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NASA NTRS1976

Radiative transfer within the earth's troposphere and stratosphere - A simplified radiative-convective model

A radiative transfer model of the troposphere and stratosphere is presented which includes both long-wave cooling and solar heating due to H2O, CO2 and O3 and has a simplified formulation which facilitates the inclusion of Doppler broadening, H2O continuum bands, hot and minor isotopic bands of CO2, and overlap of H2O bands with CO2 and O3 bands. The radiative model is used to develop an accurate radiative-convective model for studying the global surface temperature, stratospheric thermal structure and the net outgoing long-wave flux.

Ramanathan, V.↗

NASA NTRS1990

Radiative transfer in the dynamic atmospheres of long period variable stars

An iterative procedure is presented for determining the thermal structure and dynamics of Mira-type stellar atmospheres, where the non-LTE radiative transfer code PANDORA is used in conjunction with the Bowen hydrodynamics code of Iowa State University. Preliminary results are reported for an atmospheric model of a pulsating AGB star of 1 solar mass, 240 solar radii, Teff = 3000 K, and a period of 320 days. At the present time, H, H(-), Mg I, and Mg II radiative transfer calculations have been completed and synthetic spectra are shown for H-alpha. The radiative transfer calculations demonstrate that cooling in the innermost shock of the original Bowen model is underestimated due to the omission of various hydrogen transitions. These initial results suggest that the main shock of the Bowen models are too hot and/or too deep.

Luttermoser, Donald G.↗

NASA NTRS1994

Super-Eddington radiation transfer in soft gamma repeaters

Bursts from soft gamma repeaters (SGRs) have been shown to be super-Eddington by a factor of 1000 and have been persuasively associated with compact objects. Super-Eddington radiation transfer on the surface of a strongly magnetic (greater than or equal to 10(exp 13) G) neutron star is studied and related to the observational constraints on SGRs. In strong magnetic fields, Thompson scattering is suppressed in one polarization state, so super-Eddington fluxes can be radiated while the plasma remains in hydrostatic equilibrium. We discuss a model which offers a somewhat natural explanation for the observation that the energy spectra of bursts with varying intensity are similar. The radiation produced is found to be linearly polarized to one part in 1000 in a direction determined by the local magnetic field, and intensity variations between bursts are understood as a change in the radiating area on the source. The net polarization is inversely correlated with burst intensity. Further, it is shown that for radiation transfer calculations in limit of superstrong magnetic fields, it is sufficient to solve the radiation transfer for the low opacity state rather than the coupled equations for both. With this approximation, standard stellar atmosphere techniques are utilized to calculate the model energy spectrum.

Ulmer, Andrew↗

NASA NTRS1986

Comparative accuracy of the Albedo, transmission and absorption for selected radiative transfer approximations

Illustrations of both the relative and absolute accuracy of eight different radiative transfer approximations as a function of optical thickness, solar zenith angle and single scattering albedo are given. Computational results for the plane albedo, total transmission and fractional absorption were obtained for plane-parallel atmospheres composed of cloud particles. These computations, which were obtained using the doubling method, are compared with comparable results obtained using selected radiative transfer approximations. Comparisons were made between asymptotic theory for thick layers and the following widely used two stream approximations: Coakley-Chylek's models 1 and 2, Meador-Weaver, Eddington, delta-Eddington, PIFM and delta-discrete ordinates.

King, M. D.↗

NASA NTRS1991

The coupling of radiative transfer to quasi 1-D flows with thermochemical nonequilibrium

Quasi-one-dimensional nonequilibrium nozzle flows with coupled radiative transfer are considered. The strongly coupled formulation of radiation and flowfield leads to a governing set of integro-differential equations. A fully implicit numerical method using the full matrix inversion or block iteration methods is presented to solve these equations. The nonequilibrium gas model consists of two chemical species, molecular and atomic nitrogen. The thermodynamic state of the gas is described by two temperatures, translational-rotational and vibrational, and the thermal radiation is assumed to be governed by the vibrational temperature. In radiative transfer, gases are assumed to be absorbing and emitting, and a detailed spectral dependency of the absorption coefficient is prescribed for a non-gray gas. The numerical solutions of strongly radiating nonequilibrium flows are presented for both gray and non-gray gases.

