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Precipitation scatter interference on communication links with emphasis on the melting-snow layer Hulays, Rafeh Ahmad 1992

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PRECIPITATION SCATTER INTERFERENCE ON COMMUNICATIONLINKS WITH EMPHASIS ON THE MELTING-SNOW LAYERbyRAFEH AHMAD HULAYSB.Sc., Monmouth College, 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESTHE DEPARTMENT OF ELECTRICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAApril, 1992© Rafeh Ahmad Hulays, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Electrical Engineering The University of British ColumbiaVancouver, CanadaDate  April 13/1992 DE-6 (2/88)AbstractAbstract A geometrical model has been developed to calculate hydrometeor interferencebetween different microwave systems sharing the same frequency. The model is capableof calculating the interference for any combination of transmitter-receiver geometry andthe program is flexible enough to allow for many assumptions related to the spatialand vertical structure of the rain cell. Furthermore, it can easily accommodate differentattenuation and scattering models.The study also focuses on the melting-snow layer and it is found that this layer playsa significant role in the interference calculations. The melting layer significantly increasesthe interference in the 1-8 GHz range, and moderately in the 8-12 GHz. On the otherhand, the melting layer results in a significant decrease in the interference level at higherfrequencies, especially in the 30-40 GHz range.The study also examines the effect of the ice/snow region above the melting layer andit is concluded that this region plays an important role in the interference calculations,especially at higher frequencies.Three examples of interference geometries are examined in Chapter 4. The first dealswith the interference from an up-link to terrestrial links in the near-forward direction, thesecond deals with the interference from an up-link to terrestrial links in the near-backwarddirection and the third deals with the interference from an up-link to a satellite in theforward direction.A comparison is made between two rain-cell models in Chapter 5. The COST210 rain-cell model, which is adopted by the CCIR (International Radio ConsultativeCommittee), is compared with the more physical Capsoni rain-cell model.iiAbstractA new empirical attenuation formula for rain and melting-snow has been developed,which, unlike previous formulae, has the frequency as a separate parameter. For detailedanalysis, refer to Appendix D.iiiTable of ContentsTable of ContentspageAbstract ^  iiList of Figures  viiiList of Tables ^  xiiiList of Symbols  xivAcknowledgment ^  xviiChapter 1^Introduction ^  1Chapter 2^Hydrometeors: Structure and Characteristics ^ 32.1 Hydrometeor Structure ^  32.1.1 Rain cells^  32.1.2 Spatial structure of rain ^  52.1.2.1 The Melting-snow layer (Bright Band) ^ 52.2 Electromagnetic wave propagation in Hydrometeors ^ 72.2.1 Hydrometeor scatter ^  72.2.2 Hydrometeor attenuation  82.2.2.1 Kharadly 1st model for attenuation [10] 82.2.2.2 Kharadly 2nd model for attenuation [12] 92.2.2.3 Kharadly 3rd model for attenuation [12] 92.2.2.4 Kharadly 4th model for attenuation . . . 92.2.2.5 Empirical model 10ivTable of ContentsChapter 3^The Interference Model ^ 163.1 Approximate Radar equation ^  163.2 Antenna gain pattern [7]  193.3 The "Universal Model"^ 21Chapter 4^Interference Calculations 234.1 Introduction ^ 234.1.1 Scattering in the ice/snow region ^ 234.2 Interference from up-link to terrestrial links in thenear-forward direction ^ 244.2.1 Description 244.2.2 Computed results^ 274.3 Interference from up-link to terrestrial links in thenear-backward direction ^ 384.3.1 Description ^ 384.3.2 Computed results 384.4 Interference from up-link to satellite in the forwarddirection ^ 494.4.1 Description ^ 494.4.2 Computation results ^ 514.5 Summary^ 52VTable of ContentsChapter 5^COST 210 rain-cell model ^ 615.1 Introduction ^ 615.2 COST 210 rain cell model [7] ^  615.3 Results for sample interference geometries ^ 645.4 Conclusion ^ 65Chapter 6^Discussion and Conclusions^ 776.1 Effect of melting-snow layer 776.2 Effect of rain height, Hm ^ 786.3 Effect of rain rate ^ 796.4 Effect of frequency 796.5 Reminder^ 79Chapter 7^Suggestions for future research ^ 80Appendix A^Precipitation modeling^ 82A.1 Rain medium 82A.2 Melting-snow medium ^ 83Appendix B^Kharadly attenuation models 85B.1 Artificial dielectric model ^ 85B.2 Corrected attenuation models 86B.2.1 Kharadly 3rd model for attenuation^ 86B.2.2 Kharadly 4th model for attenuation^ 87Appendix C^Kharadly scattering model [11] ^  88Appendix D^Empirical formula for attenuation 92viTable of ContentsAppendix E^The program for the "Universal Model" ^ 101Appendix F^CCIR Document 12-3/29 (Rev. 1) and supplement . . ^ 138References  153viiList of FiguresList of FigurespageFigure 2.1^Rain rate distribution in a 20 km radius rain-cell for^4different roFigure 2.2^Two views of the radar bright band: at the left a vertical^6profile of reflectivity and Doppler velocity as measured withvertically pointing Doppler Radar; at right a PPI map at 8°elevation on which the melting layer appears as a brightring at about 12 miles.Figure 2.3(a)^A comparison of the attenuation profile of the melting layer^11between Kharadly 3rd and 4th attenuation models, and theExact calculations for f (frequency) = 1.0 and 10.0 GHz and= 0.1, 0.2, 0.3Figure 2.3(b)^A comparison of the attenuation profile of the melting layer^12between Kharadly 3rd and 4th attenuation models, and theExact calculations for f (frequency) = 20.0 and 30.0 GHzand ps = 0.1, 0.2, 0.3Figure 2.3(a)^A comparison of the attenuation profile of the melting layer^14between Kharadly 3rd attenuation model, Empirical model,and the Exact calculations for f (frequency) = 1.0 and 10.0GHz (ps = 0.1).viiiList of FiguresFigure 2.3(b)Figure 3.1Figure 3.2Figure 4.2.1Figure 4.2.2(a)Figure 4.2.2(b)Figure 4.2.2(c)Figure 4.2.2(d)Figure 4.2.2(e)Figure 4.2.3(a)Figure 4.2.3(b)Figure 4.2.3(c)Figure 4.3.1Figure 4.3.2(a)Figure 4.3.2(b)A comparison of the attenuation profile of the melting layer^15between Kharadly 3rd attenuation model, Empirical model,and the Exact calculations for f (frequency) = 20.0 and 40.0GHz (ps = 0.1).General Interference geometry^ 17Simulation of the gain of an antenna with K=-15,^20al = 0.6, (12 = 5.5.Interference from up-link to terrestrial link geometry in the^25near forward direction.Interference versus rain rate for various frequencies (f in^30GHz), ps (m = 1—p,), and for Hm = 2.0 km.Same as Figure 4.2.2(a), with Hm = 2.5 km.^31Same as Figure 4.2.2(a), with Hm = 3.0 km. 32Same as Figure 4.2.2(a), with Hm = 3.5 km.^33Same as Figure 4.2.2(a), with Hm = 4.0 km. 34Interference versus rain rate for various rain heights (Hm),^35and for f (frequency) = 1, 5, 10, 20 GHz.Same as Figure 4.2.3(a), with f = 30 GHz.^36Same as Figure 4.2.3(a), with f = 40 GHz. 37Interference from up-link to terrestrial link geometry in the^39near backward direction.Interference versus rain rate for various frequencies (f in^41GHz),p, (m = 1—p,), and for Hm = 2.0 km.Same as Figure 4.3.2(a), with Hm = 2.5 km.^42ixList of FiguresSame as Figure 4.3.2(a), with Hm = 3.0 km^43Same as Figure 4.3.2(a), with Hm = 3.5 km. 44Same as Figure 4.3.2(a), with Hm = 4.0 km.^45Interference versus rain rate for various rain heights (Hm),^46and for f (frequency) = 1, 5, 10, 20 GHz.Same as Figure 4.3.3(a), with f = 30 GHz.^47Same as Figure 4.3.3(a), with f = 40 GHz. 48Interference from up-link to satellite geometry in the^50forward direction.Interference versus rain rate for various frequencies (f in^53GHz), ps (m = 1—ps ), and for Hm = 2.0 km.Same as Figure 4.4.2(a), with Hm = 2.5 km.^54Same as Figure 4.4.2(a), with Hm = 3.0 km. 55Same as Figure 4.4.2(a), with Hm = 3.5 km.^56Same as Figure 4.4.2(a), with Hm = 4.0 km. 57Interference versus rain rate for various rain heights (Hm),^58and for f (frequency) = 1, 5, 10, 20 GHz.Same as Figure 4.4.3(a), with f = 30 GHz.^59Same as Figure 4.4.3(a), with f = 40 GHz. 60COST 210 rain-cell model^ 62A comparison between Capsoni and COST 210 rain cell^66models with and without a melting snow layer for Hm = 2.0km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.Figure 4.3.2(c)Figure 4.3.2(d)Figure 4.3.2(e)Figure 4.3.3(a)Figure 4.3.3(b)Figure 4.3.3(c)Figure 4.4.1Figure 4.4.2(a)Figure 4.4.2(b)Figure 4.4.2(c)Figure 4.4.2(d)Figure 4.4.2(e)Figure 4.4.3(a)Figure 4.4.3(b)Figure 4.4.3(c)Figure 5.1Figure 5.2(a,b)List of FiguresFigure 5.2(c,d) A comparison between Capsoni and COST 210 rain cell^67models with and without a melting snow layer for Hm = 2.0km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Figure 5.3(a,b) A comparison between Capsoni and COST 210 rain cell^68models with and without a melting snow layer for Hm = 2.5km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.Figure 5.3(c,d) A comparison between Capsoni and COST 210 rain cell^69models with and without a melting snow layer for Hm = 2.5km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Figure 5.4(a,b) A comparison between Capsoni and COST 210 rain cell^70models with and without a melting snow layer for Hm = 3.0km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.Figure 5.4(c,d) A comparison between Capsoni and COST 210 rain cell^71models with and without a melting snow layer for Hm = 3.0km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Figure 5.5(a,b) A comparison between Capsoni and COST 210 rain cell^72models with and without a melting snow layer for Hm = 3.5km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.Figure 5.5(c,d) A comparison between Capsoni and COST 210 rain cell^73models with and without a melting snow layer for Hm = 3.5km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Figure 5.6(a,b) A comparison between Capsoni and COST 210 rain cell^74models with and without a melting snow layer for Hm = 4.0km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.xiList of FiguresFigure 5.6(c,d) A comparison between Capsoni and COST 210 rain cell^75models with and without a melting snow layer for Hm = 4.0km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Figure C.1^Scattering geometry of a rain particle due to an incident^89electromagnetic wave.Figure D.1^A comparison of the attenuation profile of the melting layer^97between Kharadly 3rd attenuation model, Empirical model,and the Exact calculations for f (frequency) = 1.0 and 5.0GHz (p3 = 0.1).Figure D.2^A comparison of the attenuation profile of the melting layer^98between Kharadly 3rd attenuation model, Empirical model,and the Exact calculations for f (frequency) = 10.0 and 20.0GHz (ps = 0.1).Figure D.3^A comparison of the attenuation profile of the melting layer^99between Kharadly 3rd attenuation model, Empirical model,and the Exact calculations for f (frequency) = 30.0 and 40.0GHz (p s = 0.1).Figure D.4^A comparison of the attenuation profile of the melting layer^100between Kharadly 3rd attenuation model, Empirical model,and the Exact calculations for f (frequency) = 70.0 and100.0 GHz (ps = 0.1).xiiList of TablesList of Tables Chilbolton-Baldock path parameters [7]Measured transmission loss for the Chilbolton-Baldockpath at 11.2 GHz as a function of rain rate and percentageof timeThe converted input parameters for the model-programParameters used for the interference calculations fromup-link to satelliteDrop size distribution and their velocities for variousprecipitation rates [14]Table 4.1Table 4.2Table 4.3Table 4.4Table A.1page2426274982List of SymbolsList of Symbolsa • representative rain drops radius.^ant i^melting-snow particles radius.^aRi^rain drops radius.^dc^diameter of the COST 210 rain-cell.frequency.fr ▪the resonant frequency of the melting-snow particle.• low-frequency polarizability.^ge^high-frequency polarizability.^gr (0)^normalized radiation pattern of the receiving antenna at anangle Co from the main lobe axis.^n(d)^the raindrop-size distribution.Pi fraction of the volume of rain VR composed of the rain dropsof radius aRt•r,^the distance at which the rainfall rate decrease by a factor oflie (Capsoni rain cell).ref f effective Earth radius.^f m^the truncated Capsoni rain cell radius.rrt link length between transmitter and receiver.vmi fall velocity of the melting-snow spheres of radius a rm.vRi fall velocity of the rain drop of radius aRi.^(xc, Yc, zc)^the rectangular coordinates of the bottom of the rain cell.(xr , yr, zr)^the rectangular coordinates of the receiver.^(xt, yt, zt)^the rectangular coordinates of the transmitter.• sum of the sixth powers of the diameters of all hydrometeorsper unit volume (reflectivity)Aa • Attenuation coefficient due to atmospheric gases.• the normalized melting-snow attenuation.xivList of SymbolsAp • Attenuation coefficient due to precipitation.Gr receiving antenna gain.Gt •transmitting antenna gain.He the rain cell height.Hm rain height; also the height of the top of the melting layer.a parameter connected with the receiver normal radiationspattern. It determines the gain level of the side lobe of theantenna.• transmission loss.number of representative rain drops of radius a per unitvolume.Nm number of melting-snow particle per unit volume (rain dropdensity).Pr average interference power received.Pt transmitted power.R rain rate.Rr distance from the common volume to receiver.Rm in the rain rate where the Capsoni rain cell is truncated.^Rt^distance from the transmitter to the common volume.RM the peak rain rate at the centre of the rain cell (Capsoni raincell).• ratio of the melted to the total volume in the melting-snowparticle.S. surface area of the narrow beam antenna perpendicular to themain beam axis (also known as the 3dB foot-print).• melting-snow layer thickness.VR volume of rain.a2) parameters connected with the receiver normal radiationspattern.• phase coefficient due to precipitation.^7(Rt, Rr)^the propagation loss due to precipitation and atmospheric gasesalong the path Rt + Rr •xvPList of Symbolsskin depth of water.= complex permitivity of water.^CO^complex permitivity of free space.receiver loss factor.^Tit^transmitter loss factor.• double-sided half power beamwidth of the narrow beamantenna.(Or, Or) • the rectangular coordinates of the receiver main lobe axisrelative to the receiver coordinate axes.(et, 0i) the spherical coordinates of the transmitter main lobe axisrelative to the transmitter coordinate axes.A wavelength of the transmitter electromagnetic wave.▪ the rain cell radius.• the density of snow in the melting-snow particle.bistatic scattering cross section in the direction of O and(Figure C.1).• the bistatic cross section of a drop of equi-volume radius a inobi^cb, a-) the direction of (O, cb) .Qs •Rayleigh scattering.FR attenuation outside the COST 210 rain-cell.xviAcknowledgmentAcknowledgmentI would like to express my appreciation to Dr. M.M.Z. Kharadly who has providedme with much needed support, supervision and suggestions throughout the course of mystudies at UBC.I also would like to thank Dr. R.L. Olsen and Dr. D.V. Rogers of the Communica-tions Research Centre for their assistance and helpful advice. I would also like to thankMr. Tim Vlaar and Mr. Smrz Honza for their help during the summer of 1991. Thehelp of Mr. Vlaar in developing the empirical model is greatly appreciated.I would like to thank all my friends and teachers since everyone of them left theirmark in my life and character.This research was supported by the Communications Research Centre, Departmentof Communication, under contract number 36001-0-3596/01—SSFinally, I would like to thank my mother and father, whom I long to see soon andwhose advice has always been with me.xviiChapter 1—IntroductionChapter 1 IntroductionThe ever increasing demand on a limited radio-frequency spectrum has necessitatedthe sharing of frequencies by a number of services. This frequency sharing increases thepossibility of interference. In system planning, an engineer has to be able to establisha reliable system which can distinguish between the incoming signal and interferencecaused by other systems using the same frequency. To do this, it is necessary to estimatethe mutual interference between the different radio systems. This is by no means aneasy task (and is getting harder with the increasing congestion of the radio-frequencyspectrum).There are many mechanisms that can cause interference [6]:— line of sight;— diffraction over isolated obstacles;— diffraction over irregular terrain;— tropospheric forward scatter;superrefraction, with or without reflection;ducting;scatter from hydrometeors;reflections from aircraft.Microwaves are scattered by hydrometeors such as rain, snow, melting-snow, andice particles. This scattering is one of the possible causes of interference betweencommunication links operating at the same frequency. It becomes then necessary toquantify this interference in order to be able to design more reliable communication links.1Chapter 1—IntroductionRecently, considerable work has been done on interference caused by hydrometeor[1,2,7]. So far, however, the issue of the melting-snow layer has not been considered,even though the presence of the melting layer tended to be a significant source of errorin radar measurement of rain rate [17]The purposes of this study are:1. to develop a general geometrical model which can be used in conjunction with anyattenuation and scattering model;2. to develop a "universal" program to calculate the interference for a wide range ofgeometries and variables;3. to study the effect of those variables and geometries on interference due to rain, and4. to study the effect of the melting-snow layer on the interference problem.The possible geometries involved in the interference calculations are numerous. Toovercome this, a "universal" model-program has been developed. While this programis capable of calculating the interference for all geometries and variables, only the mostlikely scenarios (which are still very numerous) will be considered (e.g., geometriesinvolving the interference from up-link to satellite, interference from up-link to terrestriallink and variables such as antenna gain, rain rate and rain-cell structure).2Chapter 2—Hydrometeors: Structure and CharacteristicsChapter 2 Hydrometeors:Structure and Characteristics 2.1 Hydrometeor StructureHydrometeor scattering is observed when a rain cell overlaps with the commonvolume of transmitting and receiving antennas. This scattering and the subsequentinterference depends on the rain cell, its rain intensity, height, radius, etc. It thusbecomes very important to model the rain cell as accurately as possible for interferencecalculations. Many models have been developed to describe rain processes [eg. 3,6,7];the most realistic is that of Capsoni [3]. The Capsoni model will be the basis for thespatial distribution of rain in the present work.2.1.1 Rain cellsThe horizontal pattern of the rain cell has been represented by an analytical expressionwith an exponential shape having rotational symmetry [2]:R(z , y) = Rme ro^(2.1)where r is the distance of the point (x, y) from the rain cell centre, ro is the radius atwhich rainfall rate decreases by a factor of 1/e, and RM is the peak rain rate at the centreof the cell (Figure 2.1)The rain cell is truncated at a certain distance f,,, where the rain rate is Rm in [2]:Rmin = Rme —i."1 /r°^ (2.2)30.90.80.73c40.60.50.40.30.20.1Chapter 2--Ifydrometeors: Structure and Characteristics-15^-10^-5^0^5^10^15^20distance (r) from the centre of the rain cell in kmFigure 2.1 Rain rate distribution in a 20 km radius rain-cell for different I-.Chapter 2--Ilydrometeors: Structure and CharacteristicsBeyond this point, we assume that the effect of rain is negligible. Equation 2.2 can nowbe rewritten as:r° =^In(RA I I Rmsn)^ (2.3)The radius of the rain cell is given by:= 10 — 1.5 x log io Rm^(2.4)where^is in km and RM is in mm/h.2.1.2 Spatial structure of rainTwo rain-cell structures are considered. The first is a rain-only medium. The otheris when snow forms and then melts introducing a melting-snow layer.2.1.2.1 The Melting-snow layer (Bright Band)When it is warm enough for the snow to melt before reaching the ground, there isoften observed a layer of high reflectivity just below the 0°C isotherm. This phenomenonwas observed as far back as the forties and it became known as the radar "bright band."The melting-snow layer is the region in which the precipitation changes from snow to rain(Figure 2.2). As snowflakes descend into the melting-snow layer, they become highly"reflective."The most important reason for the increase in reflectivity is that the dielectric constantof water is four times higher than that of ice [19]. Another reason for the high reflectivityis the large size and low velocity of the melting-snow particles relative to those of raindrops. Continuing to melt while descending, the snowflakes become smaller in size and5Chapter 2--Hydrometeors: Structure and CharacteristicsRefiechinfy foe* dalFigure 2.2 Two views of the radar bright band: at the left a vertical profile of reflectivity andDoppler velocity as measured with vertically pointing Doppler Radar; at right a PPI map at 8°elevation on which the melting layer appears as a bright ring at about 12 miles. [Rogers]Chapter 2—Hydrometeors: Structure and Characteristicsfaster with less concentration. This will cause a decrease in the reflectivity as the rainmedium is approached.A formula for the melting layer thickness (in meters) has been suggested by Klassen[13]:T = 100z0 ' 17^(2.5)where z is the reflectivity as given in [6]:z = 400// 1.4^(2.6)where R is the rain rate in mm/h. The melting layer disappears at high rain rates; it isusually assumed that it disappears above a rain rate of 30 mm/h.2.2 Electromagnetic wave propagation in HydrometeorsThe most accurate method to model melting layer scattering and attenuation is throughthe use of Mie scattering techniques for spherical rain droplets [11]. The advantage ofusing this technique is obvious — its accuracy. This method is quite complicated andthus undesirable in computer models. Another technique is to have the data for scatteringand attenuation stored in files. Unfortunately, such files occupy a very large chunk ofmemory and they slow the system considerably. New models, that are simpler, but lessaccurate, have been developed in order to model hydrometeor scattering and attenuation[6, 10, 11, 12].2.2.1 Hydrometeor scatterA Hydrometeor scattering model has been developed by Kharadly [11]. This modelis both simple and relatively accurate in the 1-40 GHz range. A thorough description of7Chapter 2—Hydrometeors: Structure and Characteristicsthe model is given in Appendix C. The model has "good" agreement with the "exact"results calculated by Kishk using Mie scattering [11]. At the top of the melting layer(S=O, where S is the ratio of the melted to the total volume in the melting-snow particle),the reflectivity is assumed to be the same as that of rain (S=1). The reflectivity thendecreases by —6.5 dB per kilometer.2.2.2 Hydrometeor attenuation )Attenuation plays an important role in the interference problem. On one hand, anincrease in attenuation may decrease the interference. On the other hand, it may forcethe transmitting station to increase its transmitting power thus further aggravating theinterference. Since attenuation affects the incident and scattered signals and since thisattenuation varies as a function of rain rate and melting ratio (S), accounting for it occupiesmuch of the computer time in the interference calculations. It is then desirable to usemodels that are reasonably accurate and simple. The models developed by Kharadly[10, 12] are simple and flexible; they can readily accommodate changes in physicalassumptions relating to drop-size distributions, rain drop shapes, the density of the snow inthe melting-snow particle, etc. An empirical formula has also been developed (AppendixD). While this formula is simpler, it is not flexible.2.2.1 Kharadly 1st model for attenuation [10]The melting-snow particles are considered to be spherical, of the same number and(relative) size distribution as the resulting rain drops. The radius of the representativeparticle is calculated using equation A.4.1^For a thorough analysis refer to the Appendix A and B (Kharadly's models [10, 12]) and Appendix D for empirical model.8Chapter 2—Hydrometeors: Structure and Characteristics2.2.2 Kharadly 2nd model for attenuation [12]The above model does not satisfy the conservation of mass criterion since it does nottake into account the effect of the changing velocities of the melting-snow particles onthe number density and hence the drop-size distribution. This model has been amendedto include the effect of the velocity.2.2.3 Kharadly 3rd model for attenuation [12]Because of the deviation of the results of the 1st model from that of the exact valuesfor the melting-snow layer, Kharadly introduced a correction factor that brought theresults of the model closely to the exact attenuations calculated using Mie scattering.The correction factor is given by [12]:ni(2^+ 1] { 2 — 51 (1-s)xFactorl =  ^ (2.7)-1-- + 2 — S 2 + Swhere f is the frequency in GHz, fr is the resonant frequency of the melting-snowparticle, S is the melting degree , defined as the melted to the total volume in therepresentative melting-snow particle, and n is defined in Appendix B.2.2.4 Kharadly 4th model for attenuationBecause of the deviation of the results of the 2nd model from that of the exactvalues for the melting snow layer, Kharadly introduced a correction factor that broughtthe results of the model closely to the exact attenuations calculated using Mie scattering.The factor is given by:n2e/(1 S)— ^[ 1110Factor2 = [fn S(1 — nil {1 +^26^1 + (1 — 58)1 (2.8)9Chapter 2—Hydrometeors: Structure and Characteristicswhere a is the radius of the representative particle, 6. is the skin depth of water =^ with C1 = 20.958, f is the frequency in GHz and e is the complexReal[fpermittivity of water as given in Appendix B.The range of applicability of Kharadly formulas is between 1-40 GHzAlthough the above formulas were developed with the assumption that the density ofthe snow core in the melting layer (AO is 0.1, they still apply with a reasonable degree ofaccuracy for a wide range of A, (typically between 0.1 and 0.3). Figure 2.3 shows howclose the 3rd and the 4th attenuation models are to the "exact" results for this range. Wealso note that Kharadly 3rd model yields the best results.2.2.5 Empirical modelSince the frequency stays constant during the interference calculations, it would beuseful to have an equation where the frequency variable is separable from all othervariables, which is not the case in any of the above models. This has been achievedthrough the development of an empirical formula for attenuation based upon the exactvalues [12] and is given by:where,Ap An(R,^) x aleAn(R S) mi sal —1 e—biSal m2 sa2-1 e —b2 S°2 m3e—b3S 1, (2.9)(2.10)with,with S < 1Ali(R) = Co + CiRm°3c+ 2Ro.0002M2(R) = Do + Di R°.