Radiative transfer

The Simple Model of the Atmospheric Radiative Transfer of Sunshine (SMARTS) is a computer program designed to evaluate the surface solar irradiance components in the shortwave spectrum (spectral range 280 to 4000 nm) under cloudless conditions. The program, written in FORTRAN, relies on simplifications of the equation of radiative transfer to allow extremely fast calculations of the surface ...

Radiative transfer equation (RTE) is the commonly accepted continuum scale governing equation for radiative heat transfer in particulate system. However, its applicability is questionable for non ...Radiative Transfer; Atmospheric Radiation; Special Issue on Advancement of polarimetric observations: calibration and improved aerosol retrievals (APOLO-2017) Special Issue: Laser-light and Interactions with Particles 2020; Special Issue: HITRAN2020; Special Issue: Atmospheric Light Scattering and Radiative TransferIf you need to quickly send money to a friend or family member in another country, there are a few different ways to do so. Keep reading to learn more about your options for sending cash internationally.The three ways that heat can be transferred are conduction, convection and radiation. Conduction is most efficient in solids, convection occurs in liquids and gases and radiation occurs through anything that allows radiation to pass through...Apr 25, 2019 · Although radiative transfer is determined by traits with relevance for plant functioning, few studies have explicitly linked RTMs and plant functioning 19,23,24. Such RTMs are particularly ... For radiative transfer problems with 2-D/3-D spatial dimensions, the basic principles of the numerical integration method can be directly generalized. One important difference between the 1D vs higher dimensional problems is that each light ray passing through the grid would will intersect with the cell walls multiple times and get divided into ...Radiative Heat Transfer in Advanced Thermal Insulations. It is known that materials with high porosity and small pore size are preferred for thermal insulation at both high and moderate temperatures. High porosity reduces the contribution of heat conduction in the carrier material, while the small pore size (less than the mean free path of gas ...Radiative forcing by individual long-lived greenhouse gases since the mid-18th century is on the order of 1 W m −2 or less. Therefore, highly accurate radiative transfer in GCMs is essential to model effectively the radiative contribution of LLGHGs to global climate change.

RTE+RRTMGP is a set of codes for computing radiative fluxes in planetary atmospheres. This fork uses neural networks for the gas optics computations and optimized code for the radiative transfer. neural-networks climate-models radiative-transfer-models correlated-k. Updated on Dec 8, 2022.In the study of heat transfer, Schwarzschild's equation is used to calculate radiative transfer (energy transfer via electromagnetic radiation) through a medium in local thermodynamic equilibrium that both absorbs and emits radiation.To measure the radiative heat transfer, it is preferred to ensure that thermal radiation is the dominant transfer mode across the sample. Note that the effect of gas conduction is eliminated by maintaining the pressure in the chamber below 3 × 10 −4 Pa. Although near-field radiative transfer increases considerably as gap spacings approach ...In Chapter 6, we alluded to energy transfer by radiation as a mechanism for heat flow, but due to the entirely different natures of conduction and radiation, only a limited discussion of radiation appeared prior to this chapter. ... Radiative Transfer, McGraw-Hill, New York, NY, 1967. Google Scholar E. M. Sparrow and R. D. Cess, Radiation Heat ...The radiative transfer theory provides the most logical linkage between observations and physical processes that generate signals in optical remote sensing. The radiative transfer equation, therefore, is an integral part of Earth remote sensing, since it provides the most efficient tool for accurate retrievals of Earth properties from satellite ...This book is a valuable resource for researchers in the field of radiative transfer theory whose interests transcend the physical and numerical aspects of the interaction of light with matter. Show less. Pure and Applied Mathematics, Volume 74: Radiative Transfer on Discrete Spaces presents the geometrical structure of natural light fields. ...Energy transfer is the conveyance of energy from one item to another; the transfer occurs among different scales and motions. Energy transfer may mean different things in different sciences.The radiative heat transfer processes are complicated and difficult to model, usually including absorption, emission, and scattering of radiant energy in both the gas and condensed phases, as well as surface absorption, transmission, and reflection. In this work, the focus is on a CO2 laser with a wavelength of 10.6 μm.

