Backward Monte Carlo Method Research Articles

Inverse radiation analysis of simultaneous estimation of temperature field and radiative properties in a two-dimensional participating medium

An inverse radiation analysis is presented for simultaneous estimation of temperature field and radiative properties including absorption and scattering coefficients in a two-dimensional rectangular, absorbing, emitting and scattering gray medium from the knowledge of the exit radiative energy received by charge-coupled device (CCD) cameras at boundary surfaces. The backward Monte Carlo method was introduced to describe the radiative heat transfer for its efficiency. The inverse problem is formulated as an optimization problem and solved by the least-square QR decomposition (LSQR) method. The effects of measurement errors, optical thickness and search step length on the accuracy of the estimation were investigated and the results show that the temperature field and radiative properties can be reconstructed accurately for the exact and noisy data.

Global analysis of cloud phase and ice crystal orientation from Cloud‐Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data using attenuated backscattering and depolarization ratio

A method for discriminating cloud particle types was developed using lidar backscattering copolarization and cross‐polarization channel measurements from Cloud‐Aerosol Lidar With Orthogonal Polarization (CALIOP) on board Cloud‐Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO). In spaceborne lidar measurements, significant multiple scattering effects discriminate between cloud water and ice difficult using the depolarization ratio (δ). We theoretically estimated the relationship between δ and cloud extinction on the basis of the backward Monte Carlo method. Cloud particle type was determined by the combined use of δ and the ratio of attenuated backscattering coefficients for two vertically consecutive layers. Ice particles were further classified into two categories: randomly oriented ice crystals (3‐D ice) and horizontally oriented plates (2‐D plate). The method was applied to CALIOP data for September–November 2006. We found that 3‐D ice generally occurred colder than −20°C, whereas 2‐D plate occurred between −10°C and −20°C, with high‐occurrence frequency in high‐latitude regions. We compared the results to those obtained using the vertical feature mask (VFM). The VFM tended to show a homogeneous cloud type through the entire cloud layer in vertical directions and misclassified 2‐D plate as water. The ratio of water particles relative to ice particles decreased with decreasing temperature. By the proposed method, water cloud occurrence in subtropical and high‐latitude regions was greater (up to 20%) than in the other regions below −10°C; however, the VFM results did not show such dependence on latitude. Comparison of ice and water cloud between our results and Moderate Resolution Imaging Spectroradiometer (MODIS) products showed better agreement for water cloud than for ice cloud.

Multi-wavelength simulations of atmospheric radiation from Io with a 3-D spherical-shell backward Monte Carlo radiative transfer model

Conflicting observations regarding the dominance of either sublimation or volcanism as the source of the atmosphere on Io and disparate reports on the extent of its spatial distribution and the absolute column abundance invite the development of detailed computational models capable of improving our understanding of Io’s unique atmospheric structure and origin. Improving upon previous models, Walker et al. (Walker, A.C., Gratiy, S.L., Levin, D.A., Goldstein, D.B., Varghese, P.L., Trafton, L.M., Moore, C.H., Stewart, B. [2009]. Icarus) developed a fully 3-D global rarefied gas dynamics model of Io’s atmosphere including both sublimation and volcanic sources of SO 2 gas. The fidelity of the model is tested by simulating remote observations at selected wavelength bands and comparing them to the corresponding astronomical observations of Io’s atmosphere. The simulations are performed with a new 3-D spherical-shell radiative transfer code utilizing a backward Monte Carlo method. We present: (1) simulations of the mid-infrared disk-integrated spectra of Io’s sunlit hemisphere at 19 μm, obtained with TEXES during 2001–2004; (2) simulations of disk-resolved images at Lyman- α obtained with the Hubble Space Telescope (HST), Space Telescope Imaging Spectrograph (STIS) during 1997–2001; and (3) disk-integrated simulations of emission line profiles in the millimeter wavelength range obtained with the IRAM-30 m telescope in October–November 1999. We found that the atmospheric model generally reproduces the longitudinal variation in band depth from the mid-infrared data; however, the best match is obtained when our simulation results are shifted ∼30° toward lower orbital longitudes. The simulations of Lyman- α images do not reproduce the mid-to-high latitude bright patches seen in the observations, suggesting that the model atmosphere sustains columns that are too high at those latitudes. The simulations of emission line profiles in the millimeter spectral region support the hypothesis that the atmospheric dynamics favorably explains the observed line widths, which are too wide to be formed by thermal Doppler broadening alone.