°°3^2Ro.000210(2.11)f = 1.0 GHz^ Kharadly 3rd attenuation model Kharadly 4th attenuation model  Exact calculations, Ps = 0.1x Exact calculations, Ps = 0.2+ Exact calculations, Ps = 0.3,--.^-- I , 1P ; ,- ? t. i,■   Kharadly 3rd attenuation model_^,,t   Kharadly 4th attenuation model.,ti:^'At Exact calculations, Ps = 0.1.- ;^'t^x Exact calculations, Ps = 0.2i 'tx.^\ + Exact calculations, Ps = 0.3- i ,...--^k.I ,:^IC,^t.'t.If .' \^'.;,- I): rr. ,^s•^..%i‘ /,' ^- -4.li,: .%,`i•....f = 10.0 GHz0.00^0.20^0.40^0.60^0.80^1.00Degree of melting (S)Chapter 2-Hydrometeors: Structure and Characteristics100.0090.00so.00A 70.00m 60.00C30.0040.00v 30.0020.0010.000.007.006.00E3.00*•-•• 4.000ro= 3.00C< 2.001.000.000.00 0.20 0.40 0.60 0.80^1.00Degree of melting (S)Figure 2.3(a) A comparison of the attenuation profile of the melting layer between Kharadly3rd and 4th attenuation models, and the Exact calculations for R (rain rate) =12.5 mm/h, f (frequency) = 1.0 and 10.0 GHz and pa = 0.1, 0.2, 03110.000.00 0.20 0.40^0.60 0.80 1.0014.00• 12.0010.0o08.006.0016.0018 .00f= 20.0 GHz^ Kharadly 3rd attenuation model^ Kharadly 4th attenuation model  Exact calculations, Ps = 0.1x Exact calculations, P = 0.2+ Exact calculations, s = 0.3I4x,,t- ''^• '4.002.000.00 0.20 0.40 0.60 0.80 1.0025.0020.00E15.00T7. 0C010.0075.00rYxf = 40.0 GHzKharadly 3rd attenuation modelKharadly 4th attenuation modelExact calculations, Ps = 0.1x Exact calculations, PS = 0.2+ Exact calculations, Ps = 0.30.00/,' -/-^,'It,'-Chapter 2-Hydrometeors: Structure and CharacteristicsDegree of melting (S)Degree of melting (S)Figure 2.3(b) A comparison of the attenuation profile of the melting layer betweenKharadly 3rd and 4th attenuation models, and the Exact calculations for R (rainrate) = 12.5 mm/h, f (frequency) = 20.0 and 40.0 GHz and p, = 0.1, 0.2, 0.312Chapter 2—Hydrometeors: Structure and CharacteristicsCo, C1, C2, Do, D1, D2, al, a, # are frequency dependent constants.An (R ,^) approaches unity when S = 1.The advantage of this formula is its simplicity and ease of use. Its disadvantage isthat the formula does not, so far, take into account the average density of the snow inthe melting-snow particle. The formula does represent the attenuation "quite well" from1-100 GHz, however (Figure 2.4(a,b)). For a complete description, refer to AppendixD.130.00^0.50^1.00Degree of melting (S)Attatuation in dB/km x le210.00200.00190.00180.00170.00160.00150.00140.00130.00120.00110.00100.0090.00i•-• 80.004:•70.0060.0050.0040.0030.0020.0010.000.00-10.000.00Attenuadon in dB/km16.0015.0014.0013.0012.0011.0010.009.008.007.006.005.004.003.002.001.000.000.50^1.00Degree of melting (S)Figure 2.3.(a) A comparison of the attenuation profile of the melting layer between Kharadly 3rd attenuationmodel, Empirical model, and the Exact calculations for f (frequency) = 1.0 and 10.0 GHz (p. = 0.1).Attenuation in dB/km36.0034.0032.0030.0028.0026.0024.0022.0020.0018.0016.0014.0012.0010.008.006.004.002.000.000.00^0.50^1.00Degree of melting (S)Attenuation in dB/l®45.0040.0035.0030.0025.0020.0015.0010.005.000.000.00 0.50^1.00Degree of melting (S).xact calculations, in•0.9Empirical formulaKharadly 3rd attenuation modelFigure 2.3.(b) A comparison of the attenuation profile of the melting layer between Kharadly 3rd attenuationmodel, Empirical model, and the Exact calculations for f (frequency) = 20.0 and 30.0 GHz (p, = 0.1).Chapter 3—The Interference ModelChapter 3 The Interference Model3.1 Approximate Radar equationThe interference power received by an antenna due to the scattering of the electro-magnetic wave by precipitation is given by [1] [8]:1_ Pr _ A 2 GtGoor [ gi(OfirMa Ce ') L 71);^(4703^i^Rpt?^-Y(Rt, , RO.dV^(3.1)VolWhereL =Pr =Pt =G1 =Gr =transmission lossaverage interference power receivedtransmitted powertransmitting antenna gainreceiving antenna gain= normalized radiation pattern of the transmitting antenna at anangle 14 from the main lobe axis= normalized radiation pattern of the receiving antenna at anangle 3 from the main lobe axis= transmitter loss (loss factor < 1) - for simplicity assume 1 (noloss)71r^= receiver loss (loss factor < 1) - for simplicity assume 1 (noloss)distance from the transmitter to dVdistance from dV to receiverwavelength of the transmitter electromagnetic wavegt (0gr (0)77tlit =Rr =A =16Chapter 3—Intetference Model and System parametersFigure 3.1 General Interference geometry17Chapter 3—The Interference Model7(11t, Rr) = the propagation loss due to precipitation and atmospheric gasesalong the path Ri + R,• bistatic scattering cross section in the direction of B and(Figure C.1)The propagation loss y is given by [1]:lt+1,—0.1 f Apdr-0.1 f As dr^7 = 10^(3.2)where,Ap • Attenuation coefficient due to precipitationAa Attenuation coefficient due to atmospheric gases. Forsimplicity we will assume that the attenuation due to gases isnegligible (Aa = 0)it, lr •the distances that the electromagnetic wave traverses the raincell along the transmitter and receiver directions, respectivelyThe bistatic cross section a (O, c'.b) is given byamaxa 0,^=^4,,^= / n(a)cybi (0,i4,a)da^(3.3)0where n(d) is the raindrop-size distribution, a is the radius of the raindrop, andObi (a, a) is the bistatic cross section of a drop of equi-volume radius a in the di-rection of (9, (¢).In order to simplify the Radar equation, the narrow beam approximation to either oneof the antennas may safely be introduced. Since the transmitter and receiver parameters18Chapter 3—The Interference Modelare interchangeable, we will assume that the antenna with the narrow-beam approximationhas the subscript '1' and the other antenna has the subscript '2' as shown below:^L^Pt^(4703 Vol1= Pr A 2 GtGr f 91 (0g2 (0 ) ()92(0)o. (e,134113^^y.dV^(3.4)Using the narrow-beam approximation, dV = Sa dr(where S. is the 3dB circularsurface area perpendicular to the main beam axis), equation 3.4 becomes1 1+ 1 2re^tA, c) —0.1 f Ar dr^2P^ (r A 2 GiG,0 2h f dr gSs9)cy— = _ 0L^Pt^2567r2^113  x 10^(3.5)To3.2 Antenna gain pattern [7]The standard method for representing the main lobe of an antenna is through theGaussian-shaped pattern [7]:G1(B) = e —41n(^(3.6)where G i (B) is the gain at angle B from the main axis and al is the double-sidedhalf-power bandwidth.In order to represent the secondary lobe, we also assume a Gaussian-shaped pattern,but with a larger half-power bandwidth and a gain of K dB below the main lobe (Figure3.2) :G20) = 100.1K x e—iin2(*)^(3.7)19Chapter 3—Interference Model and System parameters0.1,,.1^4is^i^(is^2angle in degreesFigure 3.2 Simulation of the gain of an antenna with K=-15. al = 0.6, a3 = 5.5.Chapter 3—The Interference ModelThe total radiation pattern thus becomes:G^Gi(e) + G2(e)(9) = 1 + 100.1K^ (3.8)3.3 The "Universal Model"A program have been developed to implement the above equations. This programcan calculate the interference for any configuration of transmitter-receiver geometry. Itaccepts the following input variables:1. the rectangular coordinates (xi, yi, z2) of the transmitter. Initially, we will considerthat the transmitter is located at the centre of the main coordinate system, and hencethe coordinates of the transmitter are (0,0,0)2. the spherical coordinates (Ot, (ki) of the transmitter main lobe axis relative to thetransmitter coordinate axes3. the rectangular coordinates (xr , yr , zr ) of the receiver4. the spherical coordinates (Or , Or ) of the receiver main lobe axis relative to the receivercoordinate axes5. the polarization of the transmitter 26. the transmitter and receiver gains7. the transmitter double-sided half-power bandwidth8. the parameters connected with the receiver normal radiations pattern (a l , a2 , K)9. the rectangular coordinates (xe , yc , z,) of the bottom of the rain cell10. the rain cell radius (p) and Height (Hc)2^We assume that the receiver accepts input electromagnetic wave regardless of polarization21Chapter 3—The Interference Model11. the height (Hm — T) and the thickness (T) of the melting snow layer. Thicknesswill be zero in the absence of a melting snow layer12. the rain rate at the centre of the rain cell RM and the distance (ro ) at which rainfallrate decrease by a factor of lie13. the integration steps which largely determine the accuracy of the program14. the frequency used15. the density of the snow in the melting snow particle A,16. the scattering and attenuation model to be used in the calculations. For scattering,we are limited to Kharadly's model. For attenuation, we can choose from Kharadly's1st, 2nd, 3rd, 4th models and the empirical formula.Also note that:1. The z-axis for all the above mentioned coordinate systems is in the direction of thevertical edge of the rain cell, in the direction opposite to the rain fall.2. In order for the program to work correctly, at least one of the antennas has to satisfythe narrow-beam approximation.The program can also compute the interference for different melting layer profiles.However, a different subroutine is needed for each profile. Another method, which hasnot yet been implemented, is to have an external data file that contains the shape of themelting layer. The advantage is to avoid changing the program and recompiling it everytime we introduce a different profile. The disadvantage of this procedure is that usingan external file will add to the computation time.22Chapter 4--interference CalculationsChapter 4 Interference Calculations4.1 Introduction4.1.1 Scattering in the ice/snow regionRayleigh scattering is generally assumed for the ice/snow region above the melting-snow layer in the rain cell. The scattering cross section per unit volume at the top ofthe melting layer is given by [7]:7r4Crs = A4 2Z x 10 —18c — 1 m2 /m3^(4.1)+ 2where c = complex relative permittivity of water, A is the wavelength, and z is the sumof the sixth powers of the diameters of all hydrometeors per unit volume. The magnitudeof z is also given by the following empirical formula [6]:z = 400R1 '4 772 6 77"/ —3 (4.2)where R is the rain rate. The scattering decreases by —6.5 dB/km as we move higherinto the ice/snow region.On the other hand, the attenuation in the ice/snow region is negligible and is assumedto be zero.Several transmitter-receiver systems will be considered below, in our study ofinterference caused by the rain and melting-snow. It will seem that the interference willvary depending on several factors, which will include frequency, rain rate, the height ofthe melting snow layer, its thickness, and the density of the snow in the melting-snowparticle.23Chapter 4—Interference Calculations4.2 Interference from up-link to terrestriallinks in the near-forward direction4.2.1 DescriptionThe calculations are performed for an experimental link which is part of the EuropeanCOST 210 project [7] dealing with the influence of the atmosphere on interferencebetween radio communication systems. The Chilbolton-Baldock (England) path [7] hasbeen chosen because of the availability of the measured transmission loss. The geometryof interference is shown in Figure 4.2.1. A radio wave transmitted by an up-link towarda satellite is scattered by rainfall. The scattered electromagnetic wave interferes witha terrestrial receiving station operating at the same frequency and sharing a commonvolume. In this case the main lobe axes of the two antennas intersect. In order tomaximize the interference, the centre of the rain cell is positioned at the intersection ofantenna beam axes. The parameters used in the calculations are listed below, in Table4.1. The measured (experimental) transmission loss of the path for 11.2 GHz frequencyChilbolton-Baldock pathStation separation in km (rrt) 131 kmScatter geometry Vertical planeTransmitting antenna gain in dB 59.0 dBReceiving antenna gain in dB 40.5 dBTransmitting antenna 3dB Beamwidth in degrees 0.18 degreesReceiving antenna 3dB Beamwidth in degrees 1.6 degreesTransmitting antenna elevation angle in degrees 20.0 degreesReceiving antenna elevation angle in degrees(f r ) 1.0 degreesTransmitting antenna height from sea level in km (h e ) 0.12 kmReceiving antenna height from sea level in km (hr ) 0.086 kmTable 4.1 Chilbolton-Baldock path parameters [7]24Terrestrial receivingstationChapter 4—Interference Calculations(Graph not to scale)rain cellTransmitting antennaFigure 4.2.1 Interference from up-link to terrestrial link geometry in the near forward direction.25Chapter 4--Interference Calculations% of time Rain Rate in mm/h Transmission loss in dB1.0 1.9 149.20.3 4.3 143.70.1 8.3 139.70.03 15.0 136.60.01 26.3 134.60.003 42.0 133.40.001 62.0 132.5Table 4.2 Measured transmission loss for the Chilbolton-Baldockpath at 11.2 GHz as a function of rain rate and percentage of timeand 2.1 km average rain height (Hm) is given in Table 4.2 as a function of rain rateand percentage of time.The geometrical parameters in Table 4.1 were converted to the common Cartesiansystem used in the model-program. The transmitting antenna is chosen as the origin ofthe system, with the horizontal plane as the x-y plane, the x axis pointing in the directionof the receiver, and the z axis pointing vertically upward.We now define an angle b, subtended at the Earth's centre by the link length, rrt,assuming an effective Earth radius of reff = 8500 km:= rri^ rad^ 4.3reffThe Cartesian receiver angle is then calculated by:f r 1 = 90 — Br = arcsin(coser sinb siner cos(5)^4.4and the coordinates of the receiving antenna becomes(xr, yr, zr) = (rri, 0, hr — ht — rrt 2 )^4.5The converted input parameters for the model-program are given in Table 4.3:26Chapter 4--Interference Calculations4.2.2 Computed resultsThe results of the computations for this case are plotted in Figures 4.2.2(a,b,c,d,e)and 4.2.3(a,b,c). Figures 4.2.2(a,b,c,d,e) show the transmission loss versus rain rate forHm = 2.0, 2.5, 3.0, 3.5, 4.0 km, respectively. The transmission loss calculated for thefollowing frequencies, f = 1.0, 5.0, 10.0, 20.0, 30.0 and 40.0 GHz is shown in each oneof these figures. Also, we calculated the interference caused by a rain-only cell, and arain cell with a melting-snow layer with ps = 0.1, 0.2, 0.3 at each frequency.Scattering Kharadly scattering modelAttenuation Kharadly 3rd attenuation modelProfile of the melting layer S = h/H (linear)(xt, Yt, zt) of the transmitter (0, 0 , 0) in km(9i , fit ) of the transmitter (70, 0) degreesPolarization of the transmitter 0 degrees (vertical)01/2 of the transmitter 0.00314 rad(xr , yr , zr ) of the receiver (131, 0, -1.0435) km(Or, Or ) of the receiver (88.117, 180) degrees(ai,a2,K) of the receiver (1.6, 4.5, -15)rain cell height (He ) 10.0 kmGain of the transmitter 794328Gain of the receiver 11220(xc , yc, zc ) of the rain cell (7.912,0,0) kmFrequency 1, 5, 10, 20, 30, 40 GHzRain rate 0.5-150 mm/h.Hm 2.0, 2.5, 3.0, 3.5, 4.0 kmp., 0.1, 0.2, 0.3Table 4.3 The converted input parameters for the model-program27Chapter 4—intelference CalculationsThe centre of the common volume in this geometry is at 3 km from the ground level(Hm = 3.0 km). We notice that it is when the rain height is in the common volume that weget the maximum effect of the melting-snow layer. The layer increases the interferenceat the lower frequencies and decreases it for the higher frequencies.At optimum rain height (Hm = 3 km) and at a frequency of f=1.0 GHz (Figure4.2.2(c)), the interference enhancement caused by the melting layer for ps = 0.1 is 2.0,4.2, 7.0, 10.5 dB for rain rate of 1.0, 3.0, 10.0, 30.0 mm/h, respectively. The interferencelevel decreases for A, = 0.2 and ps = 0.3. Nonetheless the enhancement remains significantat 1.5, 3.0, 5.0, 8.0 dB for ps = 0.2 and 1.0, 2.0, 4.0, 6.5 dB for A, = 0.3.As the frequency is increased, we note that the effect of the melting-snow layer on thetransmission loss decreases. The melting-snow layer enhancement decreases to 2.0, 4.0,6.1, 7.5 dB, and 1.8, 3.0, 3.0, 0.0 dB for f = 5.0 and 10 GHz respectively. An interestingobservation occurs when the frequency is increased further. The melting layer starts todegrade, instead of enhance, the interfering signal. For f = 20 GHz, the melting-snowlayer causes a drop in the interfering signal by —2.0 and —7.5 dB for rain rate of 10.0and 30.0 mm/h, respectively. This degradation becomes more pronounced at still higherfrequencies. For A, = 0.1, the degradation becomes 0.0, —0.8, —4.0, —12.0 dB for f =30.0 GHz and —0.5, —1.9, —6.0, —18.0 dB for f = 40.0 GHz. Higher values of ps tendsdecrease this gap but not by much. For A, = 0.2, the gap becomes —0.5, —1.2, —4.8,—16.0 dB and for A, = 0.3, the gap reduces to —0.5, —1.1, —4.0, —12.0 dB.As the rain height moves out of the centre of the common volume, the enhancementdue to the melting-snow layer declines considerably. At Hm = 2.5 or 3.5 km (Figure4.2.2(b) and Figure 4.2.2(d), respectively), the effect of the melting layer is still consid-erable at 1.5, 2.75, 5.0, 7.5 dB for f = 1 and 1.2, 2.5, 4.5, 6.0 dB for f = 5 GHz and Hm =28Chapter 4—Interference Calculations3.5 km. The enhancement is slightly greater for Hm = 2.5 km. For Hm = 2.0 and 4.0 km(Figure 4.2.2(a) and Figure 4.2.2(e), respectively), the enhancement becomes very small.For Hm = 4.0 km, the enhancement becomes 0.8, 1.2, 2.2, 2.5 for f = 1.0 GHz and 0.5,1.0, 2.0, 2.5 for f = 5 GHz. For Hm = 2.5 km, the enhancement is slightly greater.Figures 4.2.3(a,b,c) shows the transmission loss versus rain rate for f = 1.0, 5.0, 10.0,20.0, 30.0, 40.0 GHz and Hm = 2.0, 2.5, 3.0, 3.5, 4.0 km for a rain-only cell. We observethat for f = 1.0, 5.0, 10.0 GHz, the interference increases with Hm. This is due to thehigher reflectivity of rain compared to that in the ice/snow region. For f = 20 GHz,the interference starts to decrease as Hm is increased, in the high rain rate region. Forhigher frequencies this phenomenon becomes more severe and the interference at Hm =2.0 is 68.5 dB higher than the interference at Hm = 4.0 for rain rate of 100 mm/h and f= 40.0 GHz (Figure 4.2.3(c)). This leads us to conclude that at higher frequencies andrain rates, the effect of the ice/snow region in the rain cell is more significant than thatof rain despite its lower reflectivity.Even though an exact comparison between the measured transmission loss (Table4.2) and our calculations is not possible because of frequency difference and because, inreality, Hm acts as a random variable rather than the deterministic values we assume,we observe that the experimental transmission loss adjusted for atmospheric attenuation(discrete data in Figure 4.2.2(a)) agrees well with our calculations for f = 10.0 GHz(Figure 4.2.2(a)).29Rain Rate in mm/h.le+00 3 le+01 3 le+02Transmission loss in dB-120.00RainM_L,m=0.9M_L,m=0.8M_L,m=0.7Chapter 4--interference CalculationsFigure 4.2.2(a) Interference versus rain rate for variousfrequencies (f in GHz), p, (m = 1—p,), and for Hm = 2.0 km.30Chapter 4—Interference CalculationsTransmission loss in dBRainM_L,m=0.9M_L,m=0.8M_L,m=0.7 Rain Rate in mm/h.le+00^3^le+01^3^Ie+02Figure 4.2.2(b) Same as Figure 4.2.2(a), with Hm = 2.5 km.31Chapter 4—Interference CalculationsI 1^1^13 Ie+01 3 Ie+02Transmission loss in dB-128.00 --130.00 --132.00 --134.00 --136.00 --138.00 --140.00 --142.00 --144.00 --146.00 --148.00 --150.00 --152.00 — 4*-154.00-156.00'....-158.00-160.00-162.00 --164.00 --166.00 --168.00 --170.00 — •a-172.00 --174.00RainM_L,m=0.9M_L,m=0.8M_L,m=0.7Rain Rate in mm/h.IIle+00Figure 4.2.2(c) Same as Figure 4.2.2(a), with Hm = 3.0 km.32Chapter 4--Interference Calculations- Transmission loss in dB-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00-180.00-185.00-190.00-195.00-200.00-205.00-210.00RainM_L,m=0.9M_L,m4.7le+00 3 le+01 3 le+02Rain Rate in nun/h.Figure 4.2.2(d) Same as Figure 4.2.2(a), with Hm = 3.5 km.33Chapter 4—Interference CalculationsTransmission loss in dB-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00-180.00-185.00-190.00-195.00-200.00-205.00-210.00-215.00RainM_L,m=0.9M_L,m=0.8M_L,m4.7le+00^3^le+01^3^le+02^Rain Rate in mm/h.Figure 4.2.2(e) Same as Figure 4.2.2(a), with Hm = 4.0 km.34Chapter 4—Interference CalculationsTransmission loss in dB-125.00-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00Hm=2.0 kmHm=2.5 kmHm=3.0 kmHm=3.5 kmHm=4.0 kmRain Rate in nun/h.le+00^3^le+01^3^le+02Figure 4.2.3(a) Interference versus rain rate for various rainheights (Hm), and for f (frequency) = 1, 5, 10, 20GHz.Transmission loss in dB-120.00OIM-125.00-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00-180.00-185.00I^I^I le+00^3 le+01 le+02Chapter 4--,Interference CalculationsHm=2.0 kmHm=2.5 kmHm=3.0 kmHm=3.5 kmFin3=1.6k1Rain Rate in mm/h.Figure 4.2.3(b) Same as Figure 4.2.3(a), with f = 30 GHz.36.. ..^....................-..=, .. .^-. ......■ Ik e. ............—...^ "...`"C.^•.....♦ 5,..•■ ..%••■•♦♦^• • s%`%1==40.0 GHzChapter 4—Interference CalculationsTransmission loss in dB-120.00 —-125.00 --130.00 --135.00 —-14o.00 ..........