Radiative transfer

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. Atmospheric radiative transfer involves gas absorption coupled with molecular Rayleigh scattering, in addition to scattering and absorption by clouds and aerosols. Further, computation of heating rates are dependent on absorption and emission of radiation, processes that have a complex dependence on various quantities.

which states the obvious fact that in the absence of internal sources, the upward radiation (and ultimately the radiation field at any optical depth ) is completely determined by the intensity of inward radiation. Indeed, taking into account that. is well known in the radiative transfer theory ( Sobolev 1963 ).

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)After several decades’ development of retrieval techniques in aerosol remote sensing, no fast and accurate analytical Radiative Transfer Model (RTM) has been developed and applied to create global aerosol products for non-polarimetric instruments such as Ocean and Land Colour Instrument/Sentinel-3 (OLCI/Sentinel-3) and Meteosat Second Generation/Spinning Enhanced Visible and Infrared Imager ...The radiative transfer equation (RTE), which describes the propagation of radiation energy in participating media, plays an important role in many scientific and engineering fields, such as atmospheric radiative transfer [1], optical tomography [2], astrophysics [3], combustion processes [4], as well as nuclear engineering [5]. The RTE …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.Results are summarized for a scientific project devoted to the comparison of four atmospheric radiative transfer codes incorporated into different satellite data processing algorithms, namely, 6SV1.1 (second simulation of a satellite signal in the solar spectrum, vector, version 1.1), RT3 (radiative transfer), MODTRAN (moderate resolution atmospheric transmittance and radiance code), and SHARM ...lution of the Equation of Radiative Transfer 253 10 Solution of the Equation of Radiative Transfer . . . One-half of the general problem of stellar atmospheres revolves around the solution of the equation of radiative transfer. Although equation (9.2.11) represents a very general formulation of radiative transfer, clearly the specific nature of the

Through use of accurate but complex radiative transfer models (RTMs) such as Second Simulation of a Satellite Signal in the Solar Spectrum (6S; Vermote et al., 2006), Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART, where DISORT represents “discrete-ordinate-method radiative transfer”; Ricchiazzi et al., 1998), …Context: The Monte Carlo method is probably the most widely used approach to solve the radiative transfer problem, especially in a general 3D geometry. The physical processes of emission, absorption, and scattering are easily incorporated in the Monte Carlo framework. Net stimulated emission, or absorption with a negative cross section, does not fit this method, however. Aims: We explore ...The radiative transfer equation was solved in all cases using the MURaM solver (Vögler et al., 2005). To this end we implemented a diagnostic radiative transfer that computes the intensity along twelve different outgoing ray-directions plus the vertical one.Radiative transfer Bookreader Item Preview remove-circle Share or Embed This Item. Share to Twitter. Share to Facebook. Share to Reddit. Share to Tumblr. Share to Pinterest. Share via email. EMBED. EMBED (for wordpress.com hosted blogs and archive.org item <description> tags) Want more? Advanced embedding details, examples, and help! …An Introduction to Radiative Transfer presents these techniques as applied to stellar atmospheres, planetary nebulae, supernovae, and other objects with similar geometrical and physical conditions. Accurate methods, fast methods, probabilistic methods and approximate methods are all explained, including the latest and most advanced techniques. ...Conceptual representation of 6SV radiative transfer. The 6S (Second Simulation of the Satellite Signal in the Solar Spectrum) ( Vermote et al., 1997) is a computer code that can accurately simulate the radiative transfer of an optical electromagnetic signal through the atmosphere. The 6S code is an improved version of 5S, developed by the ...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 ...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.

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 ...Radiation is responsible for most of the heat transferred into the room. Heat transfer also occurs through conduction into the room, but much slower. Heat transfer by convection also occurs through cold air entering the room around windows and hot air leaving the room by rising up the chimney. Exercise 1.7.1.An Introduction to Radiative Transfer applies these techniques to stellar atmospheres, planetary nebulae, supernovae, and other objects with similar geometrical and physical conditions. Accurate ...Near-field radiative heat transfer (NFRHT) occurs between objects separated by a distance smaller than the wavelength of thermal photons. Some materials (as \(\hbox {SiO}_2\) or \(\hbox {SiC}\) 1 ...

