POSTER SESSION I

ACCURATE SEGMENTATION OF COMPLEX SATELLITE SCENES

Accurate cloud detection in Advanced Very High Resolution Radiometer (AVHRR) data over land is a difficult task complicated by spatially and temporally varying land surface reflectances and emissivities. The AVHRR Split-and-Merge Clustering (ASMC) algorithm for cloud detection in AVHRR scenes over land provides a computationally efficient, scene specific, objective way to circumvent these difficulties. The algorithm consists of two steps: 1) a split-and-merge clustering of the input data (calibrated channel 2 reflectance, calibrated channel 4 temperature, and a channel 3 - channel4 temperature difference) which segments the scene into its natural groupings; and 2) a cluster labeling procedure which uses scene specific joint three-dimensional adaptive thresholds (as opposed to constant static thresholds) to label the clusters as either cloud, cloud-free land, or uncertain. The uncertain class is used for those pixels whose signature is not clearly cloud-free land or clouds (e.g., pixels at cloud boundaries which often contain subpixel cloud and land information which has been averaged together by the integrating aperture function of the AVHRR instrument). Results show that the ASCM algorithm is neither regionally nor temporally specific and can be used over a large range of solar altitudes. Sensitivity of the segmentation and labeling steps to the choice of input variables also was studied. Results obtained with the ASMC algorithm also compare favorably with those obtained from a wide range of currently used algorithms to detect cloud over land in AVHRR data. Moreover, the ASMC algorithm can be adopted for use with data to be taken by the Moderate Resolution Imaging Spectrometer-Nadir (MODIS-N).

The accurate segmentation of sea ice from cloud and from cloud-free ocean in polar AVHRR imagery is important for many for many scientific applications (e.g., sea ice - albedo feedback mechanisms, heat exchange between ocean and atmosphere in polar regions; studies of the stability of surface water in polar regions). Unfortunately, it is a difficult task complicated by the common visible reflectance characteristics of sea ice and cloud. Moreover, AVHRR channel 3 data historically have been contaminated by their use in the classification of polar scenes. Likewise, polar scenes often contain pixels with mixed classes (e.g., sea ice and cloud). This paper uses a combination of fuzzy logic classification methods, noise reduction in AVHRR channel 3 data using Wiener filtering methods (Simpson and Yhann, 1994), and a physically motivated rule base which makes effective use of the Wiener fil-tered channel 3 data to more accurately segment polar imagery. The new method's improved classification skill compared to more traditional methods, as well as its regional independence, is demonstrated. The algorithm is computationally efficient and hence is suitable for analyzing the large volumes of polar imagery needed in many global change studies.

SIMULATION OF THE EXTINCTION OF A LASER BEAM USING THE MONTE CARLO METHOD

Extinction of light in participating media has been extensively used in applications such as laser diagnostics and inverse radiation problems. The accuracy of these techniques is always judged upon the adequacy of the underlying modeling. In that sense, the rigorous modeling of the radiative phenomena is expected to improve substantially the accuracy of the applied techniques. In the present paper a direct statistical Monte Carlo method is adopted, together with detailed treatment of the radiative properties of particles calculated using the Mie theory. The method is firstly applied for the experiment of Boothroyd et al. (Boothroyd, S.A., Jones, A.R., Nicholson, K.W., and, Wood, R., Combust Flame 69, 235-241, 1987) concerning extinction of an expanded laser beam by fine streams of fly-ash particles. This experiment is depicted in Fig. 1. For sampling of the directions followed by the bundles after a scattering event the exact, according to Mie theory, phase function is used. The effects of polarization is not taken into account, since the laser beam is appropriately prepared to simulate unpolarized light. Comparisons are made between the measured and calculated angular distribution of the intensity and satisfactory agreement is found (Fig. 2). The value of the fly-ash refractive index is initially taken as suggested by the authors (n+ik=1.5+i0.012).

Due to the uncertainties concerned to the dependence of the refractive index from the chemical composition of the ash, as well as the sensitivity of Mie calculations on this index, lower values of its imaginary part are considered, as measured by Goodwin and Mitchner (Goodwin, D.G., and Mitchner, M.; Int. J. Heat Mass Transfer, 32, 627-638, 1989). This consideration reveals significant discrepancies of the calculated angular intensities (Fig. 3). For the specific wavelength of the He-Ne laser, a backward lobe is apparent for all the diameters of the examined psd. The most drastic change is concerned with the alteration of the scattering behavior. The calculated scattering albedo was found in the order of 0.99. Thus, ashes characterized by imaginary part of the refractive index as low as measured by Goodwin, are almost conservative scatterers.