-145.00 —-150.00 --155.00 --160.00 --165.00 --170.00 --175.00 --180.00 —-185.00 --190.00 ---195.00 —-200.00 --205.00 --210.00 --215.00 —1^1^I^1^1 le+00^3^le+01^3^le+02Hm=2.0 kmHm=2.5 kmHm=3.0 kmHm=3.5 kmani.1.6k11^1^ 1—1Rain Rate in mm/h.Figure 4.2.3(c) Same as Figure 4.2.3(a), with f = 40 GHz.37Chapter 4—interference Calculations4.3 Interference from up-link to terrestrial linksin the near-backward direction4.3.1 DescriptionThe geometry of the interference is close to that of the near-forward scattering (Figure4.3.1). The only difference is that the receiving antenna is 180 degrees from the previouscase but maintaining the same distance to the common volume. The common volumeremains 3km high.4.3.2 Computed resultsThe results of the computations in this example are given in figures 4.4.2(a,b,c,d,e)and 4.4.3(a,b,c). Figures 4.4.2(a,b,c,d,e) show the transmission loss versus rain rate forHm = 2.0, 2.5, 3.0, 3.5, 4.0 km, respectively. The transmission loss calculated for thefollowing frequencies, f = 1.0, 5.0, 10.0, 20.0, 30.0 and 40.0 GHz is shown in each ofthese figures. Also, we calculated the interference caused by a rain-only cell, and a raincell with a melting-snow layer with ps = 0.1, 0.2, 0.3 at each frequency.The maximum effect of the melting snow layer occurs when Hm = 3.0 km (Figure4.3.2(c)). For f = 1.0 GHz, the interference enhancement caused by the melting snow layerfor ps = 0.1 is 1.8, 3.0, 6.0, 9.0 dB for rain rate of 1.0, 3.0, 10.0, 30.0 mm/h, respectively.This interference decreases for ps = 0.2 and p, = 0.3. Nonetheless the enhancementremains considerable. The values of the interference enhancement calculated in this caseare slightly lower than those calculated in the near-forward direction.As we increase the frequency, the melting layer enhancement decreases to 1.5, 2.5,5.25, 6.0 dB and 1.1, 2.1, 2.5, 0.8 dB for f = 5.0 and f = 10 GHz respectively. At higherfrequencies (f = 20.0, 30.0, 40.0 GHz) the melting snow layer degrades the interferencesignal. For A, = 0.1, the degradation becomes —0.4, —1.0, —2.5, —4.0 for f = 30 GHz38Transmitting antennaChapter 4—Interference Calculations(Graph not to scale)rain cellFigure 4.3.1 Interference from up-link to terrestrial link geometry in the near backward direction.39Chapter 4—Interference Calculationsand-0.5, —1.5, —2.5, —1.75 for f = 40.0 GHz. Higher ps values help reduce the gap.This reduction is significantly lower than the one experienced in the previous example.As Hm moves away from the centre of the common volume, the effect of the melting-snow layer decreases. At Hm = 3.5 km (Figure 4.3.2(d)), the effect of the melting layeris still considerable at 1.2, 2.5, 4.0, 6.25 dB for f = 1.0 and 1.0, 2.0, 3.0, 3.7 dB for f= 5 GHz. The enhancement is slightly greater for Hm = 2.5 km (Figure 4.3.2(b)). Thisgreater enhancement is due to the closer proximity of the melting snow layer to the centre ofthe common volume. Again the interference enhancement is slightly less than the previousexample. For Hm = 2.0, and Hm = 4.0 the interference enhancement decreases significantly.For Hm = 4.0 km, the enhancement becomes 0.8, 1.4, 2.0, 2.5 dB for f = 1.0 GHz and 0.5,1.0, 1.3, 1.5 dB for f = 5.0 GHz. For Hm = 2.0 km, the enhancement is slightly greater.Figures 4.3.3(a,b,c) show the transmission loss versus rain rate for f = 1.0, 5.0, 10.0,30.0, 40.0 GHz and Hm = 2.0, 2.5, 3.0, 3.5, 4.0 km for a rain-only cell. We observe thatfor f = 1.0, 5.0, 10.0 GHz, the interference increases with Hm at the lower frequencies. Thisis also true for the higher frequencies coupled with low rain rate. However, the interferencedrops considerably with high rain rates as Hm increases. For rain rate of 100 mm/h and f= 40 GHz (Figure 4.3.3(c)), the interference for Hm = 2 km is 14.5 dB higher than that forHm = 4.0 km. We also observe that the reduction of the interference signal is much lessthan in the previous example.Comparing the current results with those in the near-forward case, we observe thatthe two are comparable for lower frequencies and rain rates. For a combination of higherfrequency and high rain rate, the difference between the two is very large to be accountedfor by scattering properties alone. This difference can only be due to different attenuationpaths for the transmitted and scattered waves between both cases.40Chapter 4---Interference CalculationsTransmission loss in dB-120.00-125.00-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00RainM_L,m=0.9M_L,m=0.8M_L,m=0.7Rain Rate in nun/h.le+00^3^le+01^3^le+02Figure 4.3.2(a) Interference versus rain rate for variousfrequencies (f in GHz), p, (m = 1—p,), and for Hm = 2.0 km.41Chapter 4--Interference CalculationsTransmission loss in dB-125.00-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00RainM_L,m=0.9M_L,m=0.8M_L,m=0.7Rain Rate in mm/h.le+00^3^le+01^3^le+02Figure 4.3.2(b) Same as Figure 4.3.2(a). with Hm = 2.5 km.42Chapter 4--Interference CalculationsTransmission loss in dB-125.00-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00RainM_L,m=0.9M_L,m41.8M_L,m=0.7Rain Rate in mm/h.le+00^3^le+01^3^le+02Figure 4.3.2(c) Same as Figure 43.2(a), with Hm = 3.0 km.433 3le+01 le+02le+00-125.00 —-130.00 —-135.00 —-140.00 —-145.00 —-150.00 —-155.00 —-160.00 —-170.00-165.00RainM_L,m=0.8M_L,m=0.7Rain Rate in mm/h.Figure 4.3.2(d) Same as Figure 4.3.2(a), with Hm = 3.5 km.Chapter 4--Inserference CalculationsTransmission loss in dB44Chapter 4--Interference Calculations..•Transmission loss in dB-125.00-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00RainM_L,m=0.9M_L,m.8M_L,m.7Rain Rate in mm/h.le+00^3^Ie+01^3^le+02Figure 4.3.2(e) Same as Figure 4.3.2(a). with Hm = 4.0 km.45Hm=2.0 kmHm=2.5 kmHm=3.0 kmHm=3.5 kmHm=4.0 km-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00Rain Rate in mm/h.1331le+00 le+02-125.00-130.00Chapter 4—Interference CalculationsTransmission loss in dBFigure 4.3.3(a) Interference versus rain rate for various rainheights (Hm), and for f (frequency) = 1, 5, 10, 20GHz.Chapter 4--Interference CalculationsTransmission loss in dB-122.00-123.00-124.00-125.00-126.00-127.00-128.00-129.00-130.00-131.00-132.00-133.00-134.00-135.00-136.00-137.00-138.00-139.00-140.00-141.00-142.00-143.00-144.00-145.00Hm=2.0 kmHm=2.5 kmHm=3.0 kmHm=3.5 kmHm=4.0 kmRain Rate in mm/h.Ie+00^3^1e+01^3^1e+02Figure 4.3.3(b) Same as Figure 4.3.3(a), with f = 30 GHz.47Chapter 4--Interference CalculationsTransmission loss in dB-122.00-123.00-124.00-125.00 --126.00 --127.00 --128.00 --129.00 --130.00 --131.00 --132.00 —-133.00 --134.00 --135.00 --136.00 --137.00 --138.00 --139.00 --140.00 --141.00 — "-142.00 --143.00 --144.00 LHm=2.0 kmHm=2.5 kmHm=3.0 kmHm=3.5 kmHm=4.0 km1=40.0 GHzle+00^3^le+01^3^le+02Rain Rate in nun/h.Figure 4.3.3(c) Same as Figure 4.3.3(a), with f = 40 GHz.48Chapter 4—Intelference Calculations4.4 Interference from up-link to satellite in the forward direction4.4.1 DescriptionThe geometry of the interference is shown in Figure 4.4.1. A radio-wave transmittedby an up-link toward a satellite is scattered by rainfall. The scattered electromagneticwave interferes with another nearby satellite operating at the same frequency.The parameter used in these calculations are listed in Table 4.4. The geometricalparameters are given in Cartesian coordinates .Scattering Kharadly's scattering modelAttenuation Kharadly 3rd attenuation modelProfile of the melting layer S = h/H (linear)(xs, yt, zt) of the transmitter (0, 0 , 0) in km(Os , Os ) of the transmitter (70, 0) degreesPolarization of the transmitter 0 degrees (vertical)01 /2 of the transmitter 0.00314 rad(x i., yr, zr) of the receiver (3291, 0, 1900) km(Or , (/),.) of the receiver (110, 180) degrees(a l , a2, K) of the receiver (3.0, 7.5, -10)rain cell height (11s ) 10.0 kmGain of the transmitter 794328Gain of the receiver 5011.87(x c , Yc, zc) of the rain cell (7.912,0,0) kmFrequency 1, 5, 10, 20, 30, 40 GHzRain rate 0.5-150 mm/h.Hm 2.0, 2.5, 3.0, 3.5, 4.0 kmm (m = 1 — AO 0.9, 0.8, 0.7Table 4.4 Parameters used for the interference calculations from up-link to satellite49rain cellTransmitting antennaChapter 4—Interference Calculations(Graph not to scale)receiving satelliteFigure 4.4.1 Interference from up-link to satellite geometry in the forward direction.50Chapter 4--Inuetference Calculations4.4.2 Computation resultsThe results of the computations in this example are given in figures 4.4.2(a,b,c,d,e)and 4.4.3(a,b,c). Figures 4.4.2(a,b,c,d,e) show the transmission loss versus rain rate forHm = 2.0, 2.5, 3.0, 3.5, 4.0 km respectively. The transmission loss calculated for thefollowing frequencies, f = 1.0, 5.0, 10.0, 20.0, 30.0 and 40.0 GHz is shown in each oneof these figures. Also, we calculated the interference caused by a rain-only cell, and arain cell with a melting snow layer with ps = 0.1, 0.2, 0.3 at each frequency.In this case, it is noticed that for f = 1, 5, 10 GHz, the enhancement caused by themelting layer is not only significant but it remains strong for a wide range of Hm. Witha rain rate of 30 mm/h and frequency of 5.0 GHz the enhancement is 4.0, 6.0, 8.8, 8.0,3.75 dB for Hm = 2.0, 2.5, 3.0, 3.5, 4.0 km, respectively (Figures 4.4.2(a), (b), (c), (d)and (e), respectively). The interference level is also significant at 10.0 GHz where, for30 mm/h, the enhancement becomes 3.0 ,4.0 ,5.0 ,3.7, 1.2 dB. At higher frequencies, weobserve that the melting layer tends to reduce the interference signal for higher rain rates.This reduction increases with frequency, rain rate and Hm. For a rain rate of 30.0 mm/hand a frequency of 40.0 GHz, the interference signal is reduced by 4.0, 6.0, 6.2, 7.5, 8.0dB for Hm = 2.0, 2.5, 3.0, 3.5, 4.0 km, respectively. We again observe that !Is plays animportant role in enhancing or reducing the interference level.Figures 4.4.3(a,b,c) show the transmission loss versus rain rate for f = 1.0, 5.0, 10.0,20.0, 30.0, 40.0 GHz and Hm = 2.0, 2.5, 3.0, 3.5, 4.0 km for a rain-only cell. It isobserved that at the lower frequencies (f = 1, 5, 10 GHz), the interference increases withhigher Hm. At the higher frequencies, the same is true for low rain rates, but for highrain rates, the interference decreases sharply for higher values of Hm. For a rain rateof 100 mm/h and a frequency of 40.0 GHz, the interference for Hm = 2.0 km is 36 dB51Chapter 4—Interference Calculationshigher than that for Hm = 4.0 km (Figure 4.4.3(c)).4.5 SummaryThe above three examples show that the melting-snow layer significantly affects thetransmission loss. The maximum effect occurs when the melting-snow layer exists in thecommon volume. But even outside the common volume, we noticed that the melting layerdid exert considerable influence. We observed also that the melting layer tends to increasethe interference level at the lower frequencies and decrease it for higher frequencies.We also observed that the ice/snow region significantly contributes to the interferencelevel at the higher frequencies. The attenuation by rain and melting-snow at highfrequencies degrades the scattered signal, thus considerably reducing the interferencelevel from rain and melting-snow. The scattered wave from the ice/snow region doesnot suffer from attenuation (except if the scattered wave intersects the melting layer orrain. This is limited to the lower parts of the ice/snow region) and thus contributessignificantly to the interference level.52Chapter 4--Interference CalculationsTransmission loss in dB-195.00-200.00-205.00-210.00-215.00-220.00-225.00-230.00-235.00-240.00-245.00RainM_L,m=0.9M_L,m=0.8M_L,m4.7le+00^3^1e+01^3^le+02^Rain Rate in mm/h.Figure 4.4.2(a) Interference versus rain rate for variousfrequencies (f in GHz), p, (m = 1—p,), and for Hm = 2.0 km.53Transmission loss in dB-200.00-205.00-210.00-215.00-220.00-225.00le+00 3 3 le+02-230.00-235.00-240.00-245.00Rain Rate in mm/h.1RainM_L,m=0.9M_L,m=0.8M_L,m=0.7Chapter 4--Interference CalculationsFigure 4.4.2(b) Same as Figure 4.4.2(a). with Hm = 2.5 km.54le+01 33I^—1e+02H^Ile+00Rain Rate in mm/h.RainM_L,m=0.9M_L,m=0.80 Go1..Chapter 4—Interference CalculationsTransmission loss in dB-200.00-202.00-204.00-206.00-208.00-210.00-212.00-214.00-216.00-218.00-220.00-222.00-224.00-226.00-228.00-230.00-232.00-234.00-236.00-238.00-240.00-242.00-244.00-246.00Figure 4.4.2(c) Same as Figure 4.4.2(a). with Hrn = 3.0 km.55Chapter 4--Interference CalculationsTransmission loss in dB-202.00-204.00-206.00-208.00-210.00-212.00-214.00-216.00-218.00-220.00-222.00-224.00-226.00-228.00-230.00-232.00-234.00-236.00-238.00-240.00-242.00-244.00RainM_L,m=0.9M_L,m=0.8M_L,m=0.7le+00^3^le+01^3^le+02^Rain Rate in mm/h.Figure 4.4.2(d) Same as Figure 4.4.2(a). with Hm = 3.5 km.56Chapter 4--Interference CalculationsTransmission loss in dB/Sr-216.00 —^ ..•■%,218.00 —1.. ../:--220.00 —^f^...%-^ •■ ...,.e.s^/'^...%W—...%.:/i" •^%-222.00 —ive.%-224.00 —^/'''%-226.00 -228.00 —-230.00 —\\t-232.00 I—^ /;•7 0/44'^ CI-234.00 — 1.. _-236.00 --238.00 --240.00 --242.00 --244.00 —-202.00-204.00-206.00-208.00-210.00-212.00-214.00RainM_L,m=0.9M_L,m=0.8M_L,m=0.7Rain Rate in mm/h.le+00^3^le+01^3^le+02Figure 4.4.2(e) Same as Figure 4.4.2(a), with Hm = 4.0 km.57Rain Rate in mm/h.1 1 1f',• 0..10 .•^.,...„..""-=-:...-•••^ # .4. •^.„ ,, 1GP: f:-;:-.**** ,itf.„-Z^ii,/0P--?-':"--e^-, '-,-- s:,-.',-..: • „'-'-'..,-..••-....„--.:---.:,•-•-200.00-205.00-210.00-215.00-220.00-225.00Hm=2.0 kmHm=2.5 kmHm=3.0 kmHm=3.5 kmHm=-4.0 km-230.00-235.00,„ , 1 .0 ol't-240.00-245.001^1^1^1^1 le+00^3^1e+01^3^le+02Chapter 4--Interference CalculationsTransmission loss in dBFigure 4.4.3(a) Interference versus rain rate for various rainheights (Hm), and for f (frequency) = 1. 5, 10, 20GHz.Chapter 4—lnierference CalculationsTransmission loss in dB196.00 —^I^I^I^I^I^— Hm=2.0 km- Hm=2.5 kmHm=3.0 kmHm=3.5 kmHm=4.0 km5^•^—5 sN.^5 •s-210.00 — ^ , -..:''......^N. 5N.^5 .^'-212.00 — - . .A"::::.." ....^. ^,^ -^="::" \-214.00 — ...*^ N^5 —-216.00 —^f=30.  GHz^■\ ..%^.-218.00 r ,-220.00 7^^ ^. •-222.00 — ■-224.00 —^ ^ —-226.00 — A^-A-228.00^ t^—t-230.00 L % --232.00 7^ %^I ^1^I^I^1 le+00^3^le+01^3^le+02Figure 4.4.3(b) Same as Figure 4.4.3(a), with f = 30 GHz.-198.00 --200.00 --202.00 --204.00 --206.00 — .1..".- ..,,s s-208.00 —^ .Rain Rate in mm/h.59Chapter 4—Interference CalculationsTransmission loss in dB-194.00-196.00-198.00-200.00-202.00 .......... ...................-204.00 —^ ..............-206.00 — ..•-0'........-208.00 —-210.00 —^0:- ....^.. .^.‘..---::::-..--'^ .^.. ..,-212.00 — :::.-- .^. . .^s..,-220.00S.-222.00 —^ f- 40.0 GHz-224.00 —-226.00 —-228.00 r--230.00-232.00 --234.00 —-236.00-238.00 1—-240.00 --Ie+00^3^le+01^3^le+02-214.00 —-216.00 —-218.00 —^ •Hm=2.0 kmHm=2.5 kmHm=3.0 kmHm=3.5 kmHm=4.0 kmRain Rate in mm/h.Figure 4.4.3(c) Same as Figure 4.4.3(a), with f = 40 GHz.60Chapter 5—COST 210 rain-cell modelChapter 5 COST 210 rain-cell model5.1 IntroductionThe CCIR working party 5C has recently adopted the COST 210 model [7] as abasis for predicting transmission loss [5]. An accompanying document was presented byCanada [4] which showed that, using the COST 210 rain cell model, the introduction of amelting snow layer in an optimum position significantly affects the transmission loss up to11 GHz. It also concluded that the melting layer should be taken into consideration whilecalculating the interference level, since the interference level introduced by the presenceof the melting layer is larger than that introduced in changing from one composite climateto another. This is an attempt to expand on the original study and to compare the COST210 rain model with Capsoni's model and to see if the COST 210 rain cell is ableto model the effect of the melting snow layer for a wide range of rain heights andfrequencies. Readers should be reminded that it is only the COST 210 rain cell geometrythat is implemented and not their interference calculation methodology. To calculate theinterference, the method outlined in Chapter 3 was applied with provisions to account forthe attenuation outside the rain cell (refer below). This method yielded results similar tothose calculated by the COST 210 program for the Chilbolton-Baldock path [7].5.2 COST 210 rain cell model [7]The rain cell centre is assumed to be at the intersection of the main beam antennaaxes (i.e. centre of the common volume). Scattering is assumed to occur within onefixed, cylindrical rain cell of circular cross-section. The diameter of the cell depends on61Chapter 5—COST 210 rain-cell model-cast .II ■aXilliFf.-110:4110:412ILE,,,, LTACMLTICBCt"1.2"Zi.!.:116.15ttMaSrillICt;Z152.11.';;;;Iirr,exti::Figure 5.1 COST 210 rain-cell model62Chapter 5—COST 210 rain-cell modelthe rainfall rate as:dc = 3.3R-0.08^ 5.1On the other hand, attenuation occurs inside and outside the rain cell. Inside the raincell, the empirical formula for attenuation is used. Outside the rain cell, the attenuationFR , between the edge of the rain cell and a point at distance d is given by the followingexponential function:rR = Ap rm1 — e-d/r,ndB/km^5.2 where rm , the scale length for rain attenuation, is given by:rm = 600R-0.510- (R+1)° 19 km^ 5.3= elevation angle, and Ap is the specific attenuation for rain, calculated from theattenuation empirical formula, in dB/km.Equation 5.2 is valid if the whole path is below the rain height Hm. If only partof the path — let us say between distances di and d2 from the edge of the rain cell —is below the rain height:FR = (e–du/rm^e–d2 /rni )dB/km^5.4COSEFor those portions of the propagation path that are above Hm, zero attenuation is assumed.The diameter of the melting layer cell is assumed to be the same as that of the rainbelow it. The melting layer attenuation is assumed to reduce at the same exponentialrate as the rain attenuation outside the core cell. Since the specific attenuation varieswith the height within the melting-snow layer, a numerical integration is carried out inthe vertical direction:FR = rm ^Api (e—d,/rm e—ds+iirni)COSE .i=15.563Chapter 5—COST 210 rain-cell modelwhere Apt is the average specific attenuation in the region between di and di +i in themelting-snow layer. n is the number of integration steps. Despite this addition to therain cell, we will continue to refer to it as the COST 210 rain cell.5.3 Results for sample interference geometriesThe calculations are done for the geometry described in section 4.2 of Chapter 4.Figures 5.2(a,b,c,d)-5.6(a,b,c,d) show the transmission loss at f = 1.0, 5.0, 10.0, 20.0,30.0, 40.0 GHz and Hm = 2.0, 2.5, 3.0, 3.5, 4.0 km for both the Capsoni rain cell modeland the COST 210 rain cell model. The scattering model used in both cells is that of Dr.Kharadly. The Empirical model is used for attenuation. This is somewhat different fromthe COST 210 model where they use modified Rayleigh scattering for rain and a differentattenuation model. Neither COST 210 attenuation nor scattering models account for themelting-snow region.For the rain-only cells, we observe that both models predict similar transmissionlosses for all Hm and rain rates at lower frequencies (f = 1.0, 5.0, 10.0 GHz). However,the two models' results differ considerably at higher frequencies and especially for thelower rain rates. For Hm = 3.0 km and f = 40 GHz (Figure 5.4 (d)), the Capsonimodel interference level is 15.0, 16.0, 13.5, 4.2, 1.5 dB higher than the interference levelcalculated using COST 210 rain cell for R = 1.0, 3.0, 10.0, 30.0 mm/h, respectively. AsHm increases, the two models' interference curves seems to produce better agreement.For Hm = 3.0 km (Figures 5.4 (a),(b),(c),(d)), which is the optimum position ofthe melting layer in the common volume, the COST 210 rain cell models the effectof the melting snow layer very nicely. For Hm = 3.5 km (Figures 5.5 (a),(b),(c),(d)),the COST 210 cell tends to overestimate the enhancement caused by the melting snow64Chapter 5—COST 210 rain-cell modellayer. This is in contrast to Hm = 2.5 km (Figures 5.3 (a),(b),(c),(d)), where the COST210 model underestimates its effect considerably. For Hm = 2.0, and 4.0 km (Figures5.2 (a),(b),(c),(d) and Figures 5.5 (a),(b),(c),(d), respectively), the melting layer does notenter into consideration since it is out of the path of the transmitting beam. We observefrom the Capsoni model that for Hm = 2.0 and 4.0 km, the melting layer does play a role(albeit reduced) in the interference problem. The reason that the COST 210 cell does notaccount for the melting layer is the small radius of the COST 210 cell.5.4 ConclusionThe computation time for the COST 210 model is much less than that of the Capsonirain model. This is directly related to the radius of the core rain cell of COST 210. Forrain rates of 0.5, 2.5, 5.0, 12.5, 25.0, 50.0, 100.0, 150.0 mm/h, the radius of the Capsonirain cell is 10.45, 9.4.0, 8.95. 8.35, 7.90, 7.45, 7.00, 6.74 km respectively. On the otherhand the radius of the COST 210 rain cell is 1.74, 1.53, 1.45, 1.35, 1.28, 1.21, 1.14, 1.11km. We can see readily that the COST 210 rain cell, which is about 6 times smaller thanthe Capsoni model, will save a considerable amount of computer time.For lower frequencies, we notice that the Capsoni and COST 210 rain models yieldsimilar results for all Hm values. For higher frequencies, we see that there is a largedifference between the two models. The COST 210 model interference level is muchlower than that of the Capsoni cell for lower rain rate. For a high rain rate and lowerfrequencies, the COST 210 model yields the higher interference level. Since the Capsonirain cell is the more realistic, it is safe to assume that the COST 210 model willunderestimate the interference at higher frequencies (and large station separation) andrain rate.65-126.00-128.00-130.00-132.00-134.00-136.00-138.00-140.00142.00-144.00-146.00-148.00-150.00-152.00-154.00-156.00-158.00Transmission loss in dB1e+00^3^1e+01^3^le+02-130.00-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00-180.00le+00^3^1e401^-3^Ie+02psomunNPsOnTAW§.--Cost,ramRain Rate in tnin/h. Rain Rate in mm/h.Figure 5.2(a,b) A comparison between Capsoni and COST 210 rain cell models with and without amelting snow layer for Hm = 2.0 km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.Transmission loss in dB^ Transmission loss in dB -122.00-124.00-126.00-128.00-130.00-132.00-134.00-136.00-138.00-140.00-142.00-144.00-146.00-148.00-150.00-152.00-154.00-156.00-158.00-120.00-122.00-124.00-126.00-128.00-130.00-132.00-134.00-136.00-138.00-140.00-142.00-144.00-146.00-148.00-150.00-152.00-154.00-156.00-158.00-16000Capsoni,rainGpsamm0.9Cost,rainle+00^3^le+01^3^le+02^le+00^3^le+01^3^le+02Rain Rate in nun/h.^ Rain Rate in nun/h.Figure 5.2(c,d) A comparison between Capsoni and COST 210 rain cell models with and withouta melting snow layer for Hm = 2.0 km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Transmission loss in dB-120.00-122.00-124.00-126.00-128.00-130.00-132.00-134.00-136.00-138.00-140.00-142.00-144.00-146.00-148.00-150.00-152.00-154.00psoru,n—riainCost.rainNsi,r7);0-.0-1e400^3^1e401^3^1e+02le+00 3 le+01 3 1e+02Transmission loss in dB-125.00-130.00-135.00-140.00-145.00-150.00-155.00O. -16o.0000-165.00-170.00-175.00Rain Rate m mm/h.^ Rain Rate in MITI&Figure 5.3(a,b) A comparison between Capsoni and COST 210 rain cell models with and without amelting snow layer for Hm = 23 km, an& (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.1e400^3^le+01^3^le402Rain Rate in mm/h.le+00^3^1e401^3^1e402Rain Rate in trviiih.Transmission loss in dB-118.00-120.00-122.00-124.00-126.00-128.00-130.00-132.00-134.00-136.00-138.00-140.00-142.00-144.00-146.00-148.00-150.00-152.00-154.00-156.00Transmission loss in dB-116.00-118.00-120.00-122.00-124.00-126.00-128.00-130.00-132.00-134.00-136.00-138.00-140.00-142.00-144.00-146.00-148.00-150.00-152.00-154.00-156.00-158.00-160.00Capsoni,raintapsommii0.§-Cost,ramtost.nn.0.9Figure 5.3(c,d) A comparison between Capsoni and COST 210 rain cell models with and withouta melting snow layer for Hm = 2.5 km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Transmission loss in dB-130.00-135.00-140.00-145.00-150.00-155.00-160.00O-165.00-170.00-175.00le+00Transmission loss in dB-133.00-134.00-135.00-136.00-137.00-138.00-139.00-140.00-141.00-142.00-143.00-144.00-145.00-146.00-147.00-148.00-149.00-150.00-151.00-152.00le+00Capsom,raintitiTontiiRiV-Cost,nunle+023^le+01^3^le+02 3^le+01^3Rain Rate in mm/h.^ Rain Rate in nvn/h.Figure 5.4(a,b) A comparison between Capsoni and COST 210 rain cell models with and without amelting snow layer for Hm = 3.0 km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.-138.00-140.00-142.00-144.00-146.00-148.00-150.00-152.00-154.00-156.00-158.00-160.00-162.00-164.00• -166.00-168.00-170.00-172.00-174.00-176.bo-178.001e400^3^1e+01^3^le+02Rain Rate in mm/h.-136.00-138.00-140.00-142.00-144.00-146.00-148.00-150.00-152.00-154.00-156.00-158.00-160.00-162.00-164.00-166.00Transmission loss in dB^Transmission loss in dBle+00^3^le+01^3^le+02Rain Rate in mm/h.Figure 5.4(c,d) A comparison between Capsoni and COST 210 rain cell models with and withouta melting snow layer for Hm = 3.0 km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Transmission loss in dB-133.00-134.00-135.00-136.00-137.00-138.00-139.00-140.00-141.00-142.00-143.00-144.00-145.00-146.00-147.00-148.00-149.00-150.00-151.00-152.00-153.00-154.00-155.00-156.00Capsommunle+00 3 Ie+01 3 le+02Transmission loss in dB-130.00-135.00-140.00-145.00-150.00-155.00ts..)^ -160.00-165.00-170.00-175.00le+00 3^1e+01^3^le+02Rain Rate in mint. • Rain Rate in mm/h.Figure 5.5(a,b) A comparison between Capsoni and COST 210 rain cell models with and without amelting snow layer for Hm = 33 km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.Transmission loss in dB-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00-180.00-185.00-190.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00-180.00-185.00-190.00-195.00-200.00-205.00-210.00-215.00-220.00Cost,rainle+00^3^Ie+01^3^le+02^le+00^3^15+01^3^15402Rain Rate in =Va. Rain Rate in nun/h.Figure 5.3(c,d) A comparison between Capsoni and COST 210 rain cell models with and withouta melting snow layer for Hm = 3.5 km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.