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The total change of radiation The sum of (2) and (4) gives the combined effect, which gives a differential equation describing radiative transfer in the absence of scattering dIl ds = rkl (Bl (T) - Il). (5) Integrating the radiative transfer equation Multiplying (5) by the integrating factor exp É , gives s 0 rkl ds' dIl ds exp É s 0 rkl ds ...Nonreciprocal 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 ...SCIATRAN is a comprehensive software package for the modeling of radiative transfer processes in the terrestrial atmosphere and ocean in the spectral range from the ultraviolet to the thermal infrared (0.18 - 40 μm) including multiple scattering processes, polarization, thermal emission and ocean-atmosphere coupling. The software is capable of modeling spectral and angular distributions of ...2.2 Radiative transfer model for seafoam. As shown in Figure 1, considering thermal emission from a layered medium with particles embedded in a background medium (i.e., seawater), the radiative transfer equation (RTE) describing the radiant field in a layered medium has the following form (Evans and Stephens, 1991; Jin et al., 2020):Fluorescence Resonance Energy Transfer (FRET) is a special technique to gauge the distance between two chromophores, called a donor-acceptor pair. The limitation of FRET is that this transfer process is effective only when the separating distance of donor-acceptor pair is smaller than 10 nanometers. However, FRET is a highly distance-dependent ...The Limb Radiation Retrival Transfer group (LRRT) is based on the Institute of Umweltphysik (IUP), at the University of Bremen, Germany. The group is led by Dr.

In this paper, we present two machine learning algorithms to identify D mesons produced in a colour singlet state from radiative W boson decays at the LHC. …The radiative transfer equation (RTE), equation (17.1), is a five-dimensional integro-differential equation, with three spatial and two directional coordinates. For a numerical solution both, spatial and directional dependencies must be discretized. Various methods of discretization are available, such as finite differences, finite volumes ... Radiative transfer (RT) codes are scientific software that numerically simulate the propagation of electromagnetic radiation through a medium. RT simulations are used in various disciplines including astrophysics, planetary and Earth science, and remote sensing. RT codes are a fundamental component in remote sensing retrieval algorithms of ...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 recent theoretical derivations that relate it directly to the Maxwell's equations (Mishchenko, 2014). Radiative transfer calculates spectral radiances and radiative fluxes.Radiative transfer models are incorporated into atmospheric correction through the inversion of a coupled surface and atmospheric equation (Tanré et al., 1979; Vermote and Vermeulen, 1999), which describes how light interacts with the atmosphere and surface prior to arriving at a sensor.Radiative flux. The monochromatic . radiative flux. at frequency gives the net rate of energy flow through a surface element. dE ~ I cos. θ. d. ω integrate over the whole solid angle ( 4 ): We distinguish between the outward direction (0 < < /2) and the inward direction ( /2 < so that the net flux is π. F. ν = 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.This finding suggests that the radiative transfer model inversion using machine learning regression algorithms is a robust and fast approach when predicting biodiversity variables of terrestrial surfaces from remote sensing data. The present results are significant in at least two respects. One of the benefits is that the training of the ...The proposed remote sensing tool, based on the hybrid inversion of radiative transfer models (RTMs) to retrieve fractional vegetation cover (FVC) at high spatial resolution, has proved its reliability and applicability to monitor ecosystem engineering resilience in heterogeneous burned landscapes affected by mixed severity wildfires. The ...Radiative transfer is at the heart of the mechanism to explain the greenhouse effect based on the partial infrared opacity of carbon dioxide, methane and other greenhouse gases in the atmosphere. In absence of thermal diffusion, the mathematical model consists of a first order integro-differential equation coupled with an integral equation for the light intensity and the temperature, in the ...