The concentration of the ash particles in the previously examined experiment is found to be dilute enough to practically avoid multiple scatterings. In order to gain a better insight on this phenomenon, a numerical experiment is performed concerning the extinction of the same laser beam by a suspension of particles with considerably higher optical depth. At elevated concentrations, bundles undergo multiple scatterings before reaching the photomultiplier. This procedure is quantified by calculating the ratio of the bundles reaching the photomultiplier after multiple scattering over the total number of the received bundles. The angular distribution of this ratio is presented in Fig. 4. From this figure it is evident that for a wide angular interval the received scattered intensity originates mostly from multiple scatterings. From the same figure, angular positions where this ratio is minimized are easily identifiable. Furthermore, the comparison between the angular distributions of the singly scattered bundles and totally received ones imply that a medium tends to be sensed as an increasingly isotropic scatterer as the proportion of the multiple scatterings also increases.

DEPENDENCE OF RADIATIVE TRANSFER CHARACTERISTICS FROM GEOMETRY OF AN ABSORBING, EMITTING AND SCATTERING MEDIUM

For power production systems, it is necessary to know the values of the incident and net radiant fluxes and their distributions along the boundary surfaces. However, the analysis of literature shows that these problems are not enough investigated yet. In present work the theoretical investigation of the influence of geometric form of an absorbing, emitting and scattering medium on the incident radiant flux and its distribution along the boundary surface is proposed. The problem is solved for a closed two-dimensional domain.

The presented investigation is based on the numerical solution of the well-known integro-differential equation of radiative transfer with the boundary conditions which are including the radiation and reflection processes on the heat-absorbing surfaces. Resolution algorithm of the mentioned above equation is a combination of the finite element method, discrete-ordinate method and method of iterations. The idea of this method is following: a) according to the discrete ordinate method, few directions for calculation are selected and the mentioned above equation is written for every selected direction; b) obtained equations are solved by well-known method of finite elements; c) so as the radiative transfer equation is non-linear an iteration process is organized for calculation the values of the radiation intensity at the nodes of the considering domain.

On the base of proposed method the dependence of radiative characteristics (density of incident and net radiative fluxes, structure of radiation field, etc.) from geometrical form of an absorbing, emitting and scattering medium is researched for domains with various geometry. The results of investigations show possibility of discontinue the radiant flux density at the corner point of domain. It is shown that the discontinue take place on the condition when the bisector of corresponding corner is not the symmetry axis of the domain or the optical properties of medium. The influence of the optical and geometrical properties of medium on the values of discontinue is considered. The behavior of falling radiant flux distribution along the boundary for various optical, heat-physical and geometrical characteristics of medium is investigated. It is shown that inhomogeneity of this distribution is increased with the increasing relative difference between the boundary radiation and the own medium radiation. The carried out investigation shows that the form of domain filled with an absorbing, emitting and scattering medium essentially effects the radiant flux distribution along its boundary surfaces.

Authors are thankful to the Belarus Foundation of Fundamental Investigations for the financial support of this work.

DEPENDENCE OF RADIATIVE TRANSFER CHARACTERISTICS FROM OPTICAL PROPERTIES OF AN ABSORBING, EMITTING AND SCATTERING MEDIUM

Study of the mechanism of radiation propagation in two-phase media (gas and solid particles) has a significant number of applications in applied physics and engineering. These include radiative and combined heat transfer, direct and inverse problems in spectroscopy of scattering medium, heat transfer enhancement in thermal and nuclear engineering and metallurgy and so on. The development of modern technology and enhancement due to the increasing capacity of heat power plants have influenced a growing interest in radiative heat transfer in new types of equipment. As a result, new, more stringent requirements for analysis of radiative transfer and correct and timely solutions of problems in this field are needed. At present time many methods for resolution of transport equation are known. But these methods do not estimate complex geometrical form of real objects. That is why the authors propose a resolution method for the integro-differential equation of radiative transfer, which is free from mentioned above demerit at least.