-134.00-136.00-138.00-140.00-142.00-144.00-146.00-148.00-13o.00-152.00-154.00-156.00le+00^3^1e401^3^le+02Rain Rate in nun /h.Transmission loss in dB^ Transmission loss in dBCapsoni.rainCos t.rai n—Rain Rate in nun/h.Figure 5.6(a,b) A comparison between Capsoni and COST 210 rain cell models with and without amelting snow layer for Hm = 4.0 km, and: (a) f (frequency) = 1, 5, 10 GHz, (b) f = 20 GHz.le+00^3^1e401^3^le+02Rain Rate in mm/h.Npsoni,m=0.9Cost,raintost.rn.0.9Transmission loss in dB-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00-180.00-185.00-190.00-195.00-200.00-205.00-210.00-215.00-220.00Transmission loss in dB-135.00-140.00-145.00-150.00-155.00-160.00-165.00-170.00-175.00-180.00-185.00-190.00le4.00^3^1e401^3^le+02Rain Rate in mm/h.Figure 5.6(c,d) A comparison between Capsoni and COST 210 rain cell models with and withouta melting snow layer for Hm = 4.0 km, and: (c) f (frequency) = 30 GHz, (d) f = 40 GHz.Chapter 5—COST 210 rain-cell modelAlso, there are inherent weaknesses in the COST 210 rain model. The model is nota physical one where it accurately describes an actual rain cell.As we stated before, themajor advantage of the COST 210 rain cell is its small radius. This advantage turns intoa disadvantage when modeling the melting snow layer. As we observed, the COST 210rain cell models the effect of the melting layer quite nicely when that region is near thecenter of the common volume. On the other hand, if the melting layer height (which isa random variable) moves upward or downward, the model will not be able to accountfor its effect beyond a relatively short distance.In general, the COST 210 model seems to be acceptable for modeling the interferencefor terrestrial stations. It would be quite interesting to extend the model to find out if itcan reasonably estimate interference on receiving satellites.To better judge the COST 210 rain cell, a comparison of the statistical transmissionloss is in order. This is currently beyond the scope of this thesis, but should be dealtwith at a future date.76Chapter 6—Discussion and ConclusionsChapter 6 Discussion and Conclusions6.1 Effect of melting-snow layerThe results introduced in Chapter 4 show that the melting-snow layer plays animportant role in the transmission loss in the 1-40 GHz frequency spectrum. This roleis by no means uniform. At lower frequencies (f = 1-10 GHz), the melting-snow layerplays a significant role in increasing the interference level. This enhancement is muchhigher for the f = 1 and 5 GHz than for f = 10 GHz. This is the region where most oftoday's radio communications is handled. The congestion of the frequency spectrum ispushing for the use of the higher frequencies. Because of the high attenuation associatedwith these frequencies in the melting-snow layer, outages will become more frequent.These outages will become more important to system engineers than signal interference.On the other hand, stations might increase their transmission power to avoid outages.This will generate a stronger scattered signal and thus a higher interference potential.Because of increased attenuation, the melting-snow layer decreases the effect of theice/snow region. This is especially true for higher frequencies. However, the effect ofthis attenuation is limited to the lower part of the ice/snow region because of the smallelevation angle of the scattered wave. Because of the importance of the ice/snow regionat higher frequencies, more research is needed to model the scattering more accurately.At low frequencies, the attenuation is small enough that it will not offset the increasein reflectivity of the melting-snow layer. At high frequencies, the attenuation by themelting-snow layer becomes great enough to smother any increase in the scattering ofthe melting-snow layer.77Chapter 6—Discussion and ConclusionsIt is also observed that for a high directivity antenna, the melting-snow layerinterference can increase or decrease depending on the position of the main lobe axisof the receiver relative to the melting-snow layer. If the main lobe axis of the highdirectivity antenna intersects or is near the melting-snow layer, its effect will be greater.Also we notice that the density of the core of the melting-snow particles plays aneffect — albeit not great — in the calculations. We see that the higher the density is,the smaller is the effect of the melting layer. This can be attributed to the reduction ofthe particle sizes resulting from higher average density.The melting layer has been assumed to have a linear melting ratio (S=h/H; where his the distance down from the top of the melting layer, H is the thickness of the meltinglayer, S is the ratio of the melted volume to the total volume). This profile provides fora narrow region in the melting layer where attenuation and scattering peaks (around S =0.1). Kharadly [1992] suggests that this profile underestimates the effect of the meltinglayer and that different profiles might have to be used.6.2 Effect of rain height, HmThe effect of increasing rain height in the rain cell is quite interesting. We can seethat for lower frequencies, the higher Hm causes a higher interference level meanwhileat higher frequencies, the interference decreases with a higher Hm.The reason for this phenomenon is the ice/snow region above the rain region. In thisregion we have scattering but no attenuation and since scattering increases but with noattenuation to offset it, the interference increases. This leads us to the conclusion thatconsiderable interference for high frequency can be achieved if a high directivity antennaintersects the ice/snow region.78Chapter 6—Discussion and Conclusions6.3 Effect of rain rateIt is very hard to talk about the effect of rain rate without mentioning frequency. Forlower frequencies, interference increases with rain rate, since higher rain rates translatesinto higher scattering cross section. For higher frequencies, higher rain rates translateinto very high attenuation levels and thus lower interference.6.4 Effect of frequencyFor lower frequencies, rain and melting-snow attenuation is negligible and interfer-ence can present problems for radio systems operating at the same frequencies.For higher frequencies, the interference problem seems to disappear since the highattenuation will smother any potential interference wave. Outages, due to the highattenuation level, seems to be a much more serious problem for higher frequency systems.Yet because of this high attenuation level, systems will be forced to increase theirtransmitting power during these periods and thus increasing the scattered power andthus the interfer6nce.6.5 ReminderA model-program has been developed to calculate the interference caused by hydrom-eteors. This model-program is — unlike the COST 210 model — capable of calculatingthe interference for any given geometry.Also a study was conducted about the effect of the melting layer on interference.It was found that the melting layer significantly enhances the interference for lowerfrequencies and should not be ignored. This is especially true in the case of satelliteinterference.79Chapter 7—Suggestions for future researchChapter 7 Suggestions for future researchThere is much work — both theoretical and experimental — that needs to be doneon the subject in the future. Some suggestions for future work are:1. There should be further work on the program to make it more efficient. This canbe done by utilizing more efficient routines or by fitting some of the parametersused in Kharadly models into equations. These parameters include the radius of therepresentative particle and the number of particles per unit volume. The equationswill be a function of rain rate and the melting ratio (S). This will make it unnecessaryto interpolate them from Table A.1 every time we need to calculate the attenuation.2. More work needs to be done on the program to make it user-friendly.3. Introduce the statistics of rain to the model. To do that, more study is required onthe statistics of the melting layer, its thickness and height and if any relation existsbetween them. Currently, there is considerable work being done in this field by theAlberta Research Council [9]4. Include real earth and space coordinates into program (longitude, latitude).5. Use the program to study more diverse geometries and a wider range of parameters.6. Include gaseous attenuation into the calculations since for f = 50 GHz the attenuationis 15 dB/km. Fog attenuation might also be significant over long distances. Fogattenuation is 0.1 dB/km for f = 50.0 GHz. This will translate into 10.0 dB for a100.0 km path length.7. Further research is needed to see if the COST 210 model can be extended tointerference on satellites.80Chapter 7—Suggestions for future research8. More work is needed on the interference caused by hydrometeors on low gain systems.This can be useful in cellular communications.9. Since the Kharadly scattering model does not extend to the snow region, moreresearch should be done to extend it. Also more work should be done to makeit more accurate.10. Develop formulas for scattering and attenuation for higher frequencies. As a first step,it will be useful to extend the scattering formulas to 100.0 GHz since the empiricalmodel for attenuation is valid over that range.11. More research is needed concerning the structure of the melting-snow region includ-ing its profile. The Alberta research [9] can provide valuable information on thesubject.12. More research is needed in the area above the melting snow layer. Again, the Albertaresearch [9] is bound to shed light on this subject.81Appendix A- Precipitation modelingAppendix A Precipitation modelingA.1 Rain mediumThe rain medium consists of drops of water drops of different sizes falling at avelocity depending on the size of the drop. For most applications, it is reasonable toassume that these particles are spheres. The size distribution of the spheres and theirvelocities v are given in Table A.1 [14].Precipitationrate (mm/h)0.25 1.25 2.5 5 12.5 25 • 50 100 150Drop size (cm) Percent of the total volumev(m/s)0.05 28.0 10.9 7.3 4.7 2.6 1.7 1.2 1.0 1.0 2.060.1^• 50.1 37.1 27.8 20.3 11.5 7.6 5.4 4.6 4.1 4.030.15 18.2 31.3 32.8 31.0 24.5 18.4 12.5 8.8 7.6 5.400.2 3.0 13.5 19.0 22.2 25.4 23.9 19.9 13.9 11.7 6.490.25 0.7 4.9 7.9 11.8 17.3 19.9 20.9 17.1 13.9 7.410.3 1.5 3.3 5.7 10.1 12.8 15.6 18.4 17.7 8.060.35 0.6 1.1 2.5 4.3 8.2 10.9 15.0 16.1 8.530.4 0.2 0.6 1.0 2.3 3.5 6.7 9.0 11.9 8.830.45 0.2 0.5 1.2 2.1 3.3 5.8 7.7 9.000.5 0.3 0.6 1.1 1.8 3.0 3.6 9.090.55 0.2 0.5 1.1 1.7 2.2 9.130.6 0.3 0.5 1.0 1.2 9.140.65 0.2 0.7 1.0 9.140.7 0.3 9.14Table A.1 Drop size distribution and their velocities for various precipitation rates [14]82Appendix A— Precipitation modelingThe model can further be simplified by considering the rain medium to be composedof rain drops of a representative radius a. The rain rate (R) can then be given by:R= 48r x 105 d9 vN^ A. (30)where,] —1/3a = [1/ E Pi^ A. (31),3i^...„Ripi is the fraction of the volume of rain VR composed of the rain drops of radius a R i .The number of representative rain drops in this fictitious rain medium is given by:N —^487r x 105 a 3 v A. (32)where R is measured in mm/h, a in cm, v in m/s, and N in cm-3 . The velocity can befound using Table A.1.A.2 Melting-snow mediumUnlike the rain medium, the melting snow layer is "essentially inhomogeneous". Itis the region at the zero isothermal where snow melts into rain. Because of the differencein density between the snow and water, the snow particle starts to decrease in size asit melts with the water forming a layer on the outside of the snow particle. The regionbetween where the melting starts and where the melting ends is called the "melting-snowlayer". For our melting-snow layer, we assume the following:1. The melting layer has a steady thermal structure.2. A steady supply of snowflakes of prescribed size is maintained at the 0°C level, atthe top of the melting region. The relative distribution of those particles is the sameas that in Table A.1.83Appendix A— Precipitation modeling3. There is no aggregation or breakup of snowflakes in the melting region.4. Snowflakes have spherical shapes.5. The melted water forms a coat around the snowflake.6. Growth by collision and coalescence with cloud drops and by condensation of watervapor is ignored.7. The melting particle increases in size as we move from the rain medium (S = 1) inthe bottom of the melting layer to the top of the melting layer (S = 0). The radiusof the representative melting snow layer is given by:a= [ ( Ps + (1 — p.,)S)Y  PivRi a' .vM •RtI —1/3A. (33)Where^Ps^density of the snow core of the particle^vRi^•^fall velocity of the rain drop of radius aR,• fall velocity of the corresponding melting-snow spheres with adegree of melting SThe velocity of the melting snow particle is given by:vrn i = 1.5 + (vRi — 1.5) sin (-7 )^A. (34)S is the ratio of the melted volume of water to the total volume of the melting snowparticle.Two models have been developed by Kharadly [10, 12] for the melting-snow layer.In [10], the effect of the fall velocity on number density is ignored which led to theviolation of the conservation of mass criterion. In [12], the effect of fall velocity is takeninto consideration.84Appendix B- Kharadly attenuation modelsAppendix B Kharadly attenuation modelsB.1 Artificial dielectric modelThe specific attenuation Ap and the phase # are given from the general expressionfor the propagation characteristic [10]:-y Ap + j#=-- 21-f (—itoe) 1 /2^B.1From the above expression the attenuation and phase can be easily approximated by:Ap 9.1g, N f x 104B.2A# 6g: N f x 10 5where the effective value of the polarizability at high frequencies ge = ge — jgen is givenby:g ge =1 +2 + Y(*)m n =1 + (Y + 1) (-krfr - 27rawhere m = 2, Y = 100, and ( = 0.81. The low-frequency value of the polarizability fora two-concentric sphere is given by:3(e2^1 )(2€2 + el) — ( IL) (e2 c1)(2€2 + 1)a2g =^ 3(e2 2)(2f2 + El) — 2( 1' ) (e2 el)(E2 — 1)02B.5with,and,B.3B.485Appendix B—Kharadly attenuation modelswhere ai, a2, El, E2 are the radius of the inner sphere, the radius of the outer sphere, thepermittivity of the inner sphere, and the permittivity of the outer sphere, respectively.The permittivity of water, 6, is given in [18]:IIIE_ 1 -11^ B.6(Es — 100 ) [1 + (A s /A) 1 ' sin (wt. /2)]I = coo + ^B.71 + 2(A s /A) 1 ' sin (air/2) + (A s /A) 2(1—a). ^(Es — c„,,)(A s /A) l—a cos (air/2)^TA 1 + 2(As /A) 1 ' sin (air/2) + (A s /A) 2(1—a) + 18.8496 x 10 10whereEs = 78.54 x [1.0 — 4.597 x 10 -3 (t — 25.0) + 1.19 x 10 -5 (t — 25.0) 22.8 x 10 -8 (t — 25.0) 3 ]T = 12.5664 x 10 8cc, = 5.27137 + 0.0216474t — 0.00131198t 2a =^—16.8129 t+273 + 0.0609265As = 0.00033836e 2513.98 /(t+273 )B.2 Corrected attenuation modelsB.2.1 Kharadly 3rd model for attenuationBecause of the deviation of the results of the 1st model from that of the exact valuesfor the melting-snow layer, Kharadly introduced a correction factor that brought theresults of the model closely to the exact attenuations calculated using Mie scattering.The correction factor is given by [12]:1 n {(2 + S)1; + 1] 1 1 2 — S1f( 1—s)Factor 1 = + 2 — S^x t 2 -1-Sf (2.7)rtE B.886Appendix B—Kharadly attenuation modelswhere f is the frequency in GHz, fr is the resonant frequency of the melting-snowparticle, S is the melting degree , defined as the melted to the total volume in therepresentative melting-snow particle.B.2.2 Kharadly 4th model for attenuationBecause of the deviation of the results of the 2nd model from that of the exactvalues for the melting snow layer, Kharadly introduced a correction factor that broughtthe results of the model closely to the exact attenuations calculated using Mie scattering.The factor is given by:n2d(1 —^ — 5ill (1- S)Factor2 = [{n + S(1— n)}{1+ ^26S )[^(1 5 frS)f1+ (2.8)where a is the radius of the representative particle, b is the skin depth of water =^ with C1 = 20.958, f is the frequency in GHz and E is the complexReal[fpermittivity of water.The range of applicability of Kharadly's formulas is between 1-40 GHz87Appendix C—Kharadly scattering modelAppendix C Kharadly scattering model [11] When an electromagnetic wave is incident on a dielectric sphere, it scatters (FigureC.1) . This scattering can be calculated using Mie scattering. This technique is computerintensive, and thus, not efficient to use. Other approaches have been developed byresearchers in the fieldOne of the simpler techniques to model the scattering from rain has been developedby Kharadly [11]. Kharadly has based his model on two assumptions1. A rain drop or a melting-snow particle, under the effect of an incident electric field,behaves as a point dipole.2. The rain medium which has particles of different sizes can be represented with afictitious medium of particles of the same geometry, but with the same particle size.After introducing correction factors to deal with some of the inaccuracy introducedas a result of the simplification of the model, Kharadly concluded the following formulafor hydrometeor scattering [11]:Q(0, (19) = cr(d) x F(M") x F(n) x F(S) x Nm^C.1where,er (a) = (ko d) 2n2^7ra-22n F ( 1) 4) )(f)c — c oE ± 2E0[LF(0, c/)) = sin! 0 ± 1+f' i- 2 (^4)sin s 0 cos -1--1 cos4 0)C.1(a)C.1(b)M" [^M"^R )} sin 0 cos 4)"")= 1 2.6 1 — 2.6 ( 1 600^C.1(c)88Appendix C—Kharadly Scattering modelFigure C.1 Scattering geometry of a rain particle due to an incident electromagnetic wave.Appendix C—Kharadly scattering modelF(n) =( /^n) 2  [  n 2 ^ln i+ R^(f)2 300 ±2n(2.5n — 1) 1 ± n 2 L^2^1 ±1 (1—.9 425S^( R )1 + (6'.52 [ 150 .100 )F(S) = {n /50 ± R X^021 ± (f) [^2R + 100 (1 0.5 f sin2 J_ ±)ga202100^frwhere,ko = -24Ao = free-space wavelength2+200(17) 3n = 1+201(f) 3f = frequencyfr = t, where c is the velocity of light in free spaceAr - 27itiouter radius of the representative melting-snow sphere= 0.866(1 + 1.5 x 10 -4f), where f is in GHzco = permittivity of free space= permittivity of waterM = M' - N H , is the refractive index of water (= e r1/2 )Xcos 0 sin 0 } 1—gC.1(e)0,0 = polar and azimuthal angles, as in FigA.1N. = number of melting-snow particle per unit volume (rain drop density)S = degree of melting — volume of melted snowtotal volumeThe radius of the representative melting snow sphere is given by:90Appendix C—Kharadly scattering model=[(0 .1 + 0 .9S)V  P VRi —113as . vRs nuwherepi = fraction of rain drop of radius aRivRi = fall velocity of rain drop of radius aRivmi = fall velocity of corresponding melting-snow spheres with a degree of melting S= 1.5 + ( vR, — 1.5) sin V91Appendix D—Empirical formula for attenuationAppendix D Empirical formula for attenuationThe most convenient method for modelling the attenuation of rain is by putting itin the following form [16]:Ap = a(f)R1 ^D.1where a and /3 have been found using a program which implements the least square datafitting technique. Given a value of 13, the program will find the a that corresponds to themost accurate fit with the original (given) data. a, and j3 have been calculated for 27frequencies ranging from 1-100 GHz. The original values of attenuations are the Miecalculations done by Kishk [12]. a, and /3 have then been fitted in two equations infunction of frequency. These two equations are:/3(f) = [ 1 * f2 f3 f4 f2 e-f }]+1.16933000000 --0.25154000000-2.45000 x 10 -4+3.50920 x 10-6-1.46357 x 10 -8-0.44110000000_ +0.14282500000 _D.1(a)a(f) = [f2.1 f6 f2.5 f4 f8 f71+3.4777654 x 10 -88-+3.8866095 x 10 -12+2.9044983 x 10 -85-3.8528788 x 10 -08+2.3261638 x 10 -18-4.8164211 x 10 -14D. 1(b)92Appendix D—Empirical formula for attenuationThe next step was to extend the formula to the melting snow layer. We did thatby dividing the values of the attenuations for the different melting degrees (S) by theattenuation for rain. We call the result value of division as the melting snow layernormalized attenuation. A formula is found that gives a good fit for the normalizedattenuation:An(R,f =^sai-1 e—bi^+ m2 sa2 —1 e— b2 Sa2 + m3 e —b3 S + 1^D.2Then,Ap = An x a(f) len^ D.3In order to simplify equation D.2, the following assumptions can be safely made:= 18b2 = 6.3a2= 1.7M3 = —1b3 = 230Equation D.2 then becomes:A n(R, f ,S) =^sai —1 e -18Sal + m2 SO.7 e -6.3S 1^e -230S + 1^D.4A formula to fit al is found:93Appendix D—Empirical formula for attenuation+1.6806—2.791 x 10 -3491(f) =[ 1if_ 711 f2.1 e— f]—3.41706+5.0493D4(a)+0.4707755—2.26293M1 and M2 are found to satisfy the following equations:Ml(R,f) = C0(f) Cicoli c1 C2(f) Re2^D.5M2(R,f) = Do(f) DicoRdi D2(f)Rd2whereCl = d1 = 0.003c2 = d2 = 0.0002Equation D.5 then becomes:Ml(R,f)^Co(f) C1(f) R0.003^y 2(f ) R0.0002^D.6M2(R,f) = Do(f) Di(f)Rdl + D2( f)Rd2Where Co(f), CO), C2(f) are given by:f2 e— f f.2^-.01 f. 7 e— f sin (-0 ] [Xin]for 1.0 < f < 12.0 in Hzton ef-100 ^ In (f) 1 cosh(f —20)^cosh( f —40)for 12.0 < f < 100.0 in GHzsin (43 ) ] [Y1,2 ]D.6(a)94Appendix D- Empirical formula for attenuationn = 0- 4.46871 x 10 10+1.40323 x 1008-6.96003 x 10 08+4.50656 x 10 10- 6.42129 x 10 07+8.73118 x 10 08+1.40150 x 10 06n = 0-6.29528 x 10 10+6.29636 x 10 10+5.96653 x 10 05- 3.88357 x 10 °5- 1.92394 x 10 08-1.82230 x 10 05+8.65689 x 10 °4n = 1- 3.17499 x 10°9+1.00081 x 1007- 4.93871 x 10 °7+3.20179 x 10 °9- 4.56513 x 1006+6.21166 x 10 °7+9.94801 x 10 °4n = 1-4.08460 x 10 09+4.08533 x 1009+4.25990 x 10 °4- 2.78377 x 10 04-1.24892 x 10 07-1.28176 x 10 04+6.23398 x 1003n = 2+4.78623 x 10 10- 1.50331 x 1008+7.45011 x 10 08- 4.82676 x 10 10+6.87778 x 1007- 9.35236 x 10 °8- 1.50098 x 1006n = 2+6.70282 x 10 10-6.70397 x 101°- 6.39256 x 1005+4.16678 x 1005+2.04855 x 1008+1.95046 x 1005- 9.28018 x 1004X1 n =Yin =Also, Do(i), Di(f), D2(f) are given by:1[1 f f2 f3 fe-f f2 e-f sin (0.6(f - 2.8)) in (1)][X2n]for 1.0 < f < 20.0 in GHzDn(f) =^[ 1 f f2 f3 fe-f f2e-f sin (0.6(f - 2.8)) In (f)1[Y2n]for 20.0 < f < 100.0 in GHzD.6(b)X2n =n = 0- 2.09914 x 10 °7+1.40003 x 10 07-8.88279 x 10 °5+1.98926 x 10 °4+4.17453 x 10 06+1.59365 x 10 °7+7.50124 x 10 05_ -2.08356 x 10 07n = 1-1.49368 x 10 06+9.95647 x 1005-6.31410 x 10 °4+1.41351 x 10 °3+2.97214 x 10 °5+1.13469 x 10 06+5.31790 x 10 04- 1.48261 x 10 06n = 2+2.24852 x 1007-1.49959 x 10 07+9.51422 x 10 °5- 2.13062 x 10 04- 4.47162 x 1006- 1.70713 x 1007- 8.03303 x 1005+2.23186 x 1007 951/2n =n = 0—4.43961 x 10 07—8.94385 x 10 05+6.29234 x 10 03—1.90282 x 1001—2.52272 x 10 15+1.27660 x 10 14—2.29312 x 10 04+1.95225 x 10 07Appendix D--Empirical formula forn = 1^n = 2^-^—3.15028 x 10 06^+4.75465 x 10°7^ 6.3347 x 10°4^+9.57732 x 10 °5^+4.45502 x 1002^—6.73784 x 1003—1.34692 x 100°^+2.03751 x 1001—1.80339 x 10 14^+2.70306 x 10 15+9.12578 x 10 12^—1.36786 x 10 14^- 1.62315 x 10°3^+2.45541 x 10°4+1.38423 x 1006^—2.09068 x 10 °7attenuationFigures D.1-4 show that the empirical model agrees with the exact calculations.Although the formulas seems to be huge, their computer running time is quite short.Also, since the frequency remains constant during the integration, we can calculate thevariables which are function of frequency at the beginning of the program and then wewill be left with a simple formula for attenuation.Unfortunately, this formula assumes that the density of the core in the melting snowparticle to be 0.1. However it should not be very difficult to incorporate the density ofthe core into the equation without increasing the computer-running time of the formulaconsiderably.96Attenuation in dB/kut4.504.003.503.002.502.001.501.000.500.00Attenuation in dB/km x 10 -3210.00200.00190.00180.00170.00160.00150.00140.00130.00120.00110.00100.0090.0080.0070.0060.0050.0040.0030.0020.0010.000.00-10.000.00^0 in^1.00^0.00^0.50^1.00Degree of melting (S)^ Degree of melting (S)Figure D.1 A comparison of the attenuation profile of the melting layer for Kharaclly 3rd attenuationmodel, Empirical model, and the Exact calculations for f (frequency) = 1.0 and 5.0 GHz (p, = 0.1).Attenuation in dB/kmAttenuation in dB/km16.0015.0014.0013.0012.0011.0010.009.008.007.00,t)coo 6.005.004.003.002.001.000.00Exact calculations, m-0.9Empirical formulaKhamcUy 1rd attenuation model36.0034.0032.0030.0028.0026.0024.0022.0020.0018.0016.0014.0012.0010.008.006.004.002.000.000.00^0.50^1.00^0.00^0.50^1.00Degree of melting (S)^ Degree of melting (S)Figure D.2 A comparison of the attenuation profile of the melting layer between Kharadly 3n1 attenuationmodel, Empirical model, and the Exact calculations for f (frequency) = 10.0 and 20.0 GHz (p, = 0.1).0.00 0.50Degree of melting (S)Attenuation in dBAmt45.0040.0035.0030.0025.0020.0015.0010.005.000.001.00^0.00 0.50Degree of melting (S)Attenuation in dB/lm44.0042.0040.0038.0036.0034.0032.0030.0028.0026.0024.0022.0020.0018.0016.0014.0012.0010.008.006.004.002.000.00-2.001.00Figure D3 A comparison of the attenuation profile of the melting layer between Kharadly 3rd attenuationmodel, Empirical model, and the Exact calculations for f (frequency) = 30.0 and 40.0 GHz (p, = 0.1).0.00 0.50 