Standard radiative transfer Monte Carlo model: scalar approachThe radiative transfer model presented in this study follows the standard approach of a forward Monte Carlo model [34], [35], [6], [7]. The 3D medium is defined in a Cartesian coordinates system OXYZ with N X × N Y × N Z regular cubic cells containing the medium properties.

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 TRadiative transfer is the transport of energy by electromagnetic waves through a gas. This example highlighting the Earth’s Energy Budget depicts energy exchanges between the Earth's surface, the Earth's atmosphere, and space. A better understanding of Earth’s present and future requires computer codes that accurately simulate the movement ... 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.Radiative Transfer. Subrahmanyan Chandrasekhar. Courier Corporation, Jan 1, 1960 - Science - 393 pages. This book by a Nobel Laureate provides the foundation for analysis of stellar atmospheres, planetary illumination, and sky radiation. Radiation transfer has been investigated as a phenomenon of astrophysics, and it has attained wider interest ...Nov 1, 2020 · After several decades’ development of retrieval techniques in aerosol remote sensing, no fast and accurate analytical Radiative Transfer Model (RTM) has been developed and applied to create global aerosol products for non-polarimetric instruments such as Ocean and Land Colour Instrument/Sentinel-3 (OLCI/Sentinel-3) and Meteosat Second Generation/Spinning Enhanced Visible and Infrared Imager ... The transient radiative transfer in a two-layer medium is first investigated, and the time-resolved results are validated by comparing with those by the Monte Carlo method (MCM). Of particular interest, the angular intensities along the slab at different times are presented to illustrate a variety of interesting phenomena, and the discontinuous …Jun 6, 2020 · Radiative transfer theory. The study of the passage of electromagnetic radiation, gamma rays, neutrons, etc., through matter, examined by means of a linear kinetic equation or transport equation (see Kinetic equation ). The problem of the determination of the radiation field in the atmosphere and the scattering of light in accordance with known ... Radiative transfer theory, i.e. the study of how electromagnetic radiation propagates through a medium, is described by the Radiative Transfer Equation (RTE). The latter mathematically describes how particles moving through a medium are affected by a variety of physical processes, including absorption, scattering and emission.

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The Community Radiative Transfer Model (CRTM) is a powerful and versatile scalar radiative transfer model for satellite data assimilation and remote sensing applications. It is implemented as an object-oriented Fortran library, enabling flexible code development and optimal runtime performance on clusters. The downsides of the Fortran interface ...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 ... Radiative transfer. Radiative transfer (also called radiation transport) is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative transfer describes these interactions mathematically.This book discusses analytic and asymptotic methods relevant to radiative transfer in dilute media, such as stellar and planetary atmospheres. Several methods, providing exact expressions for the radiation field in a semi-infinite atmosphere, are described in detail and applied to unpolarized and polarized continuous spectra and spectral lines.The discrete ordinates method is employed to find the single-layer solution for vector thermal radiative transfer; this is an extension of the approach for scalar radiative transfer, with the I- and Q-components being dealt with in a parallel way by using a doubled dimension in the discrete ordinate space. Chandrasekhar's invariance principle ...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.Tools. Although near-field radiative heat transfer was introduced in the 1950s, interest in the field has only recently revived, as the effect promises improved performance in various applications where contactless temperature regulation in the small-scale is a requirement. With progress in computational electromagnetics as well as in ...We discuss the architecture and design principles that underpin the latest version of SKIRT, a state-of-the-art open source code for simulating continuum radiation transfer in dusty astrophysical systems, such as spiral galaxies and accretion disks. SKIRT employs the Monte Carlo technique to emulate the relevant physical processes including scattering, absorption and emission by the dust. The ...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. ….