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 ...The zone method of allowing for the effect, on radiative transfer, of the temperature variation in furnace enclosures has been applied to the problem of interaction between radiation and other modes of heat transfer. The effect of different flow patterns on the gas temperature-field and wall-flux distribution in a cylindrical furnace has been ...Radiative transfer equation: considering extinction n⋅∇ I = 0 Spatial derivative along the ray In the absence of extinction, emission, scattering. n⋅∇ I = − α tot I, where α tot is the extinction coefficient. Sources of extinction: Absorption (the photon is destroyed) Scattering (the photon changes direction) Thus we can write: α ...Radiative transfer models. Table 1 gives an overview of the participating radiative transfer models. In the following, only the MSCART model is briefly described. For short descriptions of the other models please refer to the first publication of the IPRT project [1]. Model coordinate system and Stokes vectorTopics. Review of Basic Thermal Radiation Concepts, Blackbody Radiation. Near Field Thermal Radiation, Fluctuation-dissipation Theory. This section lists the various topics …

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Radiative transfer equation is the governing equation of radiation propagation in participating media, which describes the general balance of radiative energy transport in the participating media taking into account the interactions of attenuation and augmentation by absorption, scattering, and emission processes (Howell et al. 2011; Modest 2013). ...Radiative Transfer (RT) is a fundamental topic needed to interpret all remote observations spanning airless bodies, atmospheres of exoplanets and solar system bodies, protoplanetary disks, and all other astronomical objects. These complex applications require a comprehensive toolset of custom codes and extensive databases of optical properties ...While the radiative transfer can be constrained to one or more narrow bands (at a single wavelength maximal transfer of radiation between two bodies can be achieved, as the optical transmission coefficient can reach unity), for instance due to polariton resonance(s), this can lead to reducing the exchanged power to a minute value. The Bose–Einstein …Models of SIF radiative transfer are developed hand-in-hand with the RS experimental work conducted at leaf as well as canopy scales (Aasen et al., 2019). Leaf RTMs are usually embedded in canopy-scale RTMs that can be classified according to the canopy representation as one-dimensional (1D) or three-dimensional (3D).The radiative properties are modeled by the full spectrum k-distribution method, and the radiative transfer equation is solved by the discrete ordinates method. Results show that gas and solid radiative heat fluxes are about 1300 W/m 2 and 4500 W/m 2 for the dense and dilute conditions respectively, and decrease exponentially with the solid ...Radiative Transfer in Planetary/Cometary Atmospheres and Light Scattering by Small Dust Particles. Experimental and Theoretical Study of the Scattering Behavior of Dust Particles., scattering, polarization, dust, atmospheres, comets, experiments Laurent Pilon, University of California Los Angeles, Department of Mechanical and Aerospace ...

Apr 15, 2013 · Subrahmanyan Chandrasekhar. Courier Corporation, Apr 15, 2013 - Science - 416 pages. " Radiative Transfer is the definitive work in the field. It provides workers and students in physics, nuclear physics, astrophysics, and atmospheric studies with the foundation for the analysis of stellar atmospheres, planetary illumination, and sky radiation. Asinari and co-workers [35] described the advantage of having common data structures for radiation intensity and fluid flow in radiative transfer and fluid mechanics problems. They extended the LBM to solve a benchmark radiative equilibrium problem for a 2-D rectangular enclosure, and the LBM was found to have an edge over the FVM.The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature in a biological medium makes it very challenging to numerically solve the RTE problem accurately.Radiative transfer models of the Earth’s atmosphere play a critical role in supporting Earth Observation applications such as vicarious calibration. In the solar reflective spectral domain, these models usually account for the scattering and absorption processes in the atmosphere and the underlying surface as well as the radiative coupling between these two media.Radiative transfer equation is the governing equation of radiation propagation in participating media, which describes the general balance of radiative energy transport in the participating media taking into account the interactions of attenuation and augmentation by absorption, scattering, and emission processes (Howell et al. 2011; …Solution of radiative transfer problems considering relatively more complex phenomena is possible with the Monte Carlo method without compromising the accuracy of the solution. Moreover, the implementing of these complex physical phenomena, such as spectral and directional properties, anisotropic scattering, and complex geometries, does …ving atmospheric radiative transfer problems are described. The first, Streamer, is a medium spectral resolution model suitable for studying the radiation budgets at the surface and within the atmosphere. It can also be used to simulate satellite sensor ob-servations. The second tool, FluxNet, is a neural network-based radiative transfer model ...The theory and numerical modelling of radiation processes and radiative transfer play a key role in astrophysics: they provide the link between the physical properties of an object and the radiation it emits. In the modern era of increasingly high-quality observational data and sophisticated physical theories, development and exploitation of a variety of approaches to the modelling of ...A third path for radiative transfer simulations is the spherical harmonics (P N) method. This is a spectral method, based on a linear expansion of the radiation intensity in angle using spherical harmonic basis functions. The method yields a hyperbolic system of partial differential equations for the expansion coefficients, which are just the ...Radiative transfer code (except MC) totally revised, including: Higher consistency between modules. Higher calculation efficiency. Jacobian of atmospheric variables now fully analytical. Absorption/LBL revised. Support for new lineshapes. Performance improvements. New and extended system for defining particle size distributions. DOIT improvements.