1.00Attenuation in dB/lrm55.0050.0045.0040.0035.0030.0025.0020.0015.0010.005.000.00Attenuation in d13/1cm65.0060.0055.0050.0045.0040.0035.0030.0025.0020.0015.0010.005.000.000.00 0.50^1.00tract calculations, m=0.9iircal  fornatkharadly 3rd attenuation mode!Degree of melting (S)^Degree of melting (S)Figure D.4 A comparison of the attenuation profile of the melting layer between Kharadly 3rd attenuationmodel, Empirical model, and the Exact calculations for f (frequency) = 70.0 and 100.0 GHz (p. = 0.1).The program for the "Universal Model"Appendix E The program forthe "Universal Model"The following is a listing of the program used in the calculations of the interferencefor the modified Capsoni rain model:*DOUBLE PRECISION FREQ,T,QUANTITY,THETA,PHI,• XH,YH,ZH,XTHE_T,XPHIT,• XR,YR,ZR,XXXXXX,YYYYYY,• TR_ALPHA,TR_HALF_THETA,RE_ALPHA,RE_HALF_THETA,• H_MELT,H_THICKNESS,H_RAIN,RAD,RMAX,FREQ,QUANTITY,T,• D_RHO,G1,G2,HBW1,HBW2,K,MINTINTEGER TASKNUMBER1,TASKNUMBER2,SENTINALCHARACTER*2 DECISIONCALL AT_SC_MENU(TASKNUMBER1,TASKNUMBER2)CALL POSITIONINPUT(XH,YH,ZH,XTHE_T,XPHI_T,• XR,YR,ZR,XXXXXX,YYYYYY)CALL GEO_INPUT(TR_ALPHA,TR_HALFTHETA,RE_ALPHA,• RE_HALF_THETA,DECISION,H_MELT,H_THICKNESS,H_RAIN,RAD,• RO,RMAX,FREQ,QUANTITY,T,DRHO,G1,G2,HBW1,HBW2,K,MINT)CALL GEOMETRIC_MODEL(XH,YH,ZH,XTHE_T,XPHI_T,• XR,YR,ZR,XXXXXX,YYYYYY,TR_ALPHA,T,QUANTITY,• TR_HALF_THETA,RE_ALPHA,RE_HALF_THETA,DECISION,• H_MELT,H_THICKNESS,H_RAIN,RAD,RO,RMAX,FREQ,D_RHO,G1,G2,• THETA,PHI,TASKNUMBER1,TASKNUMBER2,HBW1,HBW2,K,MINT)*STOPEND********************************************************************************************** AT SC MENU ************************************************************************ -IT**********************************************************SUBROUTINE AT_SC_MENU(TASKNUMBER1,TASKNUMBER2)INTEGER TASKNUMBER1, TASKNUMBER2*READ*,TASKNUMBER1READ*,TASKNUMBER2RETURNEND*********************************************************************************************** SUBROUTINE GE() INPUT ************************************************************************7************************************************SUBROUTINE GEO_INPUT(TR_ALPHA,TR_HALF_THETA,RE_ALPHA,• RE HALF THETA,DECISION,H MELT,H THICKNESS,H RAIN,RAD,RO,• RMÄX,FRfQ QUANTITY,T,DRT10,G1,G,HBW1,HBW2,R,MINT)DOUBLE PRECISION TR_ALPHA,TR_HALF_THETA,RE_ALPHA,• RE_HALF_THETA,H_MELT,H_THICKNESS,H_RAIN,RAD,RO,RMAX,101The program for the "Universal Model"FREQ,QUANTITY,T,DRHO,G1,G2,HBW1,HBW2,K,MINTCHARACTER*2, DECISION*READ*,TR_ALPHAREAD*,TR_HALF_THETAREAD*,RE_ALPHAREAD*,REHALF_THETAREAD*,DECISIONIF (DECISION.eq.'Y')THENREAD*,H MELTREAD*,H_THICKNESSENDIFREAD*,H RAINREAD*,RADREAD*,R0READ*,RMAXREAD*,FREQREAD*,TREAD*,QUANTITYREAD*,D_RHOREAD*,G1READ*,G2READ*,HBW1READ*,HBW2READ*,KREAD*,MINTRETURNEND********************************************************************************************** SUBROUTINE GEOMETRIC MODEL ************************************************************************T******************************************COORDINATES OF RAIN CELL (BOTTOM CENTER)- DIRECTION OF MAIN BEAM ON TRANSMITTERCOORDINATES OF RECEIVER- DIRECTION OF MAIN BEAM ON RECEIVERANGLE OF ALPHA ON TRANSMITTERTHETA (HALF) FOR THE TRANSMITTERTHETA (HALF) FOR THE RECEIVER'Y' THERE IS A MELTING LAYERHEIGHT WHERE MELTING LAYER STARTSTHICKNESS OF MELTING LAYERHEIGHT OF RAIN CELLRADIUS OF RAIN CELLRAIN RATE DISTRIBUTION VARIABLEMAXIMUM RAIN RATEFREQUENCYINCREMENT FOR POSITION OF MAIN BEAMGAIN OF TRANSMITTERGAIN OF RECEIVERDIRECTION OF TRANSMITTER MAIN LOBEDIRECTION OF RECEIVER MAIN LOBE1ST INTERSECTION OF RAIN CELL AND LOBE OF TRANSMITTER2ND INTERSECTION OF RAIN CELL AND LOBE OF TRANSMITTERINTERSECTION OF RAIN CELL AND TRANSMITTED BEAM1ST INTERSECTION OF RAIN CELL AND LOBE OF RECEIVER2ND INTERSECTION OF RAIN CELL AND LOBE OF RECEIVERCLOSEST INTERSECTION OF RAIN CELL AND LOBE OF RECEIVERLOCATION OF RECEIVER RELATIVE TO NEW AXIS (X',Y',Z')NEW POSITION OF RECEIVER AFTER TRANSLATION OF TRANSMITTERTO RAIN CELLXH,YH,ZH^-XTHE_T,XPHI_TXR,YR,ZR^-XXXXXX,YYYYYYTR_ALPHA^-TR_ HALF _ THETA -RE HALF THETA -DECISION^-H_MELTH_THICKNESSH_RAINRADRORMAXFREQD_RHOG1G2T_X,T_Y,T_ZR X,R_Y,R_ZXY,1,Z1X2, Y2, Z2X, Y, ZX1P,Y1P,Z1PX2P,Y2P,Z2PX11,Y11,Z11^-XPR,YPR,ZPR^-XDPR,YDPR,ZDPR-DPRHO,DPTHETA,DPPHI^SPHERICAL COORDINATES OF RECEIVER WHEN ORIGINALCOORDINATE SYSTEM HAS BEEN ROTATED AND TRANSLATED102The program for the "Universal Model"- TEMPERATURE- THE MASS VALUE OF THE RAIN, SNOW LAYER- THE PARAMETER A/B OF THE MELTING SNOW LAYER- BOTTOM HEIGHT OF RAIN CELL MEASURED FROM TRANSMITTER- TOTAL HEIGHT OF RAIN CELL MEASURED FROM TRANSMITTER- HEIGHT OF FREEZING LAYER MEASURED FROM TRANSMITTER- HM HEIGHT OF MELTING LAYER MEASURED FROM TRANSMITTER- HEIGHT OF BEAM IN RAIN CELL- RAIN RATE- ATTENUATION DB/KM AND FROM GAMMA RESPECTIVELY- THETA DIRECTION OF SCATTERTING- PHI DIRECTION OF SCATTERING- COORDINATES OF X,Y,Z WHEN AXIS TRANSLATED TO (XR,YR,ZR)- ANGLE BETWEEN SCATTERED BEAM BEING RECEIVED ANDDIRECTION OF RECEIVING ANTENNA- ATTENUATION DUE TO GAS AND HUMIDITY RESPECTIVELY- 3X3 MATRIX TO ROTATE AXIS- ATTENUATION TASKNUMBER- SCATTEING TASKNUMBER- HALF POWER BEAM WIDTH FOR RECEIVING ANTENNA MAIN LOBE- HALF POWER BEAM WIDTH FOR RECEIVE ANTENNA SECONDARY LOBE- GAIN OF SECONDARY LOBE RELATIVE TO MAIN LOBE- COORDINATE OF ALPHA TRANSMITTERQUANTITYSHMINHMAXHFRHMHEIGHTRATEATTEN,ATTE2THETAPHIXN,YN,ZNYYYYYYAG, AHRTTASKNUMBER1TASKNUMBER2HBW1HBW2KAX,AY,AZ** *********************** *********** *********************** ********** ************SUBROUTINE GEOMETRIC MODEL(XH,YH,ZH,XTHE T,XPHI_T,• XR,YR,ZR,XXXXXXTYYYYYY,TR_ALPHA,T,QUANTITY,• TRHALFTHETA,REALPHA,RE_HALFTHETA,DECISION,• H_MELT,H_THICKNESS,H_RAIN,RAD,RO,RMAX,FREQ,D_RHO,G1,G2,• THETA,PHI,TASKNUMBER1,TASKNUMBER2,HBW1,HBW2,K,MINT)DOUBLE PRECISION XH,YH,ZH,XTHE_T,XPHI_T,S,T,QUANTITY,• XR,YR,ZR,XXXXXX,YYYYYY,TR ALPHA,RATE,ATTEN,HMIN,• TR_HALF_THETA,RE_ALPHA,RE:HALF_THETA,HMAX1,HFR,HM,HEIGHT,• H_MELT,H_THICKNESS,H_RAIN,RAD,RO,RMAX,FREQ,D_RHO,G1,G2,GT,• A_X,A_Y,AZ,RHO,TX,T_Y,T_Z,X1,Y1,Z1,X2,Y2,Z2,• R1,R2,R,RX,RY,RZ,RT(3,3),X,Y,Z,X0,Y0,ZO,H1T,• R1P,R2P,X1P,Y1P,Z1P,X2P,Y2P,Z2P,X11,Y11,Z11,XPR,YPR,ZPR,• XTRAN,YTRAN,ZTRAN,XDPR,YDPR,ZDPR,DPRHO,DPTHETA,DPPHI,• THETA,PHI,RTATT,XN,YN,ZN,YYYYYY,AG,AH,VAR,F,VARDUM,• HBW1,HBW2,K,XI1,YI1,ZI1,XYZ,RI,G,GE,ANGI,TEML,MINT,• NARR(2,3),ANUM,BNUM,A1NUM,RADARCONSTINTEGER FLAG,TASKNUMBER1,TASKNUMBER2CHARACTER*2 DECISIONVAR=0.D0T=0.D0R=1.D0CALL SPHERE2RECT(TX,TY,TZ,XTHET,XPHIT,R)X0=0YO=0Z0=0CALL LINE CYLINDER INTERSECT(X0,YO,Z0,XH,YH,ZH,RAD,MINT,IF (FLAG.LE.0) THENPRINT*, '-99999'RETURNENDIFIF (TASKNUMBER1. EQ. 5) THENCALL A_B(FREQ,ANUM,BNUM)CALL N_CALC(FREQ,NARR)103The program for the "Universal Model"CALL Al_CALC(FREQ,A1NUM)ENDIFA X=0A Y=DSIND(TR_ALPHA)A:Z=DCOSD(TRALPHA)CALL SPHERE2RECT(RX,RY,RZ,XXXXXX,YYYYYY,R)CALL ROT_PARAMETERS(T  X,T Y,T Z,A X,A Y,A  Z,RT)RT IS A 3 X 3 ARRAY WHICH HAS X',Y',Z' IN THE FIRST, SECONDAND THIRD ROWS RESPECTIVELY.R1=DSQRT(X1**2+Y1**2+Z1**2)R2=DSQRT(X2**2+Y2**2+Z2**2)IF (R1.GT.R2) THENRHO=R2+D_RH0/2RI=R1HEIGHT=Z1ELSERHO=R1+D_RH0/2RI=R2HEIGHT=Z2ENDIF600 CALL SPHERE2RECT(X,Y,Z,XTHE_T,XPHI_T,RHO)R2=DSQRTHXR-X)**2+(YR-Y)**2+(ZR-Z)**2)XI' = X - XRYI1 = Y - YRZI1 = Z - ZRXYZ = DSQRT(XI1**2 + YI1**2 + ZI1**2)XII^XI1/XYZYI1 = YI1/XYZZI1 = ZI1/XYZCALL LINE_CYLINDER_INTERSECT(XR,YR,ZR,XH,YH,ZH,RAD,MINT,6^X1P,Y1P,Z1P,X2P,Y2P,Z2P,XI1,YI1,ZI1,FLAG)R1P=DSQRT((X1P-XR)**2+(Y1P-YR)**2+(Z1P-ZR)**2)R2P=DSQRT((X2P-XR)**2+(Y2P-YR)**2+(Z2P-ZR)**2)IF (R1P.GT.R2P)THENX11=X2PY11=Y2PZ11=Z2PELSEX11=X1PY11=Y1PZ11=Z1PENDIFFINDING (XR,YR,ZR) RELATIVE TO NEW AXIS (X',Y',Z')-->(X'R,Y'R,Z'R)XPR=RT(1,1)*XR+RT(1,2)*YR+RT(1,3)*ZRYPR=RT(2,1)*XR+RT(2,2)*YR+RT(2,3)*ZRZPR=RT(3,1)*XR+RT(3,2)*YR+RT(3,3)*ZRCALL TRANSLATION(X0,YO,Z0,RHO,Y0,Z0,XTRAN,YTRAN,ZTRAN)XDPR=XPR-XTRANYDPR=YPR-YTRANZDPR=ZPR-ZTRANCALL RECT2SPHERE(XDPR,YDPR,ZDPR,DPTHETA,DPPHI,DPRHO)FINDING SHMAX1=H_RAIN+ZH104The program for the "Universal Model"HFR=ZH+HMELT+H_THICKNESSHM=H MELT+ZHHMIN=ZHCALL GET_S(HMAX1,HFR,HM,HMIN,Z,S,DECISION)CALCULATING RAIN RATECALL RAINRATE(XH,YH,X,Y,RMAX,RO,RATE)CALCULATE THE SPECIFIC ATTENUATIONCALL ATT_TASK(FREQ,T,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,& NARR,A1NUM,ANUM,BNUM)TATT=ATTEN*DRH0/1000+TATTCALCULATE THE SCATTERING CROSS SECTIONCALL SCAT_TASK(F,DPTHETA,DPPHI,S,RATE,FREQ,T,QUANTITY,& TASKNUMBER2,DECISION,H_THICKNESS)IF (DECISION.EQ.'Y') THENH1T = HFRELSEH1T = HMAX1ENDIFIF (S.EQ.O.D0) THENTEML = 10**(-0.00065*ABS(Z-H1T))F = TEML*FENDIF**^CALCULATING TOTAL RAIN ATTENUATION*CALL RAIN_TOTAL_ATTENUATION(HMAX1,HFR,HM,HMIN,FREQ,T,& QUANTITY,X,Y,Z,X11,Y11,Z11,RTATT,XH,YH,RMAX,RO,DECISION,& TASKNUMBER1,NARR,A1NUM,ANUM,BNUM,XR,YR,ZR,H_THICKNESS,& RAD,XTHET)** TRANSLATING X,Y,Z TO THE RECEIVER AXIS. SINCE THE COORDINATES (X,Y,Z)* ARE MEASURED FROM AN AXIS AT (0,0,0) ALL I HAVE TO DO IS SUBTRACT* THE POSITION OF THE RECEIVER FROM THE POINT AND THUS GET THE* TRANSLATED POINT.*XN=X-XRYN=Y-YRZN=Z-ZR** CALCULATING ANGLE BETWEEN UNIT VECTOR AND RECEIVER MAIN LOBE*CALL ANGLE(XN,YN,ZN,R_X,R_Y,R_Z,ANGI)CALL ANTENNA_GAIN(ANGI,HBW1,HBW2,K,G)* CALL RECEIVING_GAIN(G2,ANGI,GE)CALL GAS_HUMIDITY_ATTENUATION(AG,AH)VARDUM=10**(-0.1D0*(TATT+RTATT+AG+AH))VAR=VAR+((F*G*D_RHO/(DPRHO**2))*VARDUM)RHO=RHO+D RHOIF (RHO.LT .RI) GOTO 600CALL CONST_RADAR(FREQ,TR_HALF_THETA,G1,G2,GT,RADAR_CONST)VAR=VAR*RADAR_CONSTVAR = 10.*DLOG10(VAR)PRINT*, VARRETURN105The program for the "Universal Model"END**********************************************************************************************SUBROUTINE ROT PARAMETERS ******************************************************************T*************************************************THIS SUBROUTINE FINDS THE PARAMETERS IN ORDER TO ROTATE THE X-AXIS*^IN THE DIRECTION OF PROPAGATION.********************************************************************************SUBROUTINE ROTPARAMETERS(T  X,T Y,T Z,A X,A Y,A  Z,T)DOUBLE PRECISION T X,T_Y,T_Z,A X,A Y,A_Z,& DUMMY,X,Y,Z,NIX,N_Y,N_Z,TT3,3,& Z  X,Z Y,Z Z,Y X,Y Y,Y  ZN_X=0IF ((T_X.EQ.1).AND.(T_Y.EQ.0).AND.(T_Z.EQ.0))THENZ_X=A_XZ Y=A Y_ Z Z=A_ZELSE -N_Y=-TZ/DSQRT(T_Z**2+T_Y**2)N_Z=T_Y/DSQRT(T_Z**2+T_Y**2)DUMMY=(A_Y*N_Y+N_Z*A_Z)*(1-T_X)Z_X=T_X*A_XZ_Y=N_Y*DUMMY+T_X*A_YZ Z=N Z*DUMMY+T_X*A_ZCALL tROSS_PRODUCT(A  X,A Y,A Z,N X,N Y,N  Z,X,Y,Z)Z_X=Z_X-X*DSQRT(1-T_X**2)Z_Y=Z_Y-Y*DSQRT(1-T_X**2)Z_Z=Z_Z-Z*DSQRT(1-T_X**2)ENDIFCALL CROSS_PRODUCT(Z  X,Z Y,Z Z,T X,T Y,T Z,Y X,Y Y,Y  Z)T(1,1)=T_XT(1,2)=T_YT(1,3)=T_ZT(2,1)=Y_XT(2,2)=YY.T(2,3)=Y_ZT(3,1)=Z_XT(3,2)=Z_YT(3,3)=Z_Z*RETURNEND***************************************************************************************** SUBROUTINE ANTENNA GAIN *************************************************************************T************************************************** THIS SUBROUTINE CALCULATES THE GAIN OF AN ANTENNA BY IMPLEMENTING* AN ANTENNA LOB THROUGH THE USE OF TWO GAUSSIAN APPROXIMATIONS.* G1(theta)=exp(-41n2(theta/hbw1)-2)* G2(theta) = 10"(K/10)*exp(-41n2(theta/hbw2) - 2)** G(theta) = G1 (theta) + G2(theta)* G(theta) = G(theta)/G(0)** THETA^- ANGLE OF RECEPTION* HBW1,HBW2 - HALF BEAM WIDTHS OF Gl,G2 RESPECTIVELY* K^- INPUT PARAMETER TO HELP DETERMINE THE SHAPE OF THE ANTENNA* GAIN PARAMETERS.********** ***** **************************** ***** **************************** ****SUBROUTINE ANTENNAGAIN(THETA,HBW1,HBW2,K,G)**106The program for the "Universal Model"DOUBLE PRECISION THETA, HBW1,HBW2,K,G,G1,G2CALCULATING G1(THETA) AND G2(THETA).THETA = ABS(THETA)G1=DEXP(-4.0DO*DLOG(2.0D0)*((THETA/HBW1)**2))G2=10**(K/10)*DEXP(-4.0DO*DLOG(2.0D0)*((THETA/HBW2)**2))CALCULATING FINAL GAIN - G.NOTE: G(0) HAS BEEN ALREADY SIMPLIFIED.G=(G1+G2)/(1+10**(K/10))RETURNEND********************************************************************************************** SUBROUTINE GAS HUMIDITY ATTENUATION *********************************************************T********7.****************************************SUBROUTINE GAS_HUMIDITY_ATTENUATION(AG,AH)**^DOUBLE PRECISION AG,AHAG = O.DOAH = O.DORETURNEND*************** SUBROUTINE GET S ****************************************************************************,T************************************************* THIS SUBROUTINE CALCULATES THE VALUE OF S IN THE TRANSITION STAGE* FROM SNOW TO RAIN AT ANY HEIGHT OF THE RAIN CELL.********************************************************************************SUBROUTINE GET_S(HMAX1,HFR,HM,HMIN,HEIGHT,S,DECISION)DOUBLE PRECISION HMAX1,HFR,HM,HMIN,HEIGHT,SCHARACTER*2 DECISIONIF (DECISION.EQ.'Y') THENIF ((HEIGHT.GE.HMIN).AND.(HEIGHT.LE.HM))THENS=1.D0ELSEIF ((HEIGHT.GE.HM).AND.(HEIGHT.LE.HFR)) THENS=(HFR-HEIGHT)/(HFR-HM)ELSEIF (HEIGHT.GT .HFR) THENS=0.D0ENDIFELSEIF (HEIGHT.LE.HMAX1) THENS = 1.0D0ELSES = O.DOENDIFENDIF*RETURNEND********************************************************************************************** SUBROUTINE LINE CYLINDER INTERSECT ***********************************************************7********T*************************************** THIS SUBROUTINE COMPUTES THE INTERSECTION BETWEEN A LINE IN* THREE SPACE AND A CYLINDER. THE CYLINDER IS IN THE Z-DIRECTION* XO,YO,ZO ARE THE POSITION WHERE THE LINE BEGINS, A,B ARE THE CENTER* OF THE CYLINDER AT X,Y RESPECTIVELY, H IS THE HEIGHT OF THE CYLINDER,* AND X1,Y1,Z1 AND X2,Y2,Z2 ARE THE INTERSECTION POINTS. FLAG IS107The program for the "Universal Model"A VARIABLE RETURNED TO TELL US IF THERE IS ONE INTERSECTION, TWOINTERSECTIONS OR NO INTERSECTIONS FOR FLAG =0,1,-1 RESPECIVELY.IN ADDITION, XD,YD,ZD GIVES THE DIRECTION OF THE LINE, R ISTHE RADIUS OF THE CYLINDER AND H IS THE HEIGHT OF THE CYLINDER.T1 AND T2 ARE THE VARIABLES USED FOR THE PARAMETRIC EQUATIONS* NOTE*** IF THE LINE GOES STRAIGHT THROUGHT THE MIDDLE OF THE CYLINDER* IT WILL NOT SHOW INTERSECTION, SO IT IS EASY TO PUT THE LINE ON A* SMALL ANGLE. THE RESULTS SHOULD BE VERY CLOSE.*** ******* ******************* ******* ******************* ******* *******************SUBROUTINE LINE_CYLINDER_INTERSECT(X0,YO,Z0,A,B,C,R,HH,X1,Y1,Z1,& X2,Y2,Z2,XD,YD,ZD,FLAG)DOUBLE PRECISION XO,YO,ZO,A,B,C,R,H,X1,Y1,Z1,X2,Y2,Z2,& DISCRIMINANT,AA,BB,CC,T1,T2,XD,YD,ZD,HH,A1X,A1Y,& AlZ,A2X,A2Y,A2Z,A11,A22,R1B,R2B,PHILPHI2,B11INTEGER FLAGH=HH+CAA=XD**2.000+YD**2.000BB=2.0D0*(X0*XD-A*XD+YO*YD-B*YD)CC=X0**2.0DO+YO**2.0D0+A**2.0D0+B**2.0D0-2*A*X0-2*B*Y0CC=CC-R**2.0D0DISCRIMINANT=BB**2.0D0-4*AA*CCIF (DISCRIMINANT .LT. 0) THENFLAG=-1ELSEIF (DISCRIMINANT .EQ.0) THENFLAG=0T1=-BB/(2.0DO*AA)Z1=XD*T+ZOIF ((Z1.LT.C) .OR. (21 .GT. H)) THENFLAG=-1ELSEX1=XD*T1+X0Y1=XD*T1+Y0X2=X1Y2=Y1Z2=Z1ENDIFELSEIF (DISCRIMINANT .GT. 0) THENFLAG=1T1=(-BB-DSQRT(DISCRIMINANT))/(2*AA)T2=(-BB+DSQRT(DISCRIMINANT))/(2*AA)Z1=ZD*T1+Z0Z2=ZD*T2+Z0IF (((Z1.LT.C).AND.(Z2.LT.C)).OR.((Z1.GT.H).AND.(Z2.GT.H)))&^THENFLAG=-1ELSEIF ((Z1.EQ.H).AND.(Z2.GT.H)) THENFLAG=0X1=XD*T1+X0Y1=YD*T1+Y0X2=X1Y2=Y1Z2=Z1ELSEIF ((Z1.EQ.C).AND.(Z2.LT.C)) THENFLAG=0X1=XD*T1+X0Y1=YD*T1+Y0108The program for the "Universal Model"X2=X1Y2=Y1Z2=Z1ELSEIF ((Z1.GT.H).AND.(Z2.EQ.H)) THENFLAG=OX2=XD*T2+XOY2=YD*T2+YOX1=X2Y1=Y2Z1=Z2ELSEIF ((Z1.LT.C).AND.(Z2.EQ.C)) THENFLAG=0X2=XD*T2+X0Y2=YD*T2+Y0X1=X2Y1=Y2Z1=Z2ELSEIF ((Z1.GT.H).AND.((Z2.LE.H).AND.(Z2.GE.C))) THENX2=XD*T2+X0Y2=YD*T2+Y0Z1=HT1=(Z1-Z0)/ZDX1=XD*T1+X0Y1=YD*T1+Y0ELSEIF ((Z1.LT.C).AND.((Z2.LE.H).AND.(Z2.GE.C))) THENX2=XD*T2+X0Y2=YD*T2+Y0Z1=CT1=(Z1-Z0)/ZDX1=XD*T1+XOY1=YD*T1+Y0ELSEIF ((Z1.LT.C).AND.(Z2.GT.H)) THENZ1=CZ2=HT1=(Z1-Z0)/ZDT2=(Z2-Z0)/ZDX1=XD*T1+X0Y1=YD*T1+Y0X2=XD*T2+X0Y2=YD*T2+Y0ELSEIF ((Z2.LT.C).AND.(Z1.GT.H)) THENZ2=CZ1=HT1=(Z1-Z0)/ZDT2=(Z2-Z0)/ZDX1=XD*T1+X0Y1=YD*T1+Y0X2=XD*T2+X0Y2=YD*T2+Y0ELSEIF(((Z1.LE.H).AND.(Z1.GE.C)).AND.(Z2.GT.H)) THENZ2=HT2=(Z2-Z0)/ZDX1=XD*T1+X0Y1=YD*T1+Y0X2=XD*T2+X0Y2=YD*T2+Y0ELSEIF(((Z1.GE.C).AND.(Z1.LE.H)).AND.(Z2.LT.C)) THENZ2=CT2=(22-Z0)/ZDX1=XD*T1+X0Y1=YD*T1+Y0X2=XD*T2+X0Y2=YD*T2+Y0ELSEX1=XD*T1+XO109The program for the "Universal Model"Y1=YD*T1+YOX2=XD*T2+X0Y2=YD*T2+YOENDIFENDIFIF (ABS(ZD).EQ.(1.0)) THENFLAG = 1X1 = XDYl = YDZl = CX2 = XDY2 = YDZ2 = C + HHENDIFIF (FLAG.EQ.1) THENAiX = X1 - XOA1Y = Yl - YOA1Z = Zl - ZOA2X = X2 - XOA2Y = Y2 - YOA2Z = Z2 - ZOAll = DSQRT(A1X**2 + A1Y**2 + A1Z**2)A22 = DSQRT(A2X**2 + A2Y**2 + A2Z**2)Bll = DSQRT(XD**2 + YD**2 + ZD**2)R1B = A1X*XD + A1Y*YD + A1Z*ZDR2B = A2X*XD + A2Y*YD + A2Z*ZDPHI1 = R1B/(All*B11)PHI2 = R2B/(A22*B11)IF (All.EQ.O.DO) THENPHI1 = R1B/B11ENDIFIF (A22.EQ.O.DO) THENPHI2 = R2B/B11ENDIFIF ((PHIl.LT.O.D0).AND.(PHI2.GE.O.D0)) THENX1 = XOYl = YOZl = ZOELSEIF ((PHI2.LT.O.D0).AND.(PHIl.GE.O.D0)) THENX2 = X1Y2 = YlZ2 = ZlX1 = XOYl = YOZl = ZOELSEIF ((PHIl.LT.O.D0).AND.(PHI2.LT.O.D0)) THENFLAG = -1ENDIFENDIFRETURNEND***************************************************************************************************************************************************************************** SUBROUTINE POSITIONINPUT ********************************************************************************************************************** THIS SUBROUTINE INPUTS THE POSITION OF THE RAIN CELL (XN,YN,ZN),* POSITION OF TRANSMITTER (XT,YT,ZT), DIRECTION OF TRANSMISSION* (XTHE_T,XPHI_T), POSITION OF RECEIVER (XR,YR,ZR), AND DIRECTION* OF RECEPTION (XXXXXX,YYYYYY)********************************************************************************SUBROUTINE POSITIONINPUT(XH,YH,ZH,XTHE_T,XPHI_T,&^XR,YR,ZR,XXXXXX,YYYYYY)*DOUBLE PRECISION XH,YH,ZH,XTHET,XPHIT,XR,YR,ZR,110The program for the "Universal Model"& XXXXXX,YYYYYYREAD*,XHREAD*,YRREAD*,ZHREAD*,XTHE_TREAD*,XPHI_TREAD*,XRREAD*,YRREAD*,ZRREAD*,XXXXXXREAD*,YYYYYY*RETURNEND************************************************************************************************************************************************************************* SUBROUTINE ROTATION ************************************************************************************************************************ THIS ROUTINE CALCULATES THE VALUES OF THE POINT TRANSFORMED TO THE* NEW COORDINATE SYSTEM. X,Y,Z ARE THE VALUES IN THE OLD COORDINATE* SYSTEM. XB,YB,ZB ARE THE VALUES OF X,Y,Z IN THE NEW COORDINATE SYSTEM.* THE TRANSFORMATION MATRIX IS:* IT11 T12 T131* IT21 T22 T231* IT31 T32 T331********************************************************************************SUBROUTINE ROTATION(T11,T12,T13,T21,T22,T23,T31,T32,T33,& X,Y,Z,XB,YB,ZB)DOUBLE PRECISION T11,T12,T13,T21,T22,T23,T31,T32,T33,& X,Y,Z,XB,YB,ZBCOMPUTING THE NEW X,Y,Z FROM THE TRANSFORMATION MATRIXXB=T11*X+T12*Y+T13*ZYB=T21*X+T22*Y+T23*ZZB=T31*X+T32*Y*T33*ZRETURNEND********************************************************************************************** SUBROUTINE UNIT VECTOR ***********************************************************************T************************************************ THIS SUBROUTINE CALCULATES THE UNIT VECTOR BETWEEN TWO POINT IN* SPACE.*******************************************************************************SUBROUTINE UNIT VECTOR(X1,Y1,Z1,X2,Y2,Z2,X,Y,Z)DOUBLE PRECISION X1,Y1,Z1,X2,Y2,Z2,X,Y,Z,DUMMY,DISTANCEDUMMY=DISTANCE(X1,Y1,Z1,X2,Y2,Z2)X=(X2-X1)/DUMMYY=(Y2-Y1)/DUMMYZ=(Z2-Z1)/DUMMY*RETURNEND********************************************************************************************* FUNCTION DISTANCE *************************************************************************************************************************** THIS FUNCTION CALCULATES THE DISTANCE BETWEEN TWO POINTS IN SPACE.* AND THE UNIT VECTOR BETWEEN THE TWO POINTS111The program for the "Universal Model"*******************************************************************************DOUBLE PRECISION FUNCTION 1DISTANCE(X1,Y1,Z1,X2,Y2,Z2)DOUBLE PRECISION X1,Y1,Z1,X2,Y2,Z2,X,Y,ZX=(X1-X2)**2.D0Y=(Y1-Y2)**2.D0Z=(Z1-Z2)**2.D0DISTANCE=DSQRT(X+Y+Z)*RETURNEND********************************************************************************************* FUNCTION RADAR CONST ***********************************************************************T***********************************************• THIS FUNCTION COMPUTES THE RADAR CONSTANT FROM THE INPUTS HALF_THETA• G1,G2,GT (GAINS) AND FREQUENCY IN GHz.*******************************************************************************SUBROUTINE CONST_RADAR(FREQ,HALF_THETA,G1,G2,GT,RADAR_CONST)*DOUBLE PRECISION FREQ,HALFTHETA,G1,G2,GT,RADAR_CONST*^PARAMETER(P1=3.14159265359D0,C=2.9979244574D8)GT=1.D0RADAR_CONST=(1/(256*PI**2.D0))*((C/(FREQ*1.D9))**2.D0)RADARCONST=RADARCONST*(HALFTHETA**2.D0)*Gl*G2*GTRETURNEND*************************************************************************************************************************************************************************** SUBROUTINE TRANSLATION *********************************************************************************************************************• THIS SUBROUTINE GIVES THE NEW COORDINATES XTRAN,YTRAN,ZTRAN OF THE POINT• X,Y,Z IN RELATION A NEW SET OF AXES XO,YO,ZO.****************i**************************************************************SUBROUTINE TRANSLATION(XO,YO,ZO,X,Y,Z,XTRAN,YTRAN,ZTRAN)*DOUBLE PRECISION XO,YO,ZO,X,Y,Z,XTRAN,YTRAN,ZTRAN*XTRAN=X-X0YTRAN=Y-YOZTRAN=Z-ZORETURNEND***************************************************************************************************************************************************************************** SUBROUTINE ANGLE *****************************************************************************************************************************• THIS SUBROUTINE COMPUTES THE ANGLE BETWEEN TWO 3-DIMENSIONAL• VECTORS. THE EQUATION USED IS COS(PHI)=X1*X2+Yl*Y2+Z1*Z2*SQRT(IA111A21)• WHERE PHI IS THE ANGLE BETWEEN THE VECTORS.********************************************************************************SUBROUTINE ANGLE(X1,Y1,Z1,X2,Y2,Z2,PHI)DOUBLE PRECISION X1,Y1,Z1,X2,Y2,Z2,NUM,DEN,PI,PHI,TEMPIPARAMETER(P1=3.14159265359D0)****112The program for the "Universal Model"NUM=X1*X2+Yl*Y2+Z1*Z2DEN=DSQRT((X1*Xl+Yl*Y1+Z1*Z1)*(X2*X2+Y2*Y2+Z2*Z2))TEMPI = NUM/DENIF (TEMPl.GT.1.D0) TEMPI = 1.D0PHI=DACOSD(TEMP1)RETURNEND********************************************************************************************** SUBROUTINE CROSS PRODUCT ********************************************************************************************************************THIS ROUTINE COMPUTES THE CROSS PRODUCT OF TWO VECTORS.• FOR EXAMPLE A=X1+Y1+Z1, B=X2+Y2+Z2• THE CROSS PRODUCT OF A X B IS COMPUTED.*******************************************************************************SUBROUTINE CROSS PRODUCT(X1,Y1,Z1,X2,Y2,Z2,X,Y,Z)DOUBLE PRECISION X1,Y1,Z1,X2,Y2,Z2,X,Y,ZX=Y1*Z2-Y2*Z1Y=X2*Z1-Xl*Z2Z=X1*Y2-X2*Y1RETURNEND***************************************************************************************************************************************************************************** SUBROUTINE SPHERE2RECT ***********************************************************************************************************************• THIS ROUTINE CONVERTS THE SPHERICAL COORDINATES ENTERED TO• RECTANGULAR COORDINATES. WHERE THE INPUTS ARE THETA(DEG),PHI(DEG),• RHO AND THE OUTPUTS ARE X,Y,Z*******************************************************************************SUBROUTINE SPHERE2RECT(X,Y,Z,THETA,PHI,RHO)DOUBLE PRECISION X,Y,Z,THETA,PHI,RHOX=RHO*DSIND(THETA)*DCOSD(PHI)Y=RHO*DSIND(THETA)*DSIND(PHI)Z=RHO*DCOSD(THETA)RETURNEND***************************************************************************************************************************************************************************** SUBROUTINE RECT2SPHERE ***********************************************************************************************************************• THIS ROUTINE CONVERTS THE RECTANGULA4R COORDINATES ENTERED TO• SPHERICAL COORDINATES. WHERE THE INPUTS ARE X,Y,Z AND• THE OUTPUTS ARE RHO, THETA(DEG), PHI(DEG).*******************************************************************************SUBROUTINE RECT2SPHERE(X,Y,Z,THETA,PHI,RHO)DOUBLE PRECISION X,Y,Z,THETA,PHI,RHOTHETA=DATAND(DSQRT(X*X+Y*Y)/Z)PHI=DATAND(Y/X)RHO=DSQRT(X*X+Y*Y+Z*Z)IF ((X.LE.0).AND.(Y.GE.0)) THENPHI = 180.DO + PHIELSEIF ((X.LE.0).AND.(X.LE.0)) THEN113The program for the "Universal Model"PHI = PHI + 180.DOELSEIF ((X.GE.0).AND.(Y.LE.0)) THENPHI = PHI + 360.DOENDIFIF ((ABS(Z).GT.O).AND.(X.EQ.0).AND.