Numerical solution of the well-known integro-differential equation of radiative transfer with the boundary conditions which are including the radiation and reflection processes on the heat-absorbing surfaces. Algorithm of resolution of the mentioned above equation is a combination of the finite element method, discrete-ordinate method and method of iterations. The idea of this method is following: a) according to the discrete ordinate method, few directions for calculation are selected and the mentioned above equation is written for every selected direction; b) obtained equations are solved by well-known method of finite elements; c) so as the radiative transfer equation is non-linear an iteration process is organized for calculation the values of the radiation intensity at the nodes of the considering domain. In the report this method is described in full details.

On the basis of proposed method the dependence of radiative characteristics (density of incident and net radiative fluxes, structure of radiation field, etc.) from optical properties (optical density of medium, Shuster's number, emissivity of boundary and so on) of an absorbing, emitting and scattering medium is researched. In particularly the results of investigation show that scattering processes may increase or decrease the value of leaving radiant intensity in dependence on the optical thickness of medium along the direction of propagation. This result is important for the definition of absorbing index of selective, absorbing, emitting and scattering medium in the finite spectral range and for diagnosing of such media.

Authors are thankful to the Belarus Foundation of Fundamental Investigations for the financial support of this work.

COMPARISON OF NUMERICAL QUADRATURE SCHEMES APPLIED IN THE METHOD OF DISCRETE TRANSFER

The quadrature scheme in the method of discrete transfer is considered. Since the numerical solution of the radiation problem is very time consuming, it is of the utmost importance that the most efficient numerical quadrature schemes be applied in order to obtain a solution with a prescribed accuracy with the minimum computation costs. Little research has been performed in this area and only two schemes have been put forward by Shah (1979) and Bressloff et al. (1995). Shah (1979) suggested a scheme in which the peripherential angle () and the angle () from the normal of the wall are divided into equal size angles. This type of discretisation leads to solid angles which are highly unequal and the scheme is a simple midpoint quadrature in the , space. Bressloff et al. (1995) suggested a quasi-equal solid angle discretisation of the hemisphere and obtained a better accuracy for the same computational cost. In the present paper, the Gauss-Legendre quadrature is applied for the integral of the irradiation written in three ways: (i) as a function of , (ii) as a function of , (=cos), and (iii) as a function of , 1/2². Furthermore, (iv) the quadrature schemes are compared for simple geometries with an isothermal absorbing, emitting gray gas with a prescribed constant temperature regarding the accuracy and computational costs.

BOUNDARY CONDITION FOR RADIATION MODELLED BY HIGH ORDER SPHERICAL HARMONICS

A recurrence formula is derived for coefficients in the Marshak boundary condition which is used in connection with the method of spherical harmonics when modelling radiation heat transfer in absorbing, emitting and scattering material. The case considered is a one-dimensional layer of material with azimuthally symmetry surrounded by opaque, diffusely and specularly reflecting and diffusely emitting walls. The other coefficients in the Marshak condition are related to the first mentioned coefficient by simple expressions. This new method of calculating the coefficients by recurrence is easier to apply than deriving the boundary condition by tedious manual integrations. A recurrence formula for the cumulated errors is derived and the analyses shows that acceptable low errors occur when using the appropriate type of floating point numbers in the computer program taking into account the approximation order. The coefficients found by recurrence are compared to coefficients found by numerical integration and in one case the analytical solution and the agreement is excellent. The application of the recurrence formulas is demonstrated using a computer program solving the equations of the method of the spherical harmonics for arbitrary approximation order. The intensity as function of the direction cosine at the walls is analyzed for approximation orders up to 41. High order approximations are necessary for accurate modelling of the intensity as function of the direction due to discontinuities at the walls.

RADIATION IN HYPERSONIC IONIZED TURBULENT GAS JETS

The object of the work has been the development of a semiempiric design model for radiation-convection heat-mass exchange in reactive chemically jet flows, including a technique of radio band radiation design. The design technique for electromagnetic radiation of ionized jets based on the solution of the equation of radiation transfer in isotropic medium, taking into account electromagnetic waves radiation, refraction and absorption. According to this model a basic source of the electromagnetic radiation in the radio band is bremsstrahlung, provided for interaction of electrons and heavy neutral particles. In this case a kinetic model of plasma may be described by Boltszmann equation for electrons in which the collision integral is proportional to the frequency of electrons and neutral particles. In order to simulate the hypersonic axial-symmetric jet flow it has been proposed in this work the mathematics model based on the solution of the stationary system of the equations in partial derivatives of parabola type, including the parabolized system of Navier-Stokes equations (in projection onto transverse and longitudinal coordinate axes); the equations for kinetic energy and velocity of turbulent pulsation dissipation (the K- model of turbulence), the energy equation, the diffusion equation for components and mixture elements, as well the equations of chemical kinetics and the radiation transfer equation. In order to attain numeral count stability the equations of continuity with the artificial viscosity have been used in this system of equations. The equation of energy regarding to temperature has been applied, so it has been allowed to reduce an iterative process of its determination and to rise a count rate essentially. The presented technique for chemical kinetics design allows to design both non-equilibrium and equilibrium chemical processes. Newton's method has been used for the solution of the system of the non-linear algebraic equations, determining an equilibrium composition of a mixture. It is a model of low ionized plasma, that has been applied to determine a degree of jet flow ionization. According to this model the basic chemical reactions are isolated to be used for determination of a basic chemical composition, pressure, density and temperature of a mixture.

