SESSION 1
MONTE CARLO TECHNIQUES
Chairman: J.R. Howell
SPECTROSCOPIC AND RADIATIVE TRANSFER MODELS RELEVANT TO SATELLITE REMOTE SENSING AND GLOBAL WARMING
Prasad Varanasi
Institute for Terrestrial and Planetary Atmospheres
State University of New York
Stony Brook, NY 117945000
ABSTRACT. The prospects of global warming and ozonedepletion due to the increased use of
fossil fuels and chlorofluorocarbons have motivated international efforts to (a) monitor the
increasing atmospheric concentrations of the socalled 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. Infraredactive 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
clearsky or cloudfree atmosphere. It is, of course, common knowledge that a cloudfree
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 clearsky 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 infraredactive,
clearsky 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 socalled “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 socalled
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 clearsky 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 socalled “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.
RADIATIVE HEAT TRANSFER MODEL IN ARBITRARY ENCLOSURES BY RAYTRACING
Wen CAI
Centre d'Energétique
Ecole des Mines de Paris
60, Bd Saint Michel
75272 Paris Cedex 06, France
ABSTRACT. A radiative transfer model using a raytracing 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.
A NEW COMBINED MONTE CARLO AND RFUNCTIONS TECHNIQUE IN RADIATIVE TRANSFER PROBLEMS
Vladimir D. Loktionov, Sergey V. Timkin, Nikolay I. Yaroshenko
Elektrogorsk Research & Engineering Centre on NPP Safety
Elektrogorsk, Moscow Region, 142530, RUSSIA
Fax:(+709643) 3 05 15 Email: iluha@lab2.transit.ru
ABSTRACT. A new combined Monte Carlo and Rfunctions 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 Rfunctions (Rvachev
functions) for constructing complex geometrical bodies and boundaries. Using the
Rfunctions 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 Rfunctions enjoy the properties of functions of the kvalued logic as well as
the properties of classical continuos functions (V.Rvachev, 1982). Based on the
ideas of Rfunctions 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. Rfunctions
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 Ranalogies.
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 coordinates 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 2D computer
program to calculate radiation view factors of complex geometrical objects. This
program includes the set of subroutines that realise the Rfunctions 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 twodimensional
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 threedimensional configurations.
ACCURACY OF THE MONTE CARLO METHOD REEXAMINED ON A BOXSHAPED FURNACE PROBLEM
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 MonteCarlo method was reexamined 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 boxshaped 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 MonteCarlo approaches were tested. In MC1, while the energy of
each photon bundle is kept constant, the number of photon bundle histories emitted
from each subregion is taken to be directly proportional to the emissive power of that
subregion, which is based on the centerpoint temperature of the subregion.
Conversely, in MC2 and MC3, 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 MC1 was observed to be the most efficient for the problem under
consideration as both the prediction of MC1 and the exact point values of the
radiation variables are based on the same temperature at the centerpoint of each
subregion. Small discrepencies in the predictions of MC2 and MC3 are due to the
fact that they are based on the temperatures of the various points of emissions within a
subregion.
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.
 Selçuk,N., Exact Solution for Radiative Heat Transfer in BoxShaped Furnaces,
Journal of Heat Transfer Vol. 107, pp. 648655, 1985