Chandrasekhar’s work in radiative transfer theory began in 1944 and culminated with the publication of his influential treatiseRadiative Transfer in 1950. In this review his major contributions to 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 ..."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.adshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86AIn 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.AER's radiative transfer models are well validated against atmospheric observations. A validation example of LBLRTM calculations against HIS during CAMEX is provided in Fig. 1.The HIS observations from this CAMEX case from 09/29/1993 have been used extensively in validation studies for a number of forward models [35], [36].For this case, the HIS sensor had a spectral resolution of 0.32 cm-1 ...The radiative transfer equation (RTE), which describes the propagation of radiation energy in participating media, plays an important role in many scientific and engineering fields, such as atmospheric radiative transfer [1], optical tomography [2], astrophysics [3], combustion processes [4], as well as nuclear engineering [5]. The RTE is an ...Jan 1, 2021 · Radiative transfer. A layer of air will absorb a certain fraction of the incoming radiation. The rate of absorption will depend on the wavelength. For an infinitesimally thin layer of air, the change in the intensity of a beam passing through the layer can be written as (10.6) d I λ = − I λ d δ λ, where we have introduced the ... 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, We present the open-source radiative transfer code named HELIOS, which is constructed for studying exoplanetary atmospheres.In its initial version, the model atmospheres of HELIOS are one-dimensional and plane-parallel, and the equation of radiative transfer is solved in the two-stream approximation with nonisotropic scattering. A small set of the main infrared absorbers is employed, computed ..., Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength., An advanced radiative transfer modeling system (ARMS) has been developed for satellite data assimilation and remote sensing applications. It inherits the capability of other fast radiative transfer models developed mainly for US and European satellite programs but focuses on the radiative transfer components that are specific for the assimilation of the Fengyun satellites and those sensors not ..., Longwave Radiative Transfer in a Cloudy Atmosphere. In this discussion, we refer to longwave radiation as radiation emitted by the earth's surface, or the atmosphere, having wavelengths greater than about 4 μm. The effect of clouds on longwave radiation is quite different from that of for shortwave radiation. In the case of shortwave ..., tive Transfer for TOVS) fast radiative transfer model, which is widely used in the satellite retrieval and data assimilation communities. RTTOV is a fast radiative transfer model for simulating top-of-atmosphere radiances from passive visi-ble, infrared and microwave downward-viewing satellite ra-diometers., Radiation heat transfer. The radiation heat transfer between two parallel planes is reduced by placing a parallel aluminum sheet in the middle of the gap. The surface temperatures are θ 1 = 40 °C and θ 2 = 5 °C, respectively; the emissivities are ε 1 = ε 2 = 0.85. The emissivity of both sides of the aluminum is ε a = 0.05., 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 , Each species (i) is defined by a plausible set of field plant traits (T RTM), the input of a radiative transfer model (RTM) that predicts the associated reflectance factor (R) (a). Several species (9 in this example) are gathered within a regional species pool (b). Some species feature traits with close or similar values (similar species ..., 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., They have been applied to train and validate the fast infrared radiation transfer models, such as Community Radiative Transfer Model (CRTM) and Radiative Transfer for TOVS (RTTOV) [12, 29]. This dataset is gridded on the standard 101-levels ranging from 1100 to 0.005 hPa with smoothly varying layers and is fine enough to solve the radiative ..., Radiative transfer equation (RTE) is the governing equation of radiation propagation in participating media, which plays a central role in the analysis of radiative transfer in gases ..., The radiative transfer model [39], [40] which is coupled in CanAM4 [4] applies this parameterization and gets good agreement when comparing to the satellite observations and the averaged results of all radiative transfer models in the Coupled Model Intercomparison Project Phase 5 (CMIP5) [41], [42]., " 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 phenomenon of ..., 2.2 Radiative transfer model for seafoam. As shown in Figure 1, considering thermal emission from a layered medium with particles embedded in a background medium (i.e., seawater), the radiative transfer equation (RTE) describing the radiant field in a layered medium has the following form (Evans and Stephens, 1991; Jin et al., 2020):, An advanced radiative transfer modeling system (ARMS) has been developed for satellite data assimilation and remote sensing applications. It inherits the capability of other fast radiative