Acta Polytechnica Vol. 43 No. 3/2003 A Simulation Study for Computing the Emissivity of Clouds S. Seker, M. E. Aydemir, G. Apaydin In fhis sttrdy, prnpagativn through uarious dirrriburiorc of loxy particles in clouds is investigated,. Ctou"ds nay contain seueral types of crystal forms which can be rnodclled in the physical optics scattering region such as thin long cylhtdzrs and flat plate. The bistatic scatlering patterns and emissiuities of uariorn $pes of clouds are cornputed for waaes of selected polarizations passr,ng through clouds with specifld sizes, shapes and distributions. The results are in good egreenxent with the literature. Kelword;: scattering, emissility, pfusical oplics, fonuard scattering theorem. Brigld.ness temp = l[oQ 4/t /N// ./Y.-r--{ /l/\I\ Y cloud j '-*-*-------/' where nA, no(e) = * " II I$q*l-gsin 0,d0,d(o, -o) (z) +7t JJ.: 0 0 p=tl'a n%t A. a(E= +" IT f$q#9sino,do,d(e, -o) (3)1\, 4n J J ? 0 0 p=n,a I INTRODUCTION The propagation effects due to atmospherical interfer- ence in higher microwave bands have started to be investi- gated during recent years, It was seen that rain and the formation of ice crystals in clouds are the dominant physi- cal characteristics affecting channel characteristics [l]. In parallel, modeling efforts have been intensified to simulate scattering and ernission from different types of clouds [2]. In the literature there are few studies that focus on the scatter- ing properties of ice crystals at millimeter-wave fiequencies. Models of microwave emission developed in the past decade are based on a single scattering approach. Scatterers are assumed to be equal in dimensions, permittivity and shape, so that the cloud is characterized by single scattering albedo and the optical thickness t. Recent works indicate that the present trend is to describe cloud mechanisms in more realistic detail. In this study, a cloud is modelled as a random collection of discrete scatter- ers. Flat plate crystals are modelled by circular discs and long cylinder bullets are modelled by circular cylinders. Formulas to compute the absorption cross-section of random lossy dielectric dics and cylinders in the physical optics approxima- tion are derived, and their validity is checked by means of the forward scattering theorem. The bistatic scattering patterns and emissivity plots of various clouds are drawn using the statistical cloud parameters from some published papers. 2 Definitions and approximations All substances emit radiation with an intensity propor- tional to the temperature according to the Ste{han-Boltz- mann law. However, this law represents the upper limit in ra- diation intensity that a substance could emit for a particular temperature. Such a substance is normally called a 'black body'. In order to compare the actual to the theoretical emis- sion, the emissivity concept is defined as the ratio of the actual emitted radiance to that of an ideal black body [1]. Emissivity ranges from zero to one, where one would be a black body. The emissivity can also vary with wavelength for any particular substance. As an example, the emissivity for water droplet clouds decreases as the as the wavelength decreases from 10.7 pm to 3.9 pm. When viewing a cloud one can see further into its interior with 3.9 pm imagery compared to the imagery of the 10.7 pm channel. This phenomenon is shown in lig. l. The main reason is that sub- stances that are poor emitters are also poor absorbers for any given wavelength (Kirchoff's Law). Thus a cloud that has low emissivity also has low absorptivity, and any emitted radi- ation within the cloud has a good chance of escaping. Eriglrtnesstemp- lJoQ High Emissvrty Low EmissivitY 10.7um 3.9P.ttt Fig. I : Example for emissivity of clouds 3 Numerical calculations When we deal with a wave in a medium containing many particles, it is advantageous to consider two extreme cases: tenuous and dense distributions. When the particle density is tenuous, the single scattering approximation can be assumed. As the density increases, first order multiple scattering, multi- ple scattering and diffusion approximation approaches may be utilized (F,g. 2). In this study the bistatic scattering and emissivity are obtained by averaging over the given orienta- tion disribution. In [, 3] a detailed decription of the theory and the analytical expression of the emissivity (eq) for vegeta- tion is reported t3l. The same method is applicable to clouds, considering that clouds have differently shaped and sized parameters. The emissivity of a cloud is given by the following formula: 'r(o)= I -Rq(e) -&(e), (l) 61 Acta Polytechnica Vol. 43 No. 312003 Fig. 2: (a) Single scattering, (b) first order multiple scattering, (c) multiple scattering and (d) diffusion approximation /\/\/ A- \ \- -.