The radiation energy per unit time from a black body is proportional to the fourth power of the absolute temperature and can be expressed with Stefan-Boltzmann Law as. q = σ T4 A (1) where. q = heat transfer per unit time (W) σ = 5.6703 10-8 (W/m2K4) - The Stefan-Boltzmann Constant. T = absolute temperature in kelvins (K)

3.2 Blackbody Radiation All matter emits radiation if it is at a temperature > absolute zero. A blackbody is a perfect emitter - it emits the maximum possible amount of radiation at each wavelength. A blackbody is also a perfect absorber, absorbing at all wavelengths of radiation incident on it. Therefore, it looks black. Planck's Blackbody ...Radiative transfer is the science that calculates the distribution of radiative energy in planetary atmospheres based on their composition. It is a branch of optics, thanks to …13.6 Radiative transfer, entropy and local potentials 460 13.7 Radiative transfer in masers 466 Exercises 466 References 467 Symbol index 469 Index 477. Chapter 1 Definitions of fundamental quantities of the radiation field 1.1 Specific intensity This is the most fundamental quantity of the radiation field. We shall be dealing with1.2 Formal radiative transfer equation The constancy of intensity in vacuum is a property that can be very conveniently used to describe the interaction with matter, for if space is not a vacuum but filled with some material with extinction coefficient α (in units of 1/cm) the equation of radiative transfer becomes: dI ds = −αI (1.5) 2About the journal. Papers with the following subject areas are suitable for publication in the Journal of Quantitative Spectroscopy and Radiative Transfer: Spectra of atoms, molecules: theoretical and experimental aspects; Spectral lineshape studies including models and computational algorithms; Spectroscopy of the terrestrial, planetary, and ... Abstract. Atmospheric radiative transfer models (RTMs) are software tools that help researchers in understanding the radiative processes occurring in the Earth's atmosphere. Given their importance in remote sensing applications, the intercomparison of atmospheric RTMs is therefore one of the main tasks used to evaluate model performance and identify the characteristics that differ between models.the radiative transfer equation Jianguo Huang∗, Yue Yu School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University Shanghai 200240, China Abstract The radiative transfer equation is a fundamental equation in transport theory and appli-cations, which is a 5-dimensional PDE in the stationary one-velocity case, leading to greatNonreciprocal thermal photonics is an emerging topic in thermal radiation control. Recent advances in using this approach for energy harvesting, thermal management, and even communication have stimulated substantial interest in the subject. The authors review recent developments, challenges, and opportunities in the unidirectional transfer of heat energy via light, to provide a snapshot of the ...

