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The direct method for the solution of the spherical harmonics approximation to the equation of transfer of radiation is applied to the cases of (1) scattering of the solar radiation in the atmosphere with the Lambertian boundary and (2) thermal radiation transfer.
The potential importance of longwave (LW) cloud scattering has been recognized but the actual estimate of this effect on thermal radiation varies greatly among different studies. General circulation models (GCMs) generally neglect or simplify the multiple scattering in the LW. In this study, we use a rigorous radiative transfer algorithm to explicitly consider LW multiple-scattering and apply the GCM to quantify the impact of cloud LW scattering on thermal radiation fluxes. Our study shows that the cloud scattering effect on downward thermal radiation at the surface is concentrated in the infrared atmospheric window spectrum (800–1250 cm9exp −1)). The scattering effect on the outgoing longwave radiation (OLR) is also present in the window region over low clouds but it is mainly in the far-infrared spectrum (300–600 cm(exp −1)) over high clouds. For clouds with small to moderate optical depth (τ < 10), the scattering effect on thermal fluxes shows large variation with the cloud τ and has a maximum at an optical depth of ∼3. For opaque clouds, the scattering effect approaches an asymptote and is smaller and less important. The 2-stream radiative transfer scheme could have an error over 10% with an RMS error around 3.5%–4.0% in the calculated LW flux. This algorithm error of the 2-stream approximation could readily exceed the no-scattering error in the LW, and thus it is worthless to include the time-consuming computation of multiple scattering in a 2-stream radiative transfer scheme. However, the calculation error rapidly decreases as stream number increases and the RMS error in LW flux using the 4-stream scheme is under 0.3%, an accuracy sufficient for most climate studies. We implement the 4-stream discrete-ordinate algorithm in the GISS GCM and run the GCM for 20 years with and without the LW scattering effect, respectively. When cloud LW scattering is included, we find that the global annual mean OLR is reduced by 2.7 W/m(exp 2), and the downward surface flux and the net atmospheric absorption are increased by 1.6 W/m2 and 1.8 W/m(exp 2), respectively. Using one year of ISCCP clouds and running the standalone radiative transfer offline, the global annual mean non-scattering errors in OLR, surface LW downward flux and net atmospheric absorption are 3.6 W/m(exp 2), −1.1 W/m(exp 2), and −2.5 W/m(exp 2), respectively. The global scattering impact of 2.7 W/m(exp 2) on the OLR is small when compared to the typical global OLR value of 240 W/m2, but it is significant when compared to cloud LW radiative forcing (30 W/m2) and net cloud forcing (−14 W/m(exp 2)). Overall, the effect of neglecting scattering on the thermal fluxes is comparable to the reported clear sky radiative effect of doubling CO2.
We investigate the impact of cirrus cloud heterogeneity on the direct emission by cloud or surface and on the scattering by ice particles in the thermal infrared (TIR). Realistic 3-D cirri are modeled with the 3DCLOUD code, and top-of-atmosphere radiances are simulated by the 3-D Monte Carlo radiative transfer (RT) algorithm 3DMCPOL for two (8.65 micrometers and 12.05 micrometers) channels of the Imaging Infrared Radiometer on CALIPSO. At nadir, comparisons of 1-D and 3-D RT show that 3-D radiances are larger than their 1-D counterparts for direct emission but smaller for scattered radiation. For our cirrus cases, 99% of the 3-D total radiance is computed by the third scattering order, which corresponds to 90% of the total computational effort, but larger optical thicknesses need more scattering orders. To radically accelerate the 3-D RT computations (using only few percent of 3-D RT time with a Monte Carlo code), even in the presence of large optical depths, we develop a hybrid model based on exact 3-D direct emission, the first scattering order from 1-D in each homogenized column, and an empirical adjustment linearly dependent on the optical thickness to account for higher scattering orders. Good agreement is found between the hybrid model and the exact 3-D radiances for two very different cirrus models without changing the empirical parameters. We anticipate that a future deterministic implementation of the hybrid model will be fast enough to process multiangle thermal imagery in a practical tomographic reconstruction of 3-D cirrus fields.
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A comprehensive discussion of heat transfer by thermal radiation is presented, including the radiative behavior of materials, radiation between surfaces, and gas radiation. Among the topics considered are property prediction by electromagnetic theory, the observed properties of solid materials, radiation in the presence of other modes of energy transfer, the equations of transfer for an absorbing-emitting gas, and radiative transfer in scattering and absorbing media. Also considered are radiation exchange between black isothermal surfaces, radiation exchange in enclosures composed of diffuse gray surfaces and in enclosures having some specularly reflecting surfaces, and radiation exchange between nondiffuse nongray surfaces. The use of the Monte Carlo technique in solving radiant-exchange problems and problems of radiative transfer through absorbing-emitting media is explained.
Thermal radiative heat transfer in absorbing, emitting, and scattering media
Thermal radiative transfer in nonuniform anisotropic magnetoactive plasma, correcting term of Zheleznyakov equation
This book first reviews the overall aspects and background information related to thermal radiation heat transfer and incorporates new general information, advances in analytical and computational techniques, and new reference material. Coverage focuses on radiation from opaque surfaces, radiation interchange between various types of surfaces enclosing a vacuum or transparent medium, and radiation including the effects of partially transmitting media, such as combustion gases, soot, or windows. Boundary conditions and multiple layers are discussed with information on radiation in materials with nonunity refractive indices.