Gokcen, Tahir↗

NASA NTRS2017

Active and Passive Radiative Transfer Modeling with Preferentially-Aligned Particles

The fluid dynamics of falling hydrometeors often results in preferential orientations that can affect both the intensity and polarization of electromagnetic radiation. In order to properly interpret remote sensing observations of ice and snow, such alignments should be considered when constructing databases of scattering particles; however, the inclusion of aligned particles increases the complexity of the scattering data. To demonstrate the use of scattering properties of preferentially-aligned particles, millimeter-wave brightness temperatures and radar observables, including reflectivity and linear depolarization ratio, are modeled using the Atmospheric Radiative Transfer Simulator (ARTS). The necessary scattering parameters for vector radiative transfer, particularly with respect to ARTS, are reviewed, and the exploitation of particle symmetries, as well as scattering reciprocity relationships, are detailed.

radiative transfer↗

NASA NTRS2010

A Principal Component-Based Radiative Transfer Forward Model (PCRTM) for Vertically in Homogeneous Cloud

A principal-component based radiative transfer model (PCRTM) is developed for simulating the infrared spectral radiance at the top of the atmosphere (TOA). The PCRTM approach removes the redundancy in radiative transfer calculation in high resolution infrared spectra, and saves significant amount of computational time with great accuracy. In PCRTM, both ice and water clouds are treated as effective transmissivity and reflectivity stored in a pre-calculated lookup tables. These quantities are calculated using cloud single scattering properties such as cloud optical depth, cloud particle size, cloud phase, etc. The cloud can be inserted into any pressure layer in the PCRTM model (up to 100 layers). The effective temperature of each cloud layer is treated as a function of its optical depth. To test the accuracy of this approximation, the results are compared with the more rigorous DISORT model, which treats cloud as a plane parallel layer. The root-mean-square error of PCRTM, with respect to DISORT results, is generally less than 0.5 K in brightness temperature. However, the CPU time required by PCRTM was approximately two orders of magnitude less than that required by DISORT.

Li, Hui↗

NASA NTRS1993

Session on modeling of radiative transfer processes

The session on modeling of radiative transfer processes is reviewed. Six critical issues surfaced in the discussion concerning scale-interactive radiative processes relevent to the mesoscale convective systems (MCS's). These issues are the need to expand basic knowledge of how MCS's influence climate through extensive cloud shields and increased humidity in the upper troposphere; to improve radiation parameterizations used in mesoscale and General Circulation Model (GCM) models; to improve our basic understanding of the influence of radiation on MCS dynamics due to diabatic heating, production of condensate, and vertical and horizontal heat fluxes; to quantify our understanding of radiative impacts of MCS's on the surface and free atmosphere energy budgets; to quantify and identify radiative and microphysical processes important in the evolution of MCS's; and to improve the capability to remotely sense MCS radiative properties from space and ground-based systems.

Flatau, Piotr↗

NASA NTRS2020

Electromagnetic Scattering by Discrete Random Media Illuminated by a Gaussian Beam II: Solution of the Radiative Transfer Equation

In this paper, we present numerical methods for solving the phenomenological scalar radiative transfer equation for a discrete random medium illuminated by a Gaussian beam. These rely on the Fourier transform method for the horizontal variables and the discrete ordinate method with matrix exponential for solving the underlying one-dimensional radiative transfer equation in the wavenumber domain. The problem of a Gaussian beam at oblique and normal incidence, as well as, the searchlight problem are treated. A complete description of the methods and the numerical algorithms is provided.

Gaussian beam↗

NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗

NASA NTRSDate not supplied

A Principal-Component-Based Radiative Transfer Model (PCRTM) for Hyperspectral Shortwave and Longwave Satellite Sensors and Its Applications

The radiative transfer model (RTM) or forward model is an essential component in satellite remote sensing. For modern hyperspectral remote sensors, fast and accurate RTMs are needed due to a large number of spectral dimensions and high spatial resolutions. We will describe a Principal Component-based radiative transfer model (PCRTM) which can simulate the top-of-atmosphere (TOA) radiance or reflectance spectra 250 nm to 2000 micrometers quickly and accurately. The PCRTM has been demonstrated to be extremely accurate, compared to the line-by-line RTM benchmarks, and the former is several orders more computationally efficient than the latter. We will demonstrate how the PCRTM and the associated inversion algorithms are used to infer atmospheric temperature, moisture, and trace gas profiles, as well as cloud and surface properties from hyperspectral IR sounders such as Atomspheric Infrared Souder (AIRS) and Cross-track Infrared Sounder (CrIS). High-quality climate records for a 20-year duration have been derived from these IR hyperspectral data. Finally, we will show some examples of using PCRTM to retrieve cloud properties from Earth Surface Mineral Dust Source Investigation (EMIT) and its applicability of PCRTM to future missions such as the CLARREO (Climate Absolute Radiance and Refractivity Observatory) Pathfinder (CPF) CPF and the Surface Biology and Geology (SBG).

Xu Liu↗

NASA NTRS1988

A simple formulation of the delta-four-stream approximation for radiative transfer parameterizations

A systematic development of the delta-four-stream approximation for calculations of radiative fluxes in planetary atmosphere is presented. It is shown that an analytic solution for this approximation can be derived explicitly, with minimum computational effort for flux calculations. Relative accuracy checks for reflection, transmission, and absorption for numerous asymmetry factors, single-scattering albedos, optical depths, and solar zenith angles have been performed with respect to the 'exact' results computed from the adding method for radiative transfer. Overall, results from the delta-four-stream approximation yield relative accuracies within about 5 percent. This approximation is well suited to radiative transfer parameterizations involving flux and heating calculations in aerosol and cloudy atmospheres.

