Chairman: J.R. Howell


Prasad Varanasi
Institute for Terrestrial and Planetary Atmospheres
State University of New York
Stony Brook, NY 11794-5000

ABSTRACT. The prospects of global warming and ozone-depletion due to the increased use of fossil fuels and chlorofluorocarbons have motivated international efforts to (a) monitor the increasing atmospheric concentrations of the so-called greenhouse gases and (b) study their impact on the radiation budget of the planet. Atmospheric remote sensing using infrared instruments as well as the terrestrial radiative flux calculations depend heavily on the accuracy of the available infrared spectroscopic data on the greenhouse gases. Our laboratory has pioneered the technique of measuring the spectroscopic line and band parameters at temperatures and pressures appropriate to the atmosphere. We present in this paper not only a review of our measurements and the work by other spectroscopic laboratories but also discuss their use in satellite remote sensing missions and in radiative modeling. The molecules under study are carbon dioxide, methane, nitrous oxide, sulfur hexafluoride, and several important chlorofluorocarbons. The effect of the continuum of water vapour on the radiative contributions by these greenhouse gases will also be discussed.

Earth's atmosphere consists of gases, aerosols and clouds. Infrared-active of these constituents contribute to the greenhouse effect. While the modelers continue to be cloudy about cloudy atmospheres and the subject of aerosols is foggy at best, infrared spectroscopists have the enviable privilege to contribute in the development of clear concepts of radiative transfer in a clear-sky or cloud-free atmosphere. It is, of course, common knowledge that a cloud-free atmosphere on a global scale is rare indeed. Even though our “water planet” supports an active canopy of clouds with varying amount of clear skies, a clear-sky atmospheric model is essential to the complete understanding of the radiative properties of the atmosphere, in that it forms a background to the effect of the clouds. As laboratory infrared spectroscopists this author and others of his genre provide the necessary spectroscopic data for the study of the infrared-active, clear-sky atmosphere. The data provided by them are valuable in the modeling and remote sensing of the radiatively active atmosphere. This connection between laboratory spectroscopy and the atmospheric observations has been recognised by the Department of Energy in the context of its Atmospheric Radiation Measurements (ARM) Program. The identifiable relevance of our work to the objectives of the ARM Program, especially in the interpretation of CART (Cloud And Radiation Testbed) observations which involve infrared spectrometers and radiometers and also in the understanding of the newly evolved and much discussed ARESE (“ARM Enhanced Shortwave Experiment”) will be presented. Also among the significant aspects of the ARM Program, in particular, and global warming models, in general, is the development of a clear and accurate understanding of the thermal infrared (“longwave”) radiative properties of the primary (water vapor and carbon dioxide) and the secondary (methane, nitrous oxide, and man- made compounds such as the chlorofluorocarbons) greenhouse gases under atmospheric conditions.

A newly identified source of uncertainty in general circulation models is the so-called “enhanced absorpton in the short wave region” issue. It deals with the fact that new satellite observations have suggested that atmospheric absorption of solar radiation has been underestimated by the radiative transfer models used until recently. The need to identify the source of this enhanced absorption and to properly account for it is an issue of great interest in current global warming research.

Our laboratory has been engaged to perform some vital laboratory measurements of the so-called short wave absorption spectrum of water vapor. The research has been influenced by the following queries from many colleagues. “Is there enhanced absorption in the photographic infrared, or shortwave as is called by the modelers, or isn't there? Is it due to the clear sky and/or due to clouds? If it is apparent under clear-sky conditions, is it coming from some unexplained absorption features of water vapor? Are the lingering doubts as to our ability to predict the absorption of solar radiation due to inaccurate spectroscopic databases or unexplored phenomena? Speaking of unexplored phenomena, can evidence be gathered to show that water vapor might absorb shortwave radiation differently near its saturation limit (the so-called “high relative humidity” atmospheric state) from what it would if its partial pressure were considerably lower than the saturation vapor pressure?”

The author will review various suggestions made by modelers to explain the enhanced absorption. He will also discuss the existing deficiencies in the modeling of radiative contributions from clouds and aerosols. The current status of our understanding of the opacity of water vapour will be discussed.


Centre d'Energétique
Ecole des Mines de Paris
60, Bd Saint Michel
75272 Paris Cedex 06, France

ABSTRACT. A radiative transfer model using a ray-tracing technique for arbitrary multi- dimensional geometries is presented in this article. It is a generalized method for calculation of radiation exchange in transparent or emitting, absorbing and isotropically scattering media with diffuse or specular walls. A unified formulation of thermal radiation models using transfer factors is presented. This formulation is based on the definition of'generalized exchange factors' between surface or volume elements allowing the expression of all the radiative fluxes. The enclosure geometry is represented by a general data structure easily matched with any mesh tools. The ray- tracing procedure is then detailed for the calculation of generalized exchange factors for transparent enclosures as well as participating ones which have diffuse or specular boundaries. An eff cient numerical method based on an iterative algorithm is proposed to evaluate transfer factors from the exchange factors without matrix operation. The interest of the model is investigated by a few sampling examples.


Vladimir D. Loktionov, Sergey V. Timkin, Nikolay I. Yaroshenko
Elektrogorsk Research & Engineering Centre on NPP Safety
Elektrogorsk, Moscow Region, 142530, RUSSIA
Fax:(+7-09643) 3 05 15 E-mail:

ABSTRACT. A new combined Monte Carlo and R-functions technique that reduces computer run times and improves accuracy for radiation transfer problems and approximate calculation of radiation view factors in particular is proposed. As it well known the Monte Carlo - based techniques (MCT) have been widely used for radiative heat transfer problems and for approximate calculation of radiation view factors in particular. The prediction accuracy of computer programs based on numerical simulation of rays behaviour depends especially on the average of emission information for each rays (or photon). The information for each ray includes the direction and location of emission from surface, where it stops, and etc. A larger number of rays leads to the computation run time increasing. The prediction accuracy depends considerable on representation of the boundary geometrical details too. It is essential for the complex geometry problems when blocking objects are present.