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Radiative transfer models are used to simulate satellite observations from input atmospheric profiles and surface parameters. These models have a wide range of applications, including being used as forward model to assimilate satellite observations into numerical weather prediction models or for calibration and validation of satellite measurements.Community Radiative Transfer Model (CRTM) The CRTM is composed of four important modules for gaseous transmittance, surface emission and reflection, cloud and aerosol absorption and scattering, and a solver for a radiative transfer. The CRTM was designed to meet users' needs.Topics. Review of Basic Thermal Radiation Concepts, Blackbody Radiation. Near Field Thermal Radiation, Fluctuation-dissipation Theory. This section lists the various topics covered during the course along with two sets of lecture notes files, one by the professor and one by a student. Thermal radiation is energy transfer by the emission of electromagnetic waves which carry energy away from the emitting object. For ordinary temperatures (less than red hot"), the radiation is in the infrared region of the electromagnetic spectrum. The relationship governing the net radiation from hot objects is called the Stefan-Boltzmann law:The impacts of varying relevant factors on velocity, temperature, and microbe density are thoroughly examined. Results designate that the radiation factor favorably affects the velocity and temperature profiles. The rate of mass transport of liquid oxygen rises by about 45% when the Schmidt number grows from 1 to 2.Jul 19, 2022 · For example, low-fidelity physical radiative transfer calculations can be augmented by a neural network to match those of high-fidelity calculations (Brodrick et al., 2021), radiative transfer calculations performed at a subset of wavelengths can be extended across the entire spectral range (Le et al., 2020), or a neural network is used to ... Two tools for the solution of radiative transfer problems are presented. Streamer is a flexible medium spectral resolution radiative transfer model based on the plane-parallel theory of radiative ...The main tool is the uvspec radiative transfer model. It will be described first. Secondly, the other libRadtran tools will be summarized followed by examples of usage of the vari-ous tools. The description applies to version 1.0 or later of the package. 2 The uvspec radiative transfer model The uvspec radiative transfer model calculates the ...The coupling of a CGM with a radiative transfer model offers the possibility to assimilate remote sensing data while taking into account uncertainties in input parameters. A particle filter was used to assimilate satellite data into a CGM coupled with a leaf-canopy radiative transfer model to update biomass simulations of maize. The synthetic ...Dynamic control of radiative heat transfer is of fundamental interest as well as for applications in thermal management and energy conversion. However, realizing high contrast control of heat flow without moving parts and with high temporal frequencies remains a challenge. Here, we propose a thermal modulation scheme based on optical pumping of semiconductors in near-field radiative contact. ….

Radiative Heat Transfer, Fourth Edition is a fully updated, revised and practical reference on the basic physics and computational tools scientists and researchers use to solve problems in the broad field of radiative heat transfer. This book is acknowledged as the core reference in the field, providing models, methodologies and calculations ...To associate your repository with the radiative-transfer topic, visit your repo's landing page and select "manage topics." GitHub is where people build software. More than 100 million people use GitHub to discover, fork, and contribute to over 330 million projects.Rendering radiative transfer through media with a heterogeneous refractive index is challenging because the continuous refractive index variations result in light traveling along curved paths. Existing algorithms are based on photon mapping techniques, and thus are biased and result in strong artifacts. On the other hand, existing unbiased ...However, since 3D radiative transfer calculations are computationally expensive, efficient methods need to be developed for operational applications that provide an appropriate balance between accuracy and computational cost. To fully benefit from 3D-box AMFs, 3D radiative transfer calculations require high-resolution 3D distributions of trace gases …emitting and scattering. In radiative equilibrium, depending upon the cases, either full or part of the south boundary is the radiation source, and the medium temperature is unknown. In the combined mode conduction and radiation heat transfer problem, initially, the entire system is at temperature TThe development of the Community Radiative Transfer Model (CRTM) and its subsequent improvements have created a better method for NWP models to assimilate satellite measurements made under all weather conditions. The CRTM was developed by the U.S. Joint Center for Satellite Data Assimilation (JCSDA) to provide fast, accurate satellite radiance ...The radiative transfer simulation within B-cluster has been developed based on an efficient Monte Carlo path-tracing algorithm and implemented in the LargE-Scale remote sensing data and image ...Radiative transfer (RT) modeling plays a key role in interpreting the radiance measured by multispectral sensors. Glaciers respond to variations in solar irradiance. At-sensor radiance depends upon glacier surface material composition and intermixture of materials, solar and sensor geometry, and surface topography.Radiative transfer is related to the well-known inner-filter effect in fluorescence (Lakowicz, 2006) and occurs preferentially at higher concentrations, which are irrelevant for single-molecule spectroscopy. Nonradiative energy transfer is qualitatively a different phenomenon and is strongly distance dependent. It originates from the dipolar ...The key points in basic Quantum Physics, regarding radiative heat transfer, are: Molecules have one or more electrons circling them. Their orbital height is not variable, But fixed. The electrons only orbit at set altitudes, the closer to the molecule the lower the kinetic energy of the molecule and so the lower the molecule's temperature. Radiative transfer, radiative transfer will be recounted and evaluated. These include his development of the discrete ordinates method, the invariance principles, and his formulation and solution of the transfer equation for polarized light. 1. Introduction Chandrasekha inr’s rawdioarktive transf er wof hais lityfpeilcoanlog fpattern worki ningtensively in some particul ar of fieldphysics …, The fast 3D radiative transfer package called Simulated Weather Imagery has been developed to serve the development and application needs of high-resolution atmospheric modeling. Visually and physically realistic, full natural-color (e.g., Miller et al., 2012) SWIm imagery offers, for example, a holistic display of numerical model output ..., the radiative transfer equation Jianguo Huang∗, Yue Yu School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University Shanghai 200240, China Abstract The radiative transfer equation is a fundamental equation in transport theory and appli-cations, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures. 1986. Menzel, D. H. (Ed.). Selected Papers on the Transfer of Radiation., Radiative transfer modelling. The purpose of the activity is the implementation and development of algorithms for the atmospheric radiative transfer ..., Forward radiative transfer models (RTM) are an indispensable tool for quantitative applications of satellite radiometers, e.g., for data calibration, instrument development, retrieval, and so on. In this study, we develop an accurate and efficient RTM for radiometers onboard Fengyun satellites, namely FYRTM (RTM for Fengyun …, An introduction to the basic physics of astronomy and astrophysics at the graduate level. Principles of energy transfer by radiation. Elements of classical and quantum theory of photon emission; bremsstrahlung, synchrotron radiation. Compton scattering, plasma effects, atomic and molecular electromagnetic transitions., The CRTM is a widely used fast radiative transfer model for satellite data assimilation and allows the choice between two different transmittance algorithms, one being ODAS, while the other one is Optical Depth in Pressure Space (ODPS) [8]. As the name suggests, ODPS uses a linear regression on a grid of constant pressure levels to predict …, the radiative transfer equation Jianguo Huang∗, Yue Yu School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University Shanghai 200240, China Abstract The radiative transfer equation is a fundamental equation in transport theory and appli-cations, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great, Community Radiative Transfer Model (CRTM, [6]) and Radiative Transfer for the TIROS Operational Vertical Sounder (RTTOV, [7, 8]) are two operationally fast RT models widely used in satellite data assimilation, which are developed by Joint Center for Satellite Data Assimilation (JCSDA) and EUMETSAT NWP-SAF, respectively. Different …, The radiative transfer models developed at AER are being used extensively for a wide range of applications in the atmospheric sciences. This communication is intended to provide a coherent summary ..., When modeling radiative heat transfer, we need to think about how radiation is emitted from a surface and absorbed by other surfaces, as well as how much radiation is exchanged between surfaces. We've addressed emission, reflection, and transmission in two previous blog posts in this series, and now we will finish learning the foundations of ..., Aug 20, 2021 · Importance of Radiative Transfer. Radiation has a very prominent role in astrophysics, both as the only observable and also as a dominant mechanism for energy transfer within and out of astrophysical systems. Consequently, its transport through a medium is one of the most fundamental processes that needs to be considered. , Skip to main content. EUMETSAT. Main navigation. IMAGES. IMAGES. Imagery. EUMETView (Real-time images) · Earth view. Case studies., The radiative transfer simulation within B-cluster has been developed based on an efficient Monte Carlo path-tracing algorithm and implemented in the LargE-Scale remote sensing data and image ..., The radiative transfer formulation can handle 3D geometrical settings and structured objects with variations and gradients in the optical depths across the objects …, Radiative transfer, the effect on radiation of its passage through matter, is where things really get going. 