(Y.EQ.0))THENPHI=OENDIFIF (Z.LT.0) THENTHETA = 180.DO + THETAENDIFRETURNEND********************************************************************************************** SUBROUTINE SCAT TASK ************************************************************************T************************************************SUBROUTINE SCATTASK(F,THETA,PHI,S,RATE,FREQ,T,QUANTITY,• TASKNUMBER2,DECISION,H_THICKNESS)DOUBLE PRECISION F,THETA,PHI,S,RATE,FREQ,T,QUANTITY,H_THICKNESSINTEGER TASKNUMBER2CHARACTER*2 DECISIONIF (TASKNUMBER2.EQ.1) THENCALL SCATTERING(F,THETA,PHI,S,RATE,FREQ,T,QUANTITY,DECISION,H_THICKNESS)ENDIF*RETURNEND*********************************************************************************************** SUBROUTINE SCATTERING ***********************************************************************************************************************THIS SUBROUTINE COMPUTES FO, F(D)*********************************************************************************SUBROUTINE SCATTERING(F,THETA,PHI,S,RATE,FREQ,T,QUANTITY,DECISION,H_THICKNESS)DOUBLE PRECISION F,THETA,PHI,S,RATE,FO,F THETA PHI,QUANTITY,• FMDP,FD,FS,FD1,FD2,FD3,PI,T,FREQ,AiiEP,FRfQUENCY,FREQR,• N,NUM,F01,F02,F03,K,C,XI,STEMP,H_THICKNESS,RTEMP,REFCOMPLEX*16 E,M,MDPCHARACTER*2 DECISIONPARAMETER(P1=3.14159265359D0,C=2.9979244574D10)STEMP=1.D0IF (THETA.GT.90.D0) THENTHETA=180.DO-THETAENDIFIF (PHI.GT.180.D0) THENPHI=360.DO-PHIENDIFIF (S.LT.0.008D0) THENSTEMP=SS=1.D0ENDIFIF (RATE .LT. 0.25D0) THENRTEMP = RATERATE = 0.25D0ENDIFCALL A(S,RATE,AREP,QUANTITY)**114The program for the "Universal Model"XI=0.866D0*(1.DO+FREQ*1.5D-4)FREQR=C*XI/(2.D0*PI*A_REP)FREQUENCY=FREQ*1.D9K=FREQUENCY/FREQRN=(2.D0+200.D0*(K)**3.D0)/(1.D0+201.D0*(K)**3.D0)CALL NUMBER(RATE,NUM,S,QUANTITY)CALL PERMATIVITY(T,FREQUENCY,E,M)F01=400.DO*NUM*(XI**(2.DO*N))*PI*A_REP**2.D0F02=(ABSNE-1.D0)/(E+2.D0)))**2.D0F03=((K)**(2.DO*N))/(1.D0+(K)**(2.DO*N))FO=F01*F02*F03FD1=((l.DO+N)**2.D0)/(2.DO*N*(2.5D0*N-1.D0))FD2=((N**2.DO+K)/(1.D0+(N**2.D0)*K))**NFD3=(1.DO+RATE/300.D0)/2.D0FD3=FD3+((K**2.D0)/(1.DO+K**2.D0))*(1.DO-RATE/150.D0)FD=FD1*FD2*FD3MDP=-DIMAG(M)CALL FTP_FM_FS(F_THETA_PHI,FMDP,FS,XI,K,N,RATE,S,THETA,PHI,MDP)F =FO*F_THETAPHI*FD*FMDP*FSIF (STEMP.LT.0.008D0) THENS=STEMPF=F/1.D0IF (DECISION.NE .'Y') THENF = F*1.D0ENDIFIF ((DECISION.EQ.'Y').AND.(HTHICKNESS.EQ.O.D0)) THENF = F*1.D0ENDIFENDIFIF (RATE .LT. 0.25D0) THENF = F*RTEMP/0.25D0RATE = RTEMPENDIF*IF (S.EQ.O.DO) THENREF = 400.DO*RATE**1.4F = F02*REF*(PI**5)*(1.D-18)*(FREQUENCY/(C*0.01D0))**4ENDIFRETURNEND*********************************************************************************************************************************************************************** SUBROUTINE FTP FM FS ************************************************************************T**T****************************************************SUBROUTINE FTP_FM_FS(F_THETA_PHI,FMDP,FS,XI,K,N,RATE,S,THETA,PHI,MDP)DOUBLE PRECISION F THETA PHI,FMDP,FS,XI,K,N,RATE,S,THETA,PHI,MDP,F_TH1TF_ H2TF_ H3,FMDP1,FMDP2,FS1,FS2,FS3F TH1=(DSIND(THETA))**(2.DO/N)FITH2=(K/(1.DO+K))*(XI**2.D0)F TH3=(((DSIND(THETA))**3.D0)*DCOSD(PHI))F TH3=F TH3+.5D0*(DCOSD(THETA))**4.D0FITHETAIPHI=(FTH1+FTH2*FTH3)**NFMDP1=1.D0-(MDP/2.6D0)*(1.DO+RATE/600.D0)FMDP2=(MDP/2.6D0)*DSIND(THETA)*DCOSD(PHI)FMDP=1.DO+FMDP1*FMDP2*****115The program for the "Universal Model"*FS1=((150.D0/(150.DO+RATE))*25.D0*S/(1.DO+K**2.D0))FS1=(N**2.D0)*FS1**((1.D0-S)**4.D0)FS1=FS1*DSQRT(RATE/100.D0)FS2=((RATE+100.D0)/100.D0)*(1.D0-.5DO*K*(DSIND(PHI))**2.D0)FS3=((1.DO+K**2.D0)/(2.D0*N**2.D0))*DCOSD(PHI)*DSIND(THETA)FS=(FS1*(FS2+FS3))**(1.D0-S)RETURNEND***************************************************************************************** SUBROUTINE GET ATTEN ************************************************************************T*****************************************************• THIS SUBROUTINE INTERPOLATES THE ATTENUATION TABLE TO FIND THE• ATTENUATION FOR ANY RAIN RATE BETWEEN 1.25 AND 150 mm/hr. AND• ANY S BETWEEN 0.0 AND 1.0.• NOTE: IF THE RAIN RATE IS GREATER THAN 50 mm/hr. AND S IS NOT• EQUAL TO 1.0 THEN THE RESULT WILL BE INCORRECT. WE DO NOT HAVE VALUES• FOR THESE RAIN RATES AND S.• AT_TABLE IS THE RETURNED ATTENUATION VALUE FROM THE TABLE.*• AT^- ARRAY OF ATTENUATION FOR DIFFERENT RAIN RATES AND S• RATE^- THE ENTERED RAIN RATE* S^- THE ENTERED S• AT_TABLE - THE RETRIEVED ATTENUATION FROM THE ARRAY AT(INCLUDING INTERPOLATION)• R,SS^- ARRAYS OF RAIN RATE AND S TO FIND POSITION IN ARRAY• DUM1,DUM2- DUMMY VARIABLE TO HELP CALCULATE THE INTERPOLATED RESULT.*********************************************************************************SUBROUTINE GETATTEN(AT,RATE,S,ATTABLE)DOUBLE PRECISION AT(19,9),RATE,S,AT_TABLE,R(9),SS(19),DUM1,DUM2INTEGER I,P1,R2,S1,S2RAIN RATE AND S ARRAYS RESPECTIVELY TO FIND POSITION IN ARRAYDATA R/0,1.25,2.5,5,12.5,25,50,100,150/DATA SS/0,.02,.04,.06,.08,0.1,.12,.14,.16,.18,.2,.3,.4,.5,.6,.7,.8,.9,1.0/AT(0,0)=0FINDING POSITION OF ELEMENT.DO 10 1=1,8IF ((RATE.GT .R(I)).AND.(RATE.LE.R(I+1))) THENR1=1R2=I+1ENDIF10^CONTINUEDO 20 1=1,18IF ((S.GT.SS(I)).AND.(S.LE.SS(I+1))) THENS1=1S2=I+1ENDIF20 CONTINUE*IF ((RATE.EQ.0).OR.(S.EQ.0))THENAT_TABLE=0ELSEDUM1=(AT(S1,R2)-AT(S1,R1))*(RATE-R(R1))/(R(R2)-R(R1))+AT(S1,R1)DUM2=(AT(S2,R2)-AT(S2,R1))*(RATE-R(R1))/(R(R2)-R(R1))116The program for the "Universal Model"+AT(S2,R1)AT_TABLE=(DUM2-DUM1)*(S-SS(S1))/(SS(S2)-SS(S1))+DUM1ENDIF*RETURNEND**************************************************************************************** SUBROUTINE GET ARRAY ************************************************************************T******************************************************• THIS SUBROUTINE READS FROM THE FILE 'DATA1' ALL THE S AND RAIN RATE• VALUES FOR ONE FREQUENCY. IT THEN STORES THESE VALUES IN AN ARRAY• CALLED AT(S,RATE).********************************************************************************SUBROUTINE GETARRAY(FREQ,AT)DOUBLE PRECISION FREQ,AT(19,9),F(28),FR,R,SSINTEGER I,J,KDATA F/1,1.5,2,2.5,3,3.5,4,5,6,7,8,9,9.6,10,11,12,15,20,25,30,35,40,50,60,70,80,90,100/OPEN(UNIT=10,FILE='datal',STATUS='OLD')DO 20 J=1,28IF (F(J).EQ.FREQ) THENK=JJ=28ENDIF20^CONTINUEJ=153*(K-1)DO 10 I=1,JREAD(10,*)10^CONTINUEREAD(10,*),FRDO 30 1=2,9READ(10,*),RDO 40 J=2,19READ(10,*),SS,AT(J,I)40^CONTINUE30^CONTINUEDO 50 1=1,9AT(1,I)=050 CONTINUEDO 60 1=1,19AT(I,1)=060 CONTINUE*CLOSE(UNIT=10,STATUS='KEEP')*RETURNEND***************************************************************************************** SUBROUTINE GET AFB **************************************************************************T*****************************************************• THIS SUBROUTINE INTERPOLATES THE ATTENUATION, FORWARD, AND BACKWARD• SCATTERING FOR ANY RAIN RATE BETWEEN 1.25 AND 150 mm/hr. AND• ANY S BETWEEN 0.0 AND 1.0.• NOTE: IF THE RAIN RATE IS GREATER THAN 50 mm/hr. AND S IS NOT• EQUAL TO 1.0 THEN THE RESULT WILL BE INCORRECT. WE DO NOT HAVE VALUES• FOR THESE RAIN RATES AND S.AFB_TABLE IS THE RETURNED ARRAY FORM 'datal'ARRY^- THE ARRAY IN WHICH THE VALUES OF ATTENUATION,100 * FORWARD, AND 100* BACKWARD SCATTERING.RATE^- THE ENTERED RAIN RATES^- THE ENTERED VALUE OF S117The program for the "Universal Model"• AFB_TABLE- THE VALUE OBTAINED FROM THE ARRAY AFTER INTERPOLATION,(1) ATTENUATION, (2) FORWARD SCATTERING, (3) BACKWARDSCATTERING• R,SS^- THE VALUES TO WHICH THE ENTERED RAIN RATE AND S ARE COMPARED.• DUM1,DUM2- DUMMY VARIABLES• R1,R2^- INDEX VALUES TO GIVE POSITION OF ENTERED RAIN RATE IN ARRAY R• S1,S2^- INDEX VALUES TO GIVE POSITION OF ENTERED S IN ARRAY SS*********************************************************************************SUBROUTINE GET_AFB(ARRY,RATE,S,AFB_TABLE)DOUBLE PRECISION ARRY(19,9,3),RATE,S,AFB_TABLE(3),R(9),SS(19),• DUM1(3),DUM2(3)INTEGER I,R1,R2,S1,S2*• DATA TO WHICH ENTERED RATE AND S WILL BE COMPARED TO FIND POSITION*DATA R/0,1.25,2.5,5,12.5,25,50,100,150/DATA SS/0,.02,.04,.06,.08,0.1,.12,.14,.16,.18,.2,.3,.4,.5,.6,& .7,.8,.9,1.0/IF THE RAIN RATE OR S = 0 THEN RETURN ZERO FOR ATTENUATION,FORWARD SCATTERING, AND BACKWARD SCATTERINGIF ((RATE.EQ.0).OR.(S.EQ.0)) THENAFB_TABLE(1)=0AFB TABLE(2)=0AFB_TABLE(3)=0ELSEFINDING POSITION OF RAIN RATE ELEMENT.DO 10 1=1,8IF ((RATE.GT .R(I)).AND.(RATE.LE.R(I+1))) THENR1=IR2=I+1ENDIF10 CONTINUE* FINDING POSITION OF S ELEMENT.DO 20 1=1,18IF ((S.GT.SS(I)).AND.(S.LE.SS(I+1))) THENS1=IS2=I+1ENDIF20 CONTINUE*• LINEARLY INTERPOLATING TO FIND VALUE OF ATTENUATION,• FORWARD SCATTERING, AND BACKWARD SCATTERING.*DO 30 1=1,3DUM1(I)=(ARRY(S1,R2,I)-ARRY(S1,R1,I))*(RATE-R(R1))/(R(R2)-R(R1))+ARRY(S1,R1,I)DUM2(I)=(ARRY(S2,R2,I)-ARRY(S2,R1,I))*(RATE-R(R1))/(R(R2)-R(R1))+ARRY(S2,R1,I)CALCULATING ACTUAL RESULT.AFB_TABLE(I)=(DUM2(I)-DUM1(I))*(S-SS(S1))/(SS(S2)-SS(S1))+DUM1(I)30^CONTINUEENDIF*118**The program for the "Universal Model"RETURNEND**************************************************************************************** SUBROUTINE GET AFBARRY *** * * ****************************************************************** ,T******************************************************• THIS SUBROUTINE READS FROM THE FILE 'DATA1' ALL THE S AND RAIN RATE• VALUES FOR ONE FREQUENCY. IT THEN STORES THESE VALUES IN AN ARRAY• CALLED ARRY(S,RATE).** F^- POSSIBLE FREQUENCIES• FREQ^- CORRECT FREQUENCY USED• ARRY - ARRAY CONTAINING VALUES FOR ATTENUATION, FORWARD SCATTERING,AND BACK SCATTERING• FR^- FREQUENCY IN 'datal' FILE (NOT USED)*********************************************************************************SUBROUTINE GET_AFBARRY(FREQ,ARRY)DOUBLE PRECISION FREQ,ARRY(19,9,3),F(28),FR,R,SSINTEGER I,J,KF - THE FREQUENCIES USEDDATA F/1,1.5,2,2.5,3,3.5,4,5,6,7,8,9,9.6,10,11,12,15,20,25,30,35,40,50,60,70,80,90,100/OPENING FILE 'datal' TO READ ATTENUATION, FORWARD SCATTERING, ANDBACK SCATTERING.OPEN(UNIT=10,FILE='datal',STATUS='OLD')FINDING POSITION OF FREQUENCYDO 20 J=1,28IF (F(J).EQ.FREQ) THENK=JJ=28ENDIFCONTINUESKIPPING THROUGH FILE 'datal' TO CORRECT FREQUENCY.J=153*(K-1)DO 10 I=1,JREAD(10,*)CONTINUEREADING FREQUENCYREAD(10,*),FRREADING IN ATTENUATION, FORWARD SCATTERING, AND BACK SCATTERINGFOR DIFFERENT RAIN RATES.DO 30 1=2,9READ(10,*),RDO 40 J=2,19READ(10,*),SS,ARRY(J,I,1),ARRY(J,I,2),ARRY(J,I,3)ARRY(J,I,2)=ARRY(J,I,2)*100ARRY(J,I,3)=ARRY(J,I,3)*10040^CONTINUE30 CONTINUE*SETTING ATTENUATION, FORWARD SCATTERING, AND BACK SCATTERING TO ZERO119The program for the "Universal Model"• WHEN S=0 AND/OR RAIN RATE =0'*DO 50 1=1,9ARRY(1,I,1)=0ARRY(1,I,2)=0ARRY(1,I,3)=050 CONTINUEDO 60 1=1,19ARRY(I,1,1)=0ARRY(I,1,2)=0ARRY(I,1,3)=060 CONTINUE*CLOSE(UNIT=10,STATUS='KEEP')*RETURNEND*********************************************************************************************** SUBROUTINE RAIN TOTAL ATTENUATION ************************************************************T*****V*****************************************• THIS SUBROUTINE CALCULATES THE TOTAL RAIN ATTENUATION ALONG THE• LINE CONNECTING THE RECEIVER AND THE POINT TO WHICH THE TRANSMITTER• TRANSMITS TO.*X11,Y11,Z11X, Y, ZRTATTDTXD,YD,ZDXT, YT, ZTXA, YA, ZARATEXH, YHRMAXRODECISION- COORDINATES OF INTERSECTION OF MAIN BEAM OF RECEIVERAND RAIN CYLINDER- COORDINATES WHERE TRANSMITTER TRANSMITS TO- TOTAL RAIN ATTENUATION- SMALL INCREMENT OF T ALONG BEAM AXIS- DIRECTION OF LINE CONNECTING (X11,Y11,Z11) AND (X,Y,Z)- COORDINATES OF FIRST POINT BETWEEN OTHER COORDINATES- POINTS ALONG LINE CONNECTING THE TWO POINTS- CALCULATED RAIN RATE- CENTER OF RAIN CELL- MAX RAIN RATE (AT CENTER OF CELL)- RAIN RATE DISTRIBUTION VARIABLE- IS THERE A MELTING LAYER?*******************************************************************************SUBROUTINE RAIN_TOTAL_ATTENUATION(HMAX1,HFR,HM,HMIN,FREQ,• TE11,QUANTITY,X,Y,Z,X11,Y11,Z11,RTATT,XH,YH,RMAX,RO,DECISION,• TASKNUMBER1,NARR,A1NUM,ANUM,BNUM,XR,YR,ZR,H_THICKNESS,RAD,• XTHET)DOUBLE PRECISION X11,Y11,Z11,X,Y,Z,T,RTATT,DT,XD,YD,ZD,• XT,YT,ZT,DR,XA1,YA1,ZA1,TP1,HMAX1,HFR,HM,HMIN,S,RATE,• RTATT,FREQ,TEMP,QUANTITY,XH,YH,RMAX,RO,HMAX1,• NARR(2,3),A1NUM,ANUM,BNUM,ROM,D,XR,YR,ZR,ANGEP,• H_THICKNESS,XP1,YP1,ZP1,XM1,YM1,ZM1,MELTATTEN,XA2,YA2,• ZA2,RAD,XTHE_T,TP2,TE11,ATTENCHARACTER*2 DECISIONINTEGER I,TASKNUMBER1*XD=X11-XYD=Y11-YZD=Z11-ZT=(Z11-Z)/ZDRTATT=0DT=T/20.0D0XT=XD*DT+XYT=YD*DT+YZT=YD*DT+ZDR=DSQRT((XT-X)**2+(YT-Y)**2+(ZT-Z)**2)120The program for the "Universal Model"TP1 = -DT/2.D0DO 10 1=1,20TP1=DT+TP1XA1=XD*TP1+XYA1=YD*TP1+YZA1=ZD*TP1+ZCALL GET_S(HMAX1,HFR,HM,HMIN,ZA1,S,DECISION)CALL RAINRATE(XH,YH,X11,Y11,RMAX,RO,RATE)CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR,A1NUM,ANUM,BNUM)RTATT=RTATT+ATTEN*DR/100010 CONTINUERETURNEND*********************************************************************************************** ATT TASK *************************************************************************7***********************************************************SUBROUTINE ATT_TASK(FREQ,T,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR,A1NUM,ANUM,BNUM)DOUBLE PRECISION FREQ,T,RATE,S,ATTEN,QUANTITY,ATTE2,NARR(2,3),A1NUM,ANUM,BNUMINTEGER TASKNUMBER1IF (TASKNUMBER1.EQ.1) THENCALL LP(FREQ,T,RATE,S,ATTEN,QUANTITY)ELSEIF (TASKNUMBER1.EQ.2) THENCALL C_LP(FREQ,T,RATE,S,ATTEN,QUANTITY)ELSEIF (TASKNUMBER1.EQ.3) THENCALL M_ATTENUATION(FREQ,T,RATE,S,ATTEN,ATTE2,QUANTITY)ELSEIF (TASKNUMBER1.EQ.4) THENCALL MC ATTENUATION(FREQ,T,RATE,S,ATTEN,ATTE2,QUANTITY)ELSEIF (TASKNUMBER1.EQ.5) THENCALL SATTCALC(S,NARR,RATE,A1NUM,ANUM,BNUM,ATTEN)ENDIFRETURNEND*********************************************************************************************** SUBROUTINE EMPIRICAL) ATTENUATION******************************************************************7****************************************SUBROUTINE SATTCALC(S,N,RATE,A1,A,BNUM,ALPHA)DOUBLE PRECISION S,N(2,3),RATE,A1,M1,M2,FS,A2,M3,B3,B2,B1,A,BNUM,ALPHAPARAMETER(A2=1.7,M3=1,B3=230,B2=6,B1=20)IF (S.LT.1.0D0) THENM1=N(1,1)+N(1,2)*RATE".003+N(1,3)*RATE".0002M2=N(2,1)+N(2,2)*RATE".003+N(2,3)*RATE".0002FS=Ml*DEXP(-B1*S**A1)*S**(A1-1)FS=FS+M2*DEXP(-B2*S**A2)*S**(A2-1)FS=FS-M3*DEXP(-B3*S)+1**121The program for the "Universal Model"ELSEFS=1.0D0ENDIFALPHA=FS*A*RATE**BNUMRETURNEND********************************************************************************************** Al CALL *************************************************************************T************************************************************• THIS SUBROUTINE CALCULATES al FOR THE SUBROUTINE SATTCALC TO USE• IN THE. EQUATION FOR F(S) (SEE SATTCALC)*********************************************************************************SUBROUTINE Al_CALC(FREQUENCY,A1)DOUBLE PRECISION FREQUENCY,F,C(6),A1DATA C/1.680592398562237e+00,• -2.790804733796220e-03,• -3.417061223974332e+00,5.049293127489146e+00,4.707754939384348e-01,• -2.262928752321020e+00/F=FREQUENCYA1=C(1)+C(2)*F+C(3)*F**-1+C(4)*F**-2+C(5)*DEXP(-F)*F**2.1A1=Al+C(6)*F**-3RETURNEND************************************************************************************************* N CALL *************************************************************************T***********************************************************THIS SUBROUTINE CALCULATES Ni AND N2 WHICH ARE NEEDED TO CALCULATEMI AND M2.*N[1]^([2],^[3])1. 1 OR 2 FROM M1 OR M2 RESPECTIVELY2. 1 or 2 FOR LOW AND HIGH FREQUENCY RANGES.1=1-12 GHz.,^2=12-100^GHz.^IF^[1] =^1^(M1)1=1-20 GHz.,^2=20-100^GHz.^IF^[1] = 2^(M2)3. CAN BE 1,2,OR 3 FOR THE VARIABLE N1,N2,OR N3.********************************************************************************SUBROUTINE NCALC(FREQUENCY,N)DOUBLE PRECISION F,FREQUENCY,N1(2,3,7),N2(2,3,8),N(2,3)INTEGER IDATA (N1(1,1,I),I=1,7)/-4.468710233696790e+10,1.403226146957391e+08,-6.960027662822775e+08,4.506558794171744e+10,-6.421292889699095e+07,8.731179500736722e+08,1.401495928213695e+06/*DATA (N1(2,1,1),1=1,7)/-6.295278387177499e+10,***122The program for the "Universal Model"6.296355557484093e+10,5.966553195229598e+05,-3.888357198437326e+05,-1.923936894943743e+08,-1.822301639050625e+05,8.656888811513758e+04/DATA (N1(1,2,I),I=1,7)/-3.174987655808701e+09,1.000814015141864e+07,-4.938711808841844e+07,3.201787180190318e+09,-4.565132790730321e+06,6.211655984741843e+07,9.948011000116054e+04/DATA (N1(2,2,1),1=1,7)/-4.084602058168248e+09,4.085333281240790e+09,4.259904738584688e+04,-2.783771486082181e+04,-1.248919873419444e+07,-1.281758620243883e+04,6.233978784040986e+03/DATA (N1(1,3,I),I=1,7)/ 4.786234527835458e+10,-1.503307914573111e+08,7.454010806448646e+08,-4.826764045492385e+10,6.877779221467581e+07,-9.352359718254586e+08,-1.500976973852585e+06/DATA (N1(2,3,1),I=1,7)/6.702815890731934e+10,-6.703966103497658e+10,-6.392557379690040e+05,4.166781931398259e+05,2.048548402103934e+08,1. 950457764835905e+05,-9.280180321809524e+04/DATA (N2(1,1,1),1=1,8)/-2.099142532327721e+07,1.400026226688738e+07,-8.882786193005802e+05,1.989261675140147e+04,4.174527682005403e+06,1.593655028099594e+07,7.501240296862618e+05,-2.083589564285219e+07/DATA (N2(2,1,I),I=1,8)/-4.439610851013492e+07,-8.943850388853900e+05,6.292344533547490e+03,-1.902820302670007e+01,-2.522716953072156e+15,1.276598780066267e+14,-2.293117873033613e+04,1.952254679706120e+07/DATA (N2(1,2,I),I=1,8)/-1.493679774541824e+06,9.956472852260806e+05,-6.314103317406768e+04,1.413509106519248e+03,2.972144450610339e+05,1.134692648445301e+06,5.317895603908228e+04,-1.482614399143066e+06/123The program for the "Universal Model"DATA (N2(2,2,1),1=1,8)/-3.150283332144003e+06,-6.334729039970136e+04,4.455018565359137e+02,-1.346924157214865e+00,-1.803394805985552e+14,9.125776857644061e+12,-1.623153722957795e+03,1.384227230004449e+06/DATA (N2(1,3,I),1=1,8)/ 2.248517939626698e+07,-1.499594585442772e+07,9.514215725554167e+05,-2.130616396424133e+04,-4. 471624512634573e+06,-1.707130423100917e+07,-8.033028871120176e+05,6.^ 2.231858202049057e+07/DATA (N2(2,3,I),I=1,8)/4.754646862535044e+07,9.577316084775798e+05,-6.737837935928022e+03,2.037509693681765e+01,2.703059184218280e+15,-1.367857979044508e+14,2.455407948296932e+04,-2.090678544294405e+07/F=FREQUENCYIF ((F.GE.1).AND.(F.LT.12)) THENDO 10 1=1,3N(1,I)=N1(1,I,1)+N1(1,I,2)*F*F*DEXP(-F)+N1(1,I,3)*F**.2N(1,I)=N(1,I)+N1(1,I,4)*F**.01+N1(1,I,5)*F**.7N(1,I)=N(1,I)+N1(1,I,6)*DEXP(-F)+N1(1,I,7)*DSIN(F/.9)10^CONTINUEELSEIF ((F.GE.12).AND.(F.LE.100)) THENDO 20 1=1,3N(1,1)=N1(2,I,1)+N1(2,I,2)*F**.003+N1(2,I,3)*EXP(-100+F)N(1,I)=N(1,I)+N1(2,I,4)*(1/DCOSH(F-20))+N1(2,I,5)*DLOG(F)N(1,I)=N(1,I)+N1(2,1,6)*(1/DCOSH(F-40))N(1,I)=N(1,I)+N1(2,I,7)*DSIN(F/.08)20^CONTINUEENDIFIF ((F.GE.1).AND.(F.LT.20)) THENDO 30 1=1,3N(2,I)=N2(1,I,1)+N2(1,I,2)*F+N2(1,I,3)*F**2+N2(1,I,4)*F**3N(2,I)=N(2,I)+N2(1,1,5)*F*DEXP(-F)+N2(1,I,6)*F*F*DEXP(-F)N(2,I)=N(2,I)+N2(1,I,7)*DSIN(.6*(F-2.8))+N2(1,I,8)*DLOG(F)30^CONTINUEELSEIF ((F.GE.20) .AND.(F.LE.100)) THENDO 40 1=1,3N(2,I)=N2(2,I,1)+N2(2,I,2)*F+N2(2,I,3)*F**2+N2(2,I,4)*F**3N(2,I)=N(2,I)+N2(2,I,5)*F*DEXP(-F)+N2(2,I,6)*F*F*DEXP(-F)N(2,I)=N(2,I)+N2(2,1,7)*DSIN(.6*(F-2.8))+N2(2,I,8)*DLOG(F)40^CONTINUEENDIF**RETURNEND************************************************************************************************* A g **********************************************************124The program for the "Universal Model"*******************************************************************************• THIS SUBROUTINE COMPUTES THE VALUE OF a AND B FROM THE EQUATION^*^ bATTENUATION = a*r********************************************************************************** r^- RAIN RATEa - VARIABLE DEPENDENT UPON FREQUENCY.* b^- VARIABLE DEPENDENT UPON FREQUENCY.• Cl - CONSTANTS FOR b• C2^- CONSTANTS FOR a*********************************************************************************SUBROUTINE A_B(FREQUENCY,A,B)*DOUBLE PRECISION FREQUENCY,F,A,B,C1(9),C2(11)*DATA C1/1.175693749863705D+00,-5.372610249096163D-03,-1.451430379276010D-04,2.483615756859940D-06,-1.052429358496198D-08,-4.112419378557529D-01,-1.202673982695477D-01,3.133414878851311D-02,-2.717811349173657D-02/DATA C2/3.432142878826195D-03,2.930235190132424D-09,-9.239923589608143D-11,9.776864619131741D-13,-3.485507759140589D-15,6.906393023884164D-04,5.450508196170798D-06,-1.023109914867535D-02,1.232762310835401D-02,1.752618764932525D-02,1.566935461598425D-04/F=FREQUENCYCALCULATING bB=C1(1)+C1(2)*F+C1(3)*F**2+C1(4)*F**3+C1(5)*F**4B=B+C1(6)*F*F*DEXP(-F)+C1(7)*F**(-2)+C1(8)*DLOG(F)B=B+C1(9)*(1/(DCOSH(.2*(F-13))))CALCULATING aA=C2(1)*F**1.4+C2(2)*F**5+C2(3)*F**6+C2(4)*F**7+C2(5)*F**8A=A+C2(6)*DEXP(-F)*F**3+C2(7)+C2(8)*F+C2(9)*DLOG(F)A=A+C2(10)*DEXP(-F)+C2(11)*F**-9RETURNEND*********************************************************************************************** SUBROUTINE M ATTENUATION (M L&P) **********************************************************7***************************************************^SUBROUTINE MATTENUATION(FREQ,T,RATE,S,ATTEN,ATTE2,QUANTITY)DOUBLE PRECISION FREQ,T,RATE,S,A_REP,N,FREQR,ATTEN,GEDP,NUM,EADOUBLE PRECISION FREQUENCY,QUANTITY,ATTE2,C,RTEMP125The program for the "Universal Model"COMPLEX*16 G,GE,EPSILON,GAMMAPARAMETER(P1=3.14159265359DO,EA=1.DO,C=2.9979244574D10)IF (RATE .LT. 0.25D0) THENRTEMP = RATERATE = 0.25D0ENDIFIF (S.LT..002) THENATTEN=0ATTE2=0RETURNENDIFFREQUENCY=FREQ*1.D9CALL A(S,RATE,A REP,QUANTITY)FREQR=0.866D0*C/(2.D0*PI*A_REP)N=(2.D0+100.D0*(FREQUENCY/FREQR)**2.D0)N=N/(1.D0+101.D0*(FREQUENCY/FREQR)**2.D0)CALL NUMBER(RATE,NUM,S,QUANTITY)CALL G_LOWCASE(S,A_REP,G,T,FREQUENCY)GE=G/DCMPLX(1.D0,(FREQUENCY/FREQR)**N)GEDP=-DIMAG(GE)ATTEN=9.1D0*GEDP*NUM*1.D4*FREQEPSILON=EA*(1.D0+GE*NUM)GAMMA=2.D0*PI*FREQUENCY*CDSQRT(-4.D0*PI*1.D-7*EPSILON)ATTE2=DREAL(GAMMA)IF (RATE .LT. 0.25D0) THENATTEN = ATTEN*RTEMP/0.25D0RATE = RTEMPENDIFRETURNEND************************************************************************************************ SUBROUTINE MC ATTENUATION (MC L&P)**********************************************************7*************************************************SUBROUTINE MCATTENUATION(FREQ,T,RATE,S,ATTEN,ATTE2,QUANTITY)*DOUBLE PRECISION FREQ,T,RATE,S,A_REP,N,FREQR,ATTEN,GEDP,NUM,EADOUBLE PRECISION FREQUENCY,QUANTITY,ATTE2,C,FACTOR,GAM,RTEMPCOMPLEX*16 G,GE,EPSILON,GAMMA,E,MPARAMETER(P1=3.14159265359DO,EA=1.D0,C=2.9979244574D10,C1=20.958228)IF (RATE .LT. 0.25D0) THENRTEMP = RATERATE = 0.25D0ENDIFIF (S.LT..002) THENATTEN=0ATTE2=0RETURNENDIFFREQUENCY=FREQ*1.D9CALL A(S,RATE,A_REP,QUANTITY)FREQR=0.866D0*C/(2.D0*PI*A_REP)N=(2.D0+100.D0*(FREQUENCY/FREQR)**2.D0)N=N/(1.D0+101.D0*(FREQUENCY/FREQR)**2.D0)CALL NUMBER(RATE,NUM,S,QUANTITY)CALL G_LOWCASE(S,A_REP,G,T,FREQUENCY)**126The program for the "Universal Model"GE=G/DCMPLX(1.D0,(FREQUENCY/FREQR)**N)GEDP=-DIMAG(GE)ATTEN=9.1DO*GEDP*NUM*1.D4*FREQEPSILON=EA*(1.DO+GE*NUM)GAMMA=2.D0*PI*FREQUENCY*CDSQRT(-4.D0*PI*1.D-7*EPSILON)ATTE2=DREAL(GAMMA)CALL PERMATIVITY(T,FREQUENCY,E,M)GAM=100/REAL(FREQ*C1*CDSQRT(-E))FACTOR=1+((1-5*S)/5)*FREQUENCY/FREQRFACTOR=FACTOR*((N**2)*A_REP*(1-S)/(2*GAM))+1FACTOR=(FACTOR*(N+S*(1-N)))**(1-S)ATTEN=ATTEN*FACTORIF (RATE .LT. 0.25D0) THENATTEN = ATTEN*RTEMP/0.25D0RATE = RTEMPENDIFRETURNEND************************************************************************************************ SUBROUTINE LP ********************************************************************************************************************************SUBROUTINE LP(FREQ,T,RATE,S,ATTEN,QUANTITY)DOUBLE PRECISION FREQ,T,RATE,S,AREP,N,FREQR,ATTEN,GEDP,NUM,EADOUBLE PRECISION FREQUENCY, QUANTITY, C, RTEMPCOMPLEX*16 G,GEPARAMETER(PI=3.14159265359D0,EA=1.DO,C=2.9979244574D10)IF (RATE .LT. 0.25D0) THENRTEMP = RATERATE = 0.25D0ENDIFIF (S.LT..002) THENATTEN=0RETURNENDIFFREQUENCY=FREQ*1.D9CALL NUMBER2(RATE,NUM,S,A_REP,QUANTITY)FREQR=0.866D0*C/(2.D0*PI*A_REP)N=(2.D0+100.D0*(FREQUENCY/FREQR)**2.D0)N=N/(1.D0+101.D0*(FREQUENCY/FREQR)**2.D0)CALL NUMBER(RATE,NUM,S,QUANTITY)CALL G_LOWCASE(S,A_REP,G,T,FREQUENCY)GE=G/DCMPLX(1.D0,(FREQUENCY/FREQR)**N)GEDP=-DIMAG (GE)ATTEN=9.1DO*GEDP*NUM*1.D4*FREQIF (RATE .LT. 0.25D0) THENATTEN = ATTEN*RTEMP/0.25D0RATE = RTEMPENDIFRETURNEND************************************************************************************************ SUBROUTINE C LP (CORRECTED) ***************************************************************T**********************************************************127The program for the "Universal Model"*SUBROUTINE CLP(FREQ,T,RATE,S,ATTEN,QUANTITY)*DOUBLE PRECISION FREQ,T,RATE,S,AREP,N,FREQR,ATTEN,GEDP,NUM,EADOUBLE PRECISION FREQUENCY,QUANTITY,C,RTEMPCOMPLEX*16 G,GEPARAMETER(P1=3.14159265359D0,EA=1.DO,C=2.9979244574D10)IF (RATE .LT. 0.25D0) THENRTEMP = RATERATE = 0.25D0ENDIFIF (S.LT..002) THENATTEN=0RETURNENDIFFREQUENCY=FREQ*1.D9CALL NUMBER2(RATE,NUM,S,A_REP,QUANTITY)FREQR=0.866D0*C/(2.D0*PI*A_REP)N=(2.D0+100.D0*(FREQUENCY/FREQR)**2.D0)N=N/(1.D0+101.D0*(FREQUENCY/FREQR)**2.D0)CALL NUMBER(RATE,NUM,S,QUANTITY)CALL G_LOWCASE(S,A_REP,G,T,FREQUENCY)GE=G/DCMPLX(1.D0, (FREQUENCY/FREQR)**N)GEDP=-DIMAG (GE)ATTEN=9.1DO*GEDP*NUM*1.D4*FREQFACTOR=N*((2+S)*FREQUENCY/FREQR+1)/(FREQUENCY/FREQR+2-S)FACTOR=(FACTOR**(1-S**2))*((2-S)/(2+S))**(1-S)ATTEN=ATTEN*FACTORIF (RATE .LT. 0.2500) THENATTEN = ATTEN*RTEMP/0.25D0RATE = RTEMPENDIFRETURNEND***************************************************************************************************************************************************************************** SUBROUTINE G LOWCASE **********************************************************************T***************************************************• THIS SUBROUTINE CALCULATES g FROM THE EQUATION IN TABLE III• PG. 295 OF 'IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION',• DATED FEB. 1988.^THE NAME OF THE ARTICLE IS "A SIMPLIFIED• APPROACH TO THE EVALUATION OF EMW PROPAGATION CHARACTERISTICS• IN RAIN AND MELTING SNOW. IT USES THE SUBROUTINE 'PERMATIVITY'• TO GET THE PERMATIVITY OF OUTER LAYER.