Rassvet: Backward Monte Carlo radiative transfer in spherical-shell planetary atmospheres

Validation of global numerical models of planetary atmospheres requires simulating images and spectra from the IR to UV spectral regions in order to compare them with remote observations. This paper describes Rassvet, a 3-D spherical-shell backward Monte Carlo radiative transfer model developed for such simulations. It utilizes a new methodology for calculating atmospheric brightness in scattered sunlight by introducing the concept of an “effective emission source”. This allows for the accumulation of the scattered contribution along the entire path of a ray and the calculation of the atmospheric radiation when both scattered sunlight and thermal emission contribute to the remote measurement – which was not possible in previous models. A “polychromatic” algorithm is extended for applications with the backward Monte Carlo method and implemented in the model. It allows for the calculation of radiative intensity for several wavelengths simultaneously, resulting in improved efficiency. The capabilities of the model are demonstrated by simulating remote measurements from the atmosphere of Io.

Efficient inverse radiation analysis of temperature distribution in participating medium based on backward Monte Carlo method

An efficient numerical inverse radiation analysis based on the backward Monte Carlo (BMC) method is presented to determine the three-dimensional (3-D) temperature distribution in a large rectangular enclosure containing the participating medium, using radiative intensities in the visible range received by charge-coupled device (CCD) cameras. For large radiative sources and small detectors, when the radiation onto a small spot and onto a small direction cone is desired, the BMC method is more efficient than the forward Monte Carlo (FMC) method. Because the temperature reconstruction from the measured radiative intensities is an ill-posed inverse problem, least-square QR decomposition (LSQR) method is introduced to determine the meaningful temperature distribution. In order to gain insight into the effects on the accuracy of temperature distribution reconstruction, the detailed analyses are made using numerical simulations. The results show that the temperature distribution can be reconstructed accurately for the exact and noisy data.

Noncontact temperature measurement by means of CCD cameras in a participating medium

An original technique was presented for noncontact three-dimensional temperature field measurement in a participating medium using radiative information captured by a CCD camera. This technique was based on the backward Monte Carlo method and was faster and more efficient than traditional techniques based on the forward Monte Carlo method. A numerical simulation case was adopted to validate the technique. It was found that the technique was capable of reconstructing the three-dimensional temperature field well, even with noisy input data.

Fast reconstruction of two-dimensional temperature distribution in participating medium

An original model was presented for fast reconstruction of two-dimensional temperature distribution in participating medium using radiative information captured by charge-coupled device cameras. Compared with present models for temperature reconstruction, the model developed here is based on backward Monte Carlo method and reconstruction speed is faster, it is more efficient and can describe the scattering medium better. An exact two-dimensional temperature was assumed to be the reconstruction object and results show that even if there are measurement errors, the reconstructed temperature distribution can reproduce the original temperature distribution.

Ultrafast Wigner transport in quantum wires

Two quantum-kinetic models, governing the transport of an initial highly non-equilibrium carrier distribution generated locally in a nanowire, are explored. Dissipation processes due to phonons govern the carrier relaxation, which at early stages of the evolution is characterized by the lack of energy conservation in the collisions. The models are analyzed and approached numerically by a backward Monte Carlo method. The basic difference between them is in the way of treatment of the finite collision duration time. The latter introduces quantum effects of broadening and retardation, ultrafast spatial transfer and modification of the classical trajectories, which are demonstrated in the presented simulation results.

Approximate Thermal Emission Models of a Two-Dimensional Gradient Index Semitransparent Medium

This study develops numerical models for thermal emission in a two-dimensional semitransparent graded-index medium. Two piecewise continuous refractive index models, the bar model and the slab model, are presented. The formal is a combination of rectangular bars each having its own unique refractive index. The latter is a combination of slabs, each of which has a linear refractive index distribution. Two interface hypotheses are discussed: the reflection/refraction hypothesis and the refraction/total reflection hypothesis. The backward ray tracing method and the backward Monte Carlo method are employed for calculation. The apparent directional emissivity of a semitransparent medium with linear and nonlinear refractive index distributions is calculated. The results show that piecewise continuous refractive index can be used for modeling semitransparent media with continuously variable refractive index. Emission from the medium is complex and quite different from a medium with a constant refractive index, when the absorption coefficient is small and/or the refractive index varies greatly in the medium. The refractive/totally reflective inner interface in the bar model gives a more precise emission distribution and can be extended to simulate emission from a medium with a complex three-dimensional refractive index distribution.