For the numeral solution of the parabolized system of the equations, cited above and offered for heat-mass transfer in reactive chemically jet flows, an algorithm has been proposed in which an implicit numeral scheme according to the "predictor-corrector" method has been used. On the basis of numeral simulation the investigation of heat-mass exchange and radio frequency radiation of a hypersonic under expanded jet, while its discharging into hypersonic air flow, has been worked out. As a result of the numeral computations been fulfilled the basic hydrodynamic and heat parameters distribution have been determined, such as: velocity, pressure, temperature, basic components concentration, including electrons concentration and spectral intensity of radio radiation.

RADIATIVE TRANSFER IN SEMI-TRANSPARENT MEDIUMS LIKE ISOLATING FOAM AND GLASS WOOL

There are several engineering applications of simultaneous radiation and conduction in a participating medium. For example, in heat transfer at room temperature through porous insulating materials such as fibers and foams, thermal radiation is comparable to conduction.

In such situations a separate calculation of conductive and radiation heat fluxes without any consideration of the interaction between thermal radiation and conduction may introduce error in the heat transfer results.

For the fibrous insulants an accurate modelization allows the simulation of radiative transfer starting with the optical and morphological characteristics of the medium. The absence of simplifying hypothesis allows the study of parameters influencing the transfer.

This method is impossible for the foams because the optical and morphological characteristics are complicated or unknown.

An experimental and a phenomenological approach are necessary. Measurements of thermal conductivity, using a k meter guarded hot plates apparatus, showed that the steady state thermal conductivity depends of the specimen thickness.

We make use of this property and induce the extinction parameter for the radiation transfer. The energy equation for simultaneous conduction and radiation may be solved.

Particularly the phenomenological approach for the fibrous insulants are analyzed and compared with the rigorous model showing a good agreement.

NON-STEADY RADIANT HEATING OF A COMPOSITE SLAB

This paper describes a method of predicting the thermal response of a two-dimensional composite slab which is subjected to non-linear thermal boundary conditions and which has temperature-dependent physical properties. One of the exposed faces of the composite slab is subjected to a time-dependent radiative flux whilst the other face is exposed to the ambient fluid and a radiation sink. Thus the boundary conditions involve both counteracting and combined radiative and natural convective heat transfer, which are both non-linear in temperature. The conduction equation itself becomes non-linear when the physical properties (such as conductivity) are temperature dependent. Additional problems arise from the presence of discontinuities in physical properties at the interfaces of the slab components. The analysis was developed in order to predict the temperature distribution in a composite plate rotating backwards and forwards in a beam of thermal radiation.

This problem poses considerable challenges for the analyst; of all the available methods of solution the heat balance integral (HBI) technique is particularly well suited. Of central importance to the accuracy of the HBI technique is the choice of approximation for the time-dependent temperature profile in a spreading thermal disturbance and the main contribution of this paper is the presentation of an integral solution to this complex transient conduction problem which uses Hermite polynomials as the approximations for the temperature profile.

ON THE HEAT TRANSFER PHENOMENON IN A BODY WITH WAVELENGTH-DEPENDENT PROPERTIES

In this work the coupled conduction/radiation heat transfer phenomenon in an opaque convex body with radiation properties depending on the wavelength is mathematically modelled. The considered heat transfer process is described by a partial differential equation subjected to a nonlinear boundary condition which involves the Classical Planck's law. In order to provide a more adequate description, it is constructed a modified version of Planck's law. It is presented a minimum principle which is employed for proving existence and uniqueness of the solution and which provides a way for simulating the considered nonlinear energy transfer phenomenon.