transfer models developed mainly for US and European satellite programs but focuses on the radiative transfer components that are specific for the assimilation of the Fengyun satellites and those sensors not ..., The radiative transfer theory, also called transport theory, is the theory describing the wave propagation through a medium characterized by a random distribution of scatterers. It usually applies to electromagnetic radiation, but it can be generalized to acoustic radiation. The radiative transfer theory is one of the two theories developed to ..., Abstract Demands for Monte Carlo radiative transfer modeling have grown with the increase in computational power in recent decades. This method provides realistic simulations of radiation processes for various types of application, including radiation budgets in cloudy conditions and remote measurements of clouds, aerosols, and gases. …, May 19, 2021 · Fig. 4.1. Formulation of the radiative transfer equation. The radiance L depends on the vertical coordinate z, cosine \ (\mu \) of polar angle \ (\theta \) and the azimuthal angle \ (\varphi \). The principal plane is perpendicular to the layer boundaries and comprises the incident radiation direction. , ing fluid. Furthermore, radiative transfer is usually the most effective energy-exchange mechanism within the fluid. To describe the behavior of such flows we need conservation laws that account accurately for both the material and the radiative contributions to the flow dynamics. To estilmate the importance of radiation in fixing the local ..., Radiative transfer is the theory describing how electromagnetic radiation is transmitted through a medium such as a planetary atmosphere or a stellar photosphere. The medium can emit, absorb, and scatter radiation with a behavior that may vary strongly with wavelength according to the different species composing the medium and their physical state. , Have you earned college credits from a nationally accredited school and now want to transfer them to a school with regional accreditation? Updated April 14, 2023 thebestschools.org is an advertising-supported site. Featured or trusted partn..., 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 ..., LBLRTM. Brightness temperature observations and residuals (IASI- LBLRTM) for the ARM SGP case for the HNO3 (a, b) and the OCS (c, d) spectral regions. Within atmospheric science, LBLRTM - The Line-By-Line Radiative Transfer Model is an accurate, efficient and highly flexible model for calculating spectral transmittance and radiance ., The Limb Radiation Retrival Transfer group (LRRT) is based on the Institute of Umweltphysik (IUP), at the University of Bremen, Germany. The group is led by Dr., The terms radiative heat transfer and thermal radiation are commonly used to describe the science of the heat transfer caused by electromagnetic waves. According to [16, 21], all materials ..., The synthetic data were produced using the DISAMAR radiative transfer model; therefore, we expect the online radiative transfer retrievals to be generally better than the NN-based retrievals. The aerosol model utilised in the retrieval is the same at that in Sect. 2.2 , using fixed parameters for aerosol single scattering albedo, aerosol layer ..., In modeling the canopy reflectance of row-planted crops, neglecting horizontal radiative transfer may lead to an inaccurate representation of vegetation energy balance and further cause uncertainty in the simulation of canopy reflectance at larger viewing zenith angles. To reduce this systematic deviation, here we refined the four-stream radiative transfer …, 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 ..., WeTransfer is an online platform that allows users to transfer large files for free. It has become an increasingly popular way for individuals and businesses alike to send high-volume files quickly and securely., Abstract With the increasing use of satellite and ground-based high-spectral-resolution (HSR) measurements for weather and climate applications, accurate and efficient radiative transfer (RT) models have become essential for accurate atmospheric retrievals, for instrument calibration, and to provide benchmark RT solutions. This study develops a spectral data compression (SDCOMP) RT model to ..., Radiative Transfer. Propagation of Radiation We have discussed the generation of radiation by considering the volume emissivity, η ν, which is the energy per unit time per unit volume per unit frequency bandwidth per sterradian.Note that these units are the same as intensity, except it is per unit volume instead of per unit area., The radiative transfer problem should be simplified to obtain the most important physical estimates. However, the main special features of the real problem such as the spectrum of solar radiation and spectral properties of particles have to be taken into account. The main simplifications are: (1) The plane-parallel cloud of particles is ..., 120 An Atmospheric Radiative Transfer Primer FIGURE 6.3 Plane-parallel coordinates. Atmospheric light paths are defined by µ the cosine of the zenith angle. The position of radiative quantities can then be reduced from (x, y, z) to (z). In problems of radiative transfer in plane-parallel atmospheres it is convenient to