A forward–backward Monte Carlo method for solving influence diagrams

Although influence diagrams are powerful tools for representing and solving complex decision-making problems, their evaluation may require an enormous computational effort and this is a primary issue when processing real-world models. We shall propose an approximate inference algorithm to deal with very large models. For such models, it may be unfeasible to achieve an exact solution. This anytime algorithm returns approximate solutions which are increasingly refined as computation progresses, producing knowledge that offers insight into the decision problem.

Analysis of Rocket Plume Base Heating by Using Backward Monte-Carlo Method

Analysis of Rocket Plume Base Heating by Using Backward Monte-Carlo Method

Simulation of the infrared radiation characteristics of high-temperature exhaust plume including particles using the backward Monte Carlo method

The analysis of the infrared radiation characteristics of high-temperature free-stream flow including particles is very significant for the field of target detection, combustion diagnosis and temperature measurement of flame. In this paper, the infrared radiation characteristics of high-temperature free-stream flow are calculated and analyzed using the backward Monte Carlo method, considering the effect of the directional radiation heat flux due to the particle scattering and the different boundary conditions. The calculation results of emitting, absorbing and anisotropically scattering media are compared with the forward Monte Carlo and finite-volume methods results, which shows the superiority on computational efficiency with the backward Monte Carlo method.

Backward Monte Carlo simulation for apparent directional emissivity of non-isothermal semitransparent slab

A backward Monte Carlo method based on radiation distribution factor is extended to compute the apparent directional emissivity of one-dimensional absorbing–emitting–scattering semitransparent slab with specular semitransparent surface and opaque diffuse substrate. A non-isothermal semitransparent slab is taken as an example to examine the efficiency of backward Monte Carlo method. The apparent directional emissivity of the semitransparent slab is determined by backward Monte Carlo simulation and compared with that determined by forward Monte Carlo simulation. The results show that the backward Monte Carlo method is very efficient in solving the apparent directional emissivity of the semitransparent slab. The backward Monte Carlo method converges more quickly than the forward Monte Carlo method.

A two‐dimensional Monte Carlo model of radiative transfer in sea ice

A two‐dimensional, Monte Carlo radiative transfer model was developed for the analysis of optical data from cylindrical samples of sea ice. The backward Monte Carlo method was used to solve the radiative transfer equation in a cylindrical, azimuthally symmetric domain. Horizontal layers between two depths and vertical shells between two radii can be used to simulate spatial gradients in scattering, absorption, and refractive index in the model. The top of the cylinder can be illuminated by either normally incident, collimated radiation or by diffuse radiation. Irradiance and radiance detectors can be located anywhere within or on the cylindrical domain. The model was tested by comparing predicted apparent optical properties with solutions from existing one‐dimensional and two‐dimensional radiative transfer models. Domains with the largest optical depths and smallest radii were found to be impacted most by the horizontally finite geometry. The model was used to interpret backscattered and transmitted spectral radiance data taken in the laboratory from cylindrical core samples of first‐year sea ice at −15°C. Use of a similarity parameter facilitated comparison between observations and model predictions by reducing the number of independent variables by one. Concurrent observations of ice microstructure indicated that light scattering due to inclusions of brine, gas, and precipitated salts should result in a scattering coefficient of ∼4.6 cm−1 in our samples. Combining this value with the inferred similarity parameter yielded an asymmetry parameter of 0.98 for first‐year sea ice at −15°C. Agreement between observed and predicted spectral radiances demonstrates the viability of this model as a tool for analyzing the optical properties of samples with finite geometry.

Backward Monte Carlo Simulations in Radiative Heat Transfer

Standard Monte Carlo methods trace photon bundles in a forward direction, and may become extremely inefficient when radiation onto a small spot and/or onto a small direction cone is desired. Backward tracing of photon bundles is known to alleviate this problem if the source of radiation is large, but may also fail if the radiation source is collimated and/or very small. In this paper various implementations of the backward Monte Carlo method are discussed, allowing efficient Monte Carlo simulations for problems with arbitrary radiation sources, including small collimated beams, point sources, etc., in media of arbitrary optical thickness.