Usually the complex boundary is modelled with the set of primitive sections (triangulars, parallelograms, spheres and etc.). The traditional representation of body surface by the set of primitive sections is natural, but on the other hand, such a description of a complex geometric body requires the use of a great number of faces and runs into considerable expenses of computer resources.

In present paper we combine the Monte Carlo technique and R-functions (Rvachev functions) for constructing complex geometrical bodies and boundaries. Using the R-functions theory allows the arbitrary geometric object to describe as W(x,y,z)=0 at analytical level and moreover:

W(x,y,z)>0 - for the points lying inside the body;
W(x,y,z)<0 - for the points lying outside the body.

These R-functions enjoy the properties of functions of the k-valued logic as well as the properties of classical continuos functions (V.Rvachev, 1982). Based on the ideas of R-functions theory we can make the judgements about such characteristics of a geometric body as the curvature of its surface and the direction of the vector normal to the surface at arbitrary point lying on the boundary surface. R-functions have been used to solve the inverse problem of analytical geometry : for any geometric body, find a function W(x,y,z) that is positive inside the body, negative outside it, and equal to zero on its surface. To solve this problem, it is necessary to determine the system of basic geometric objects and the complete system of operations over them. We can take a plane, a cone, an ellipsoid and other surfaces as the basic geometric objects that are described by equations of the form F(x,y,z)=0.

The procedure of constructing the normalised equation of complex geometric bodies consists of the following steps:

  • a partition the geometric object into a number of basic objects described by equation such as Fi(x,y,z)=0;
  • the construction of a predicate equation for the complex body by using the logical operations of conjunction, disjunction and negation;
  • transformation of the predicate equation to an analytical one by replacing the symbols Fi(x,y,z) in the predicate equation to their respective equations and the logical operations should be replaced by their R-analogies.

The analytical description of geometric objects has many advantages over the polygonal description (the storage of the equation describing the body needs considerably less memory than the storage of the list of faces; the process of determine the normal vector to the body surface at its arbitrary point is simpler). Moreover, it is possible always pass from the analytical description to the polygonal one.

An analytical representation of the body surface allows to simplify the algorithms for prediction of interaction between surface and emission ray. If the ray represents parcels of energy that is tracked along straight line E throughout a medium, the moving co-ordinates of the point lying on the straight line E are (Xj, Yj, Zj) and there are the following events:

Wl(Xj, Yj, Zj)<0 - point is situated outside the body Wl;
Wl(Xj, Yj, Zj)=0 - point is situated on the surface of the body Wl;
Wl(Xj, Yj, Zj)>0 - point enters and is situated inside of the body Wl.

This approach and concept considered above were implemented in a 2-D computer program to calculate radiation view factors of complex geometrical objects. This program includes the set of subroutines that realise the R-functions for describing the complex geometrical objects.

To demonstrate the usefulness of this computer program we have used this program to calculate approximate values of view factors in the following two-dimensional problems:

  • internal radiation problem with complex geometrical black surfaces;
  • a heated tube bundles with black and specula surfaces.

The alternate solutions exist for mentioned problems and comparison of the numerical results and alternate solutions were satisfactory and the accuracy of the results surpasses practical requirements.

The future stages of investigations will be linked with application of this technique for complex three-dimensional configurations.


Hakan ERTÜRK*, Faruk ARINÇ*and Nevin SELÇUK**
* Department of Mechanical Engineering
** Department of Chemical Engineering
Middle East Technical University
Ankara 06531, Turkey

The accuracy of Monte-Carlo method was re-examined by applying it to the predictions of radiative flux density and source term of a three dimensional enclosure problem and comparing the results with exact numerical solutions reported earlier [1]. The box-shaped enclosure is based on data reported previously on a large scale experimental furnace with steep temperature gradients typically encountered in industrial furnaces. The rectangular enclosure under consideration has black interior walls and an absorbing emitting grey medium of costant properties.

Three different Monte-Carlo approaches were tested. In MC-1, while the energy of each photon bundle is kept constant, the number of photon bundle histories emitted from each sub-region is taken to be directly proportional to the emissive power of that sub-region, which is based on the center-point temperature of the sub-region. Conversely, in MC-2 and MC-3, the number of photon bundles emitted from each sub- region is kept constant while the energy of each emitted photon bundle is taken to be directly proportional to the emissive power of the point of emission. The approach named MC-1 was observed to be the most efficient for the problem under consideration as both the prediction of MC-1 and the exact point values of the radiation variables are based on the same temperature at the center-point of each subregion. Small discrepencies in the predictions of MC-2 and MC-3 are due to the fact that they are based on the temperatures of the various points of emissions within a sub-region.

The comparisons show that the predictions of the Monte Carlo method are in very close agreement with the exact solutions. As the number of histories is increased, the accuracy increases up to the statistical limits as expected. It can therefore, be concluded that the predictive accuracy of the the Monte Carlo methods are sufficent for generating benchmark solutions for three dimansional radiative heat transfer problems when sufficiently high numbers of histories are used.

  1. Selçuk,N., Exact Solution for Radiative Heat Transfer in Box-Shaped Furnaces, Journal of Heat Transfer Vol. 107, pp. 648-655, 1985

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