Liou, Kuo-Nan↗

NASA NTRS1981

Radiative transfer theory for active remote sensing of a homogeneous layer containing spherical scatterers

The radiative transfer theory with a Rayleigh scattering model is used to study the effect of volume scattering for active microwave remote sensing of low-loss and scattering dominant areas by obtaining backscattering cross sections through iterative and numerical approaches. The iterative approach gives closed form solutions which are valid when the effect of scattering is small. The depolarization of the backscattered power is shown to be a second-order effect. For the general cases, a numerical approach is used to solve the radiative transfer equations. The theoretical results are compared and illustrated for the various cases.

Shin, R. T.↗

NASA NTRS1974

Radiative transfer in highly scattering materials - numerical solution and evaluation of approximate analytic solutions

Numerical solutions for radiative transport in a class of anisotropically scattering materials are presented. Conditions for convergence and divergence of the iterative method are given and supported by computed results. The relation of two flux theories to the equation of radiative transfer for isotropic scattering is discussed. The adequacy of the two flux approach for the reflectance, radiative flux and radiative flux divergence of highly scattering media is evaluated with respect to solutions of the radiative transfer equation.

Weston, K. C.↗

NASA NTRS2011

Numerical Solution of the Radiative Transfer Equation: X-Ray Spectral Formation from Cylindrical Accretion onto a Magnetized Neutron Star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. This requires developing numerical routines for the solution of the radiative transfer equation according to the expected physical conditions of the systems under study. Aims. We have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. Methods. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system pi using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. Results. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth pi produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. Conclusions. The algorithm has been implemented in the XPEC package for X-ray fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (approx > 10(exp 12) G). This latter case is expected to be of typical accreting systems such as X-ray pulsars and supergiant fast X ray transients.

Fairnelli, R.↗

NASA NTRS2018

An Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. II: Approach Based on the Dyson and Bethe-Salpeter Equations

In this paper, the vector radiative transfer equation is derived by means of the vector integral Foldy equations describing the electromagnetic scattering by a group of particles. By assuming that in a discrete random medium the positions of the particles are statistically independent and by applying the Twersky approximation to the order-of-scattering expansion of the total field, we derive the Dyson equation for the coherent field and the ladder approximated Bethe–Salpeter equation for the dyadic correlation function. Then, under the far-field assumption for sparsely distributed particles, the Dyson equation is reduced to the Foldy integral equation for the coherent field, while the iterated solution of the Bethe–Salpeter equation ultimately yields the vector radiative transfer equation.

Electromagnetic scattering↗

NASA NTRS2022

A Deep Learning Approach to Fast Radiative Transfer

Due to the sheer volume of data, leveraging satellite instrument observations effectively in a data assimilation context for numerical weather prediction or for remote sensing requires a radiative transfer model as an observation operator that is both fast and accurate at the same time. Physics-based line-by-line radiative transfer (RT) models fulfil the requirement for accuracy, but are too slow and too costly in computational terms for operational applications. Therefore, fast methods were developed to be able to perform fast RT calculations using techniques such as spectral sampling or pre-computed look-up tables. The operational fast models currently calculate the absorption and scattering coefficients from the pre-computed regression coefficients and atmospheric state and cloud profiles. As a novel solution to this problem, this work investigates a deep learning approach to replace the regression coefficients in the fast RT models. A selection of hidden-layer neural network configurations is trained against atmospheric transmittance profile data computed by an accurate line-by-line model and their performance is evaluated and their advantages and disadvantages are discussed.

Machine learning↗

NASA NTRS2018

Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. I: Approach Based on the Far-Field Foldy Equations

In this paper, we revisit, with further enhancements and clarifications, the self-consistent first-principles approach developed previously for deriving the vector radiative transfer theory for a discrete random medium with a sparse concentration of particles. We specifically consider the case of a plane-parallel particulate layer embedded in an otherwise homogeneous unbounded medium. The solution method is based on the far-field Foldy equations, an order-of-scattering expansion for the total field derived under the Twersky approximation, the computation of the coherent field by assuming that the positions of the particles are uncorrelated, and the ladder approximation for the coherency dyadic. The latter yields an integral equation for the diffuse specific coherency dyadic, defined through an angular spectrum repre- sentation for the coherency dyadic, which in turn, gives the vector radiative transfer equation for the diffuse specific intensity column vector. We analyze specifically the computation of the coherent field for inhomogeneous particulate media and multiple species of particles, the continuous extension of the far-field representation to the near field, the Foldy approximation, and the Foldy integral equation for the coherent field. Finally, we discuss the transition from the vector to the scalar radiative transfer equation.

Doicu, Adrian↗