A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam

Monte Carlo approaches to compute multiple scattering of polarized light are examined. A Backward Monte Carlo (BMC) method is developed to solve the Stokes vector of the multiple scattered light for an inhomogeneous scattering medium with boundaries. A generalized form of the BMC method in vector notation is proposed. This method can determine the scattered light with sufficient accuracy in both intensity and polarization compared to the same calculation using the doubling–adding method for a plane parallel medium. For application to a narrow incident beam and an inhomogeneous medium, a modified BMC method is developed, borrowing a concept from the Forward Monte Carlo (FMC) method for the first scattering events. Furthermore, a modification of the total scattering matrix, i.e., the combination of the derived scattering matrix with its time inverse, is discussed. This BMC method can be used successfully for model calculations of lidar and other laser measurements of polarized light.

Microwave radiative transfer through horizontally inhomogeneous precipitating clouds

Recent advances in cloud microphysical models have led to realistic three‐dimensional distributions of cloud constituents. Radiative transfer schemes can make use of this detailed knowledge in order to study the effects of horizontal as well as vertical inhomogeneities within clouds. This study looks specifically at the differences between three‐dimensional radiative transfer results and those obtained by plane parallel, independent pixel approximations in the microwave spectrum. A three‐dimensional discrete ordinates method as well as a backward Monte Carlo method are used to calculate realistic radiances emerging from the cloud. Analyses between these models and independent pixel approximations reveal that plane parallel approximations introduce two distinct types of errors. The first error is physical in nature and is related to the fact that plane parallel approximations do not allow energy to leak out of dense areas into surrounding areas. In general, it was found that these errors are quite small for emission‐dominated frequencies (37 GHz and lower) and that physical errors are highly pronounced only at scattering frequencies (85 GHz) where large deviations and biases up to 8 K averaged over the entire cloud were found. The second error is more geometric in nature and is related to the fact that plane parallel approximations cannot accommodate physical boundaries in the horizontal dimension for off‐nadir viewing angles. The geometric errors were comparable in magnitude for all frequencies. Their magnitude, however, depends on a number of factors including the scheme used to deal with the edge, the nature of the surface, and the viewing angle.

An adjoint Monte Carlo treatment of the equations of radiative transfer for polarized light

The equation of radiative transfer for a Stokes' intensity vector is used to define a four-vector Green's function. The physical quantities of interest are represented by a response vector which is found by integrating the product of a suitable response matrix and the Stokes' intensity vector over phase space. Equations adjoint to those for the Stokes' intensity vector and for the Green's function vector are given. The response vector is then expressed in terms of the adjoint vector Green's function. A Monte Carlo sampling procedure is given for the adjoint Green's function vector equation. When the adjoint source vector is given by a Dirac delta function in phase space, the response vector is the Stokes' intensity vector and the “backward Monte Carlo method” of Collins and Wells (Report RRA-T74, Radiation Research Associates, Inc.) obtains.

Monte Carlo Studies of the Sky Radiation at Twilight

Results are presented in several wavelengths of the sky intensity and polarization along the solar vertical at twilight, as calculated using the backward Monte Carlo method applied to spherical shell atmospheres. Molecular scattering with anisotropy of molecules, ozone absorption, and refraction are taken into account. The dependence of the intensity on the solar depression angle is in general agreement with calculations based upon single plus second order scattering, but the degree of polarization is much higher. It is verified that the molecular plus ozone atmosphere does not explain the purple light. The elongation of the Babinet neutral point from the sun is determined as a function of solar depression angle.

Backward Monte Carlo Calculations of the Polarization Characteristics of the Radiation Emerging from Spherical-Shell Atmospheres

A Monte Carlo procedure, designated as FLASH, was developed for use in computing the intensity and polarization of the radiation emerging from spherical-shell atmospheres and is especially useful for investigating the sunlit sky at twilight time. The procedure utilizes the backward Monte Carlo method and is capable of computing the Stokes parameters for discrete directions at the receiver position. Both molecular and aerosol scattering are taken into account as well as ozone, aerosol, water vapor, and carbon dioxide absorption within the atmosphere. The curvature of the light path due to the changing index of refraction with altitude is taken into account. Some comparisons are made between FLASH calculations for a pure Rayleigh atmosphere, a combined Rayleigh and aerosol atmosphere, and calculations reported by other authors for plane-parallel atmospheres. The comparisons show that the FLASH calculations for spherical-shell atmospheres are in good agreement with those for plane-parallel atmospheres within the range of zenith angles for which no differences could be attributed to the difference in the geometries of the two atmospheric models.