7.1 The Equation of Radiative Transfer We can use the fact that the specific intensity does not change with distance to begin deriving the radiative transfer equation. For light traveling in a vacuum along a path length s, we say that ..., The results have direct application to the design of packed/fluidized bed systems wherein thermal radiation is a significant heat transfer mode. AB - Experimental measurements are compared with theoretical predictions for radiative transfer in suspensions of 11.0 μ dia Dow latex particles using 0.6328 μ He-Ne laser light., A generalized form of the radiation transfer equation is presented, which covers both limiting cases of thin and dense atmospheres and allows a continuous transition from low to high densities, controlled by a density dependent parameter. Simulations of the up- and down-welling radiation and its interaction with the most prominent greenhouse ..., The radiative transfer equations are well known, but radiation parametrizations in atmospheric models are computationally expensive. A promising tool for accelerating parametrizations is the use of machine learning techniques. In this study, we develop a ..., The radiative transfer equation shown in the purple box of Fig. 1 is the scalar (ignoring polarization) radiative transfer equation (SRTE). It is derived in a qualitative fashion on the SRTE Heuristic Development page. There is actually a hierarchy of radiative transfer equations (RTEs)., The radiative transfer model (RTM) is a bridge that connects observations and theoretical radiation and is based on the radiative transfer equation; as a result, RTMs are widely used in …, RADMC-3D is capable of modeling radiative transfer in molecular and/or atomic lines. Due to the complexity of line radiative transfer, and the huge computational and memory requirements of full-scale non-LTE line transfer, RADMC-3D has various different modes of line transfer. Some modes are very memory efficient, but slower, while others are ..., When modeling radiative heat transfer, we need to think about how radiation is emitted from a surface and absorbed by other surfaces, as well as how much radiation is exchanged between surfaces. We've addressed emission, reflection, and transmission in two previous blog posts in this series, and now we will finish learning the foundations of ..., Radiative Transfer. " Radiative Transfer is the definitive work in the field. It provides workers and students in physics, nuclear physics, astrophysics, and atmospheric studies with the foundation for the analysis of stellar atmospheres, planetary illumination, and sky radiation. Though radiative transfer has been investigated chiefly as a ..., What is the rate of heat transfer by radiation, with an unclothed person standing in a dark room whose ambient temperature is \(22.0^oC\). The person has a normal skin temperature of \(33.0^oC\) and a surface area of \(1.50 \, m^2\). The emissivity of skin is 0.97 in the infrared, where the radiation takes place. Strategy. We can solve this by ..., Thermal radiation is energy transfer by the emission of electromagnetic waves which carry energy away from the emitting object. For ordinary temperatures (less than red hot"), the radiation is in the infrared region of the electromagnetic spectrum. The relationship governing the net radiation from hot objects is called the Stefan-Boltzmann law:, The Radiative Transfer for the TIROS Operational Vertical Sounder (TOVS) (RTTOV; Saunders et al., 1999, 2018) has been developed for the specific application of NWP data assimilation to respond to the requirement of high computational performance. For this purpose, RTTOV employs parameterizations tailored to specific microwave satellite ..., Radiative Transfer – Radiance and Lambertian Sources The exitance M gives the power per unit area, but it contains no information about the directionality or angular distribution of the light leaving the scene. This information is contained in the radiance L. The most common assumption for diffuse scenes is that the radiance is constant or independent of …, The positivity-preserving property is an important and challenging issue for the numerical solution of radiative transfer equations. In the past few decades, different numerical techniques have been proposed to guarantee positivity of the radiative intensity in several schemes; however it is difficult to maintain both high order accuracy and positivity. The discontinuous Galerkin (DG) finite ..., The radiative properties are modeled by the full spectrum k-distribution method, and the radiative transfer equation is solved by the discrete ordinates method. Results show that gas and solid radiative heat fluxes are about 1300 W/m 2 and 4500 W/m 2 for the dense and dilute conditions respectively, and decrease exponentially with the solid ..., The radiative properties are modeled by the full spectrum k-distribution method, and the radiative transfer equation is solved by the discrete ordinates method. Results show that gas and solid radiative heat fluxes are about 1300 W/m 2 and 4500 W/m 2 for the dense and dilute conditions respectively, and decrease exponentially with the solid ..., The radiative transfer mode of Norman [Norman, 1979; Norman and Jarvis, 1975; Norman et al., 1971] provides a set of discrete equations for the transmission, interception and reflection of direct and diffuse in discrete wavebands (e.g. visible, near infrared and infrared radiation) through one dimensional ca nopies.