (MMC) method coupled with the time shift and superposition (TSS) principle. The boundaries are considered as Fresnel surfaces, the refractive index at the boundary mismatches with that of the surroundings, making the reflectivity at the boundary change with the incident directions. The incident pulse consists of two parts when it hits the boundary: bundles directly reflected by the outside boundary and bundles refracted into the medium. The accuracy of the present algorithm is confirmed first. Numerical results show that by using the TSS principle, the computational efficiency is greatly improved. Afterward, the TRT in the media with different graded refractive index distributions is investigated. The time-resolved reflectance and transmittance at different locations are given. Several trends on the time-resolved signals are observed and analyzed.

Investigation of the spectral reflectance and bidirectional reflectance distribution function of sea foam layer by the Monte Carlo method.

Spectral properties of sea foam greatly affect ocean color remote sensing and aerosol optical thickness retrieval from satellite observation. This paper presents a combined Mie theory and Monte Carlo method to investigate visible and near-infrared spectral reflectance and bidirectional reflectance distribution function (BRDF) of sea foam layers. A three-layer model of the sea foam is developed in which each layer is composed of large air bubbles coated with pure water. A pseudo-continuous model and Mie theory for coated spheres is used to determine the effective radiative properties of sea foam. The one-dimensional Cox-Munk surface roughness model is used to calculate the slope density functions of the wind-blown ocean surface. A Monte Carlo method is used to solve the radiative transfer equation. Effects of foam layer thickness, bubble size, wind speed, solar zenith angle, and wavelength on the spectral reflectance and BRDF are investigated. Comparisons between previous theoretical results and experimental data demonstrate the feasibility of our proposed method. Sea foam can significantly increase the spectral reflectance and BRDF of the sea surface. The absorption coefficient of seawater near the surface is not the only parameter that influences the spectral reflectance. Meanwhile, the effects of bubble size, foam layer thickness, and solar zenith angle also cannot be obviously neglected.

Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method

Transient (time-dependent) polarized radiative transfer in a scattering medium exposed to an external collimated beam illumination is conducted based on the time-dependent polarized radiative transfer theory. The transient term, which persists the nanosecond order time and cannot be ignored for the time-dependent radiative transfer problems induced by a short-pulsed beam, is considered as well as the polarization effect of the radiation. A discontinuous finite element method (DFEM) is developed for the transient vector radiative transfer problem and the derivation of the discrete form of the governing equation is presented. The correctness of the developed DFEM is first verified by comparing the DFEM solutions with the results from the literature. The DFEM is then applied to study the transient polarized radiative transfer induced by a pulsed beam. The time-dependent Stokes vector components are calculated, plotted and analyzed as functions of the axis coordinate and discrete direction. Effects of the diffuse/specular boundary and the incident beam polarization state with respect to the Stokes vector components are further analyzed for cases of different boundary reflection modes and incident beam illuminations.

Transient radiative transfer in a graded index medium with specularly reflecting surfaces

A modified Monte Carlo (MC) method has been developed for solving transient radiative transfer in a one-dimensional scattering medium with a graded refractive index. The accuracy and computational efficiency of the algorithm are validated initially. With the introduction of time shift and superposition principle into the MC model, the computational efficiency is greatly improved. We make a comparative analysis of the time-resolved incident radiation (and radiative heat flux) distributions in the media with diffuse and specular reflection boundaries. Results show that the temporal and spatial radiative signals of the medium with specular reflection boundaries greatly differ from those having diffuse reflection boundaries.

Transient/time-dependent radiative transfer in a two-dimensional scattering medium considering the polarization effect

Transient/time-dependent radiative transfer in a two-dimensional scattering medium is numerically solved by the discontinuous finite element method (DFEM). The time-dependent term of the transient vector radiative transfer equation is discretized by the second-order central difference scheme and the space domain is discretized into non-overlapping quadrilateral elements by using the discontinuous finite element approach. The accuracy of the transient DFEM model for the radiative transfer equation considering the polarization effect is verified by comparing the time-resolved Stokes vector component distributions against the steady solutions for a polarized radiative transfer problem in a two-dimensional rectangular enclosure filled with a scattering medium. The transient polarized radiative transfer problems in a scattering medium exposed to an external beam and in an irregular emitting medium are solved. The distributions of the time-resolved Stokes vector components are presented and discussed.

Discontinuous Galerkin finite element method for radiative heat transfer in two-dimensional media with inner obstacles

Abstract A discontinuous Galerkin finite element method (DGFEM) with unstructured meshes is presented to solve the radiative transfer equation (RTE) in two-dimensional media with inner obstacles. The computation domain is discretized into a tessellation of unstructured elements and the elements are assumed to be discontinuous on the inner-element boundaries. The shape functions are constructed on each element and the continuity of the computation domain is maintained by modeling an up-winding numerical flux across the inner boundaries, which makes the DGFEM suitable and numerical stable for radiative transfer problems involved with strong non-uniformity and discontinuity induced by ray effects. The DGFEM discretization for RTE is presented and the accuracy of DGFEM is verified. Radiative transfer problems in square and irregular media with inner obstacles are investigated, the influence of medium parameters and the obstacle shielding effects are discussed.