*******************************************************************************SUBROUTINE GLOWCASE(S,A_REP,G,T,FREQUENCY)COMPLEX*16 E,G,M,NUMER,DENDOUBLE PRECISION S,AREP,PI,Z,EA,E1,T,FREQUENCYPARAMETER(P1=3.14159265359D0,E1=1.20DO,EA=1.0D0)CALL PERMATIVITY(T,FREQUENCY,E,M)Z=4.DO*PI*A_REP**3.D0NUMER=(E-EA)*(2.D0*E+E1)-(1.D0-S)*(E-E1)*(2.D0*E+EA)DEN=(E+2.D0*EA)*(2.D0*E+E1)-2.D0*(1.D0-S)*(E-E1)*(E-EA)G=Z*NUMER/DEN****128The program for the "Universal Model"RETURNEND******************************************************************************************************************************************************************************* SUBROUTINE PERMATIVITY ********************************************************************************************************************** THIS SUBROUTINE INPUTS THE TEMPERATURE T IN DEG CELSIUS AND THE* FREQUENCY IN Hz.*******************************************************************************SUBROUTINE PERMATIVITY(T,FREQUENCY,E,M)REAL*8 LS,ALPHA,EI,TAO,ES,E1,E2,T,L,C,PI,ETREAL*8 FREQUENCYCOMPLEX*16 M,EC = 2.997924574D+10PI = 3.141592654D0TAO = 12.5664D+08L = C/FREQUENCYLS=0.00033836D0*DEXP((2513.98D0/(T+273.D0)))ALPHA=-16.8129D0/(T+273.D0) + 0.0609265EI=5.27137D0+0.0216474*T-0.00131198*T**2ES=1.0D0-4.597D-03*(T-25.D0)ES= ES+1.19D-05*(T-25.D0)**2 - 2.8D-08*(T-25.D0)**3ES = ES*78.54D0**234567890123456789012345678901234567890123456789012345678901234567890ET = 1.D0 + 2.D0*(LS/L)**(1.D0-ALPHA)*DSIN(ALPHA*PI/2.D0)ET = ET + (LS/L)**(2.D0*(1.D0-ALPHA))El = (ES-EI)*(1.D0+(LS/L)**(1.D0-ALPHA)*DSIN(ALPHA*PI/2.D0))El = El/ETEl = El + EI*E2 = (ES-EI)*(LS/L)**(1-ALPHA)*DCOS(ALPHA*PI/2.D0)/ETE2 = TAO*L/18.8496D+10 + E2*E= DCMPLX(E1,-E2)M = CDSQRT(E)END******************************************************************************************************************************************************************************* SUBROUTINE NUMBER *************************************************************************************************************************** THIS SUBROUTINE CALCULATES 'NUM', THE NUMBER OF DROPS PER UNIT VOLUME.* IT USES THE SUBROUTINES WHICH CALCULATE THE RAIN VELOCITY (VELRAIN)* AND REPRESENTATIVE RAIN RADIUS WHEN S=1 (NO SNOW).*******************************************************************************SUBROUTINE NUMBER(RATE,NUM,S,QUANTITY)DOUBLE PRECISION RATE,VELR,S,NUM,A_REP,V,S2PARAMETER(P1=3.14159265359D0)S2=1.D0CALL A(S2,RATE,A_REP,QUANTITY)CALL VELRAIN(A_REP,VELR)V=(1.5D0+(VELR-1.5D0)*DSIN(S*PI/2.D0))NUM=RATE/(48.0DO*PI*1.0D5*V*(AREP**3.D0))*RETURNEND*******************************************************************************129The program for the "Universal Model"***************** SUBROUTINE NUMBER2 *************************************************************************************************************************• THIS SUBROUTINE CALCULATES 'NUM', THE NUMBER OF DROPS PER UNIT VOLUME.• IT USES THE SUBROUTINES WHICH CALCULATE THE RAIN VELOCITY (VELRAIN)• AND REPRESENTATIVE RAIN RADIUS WHEN S=1 (NO SNOW).********************************************************************************SUBROUTINE NUMBER2(RATE,NUM,S,AREP,QUANTITY)DOUBLE PRECISION RATE,VELR,S,NUM,A_REP,V,S2,QUANTITYPARAMETER(P1=3.14159265359D0)S2=1.D0CALL A(S2,RATE,A_REP,QUANTITY)CALL VELRAIN(AREP,VELR)NUM=RATE/(48.00 *PI*1.0D5*VELR*(A_REP**3))V=(1.5D0+(VELR-1.5D0)*DSIN(S*PI/2.D0))AREP=AREP/M1-QUANTITY)+QUANTITY*S)**.33333333333333D0)NUM=NUM*VELR/V*RETURNEND*********************************************************************************************** SUBROUTINE A *********************************************************************************************************************************• THIS SUBROUTINE COMPUTES THE VALUE OF A REP, WHICH IS THE• REPRESENTATIVE RADIUS OF THE SNOW AND RAIN MIXTURE. IF S• IN THE FORMULA IS SET TO EQUAL '1', THIS ROUTINE WILL RETURN THE• VALUE OF A RAIN (JUST THE RAIN RADIUS). THE VARIABLE 'RATE'• IS THE RAIN RATE IN mm/hr.********************************************************************************SUBROUTINE A(S,RATE,AREP,QUANTITY)*DOUBLE PRECISION PI,DROP(15,11),RATE,P(14),DUMMY,A_REP,NORMALIZE,S,QUANTITYINTEGER 1,J,PARAMETER(PI=3.1415926535900)OPEN(UNIT=10,FILE='hydro',STATUS='OLD')3000 FORMAT(10(D6.0,X),D6.0)READ(10,3000)((DROP(I,J),J=1,11),I=1,15)CLOSE(UNIT=10,STATUS='KEEP')DO 110 J=3,10IF ((DROP(1,J).LE.RATE).AND.(DROP(1,J+1).GE.RATE)) THENDUMMY=(RATE-DROP(1,J))/(DROP(1,J+1)-DROP(1,J))DO 100 1=2,15P(I-1)=DUMMY*(DROP(I,J+1)-DROP(I,J))+DROP(I,J)100^CONTINUEJ=10END IF110 CONTINUE*NORMALIZE=0DO 120 1=1,14NORMALIZE=NORMALIZE+P(I)120 CONTINUE*DUMMY=0DO 130 1=1,14VS=1.5+(DROP(I+1,2)-1.5)*DSIN(PI*S/2)DUMMY=DUMMY+DROP(I+1,2)*(P(I)/NORMALIZE)/130The program for the "Universal Model"(((DROP(I+1,1)/2)**3)*VS)130 CONTINUEAREP=(DUMMY*((l.DO-QUANTITY)+QUANTITY*S))**(-.3333333333D0)RETURNEND********************************************************************************************** SUBROUTINE VELRAIN ****************************************************************************************************************************• RAIN VELOCITY WITH LINEAR INTERPOLATION.• THIS SUBROUTINE TAKES AS INPUT, THE DIAMETER OF THE RAINDROP (DIA),• AND ACCORDING TO THE TABLE ON PG.552 OF 'IEEE TRANSACTIONS ON• ANTENNAS AND PROPAGATION' AN ARTICLE CALLED "RAINFALL ATTENUATION OF• CENTIMETER WAVES: COMPARISON OF THEORY AND MEASUREMENT" BY• RICHARD G. MEDHURST, DATED JULY 1965, IT GIVES THE VELOCITY.• LINEAR INTERPOLATION IS USED TO GET THE VELOCITY• FOR WHICH THE DIAMETER IS NOT SPECIFIED IN THE TABLE.********************************************************************************SUBROUTINE VELRAIN(AREP,VELR)*DOUBLE PRECISION VELR,AREP,AREP,DUMMY*AREP=AREP*2.D0*DUMMY=DEXP(-DSQRT(115.D0)*(AREP+.05D0))VELR=5.44704233688D0-6.47412769848D0*DUMMYVELR=VELR-78.0827787323D0*(AREP+.05D0)*DUMMYVELR=VELR+6.883324065D0*DSQRT(AREP)-4.278474844DO*AREP**2.D0RETURNEND******************************************************************************************** SUBROUTINE RAINRATE *****************************************************************************************************************************• THIS SUBROUTINE CALCULATES THE RAIN RATE AT ANY POINT IN A RAIN CELL.*• XO,Y0^- BOTTOM CENTER COORDINATE LOCATION OF THE RAIN CELL.• X,Y - COORDINATE LOCATION WHERE RAIN RATE IS TO BE CALCULATED.• RMAX^- MAXIMUM RAIN RATE LOCATED AT (XO,Y0).• RATE - RETURNED RAIN RATE• RO^- INPUT PARAMETER WHICH CONTROLS THE DISTRIBUTION OF THERAIN RATE IN THE RAIN CELL.*********************************************************************************SUBROUTINE RAINRATE(X0,Y0,X,Y,RMAX,R0,RATE)*DOUBLE PRECISION XO,YO,X,Y,RMAX,RO,RATE*• CALCULATION OF RAIN RATE AT LOCATION (X,Y)*RATE=RMAX*DEXP(-DSQRTUX-X0)**2+(Y-Y0)**2)/R0)*RETURNENDTo implement the COST 210 rain cell model, replace RAIN_TOTAL_ATTENUATION**131The program for the "Universal Model"by:*********************************************************************************************** SUBROUTINE RAIN TOTAL ATTENUATION ************************************************************7*****T*****************************************• THIS SUBROUTINE CALCULATES THE TOTAL RAIN ATTENUATION ALONG THE• LINE CONNECTING THE RECEIVER AND THE POINT TO WHICH THE TRANSMITTER• TRANSMITS TO.*• X11,Y11,Z11 - COORDINATES OF INTERSECTION OF MAIN BEAM OF RECEIVERAND RAIN CYLINDER• X,Y,Z^- COORDINATES WHERE TRANSMITTER TRANSMITS TO• RTATT - TOTAL RAIN ATTENUATION• DT - SMALL INCREMENT OF T ALONG BEAM AXIS• XD,YD,ZD^- DIRECTION OF LINE CONNECTING (X11,Y11,Z11) AND (X,Y,Z)• XT,YT,ZT - COORDINATES OF FIRST POINT BETWEEN OTHER COORDINATES• XA,YA,ZA^- POINTS ALONG LINE CONNECTING THE TWO POINTS• RATE^- CALCULATED RAIN RATE• XH,YH - CENTER OF RAIN CELL• RMAX^- MAX RAIN RATE (AT CENTER OF CELL)• RO - RAIN RATE DISTRIBUTION VARIABLE• DECISION^- IS THERE A MELTING LAYER?*********************************************************************************SUBROUTINE RAINTOTAL_ATTENUATION(HMAX1,HFR,HM,HMIN,FREQ,• TE11,QUANTITY,X,Y,Z,X11,Y11,Z11,RTATT,XH,YH,RMAX,RO,DECISION,• TASKNUMBER1,NARR,A1NUM,ANUM,SNUM,XR,YR,ZR,H_THICKNESS,RAD,• XTHE_T)DOUBLE PRECISION X11,Y11,Z11,X,Y,Z,T,RTATT,DT,XD,YD,ZD,• XT,YT,ZT,DR,XA1,YA1,ZA1,TP1,HMAX1,HFR,HM,HMIN,S,RATE,• RTATT,FREQ,TEMP,QUANTITY,XH,YH,RMAX,RO,HMAX1,• NARR(2,3),A1NUM,ANUM,BNUM,ROM,D,XR,YR,ZR,ANGEP,• H_THICKNESS,XP1,YP1,ZP1,XMLYM1,ZM1,MELTATTEN,XA2,YA2,• ZA2,RAD,XTHE_T,TP2,TE11,ATTENCHARACTER*2 DECISIONINTEGER LTASKNUMBER1XD=X11-XYD=Y11-YZD=Z11-ZT=(Z11-Z)/ZDRTATT=0DT=T/20.0D0XT=XD*DT+XYT=YD*DT+YZT=YD*DT+ZDR=DSQRT((XT-X)**2+(YT-Y)**2+(ZT-Z)**2)TP1 = -DT/2.D0DO 10 1=1,20TP1=DT+TP1XA1=XD*TP1+XYA1=YD*TP1+YZA1=ZD*TP1+ZCALL GET_S(HMAX1,HFR,HM,HMIN,ZA1,S,DECISION)CALL RAINRATE(XH,YH,X11,Y11,RMAX,RO,RATE)132The program for the "Universal Model"CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR, A1NUM, ANUM, BNUM)RTATT=RTATT+ATTEN*DR/100010 CONTINUECALL GETS(HMAX1,HFR,HM,HMIN,Z11,S,DECISION)CALL RAINRATE(XH,YH,X11,Y11,RMAX,RO,RATE)ROM = 600.D0*RATE**(-0.5)*10.D0**(-(RATE+1.D0)**0.19)ROM = ROM*1000.D0IF (S.EQ.1.0D0) THEND = DSQRT((X11-XR)**2+(Y11-YR)**2)CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR,A1NUM,ANUM,BNUM)ATTEN = ATTEN*ROM*(1.D0-DEXP(-D/ROM))/1000.D0ANGEP = D/DSQRT((X11-XR)**2+(Y11-YR)**2 +(Z11-ZR)**2)ATTEN = ATTEN/ANGEPENDIFIF (S.EQ.0.D0.AND.H_THICKNESS.EQ.0.D0) THENZP1 = HFRS = 1.D0D = DSQRT((X11-XR)**2+(Y11-YR)**2)CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR,A1NUM,ANUM,BNUM)XD = X11-XYD^Yll-YZD = Z11-ZXP1 = XD*(ZP1-Z)/ZD + XYP1 YD*(ZP1-Z)/ZD + YZP1 = ZD*(ZP1-Z)/ZD + ZD2 - DSQRTHX11-XR)**2+(Y11-YR)**2)D1 = DSQRTUX11-XP1)**2+(Y11-YP1)**2)ATTEN = ATTEN*(DEXP(-D1/ROM) - DEXP(-D2/ROM))/1000.D0ANGEP = D/DSQRT((X11-XR)**2+(Y11-YR)**2 +(Z11-ZR)**2)ATTEN = ATTEN*ROM/ANGEPENDIFIF (S.LT.1.D0.AND.S.GT.O.D0) THENZM1^HMXD = X11-XYD = Y11-YZD = Z11-ZXM1 = XD*(ZM1-Z)/ZD + XYM1 = YD*(ZM1-Z)/ZD + YZM1 = ZD*(ZM1-Z)/ZD + ZT=(ZM1-Z11)/(ZM1-Z11)MELTATTEN = 0.D0DT-T/20.0D0TP1 = -DT/2.D0DO 420 1=1,20TP1=DT+TP1XA1=(XM1-X11)*TP1+X11YA1=(YM1-Y11)*TP1+YllZA1=(ZM1-Z11)*TP1+Z11CALL GET_S(HMAX1,HFR,HM,HMIN,ZA1,S,DECISION)CALL RAINRATE(XH,YH,X11,Y11,RMAX,RO,RATE)CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR, A1NUM, ANUM, BNUM)D2 = DSQRTHX11-XA1)**2+(Y11-YA1)**2)IF (I.EQ.1) THEND1 = 0ELSETP2 = TP1 - DTXA2^(XM1-X11)*TP2 + X11YA2 = (YM1-Y11)*TP2 + Yll133The program for the "Universal Model"ZA2^(ZM1-Z11)*TP2 + Z11D1 = DSQRTHX11-XA2)**2+(Y11-YA2)**2)ENDIFATTEN = ATTEN*(DEXP(-D1/ROM) - DEXP(-D2/ROM))/1000.D0D = DSQRTHX11-XR)**2+(Y11-YR)**2)ANGEP = D/DSQRT((X11-XR)**2+(Y11-YR)**2 +(Z11-ZR)**2)ATTEN = ATTEN*ROM/ANGEPMELTATTEN = MELTATTEN + ATTEN420^CONTINUES = 1.D0CALL RAINRATE(XH,YH,X11,Y11,RMAX,R0,RATE)CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR,A1NUM,ANUM,BNUM)D2 = DSQRT((X11-XR)**2+(Y11-YR)**2)D1 = DSQRT((X11-XM1)**2+(Y11-YM1)**2)ATTEN^ATTEN*(DEXP(-D1/ROM) - DEXP(-D2/ROM))/1000.D0ANGEP = D2/DSQRTHX11-XR)**2+(Y11-YR)**2 +(Z11-ZR)**2)ATTEN = ATTEN*ROM/ANGEPATTEN = ATTEN + MELTATTENENDIFIF (S.EQ.O.DO.AND.H_THICKNESS.NE.0.D0) THENZP1 = HFRZM1 = HMXD = X11-XYD = Yll-YZD = Z11-ZXP1 = XD*(ZP1-Z)/ZD + XYP1 = YD*(ZP1-Z)/ZD + YZP1 = ZD*(ZP1-Z)/ZD + ZXM1 = XD*(ZM1-Z)/ZD + XYM1 = YD*(ZM1-Z)/ZD + YZM1 = ZD*(ZM1-Z)/ZD + ZT=(ZM1-ZP1)/(ZM1-ZP1)MELTATTEN = 0.D0DT=T/20.0D0TP1 = -DT/2.D0DO 40 1=1,20TP1=DT+TP1XA1 = (XM1-XP1)*TP1+XP1YA1 = (YM1-YP1)*TP1+YP1ZA1 = (ZM1-ZP1)*TP1+ZP1CALL GET S(HMAX1,HFR,HM,HMIN,ZA1,S,DECISION)CALL RAIi4RATE(XH,YH,X11,Y11,RMAX,RO,RATE)CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR,A1NUM,ANUM,BNUM)D2 = DSQRT((X11-XA1)**2+(Y11-YA1)**2)IF (I.EQ.1) THEND1 = DSQRTUX11-XP1)**2 + (Y11-YP1)**2)ELSETP2 = TP1 - DTXA2 = (XM1-XP1)*TP2+XP1YA2 = (YM1-YP1)*TP2+YP1ZA2 = (ZM1-ZP1)*TP2+ZP1D1 = DSQRT((X11-XA2)**2+(Y11-YA2)**2)ENDIFATTEN = ATTEN*(DEXP(-D1/ROM) - DEXP(-D2/ROM))/1000.D0D = DSQRTUX11-XR)**2+(Y11-YR)**2)ANGEP = D/DSQRTUX11-XR)**2+(Y11-YR)**2 +(Z11-ZR)**2)ATTEN = ATTEN*ROM/ANGEPMELTATTEN = MELTATTEN + ATTEN40^CONTINUES = 1.D0134The program for the "Universal Model"CALL RAINRATE(XH,YH,X11,Y11,RMAX,RO,RATE)CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR,A1NUM,ANUM,BNUM)D2 = DSQRT((X11-XR)**2+(Y11-YR)**2)D1 = DSQRT((X11-XM1)**2+(Y11-YM1)**2)ATTEN = ATTEN*(DEXP(-D1/ROM) - DEXP(-D2/ROM))/1000.D0ANGEP = D2/DSQRTHX11-XR)**2+(Y11-YR)**2 +(Z11-ZR)**2)ATTEN ATTEN*ROM/ANGEPATTEN ATTEN + MELTATTENENDIFRTATT = RTATT + ATTEND = SQRT(XH**2 + YH**2)ATTEN = 0.D0IF (D.GT.RAD) THEND = D - RADS = 1.D0CALL RAINRATE(XH,YH,X11,Y11,RMAX,RO,RATE)CALL ATT_TASK(FREQ,TE11,RATE,S,ATTEN,QUANTITY,TASKNUMBER1,NARR,A1NUM,ANUM,BNUM)ATTEN = ATTEN*ROM*(1.DO-DEXP(-D/ROM))/1000.D0ANGEP = 90.DO - XTHE_TANGEP = DCOSD(ANGEP)ATTEN = ATTEN/ANGEPENDIFRTATT = RTATT + ATTENRETURNENDThe following is a sample input to the program:5^, Select attenuation model [note 1]1 , Select Scattering model [note 2]0^f (X,0,y,0^, z) of the centre of the rain cell60 , THE_T_ [note 3]0^, PHI _T_ [note 3]200000^, (x,0^I y,0 , z) of the receiver89.14063, THE_R_ [note 4]180^, PHI _R_ [note 4]0 , TR_ ALPHA [note 5]0.02^, TR HALF THETA_^_ [note 6]0^, RE _ALPHA [note 7]0.02^, RE HALF THETA_^_ [note 7]Y^, Is there a melting snow layer [note 8]135The program for the "Universal Model"5200^, height of melting layer (Hm - T)800^, thickness of melting layer (T)6000^, Hc20000^, radius of the rain cell10000^ro12.5^, The maximum rain rate at the centre of the rain cell1^, Frequency in GHz0 , Temperature in degrees Celcius.9^m^ [note 9]50 , Steps of integrations in meters100000 , Transmitter gain50000^, Receiver gain0.4 [note 10]5.5 [note 10]-18^ [note 10]6000 Hcnote 1^An input to select the attenuation model to be used in the calculations."1"is used for Kharadly's first attenuation model"2"is used for Kharadly's third attenuation model"3"is used for Kharadly's second attenuation model"4"is used for Kharadly's fourth attenuation model"5" is used for the empirical formulanote 2^An input to select the Scattering model to be used in the calculations.Cuurentelly, we have only one scattering model (Kharadly's).note 3^THE_T is B tPHI_T is cbtnote 4^• THE_R is OrPHI_R is Or136The program for the "Universal Model"note 5^Determine the polarization of the transmitting antenna"0", "180", "360" is for vertical polarization"90", "270" is for horizental polarizationnote 6note 7note 8note 9note 10A number can be chosen between 0 to 360.• The double-sided half-power bandwidth of the transmitterparameter that currentelly does not enter into calculationsIs there a melting snow layer:If "N"o, then skip ignore the next two lines (do not enter them)If "Y"es, then enter (Hm - T) and TThe No case need not be used since we can enter T = 0m = 1 — psm ranges between 0.7 to 0.9The empirical formula will treat m to be 0.9 whatever the input isIn this case:(a l , a2, K) = (0.4, 5.5, — 18) for the receiver antennanote^The Transmitter is assumed to be at the centre of the main coordinatesystem.The program can be (and should be) further refined as to make it more efficient andto incorporate more features.137CCIR Document 12-3/29 (Rev. 1) and supplementAppendix F CCIR Document 12-3/29(Rev. 1) and supplementCanada's contribution to CCIR Study group (Working Party 5C), document 12-3/29(Rev. 1) titled EFFECT OF THE MELTING LAYER ON HYDROMETEOR SCATTERINTERFERENCE AND COORDINATION DISTANCE is reproduced on p. 139-148.[4]The error statistics for COST 210 [7] paths, extracted from a paper to be submittedto the IEEE Proceedings, is reproduced on p. 149-152. *Olsen, R.L., Kharadly, M.M.Z. and Hulays, R.A, "Effect of hydrometeors in and above the melting layer on scatter interference,"IEEE Proceedings on Electromagnetic Propagation in Rain, early 1993.138CCIR Document 12-3129 (Rev. 1) and supplement1DocumentsCCIR Study GroupsPeriod 1990-1994Received: 16 January 1992Delayed ContributionDocument 12-3/29 (Rev. 1)8 January 1992Driginal: EnglishEFFECT OF THE MELTING LAYER ON HYDROMETEOR SCATTER INTERFERENCE ANDCOORDINATION DISTANCE1. IntroductionThe Working Party 5C Revision of Recommendation 620 (Doc. SC/TEMPS) includesa simple modification to the model for the hydrometeor scatter mechanism of Report 724-2to take into account the 6.5 dB/km fall off in reflectivity above the rain height. Because theold method in Report 724-2 assumed a constant reflectivity up to heights above the rainheight, the effect of the modification is to significantly reduce the coordination distance Inmany circumstances. The intent of the modification to bring the model into better agreementwith physical reality in a relatively simple way Is believed to be a good one. Unfortunately,the modification may now err too much in the optimistic direction, particularly for the 4-6GHz band, because it ignores the effect of the melting layer. A Canadian document consideredby Working Party 5C at its recent meeting gave some preliminary model calculations of theeffect of the melting layer on relative interference levels. The predicted enhancement ofinterference as a result of the melting layer was the same order as that indicated by somelimited experimental results available at the time [COST 210, 1991]. This documentpresents some additional model calculations that illustrate the effect of both melting layerscattering and attenuation on coordination distance. Further comparison is also made withexperimental results available for frequencies above 11 GHz [COST 210, 1991].1. Model for scattering cross-section of melting snowflakesThe model for the scattering cross-section of melting snowflakes [Kharadly, 1990]is based on an extension of three main physically-based empirical approximationsinvestigated by Kharadly and Choi [1988) for attenuation by melting snow flakes. First ofall, it is assumed for the purposes of interference calculations that the melting snow flakescan be approximately represented by water-coated snow spheres (The density of 0.1 g/cm 3of the snow core was based on measurements of Matsumoto and Nishltsujo [1971].)Secondly, a physically-based empirical extension of the Rayleigh scattering cross-section isintroduced for frequencies above the Rayleigh region. Thirdly, it is assumed that adistribution of particle sizes can be replaced by a single particle of representative size.Three additional empirical correction factors were also introduced by Kharadly [1990] togive improved agreement with Mie scattering calculations. The particle-size distributionused to determine the representative particle size for the melting layer is such that itreduces to a Laws and Parsons drop-size distribution for the rain below and satisfies theconservation of mass criterion (Kharadly and Kishk, 1991]. (The Initial distribution usedby Kharadly and Choi [1988] for melting snow particles violated conservation of mass.)Example comparisons between the model cross-sections (Model I) and Mie scatteringcross sections for the forward scattering direction are given in Figures 1 and 2 for rain(degree of melting S.1) and a modelled melting snow medium with 10% by volume of theouter shell of the particle melted (5.0.1). (The Model II curves given are based on adifferent set of assumptions and are not used here [Kharadly, 1990].) These resultsindicate the validity of all approximations noted above except the first, the shape andcomposition of the particles themselves. An additional investigation [Kharadly, 1991a] hasdemonstrated that uniformly-randomly-oriented (and even to some extent non-uniformly-139CC1R Document 12-3129 (Rev. 1) and supplement2randomly-oriented) water-coated snow spheroids can be adequately approximated bywater-coated snow spheres for the purposes of interference calculations.The water-coated snow sphere model employed results in a radar reflectivity peak inthe melting layer of about 16 dB with respect to that of rain of equivalent rain rate. Thiscompares with some values of about 12 dB observed from radar measurements [Klassen,1988]. Any such measurements, however, will tend to reduce the peak value because ofvolumetric averaging. Even more averaging will occur in radar measurements of statisticalreflectivity profiles [e.g., COST 210, 1991]. The model is sufficiently flexible, however,so as to allow the peak reflectivity to be adjusted to fit the data. An increase in the snow coredensity, for example, will reduce the size of the model snow scatterers and therefore thereflectivity peak. Such adjustments can also be made to obtain best fits to actual meltinglayer attenuation data [Kharadly and Kishk, 1991].2. Models for specific attenuation by melting snowflakesThree models have been developed for specific attenuation of melting snowflakes[Kharadly 1991 b], all of which employ the three main physically-based empiricalapproximations noted above. The differences between the models are the additionalempirical correction factors which have been introduced to give improved agreementbetween the model calculations and Mie calculations for water coated snow spheres. Finally,a totally empirical model has been developed [Hulays, 1991] of the formA. An(R,S) aRb^ ( 1 )where R is the precipitation rate and S is the degree of melting, with aRb the well-knownform for rain [Olsen et al., 1978]. This model, which also gives good agreement with Miescattering calculations, is conveniently used for the interference calculations presented inthis document.3. Macroscopic meteorological modelsThe horizontal structure of the fixed-position rain cell employed in the rain scatterand rain attenuation calculations is that currently assumed in Revised Recommendation452-4 (Doc. 5C/TEMP9) and used previously in Report 569-4 and also by COST 210[1991]. The center of the cell is positioned at the intersection of the antenna beam axes.The diameter of the melting layer cell is assumed to be the same as that of the rain cell belowit, and the melting layer attenuation is assumed to reduce at the same exponential rate as therain attenuation outside the core cell. Since the specific melting layer attenuation varieswith height within the melting layer, a numerical integration is carried out in the verticaldirection.The depth Dm of the melting layer is assumed to vary with reflectivity factor Z of therain in the form [Klassen, 1988]Dm .100 Z 0 . 