Thermal radiation exchange between surfaces and enclosures
Radiative heat transfer and thermal structure of planetary atmospheres
A model for numerical simulation of stratus cloud layers is constructed by combining a second-order closure, turbulent transfer model with a thermal radiative transfer model. The turbulent transfer model allows water vapor saturation. The combined turbulence-radiation model is applied to both a horizontally uniform one-dimensional case and a horizontally nonuniform two-dimensional case. In the latter, the dynamics of mesoscale circulations are also incorporated. Results of the two-dimensional simulation show that the layer cloud instability occurs where the sea surface temperature is high and the large-scale subsidence is weak. The simulated instability is analyzed in view of an instability criterion, the eddy kinetic energy budget, and evaporative cooling near the cloud top.
Thermal effect of radiative transfer in atomic oxygen line
The radiosity method is introduced to plant canopy reflectance modeling. We review the physics principles of the radiosity method which originates in thermal radiative transfer analyses when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity method and the radiative transfer method, we conclude that both methods are complementary to each other. Results of sample calculations are given for canopy models with up to 20,000 discrete leaves.
A summary of the work involving the Monte Carlo method in the solution of problems in thermal radiation transfer is presented, which indicates general methods previously used for solving problems in which radiation is coupled with other modes of energy transfer. Previous work involving radiation in absorbing-emitting media is included. An example is outlined to indicate the use of the Monte Carlo method in the design of a space radiator. Suggestions are given for solution of a complex case incorporating the effects of coupled conduction, convection and radiation, wavelength dependent and selective surfaces, nonisothermal conditions, and strongly directional or nondiffuse emitting and reflecting surfaces. A discussion is given of the factors that may affect convergence, running time, and accuracy of the Monte Carlo solutions and of the advantages and disadvantages of this approach for practical problems. Also discussed are the case of programming for complex problems and the probable machine time requirements of the method.
The role of clouds remains the largest uncertainty in climate projections. They influence solar and thermal radiative transfer and the earth's water cycle. Therefore, there is an urgent need for accurate cloud observations to validate climate models and to monitor climate change. Passive satellite imagers measuring radiation at visible to thermal infrared (IR) wavelengths provide a wealth of information on cloud properties. Among others, the cloud top height (CTH) - a crucial parameter to estimate the thermal cloud radiative forcing - can be retrieved. In this paper we investigate the skill of ten current retrieval algorithms to estimate the CTH using observations from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) onboard Meteosat Second Generation (MSG). In the first part we compare ten SEVIRI cloud top pressure (CTP) data sets with each other. The SEVIRI algorithms catch the latitudinal variation of the CTP in a similar way. The agreement is better in the extratropics than in the tropics. In the tropics multi-layer clouds and thin cirrus layers complicate the CTP retrieval, whereas a good agreement among the algorithms is found for trade wind cumulus, marine stratocumulus and the optically thick cores of the deep convective system. In the second part of the paper the SEVIRI retrievals are compared to CTH observations from the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) and Cloud Profiling Radar (CPR) instruments. It is important to note that the different measurement techniques cause differences in the retrieved CTH data. SEVIRI measures a radiatively effective CTH, while the CTH of the active instruments is derived from the return time of the emitted radar or lidar signal. Therefore, some systematic differences are expected. On average the CTHs detected by the SEVIRI algorithms are 1.0 to 2.5 kilometers lower than CALIOP observations, and the correlation coefficients between the SEVIRI and the CALIOP data sets range between 0.77 and 0.90. The average CTHs derived by the SEVIRI algorithms are closer to the CPR measurements than to CALIOP measurements. The biases between SEVIRI and CPR retrievals range from −0.8 kilometers to 0.6 kilometers. The correlation coefficients of CPR and SEVIRI observations vary between 0.82 and 0.89. To discuss the origin of the CTH deviation, we investigate three cloud categories: optically thin and thick single layer as well as multi-layer clouds. For optically thick clouds the correlation coefficients between the SEVIRI and the reference data sets are usually above 0.95. For optically thin single layer clouds the correlation coefficients are still above 0.92. For this cloud category the SEVIRI algorithms yield CTHs that are lower than CALIOP and similar to CPR observations. Most challenging are the multi-layer clouds, where the correlation coefficients are for most algorithms between 0.6 and 0.8. Finally, we evaluate the performance of the SEVIRI retrievals for boundary layer clouds. While the CTH retrieval for this cloud type is relatively accurate, there are still considerable differences between the algorithms. These are related to the uncertainties and limited vertical resolution of the assumed temperature profiles in combination with the presence of temperature inversions, which lead to ambiguities in the CTH retrieval. Alternative approaches for the CTH retrieval of low clouds are discussed.
Radiative interactions between absorbing-emitting and flowing media with internal energy generation
The application is discussed of illuminographic camera techniques to the measurement of radiative form factors for satellite modeling applications. The equation for the illuminographic mirror is derived, and the advantages of the method are discussed. Proximity error for the illuminographic mirror is defined, and estimates of this error as a function of the scale factor of the model are given, together with a method for halving this error. Designs for illuminographic mirrors are presented: the first provides a further threefold reduction in proximity error; the second permits the estimation of thermal radiation transfer coefficients to interior regions of otherwise inaccessible volumes. Finally, reflex Polaroid camera techniques appropriate to the relatively small size of the illuminographic mirror are described.
A numerical study has been made of transient heat transfer and fluid flow in a cylindrical enclosure containing a two-layer gas-and-liquid system. The geometric configuration and the boundary conditions of the problem are relevant to the analysis of the preignition processes during the fire accident situation involving a pool of liquid fuel in the vicinity of an ignition source. It is demonstrated that the effects of the natural and thermocapillary convection, radiative transfer, thermal inertia and conduction of the walls bounding the enclosure, as well as, the magnitude of the gravity field play important roles in the development of the temperature and velocity fields in the container.