\ - - _-5)b (ol Itort,nlllor ,aeltrtr on.gu9of-o3'3o-t".,,o - o/\o-Y o --u.o {c) with random orientation are shown. They are obtained by av- eraging the bistatic scattering patterns of an object which as- sumes different. orientations following a uniform distribution in the azimuth (between 0o and 360") and inclination (be- tween 0'and 90') . The input parameters are listed in Thble l. The direction of the incidentwave is always 0=45" and {=g; u1 300 GHz, we then take into account cylinders of 135 and l85pm radii and lengths equal to five and seven times the ra- dius, respectively, and circular discs of radius 600pm and thickness 30pm. The plots of Fig. 4 represent scattering in the plane of incidence ({, - 0 = 0) in the horizontal polarization. The calculated scattering cross sections (which can be ob- tained by means of surface integrating the bistatic scattering patterns in Fig. 4) are in agreement with these backscatter cross sections which are measured by NAIO military radars. The effects observed in Fig. 4lead to some computa- tional problems. Fine sampling in the scattering angle is needed if one is to get a correct numerical solution of the integrals in equations (2) and (3). Since the bistatic scattering patterns are mainly forwards, power is either transmitted in the same direction as that of the incidence, or is absorbed. Therefore a scatterer layer may be simply described by a transmission function: , {(e)=.*n[ ,trpl o, \/ trigures 4(a) and 4 (b) and 5 4(c) and 5 Approximation type PO PO PO Cloud Type Thin Cirrus Cirrus Cirrostratus Scatterer Type Cylinder Cylinder Disc Radius a (pm) 185 135 600 Cylinder length 2l (pm) 800 400 Disc thickness T (pm) JlJ Frequency/(GHz) 300 300 300 Incidence angle (0) 45" 45" 45" Permittivity e, 3.13-0.01lj 3.13-0.01lj 3.13-0.01lj Number of scatterers per unit volume nAv (m-3) 104 1.2x104 10' Cloud-layer height (m) 500 800 2000 62 Acta Polytechnica Vol. 43 No. 312003 900e$o 009;006 -b- Fig. 4: Average bistatic scattering Patterns (cm2; of randomly oriented cylinders (a), (b) and discs (c) assuming Rq(O)'5 '6 U Horizonul Polarization 63 Acta Polytechnica Vol. 43 No. 312003 length- Also in Fig. 4 it is seen that objects tend to behave as absorbers when the object dimensions ar€ close to the wavelength. It follows that the exact comPutation of the emissivity of a layer of large cylinders requires very large computational resources. To solve this kind of problem, we have inroduced an 'ipproximate' method based on the assumption that cylin- ders behave likesimple absorbers, which makes the use of the cylinder absorption cross section derived in this study' Itwas seen that the results are in good agreementwith the literature [4-6]. References tll Ulaby, F. T. etal: Microwaue Remote Smsing.Yol. I and 3, New York: Artech House, 1986. t2l Altshul, E. E. Y: Clou"d Attenmtion at Mil;imcter Waae- bngth. IEEE Trans. On Ant.&Prop., Yol.37, No. 199, 1989, p. 1473-1419. l3l Ferrazzoli, P., Guerriero,L.:, Emissi'ui't1 of Vegentian: Thc- or) ad Confutntional Aspects. In: 'Journal of Electro- magnetic Waves and Applications", Vol. 10, 1996, p.609S28. t4l NASA SUCCESS Mission Overview: http://cloud l.arc.nasa. gov/espo/success [5] 'Joe P. Precipitation at the Ground: Radar Techniques: NATA ASI Snizs,Yol.145, 1996, p.227-321. t6l Painter, A. J. et al Combin'ed, Infrared Emissinn Spectra an'd' Radnr Reflectiuity Shttits of Cirnr Clolt^' IEEE Trans GSRS,Vol.3l, No. l, 1993, p.64-69. Prof. Dr. Selim Seker phone: +90 212 358 l5 00 +90 212 358 l5 40.1414 fax: *90 212287 24 65 e-mail: seker@bound.edu.tr Department of Elecrical-Electronics Engineering Bogazici University 34342 BebeVlstanbul Turkey Mustafa Emre Aydemir Department of Electronics Engineering Turkish Air Force Academy Istanbul, Turkey G