17^( 2 )Dm is related to the precipitation rate R through the relation Z • 400R 1.4 .The height of the melting layer is assumed to be fixed, but the effect of differentvalues of this fixed height have been calculated. As demonstrated elsewhere [COST 210,1991], the height of the melting layer varies considerably and the most accuratecalculations should assume a distribution of heights. However, within any given month suchas the worst month, the range in distribution of heights will be smaller and the use of a fixedheight should give a reasonably close upper bound to the effect of the melting layer.The variation in the melting profile of the melting layer (i.e., variation in S between0 at the by and 1 at the bottom) is assumed to be linear Kharadly and Choi, 1988]. Otherprofiles are considered elsewhere [Kharadly and Kishk, 1991].140CCIR Document 12-3129 (Rev. 1) and supplement3The effect of the ice and dry snow medium above the melting layer was not Included inthe calculations of the earlier Canadian document considered by Working Party 5C. Thisapproximation has now been eliminated. Rayleigh scattering by the ice and snow mediumabove the melting layer is assumed along with a reflectivity of Z • 400R 1 .4 at the lowerboundary of this medium (the so-called 'rain height") decreasing with height at the rate of-6Z dB/km as required In Revised Recommendations 620 (Doc. 5C/TEMP9) and 452-4(Doc. 5C/TEMP9). The elimination of this approximation has turned out to be moreImportant than previously believed since the attenuation of an Intervening melting layertends to reduce the contribution of this ice and snow region relative to Its contributionwithout a melting layer, the effect of course increasing with Increasing frequency. Theoverall result at the higher frequencies is that the relative effect of Including the meltinglayer in the model calculations is less, even when the melting layer is at the optimumheight. However, since existing experimental data [COST 210, 1991] are used as areference, the difference does not change the conclusions.4. Other assumptionsOther assumptions made In the calculations are consistent with the 'extended CCIRmodel" discussed elsewhere [COST 210, 1991). These include an assumption of nopolarization mismatch, a narrow-beam approximation for the earth-station antenna, andGaussian-shaped main-lobe and side-lobe patterns (highest side-lobe gain of 15 dB downassumed) for the terrestrial antenna. Atmospheric attenuation, ignored in the calculationsof the earlier Canadian document, Is now included using the model in RevisedRecommendation 452-4 (Doc. 5C/TEMP9), although the contribution is small at thefrequencies considered.5. Results for sample Interference geometriesTwo curves of transmission loss as a function of rainrate are given in Figure 3 forthe experimental parameters of the Chilbolton-Baldock link [COST 210, 1991] (e.g.,frequency of 11.2 GHz and a station separation of 131 km). The solid curve is for rain onlyand the dashed curve for rain plus melting layer. The latter is not shown above 30 mm/hbecause the existence of a melting layer above this precipitation rate Is considered unlikely.The terrestrial and earth-station elevation angles of 1.0° and 20°, respectively, place thecenter of the common volume at a height of about 3.0 km. The bottom of the melting layer ispositioned at this height, which approximately maximizes the interference effect of themelting layer. Other parameters are indicated in the caption.As seen from Figure 3, the effect of the melting layer increases with increasingrainrate (and increasing melting layer thickness) until above about 5 mm/h, where theeffect of attenuation in the melting layer begins to outweigh the effect of increased scatteringcross section. At rainrates of 8, 13, 15, 19, and 29 mm/h, the interference level isapproximately 2.5, 2.2, 2.0, 1.8, and 1.5 dB higher, respectively, than it would be if therewere rain in place of the melting layer. This compares with melting layer enhancements of1.7 and 2.7 dB exceeded for 0.1% and 0.01% of the time in the worst season (summer).These values were estimated from a comparison of actual data for summer and winter at twocommon volume altitudes (data provided courtesy of Rutherford-Appleton Laboratory; seealso Revised Recommendation 452-4 (Doc. 5C/TEMP9)). In composite rain climate C,D,E,these exceedances correspond to rainrates of 8 and 19 mm/h on an annual basis, or about 13and 29 mm/h on a worst season basis. A rainrate of about 15 mm/h is exceeded for 0.1% ofthe worst month in the same rain climate. The worst season enhancements of 1.7 and 2.7 dBat the 0.1% and 0.01% exceedance levels will also be observed in the annual distributionsbut at smaller exceedance levels. It Is interesting, but possibly a coincidence, that theannual distributions of interference level predicted for the Chilbolton-Baldock link by themethod of Revised Recommendation 452-4 (Doc. 5C/TEMP9) underestimate the measureddistributions by about the amount of the melting layer enhancement obtained from theseasonal measurements.As evident from the comparison of model and experimental estimates of theenhancement in interference caused by the presence of the melting layer, the latter is close141CCIR Document 12-3129 (Rev. 1) and supplement4to the optimum estimated value (1.7 versus 2.0 dB) at 0.1% of the worst season and greaterthan the optimum estimated value (2.7 dB versus 1.5 dB) at 0.01%. This suggests thateither the height variation of the melting layer in the summer is not large or that theexperimental estimates are a little on the high side, at least at 0.01% of the worst season.(The melting layer was known to occur approximately at the common volume height onChilbolton-Baldock link during the summer months (COST 210, 19911.) It should be noted,however, that it is possible in principal for melting layer and associated precipitationscatter a low precipitation rates to contribute to the interference levels exceeded forsmaller percentages of time than the corresponding precipitation rate. There will be someinstances, for example, when the melting layer and rain attenuation associated with thescattering will be smaller than that predicted by a model estimating the average attenuation(e.g., if the scatter volume were on the edge of the precipitation cell without muchattenuation outside the common volume). In any case, the combined experimental and modelresults suggest that the effect of the melting layer is too significant to ignore when thescatter volume is at about the height of the melting layer in any given month or season, evenat 11.2 GHz. The increase in coordination distance required to offset the effect of the meltinglayer enhancement of 1.7 dB exceeded for 0.1% of the time in the worst season is 21 km.Results are given in Figure 4 for the same parameters of the Chilbolton-Baldocklink, but at a frequency of 4 GHz. Here the height of the center of the melting layer ispositioned at the height of the center of the common volume, which approximately'optimizer the enhancement of the melting layer. The 'optimum' enhancements are 6.6,7.5, 7.8, 8.3, and 9.2 dB at rainrates of 8, 13, 15, 19, and 29 mm/h, respectively. On thebasis of a frequency scale factor of 3.4 derived from the enhancement ratio 7.5/2.2 at arainrate of 13 mm/h, the measured enhancement of 1.7 dB at 11.2 GHz scales to 5.8 dB at 4GHz. Similarly, the measured enhancement of 2.7 dB ( -optimum' estimated value of 1.5dB) at 11.2 GHz scales to 16 dB (9.2 dB for 'optimum' value) at 4 GHz on the basis of afrequency scale factor of 9.2/1.5.6.1 derived from the enhancement ratio at 29 mm/h. Amore optimistic scale factor of 3.9 derived from the enhancement ratio of 7.8/2.0 at 15mm/h would reduce the latter figure to 5.9 dB. The increase in coordination distance neededto offset a 5.9 dB enhancement for a rainrate of 15 mm/h at 4 GHz is 66 km.In agreement with calculations obtained elsewhere [COST 210, 1991], calculationsfor higher frequencies using the current model indicate that the effect of the melting layeron interference continues to diminish as a result of increasing attenuation both in the rainand the melting layer. The 2.8 dB 'optimum" enhancement estimated at 1.1.2 GHz fromFigure 3, for example, is reduced to about 0.7 dB at 20 GHz.Certain geometries for which the effect of attenuation outside the common volume isreduced should pose problems up to quite high frequencies. One such geometry is that of anintersection or near-intersection between two earth-station beams pointed at elevationangles significantly higher than that of the average terrestrial station antenna. Such ageometry was investigated at 11.4 GHz on a 9.3 km side-scatter link near Graz [COST 210,1991]. The model calculations for this link, with and without the melting layer, are givenin Figure 5. Here the top of the melting layer is positioned 0.1 times Its thickness from thecenter of the -common volume at 2.9 km height to obtain "optimum" enhancements of 5.8,6.4, and 2.9 dB at 2, 10, and 30 mm/h, respectively. (Corresponding figures for afrequency of 20 GHz are 1.9, 1.5, and 0 dB.) Rainrates of 2, 10, and 32 mm/h are exceededfor 1%, 0.1%, and 0.01% of the year for composite rain climate F-K corresponding to thatof Graz. It is interesting that the annual distributions of interference level predicted for theGraz link by the method of Revised Recommendation 452-4 (Doc. 5C/TEMP9)underestimate the measured distributions by amounts ranging from 12 dB to 6 dB betweenthe corresponding exceedance levels of 1% and 0.01% of the time on an annual basis [COST210, 1991]. The enhancement caused by the melting layer can perhaps explain much ofthis large discrepancy.142CCIR Document 12-3129 (Rev. 1) and supplement56. Discussion and ConclusionsThe model results given and supporting comparisons with experimental data suggestthat the effect of the melting layer should be taken into account in both coordination distancecalculations (such as those obtained from Revised Recommendation 620 (Doc. 5C/TEMP6))and detailed interference calculations (such as those obtained from Revised Recommendation452-4 (Doc. 5C/TEMP9)). This is most important for the 4-6 GHz band where the effectsof rain and melting layer attenuation are least significant with respect to that of thescattering. Another way of looking at the results is that the apparent increase in theInterference level introduced by the presence of the melting layer is larger than that inchanging from one composite rain climate to another (e.g., climate C,D,E to Climate F-K). Ifthe use of such "fine" climatic differences is justified, then the introduction of the apparenteffect of the melting layer would seem even more justified.Of course scattering from rain and the dry snow and ice region above the meltinglayer are only important from an interference coordination viewpoint if there Is a mainbeam Intersection. Clearly the chance of such a main-beam intersection occurring is verysmall, which is no doubt one reason that interference due to hydrometeor scatter hasapparently not been observed in practice. Even if an interference causing main-beamintersection or near-intersection had occurred in the past, it would not be surprising forthe interference to have remained unobserved. Interference due to hydrometer scatter it notgenerally as long lasting as that resulting from the clear-air mechanisms. Furthermore,performance monitoring has not been generally carried out. Even If a deterioration inperformance were observed, there would be no easy way of knowing If It were due tointerference or to attenuation of the wanted signal.At first sight the chances of having a main-beam intersection and a melting layeroccurring within it at the time of year when precipitation intensities are greatest wouldseem to be even smaller than having a main-beam intersection occurring within rain. Thisis no doubt true for short distances between terminals with the main-beam intersectionsoccurring at low altitudes. However, at the 100 km and larger distances for coordinationthe main-beam intersections occur at altitudes for which the melting layer also occurs inthe summer months, at least at temperate latitudes. Thus, it would appear that the meltinglayer should always have some influence on coordination at these latitudes in the frequencybands including and below the 11.14 GHz band.At low latitudes in rain climates for which convective rain clearly dominates theInterference statistics at the critical time percentages (e.g., 0.01%), the melting layershould not be a factor in either coordination or detailed interference prediction. Compositerain climates L,M and N,P are believed to be in this category. Melting layer scatter isbelieved to be a factor in composite rain climate F-K because scatter from the less intenseprecipitation in the melting layer dominates that from some of the more Intenseprecipitation in convective rain.Although the possible effect of melting layer scatter on the accuracy of detailedinterference calculations is mentioned in Revised Recommendation 452-4 (Doc.5C/TEMP9)), there was insufficient data and other Information available at the meeting ofWorking Party 5C to propose a suitable modification to the prediction technique forestimating hydrometeor scatter interference levels. Data and other information weresimilarly lacking to propose a suitable modification to the coordination procedure in RevisedRecommendation 620 (Doc. 5C/TEMP6). A crude modification could be carried out on thebasis of the information given in this document If it were desired to give designers of earthstations the option of including 100% of possible interference geometries. A difficulty isthat there is no corresponding method as yet in Revised Recommendation 452-4. At thevery least, the information In this document provides a much dearer Indication than waspreviously available of the potential risks Involved in Ignoring the effects of the meltinglayer in interference coordination.143CCIR Document 12-3129 (Rev. 1) and supplement6REFERENCESCOST 210 Management Committee [1991) Influence of the atmosphere on interferencebetween radio communications systems at frequencies above about 1 GHz. Final Report ofCost 210 Management Committee, EUR 12407, ISBN 92 - 826-2400-5, Commission ofEuropean Communities, Luxembourg.HULAYS, R. [1991] Precipitation scatter Interference on communication links withemphasis on the melting snow layer. MASc. Thesis in preparation, Department of ElectricalEngineering, University of British Columbia, Vancouver, Canada.KHARADLY, M.M2. [1990] A model for evaluating the bistatic scattering cross section ofmelting snow: Phase III. Final Report on Contract CRC 36100-9-0247-101-ST,Department of Electrical Engineering, University of British Columbia, Vancouver, Canada.KHARADLY, M.M.Z. [1991a] A model for evaluating the bistatic scattering cross section ofmelting snow: Phase IV. Final Report on Contract CRC 36001-0-6572, Department ofElectrical Engineering, University of British Columbia, Vancouver, Canada.KHARADLY, M.M.Z. [1991 b] Private communication.KHARADLY, M.M.Z., and CHOI, A. [1988] A simplified approach to the evaluation of EMWpropagation characteristics in rain and melting snow. IEEE Trans. Antennas Propagat., Vol.36, 2, 282-296.KHARADLY, M.M.Z., and KISHK, A. [1991] Models for estimating melting layer attenuation.Manuscript in preparation, Department of Electrical Engineering, University of BritishColumbia, Vancouver, Canada.KLASSEN, W. [1988] Radar observations and simulation of the melting layer ofprecipitation, J. Atmos. Sci., Vol. 45, 24, 3741-3753.MATSUMOTO, A. and NISHITSUJI, A. Ed. [1971] SHF and EHF propagation in snowydistricts, Monograph series of Res. Inst. of Applied Electricity, No. 19, HokkaidoUniversity, Sapporo, Japan.OLSEN, R.L., ROGERS, D.V. and HODGE, D.B. [1978] The aRb relation in the calculation ofrain attenuation, IEEE Trans. Antennas Propagat., Vol. 26, 2, 318-329.144-7-12-3/29-E0.001^to^au^asfrequency (az)0.0111.0010^6 10 16^SO^SS^SOFrequency (Gliz)SS 40100001000100CC!R Document 12-3129 (Rev. 1) and supplementFigure 1. Comparison of model (Mode! I) and Mie scattering ('exact') forward scattering , crosssections (m2./m3) of rain (S•1) as functions of frequency. R.25 mm/h, 0•C watertemperature.Figure 2. Comparison of model (Model I) and Mie scattering •eicacr) forward scattering crosssections (m 2/m 3) of melting snowflakes (S•0.1) as functions of frequency. R.25mm/h, 0•C water temperature.145-136.00-138.00-140.00-142.00-144.00-146.00-148.00-150.00-152.00-154.00-156.00-158.00CC!R Document 12-3129 (Rev. 1) and supplementTransmission loss in dB1^3^10^30^100Rainrate in mm/hFigure 3. Comparison of transmission loss with and without the melting layer as a functionof rainrate at 11.2 GHz for parameters of Chilbolton-Baldock link. — rainonly, -- rain with melting layer; 131 km station separation, 20° earth-station elevation angle, 1.0° terrestrial-station elevation angle, 3.0 kmcommon-volume height, 3.0+Dm km height to melting layer top ("rain height"),40.5 dB terrestrial antenna gain (1.6° half-power beamwidth), 59 dB earth-station gain (0.18° half-power beamwldth, 55% efficiency).146Wm,CCIR Document 12-3129 (Rev. 1) and supplement9'rransmission loss in-132.00 —-134.00 --136.00 --138.00 --140.00 --142.00 --144.00 --146.00 --148.00 --150.00 --152.00 --154.00 --156.00 --158.00 --160.00-162.00-164.00-166.00 —1^3^10^30^100Rainrate in mm/hFigure 4. Comparison of transmission loss with and without the melting layer as a functionof rainrate at 4 GHz GHz for parameters of Chilbolton-Baldock link. — rainonly, — rain with melting layer; 131 km station separation, 20° earth-station elevation angle, 1.0° terrestrial-station elevation angle, 3.0 kmcommon-volume height, 3.0+0.50in km height to melting layer top (°rainheight .), 40.5 dB terrestrial antenna gain (1.6° half-power beamwidth), 59.0dB earth-station gain (0.18° half-power beamwidth. 55% efficiency).147-122.00-124.00-126.00-128.00-130.00-132.00-134.00-136.00-138.00-140.00-142.00-144.00-146.00-148.00OEM1^3^1 0^30=MIdm.■I.CCIR Document 12-3129 (Rev. 1) and supplement1 0Transmission loss in dBRainrate in mm/hFigure 5. Comparison of transmission loss with and without the melting layer as a functionof rainrate at 11.4 GHz for parameters of Graz link. — rain only, — rainwith melting layer; 9.3 km station separation, 16.8° transmitter elevationangle, 36.3° receiver elevation angle, 2.9 km common-volume height,2.9+0.1 Dm km height to melting layer top Crain height"), 37 dB transmittingantenna gain (3.0° half-power beamwldth), 47 dB recanting antenna gain (0.6°half-power beamwidth, 55% efficiency assumed).148CCIR Document 12-3129 (Rev. 1) and supplementLong-Path Error Statistics' for COST 210 Links at 1%Path Rot 724 Rot 724 Mod(4.5 dB/km)Rpt 724 Mod(-5.0 dB/km)Rpt 724 Mod(-4.5 dB/km)Rpt 724 Mod(-4.0 dB/km)Rpt 724 Mod(-3.5 dB/km)-1.15(0.85)Chilbolton•Baldock,1312.0 dB -3.9^(-1.9) • .50(•0.50)-2.05(-0.05)•1 .60(0.40)Chilbolton-Baldock, Bb6.0 -5.4 -3.00 -2.20 -1.40 -0.6 Cap d'Antifar •Chilbohon-3.9 .3.9^(-1.9) -3.9^(-1.9) -3.9^(-1.9) -3.9^(-1.9) -3.9^(-1.9)Fulda, Ft • - • - -Fulda. Fb • • • - - -Radar Simul., S2 0.0 0.0 0.0 0.0 0.0 0.0Radar Simul., S3 0.8 0.8 0.8  0.8 0.8 0.8Radar Simul., S4 3.9 3.2 3.35 3.41 3.46 3.52Radar Simul., S5 11.0 '2.5 4.45 5.11 5.76 6.42Mean 2.7 -1.0^(-0.4) .0.1 10.5) 0.2 (0.7) 0.4^(1.0) 0.7^(1.3)Standard Div. _^4.7 _ 3.42 (2.96) 3.22 (2.68) 3.23^(2.68) _ 3.27 (2.72) _^3.35^(2.80)Short-Path Error Statistics' for COST 210 Links at 1%Path Rpt 724 Rpt 724 Mod(4.5 dB/km)Rpt 724 Mod(-6.0 dB/km) ,Rpt 724 Mod(-4.6 dB/km)Rot 724 Mod(-4.0 d13/km)Rpt 724 Mod(-3.5 dB/km)Laidschandam, L1 10.8 10.8 10.8 10.8 10.8 10.8L2,•Loldschandam, 11.4 11.4^(11.9) 11.4^(11.9) 11.4^(11.9) 11.4^(11.9) 11.4^(11.9)Laldscharrdam, 1.3 12.4 12.4 112.9) 12.4 (12.9) 12.4 (12.9) 12.4 (12.9) 12.4 (12.9)Laidsdi•ndam, 1.4 14.0 14.0 (14.6) 14.0^(14.5) 14.0 (14.6) 14.0 (14.6)„ 14.0^(14.5)Laidschandam, 1.5 16.1 12.2^(12.7) 13.1^(13.6) 13.4^(13.9) 13.7 (14.2) 14.0^(14.5)Laidschandam, 1.6 18.5 10.7^(11.2) 12.5^(13.0) 13.1^(13.6) 13.7^(14.2)..._ 14.3^(14.8)Loldschandam, L7 21.1 7.5 10.6 11.7 12.7 13.8Laidschandam, LB 22.9 2.9 7.4 9.0 10.6 12.1Darmstadt, D1 6.7 6.7 6.7  6.7 6.7 6.7Darmstadt, D2 11.7 8.5 9.2 9.5 9.7 10.0Darmstadt, D3 14.0 4.9 7.0  7.7 8.4 9.1Darmstadt, D4 18.3 2.7 6.3 7.5 8.7  9.9, Darmstadt. D5 7.0 7.0 7.0 7.0 7.0 7.0Darmstadt, D6 10.8 4.2 -0.7 0.6 1,6_ 2.8Graz -0.6 -3.9^(2.5) -3.1^(3.3) -2.9^(3.6) -2.6 (3.8) -2.4^(4.0)Radar Simul., Si 3.1 3.1 3.1 3.1 3.1 3.1Mean 12.3^.6.6 (7.1) 7.9 (8.5) 6.4 (8.9) 8.8 (9.4) 9.3 (9.8)Standard Div. 6.4 5.50 (5.07) 4.92 (4.34) 4.83^(4.21) 4.80 (4.14) 4.83^(4.15)Combined Long- and Short-Path Error Statistics' (dB) for COST 210 Links at 1%St:enndardnwDay.RIX 724 Rpt 724 Mod Rpt 724 Mod Rp1 724 Mod Rpt 724 Mod Rpt 724 Mod(4.5 dB/km) (•5.0 dB/km), (•.5 dB/km) (•4.0 dB/km) (-3.5 dB/km)6.8 4.88 (4.46) 4.39 (3.85) 4.33 (3.75) 4.32 (3.70) 4.36 (3.73)Predicted interference levels minus measured levels. Values in parentheses Include roughcorrection for melting layer.149CCIR Document 12-3129 (Rev. 1) and supplementLong-Path Error Statistics' (dB) for COST 210 Links at 0.1%Path Rpt 724 Rpt 724 Mod(-6.5 dB/km)Rot 724 Mod(•5.5 dB/km)Rpt 724 Mod(-5.0 dB/kmRpt 724 Mod(-4.5 dB/km)Rpt 724 Mod(-4.0 dB/km)Rpt 724 Mod(-3.5 dB/km)•3.15( -1.1 6)Chilbohon•Baldock,Bf0.0 -5.9^(•3.0) -4.95(-2.95)• .50(•2.50)-4.05(-2.05)-3.60(.1 .6 0)Chitbolton-Baldock, Bb3.9 -6.5 -4.90 -4.10 -3.30 -2.50 -1.70Cap d'Antiler •Chilbotton-4.7 -4.7^(-2.7) -4.7^(-2.7) -4.7^(•2.7) -4.7^(-2.7) -4.7^(-2.7) -4.7^(-2.7)Fulda, Ft • - • • - • •Fulda, Fb • - • • • • -Radar Simul., $2 0.0 0.0 0.0 0.0 0.0 0.0 0.0Radar Simul., S3 0.0 0.0 0.0 0.0 0.0 0.0 0.0Radar SImul., $4 2.8 2.1 2.20 2.25 2.31 2.36 2.42Radar Simul., S5 8.9 0.4 1.70 2.35 3.01 3.66 4.32^'Mean 1.6 •2.1^(-1.5) -1.6^(-0.7) -1.2^(-0.7) -1.0^(-0.4) -0.7^(-0.1) -0.4^(0.2)Standard Dev. 4.2 3.49 (2.98)) _^3.22 (2.75) _ 3.13^(2.51) 3.00 (2.44) 3.08 (2.41) 3.12^(2.44)Short•Path Error Statistics' (dB) for COST 210 Links at 0.1%Path Rpt 724 Rpt 724 Mod(-6.5 dB/km)Rpt 724 Mod(•5.5 dB/km)Rpt 724 Mod(-5.0 dB/km)Apt 724 Mod(-4.5 dB/km)Rpt 724 Mod(-4.0 dB/km)Apt 724 Mod(•3.6 dB/km)Lsidschandam, L1 7.2 7.2 7.2 7.2 7.2 7.2 7.2LAidschendam, 1.2 7.0 7.8 (8.3) 7.8 (8.3) 7.1 (8.3) 7.8 (8.3) 7.8 (8.3) 7.8 (8.3)Leidschendam, L3 8.9 8.0 (9.4) 8.9 (9.4) 5.9 (0.4) 8.9 (9.4) 11.9 (0.4) 5.9 (9.4)Leidsehendam, L.4 10.2 10.2 (10.8) 10.2 (10.8) 10.2 (10.8) 10.2 (10.8) 10.2 (10.8) 10.2 (10.8)Leidschendam, 1.5 12.0 8.1^(8.6) 8.70 (9.20) 9.00 (9.50) 0.30 (9.80) 0.60 (10.1) 9.90 (10.4)LaIdschendam, 1.6 14.6 6.9 (7.4) 8.00 (8.50) 8.60 (9.10) 0.20 (9.70) 9.80 (10.3) 10.40 (10.9)Leidschendam. 1.7 18.1 4.5 6.66 7.60 8.65 9.70 10.75LAidsehendam, L8 20.9 0.8 3.85 6.40 6.05 8.50 10.05Darmstadt, D1 3.3 3.3 3.3 3.3 3.3 3.3 3.3Darmstadt. D2 8.5 6.9 6.76 6.00 6.25 6.50 6.75Darmstadt, D3 9.6 0.6 1.90 2.60 3.30 4.00 4.70Darrnstadt, D4 13.3 . -2.3 0.10 1.90 2.60 3.70 4.90Darmstadt, D5 2.6 2.5 2.5 2.5 2.5 2.5 2.5Darmstadt, D6 10.6 -4.3 -2.05 -0.90 0.25 1.40 2.65Graz -0.8 • .0^(2.4) -3.65 (2.85) -3.30 (3.10) -3.05 (3.35) -2.80 (3.60) -2.55^(3.65)Radar Simul., $1 2.8 2.8 2.8 2.8 2.8 2.8 2.8Mean 9.3 3.6 (4.2) 4.6 (5.1) 4.9 (5.5) 5.4 (5.0) SA (6.4) 6.3 (6.8)Standard Dev. 6.8 4.66 (4.20) 4.07 (3.69) 3.91^(3.48) _ 3.81^(3.33) 3.79 (3.27) 3.84 (3.22)Combined Long- and Short-Path Error Statistics• (dB) for COST 210 Links at 0.1%CombinedStandard Day.Apt 724 Rpt 724 Mod Rpt 724 Mod Rpt 724 Mod Rpt 724 Mod Rpt 724 Mod Rpt 724 Mod(-6.6 dB/km) (-5.6 d111/km) (-5.0 d13/km) (-4.6 dB/km) (-4.0 dB/km) (-3.6 dB/km)6.1 4.16 (3.87) 3.76 (3.37) 3.62 (3.16) 3.64 (3.03) 8.62 (2.98) 3.56 (3.00)'Predicted Interference.levebs minus measured levels. Values in parentheses include rough correctionfor melting layer.150CCIR Document 12-3129 (Rev. 1) and supplenientLong-Path Error Statistics* (dB) for COST 210 Links at 0.01%Path Rpt 724 Rpt 724 Mod(4.5 dB/km)Apt 724 Mod(•.6 dB/km)Rpt 724 Mod(•5.0 dB/km)Rix 724 Mod(-4.6 dB/km)Apt 724 Mod(-4.0 dB/km)Rpt 724 Mod(-3.5 dB/km)-3.15(-1 .1 6 )Chilbolton•Baldock,1310 • .9^(-3.9) -4.95(-2.95).4.50(•2.50)-4.05(-2.06)-3.60(•1.60)Chilbotton-Baldock. Bb4.9 -5.6 -3.90 -3.10 -2.30 -1.60 -0.70Cap d'Antifin •Chilbolton4.3 • .3^(4.3) 4.3^(-4.3) 4.3 (4.3) 4.3^(-4.3) 4.3 (4.3) 4.3 (4.3)Fulda, Ff •1.3 -1.3 -1.3 -1.3 -1.3 -1.3 -1.3Fulda, Fb 0.0 0.0 0.0 0.0 0.0 0.0 0.0Radar Simul., S2 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6Radar Simul., S3 •1.6 -1.6 -1.6 -1.6 -1.6 -1.6 •1.6Radar Simi., 44 0.0 -0.7 -0.61 •0.65 -0.50 -0.44 -0.39Radar Simul., S5 6.9 '^-1.6 •0.31 0.35 1.01  1.66 2.32Moan 0.2 .2.6^(•2.2) -2.2^(-1.7) -2.0^(-1.5) -1.7^(-1.3) •1.6(•1.1) •1.3^(-0.9)Standard Div. 3.8 2.63^(1.92) 2.29^(1.60) _^2.24^(1.53) 2.24 (1.53) 2.28 (1.60) 2.37^(1.73)Short-Path Error Statistics' (dB) for COST 210 Links at 0.01%Path Apt 724 Rpt 724 Mod(-6.6 de/km)Apt 724 Mod(-4.5 dB/km)Rpt 724 Mod(-5.0 dB/km)Apt ra Mod(-4.6 dB/km)Apt 724 Mad(-4.0 dE►km)Apt 724 Mod(•.6 dB/km)Laidschendam, L1 3.4 3.4 3.4 3.4 3.4 3.4 3.4Laidschandam, L2 4.1 4.1^(4.6) 4.1^(4.6) 4.1^(4.6) 4.1 (4.6) 4.1 (4.6) 4.1^(4.6)Laidschandam, 1.3 6.6 6.6^(6.1) 5.6 (6.1) 6.6 (6.1) 6.6 (6.1) 6.6 (8.1) 6.6 (6.1)LaIdsc►andam, 14 7.1 7.1^(7.6) 7.1^(7.6) 7.1^(7.6) 7.1^(7.6) 7.1^(7.6) 7.1^(7.6)Loidschandam, L5 8.7 4.8 (5.3) 6.4 (5.9) 6.7 (6.2) 6.0 (6.6) 6.3 (6.8) 6.6 (7.1)Laidschandam, 16 9.8 2.0 (2.5) 3.2 (3.7) 3.8 (4.3) 4.4 (4.9) 6.0 (6.6) 6.6 (8.1)Laidschandam. L7 15.4 1.8 3.9 4.9 6.0 7.0 8.1Laidschandam, LB 18.1 -2.1 1.1 2.6 4.2 6.7 7.3Darmstadt. D1 2.9 2.9 2.9 2.9 2.9 2.9 2.9Darmstadt, D2 7.9 4.6 6.2 6.4 6.7 '^6.9 6.2Darmstadt, D3 9.2 0.1 1.6 2.2 2.9 3.6 4.3Darmstadt, 04 11.4 -4.2 -1.8 -0.6 0.6 1.8 3.0Darmstadt, D5 2.0 2.0 2.0 2.0 2.0 2.0 2.0Darmstadt, D6 8.7 -6.1 -4.0 -2.8 -1.7 -0.6 0.7Graz 0.2 -3.1^(3.3) -2.6 (3.8) -2.3^(4.1) -2.1^(4.3) -1.8 (4.6)  -1.6^(4.8)Radar Simul., Si 1.3 1.3 1.3 1.3 1.3 1.3 1.3Mean 7.2 1.6^(2.1) 2.4 (3.0) 2.8 (3.4) 3.3 (3.8) 3.7 (4.3) 4.2 (4.7)Standard Div. 6.0 3.69 (3.53) 3.09 (2.95) 2.84 (2.64) 2.71^(2.45) 2.64 (2.32) 2.71^(2.33)Combined Long- and Shod-Path Error Statistics' (dB) for COST 210 Links at 0.01%CombinedStandard Day.Rpt 724 Apt 724 Mod(4.6 dB/km)Apt 724 Mod(-5.6 dB/km)Rpt 724 Mod(•6.0 dB/km)Apt 724 Mod(4.6 d13/km)Apt 734 Mod(-4.0 dB/km)Apt 724 Mod(•.5 dB/km)4.6 3.19 (3.00) 2.78 (2.61) 2.69 (2.27) 2.50 (2.13) 2.48 12.05) 2.54 (2.10)* Predicted interference levels minus measured levels. Values in parentheses include rough correctionfor melting layer.151Long-Path Error Statistics . (dB) for COST 210 Links at 0.001%Pah Rat 724 Rpt 724 Mod(4.5 de/km)Rpt 724 Mod(-5.5 d8/km)Rpt 724 Mod(-5.0 dB/km)Rpt 724 Mod(-4.5 d8/km)Rpt 724 Mod(-4.0 dB/km)Rpt 724 Mod(-3.5 dB/km)Rpt 724 Mod(-3.0 d8/km)Rpt 724 Mod(-2.5 de/km)Chilbolton-Baidock.BI0.4 -5.5 -4.55 -4.10 -3.65 -3.20 -2.75 -2.30 -1.85ChIlbollon-Beklodi, Bb5.1 -5.3 -3.70 -2.90 -2.10 -1.30 -0.50 0.30 1.10Cap frAntiffor -CfillboNon-5.9 -5.9 -5.9 -5.9 -5.9 -5.9 -5.9 -5.9 -5.9Fulda. Ft -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7Fulda, Fb _ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Radar Smut.. 62 -2.6 • .6 -2.6 -2.6 -2.6 -2.6 -2.6 -2.6 -2.6Radar Shut. &I -6.2 -6.2 -5.2 -5.2 -5.2  -6.2 -5.2 -6.2 -5.2Radar 8Inst, 64 -5.2 -8.6 -5.81 -5.75 -5.70 -5.64 -5.59 -5.53 -5.46^,Shaul.. 65, Radar 2.9 -5.6 -4.31 -3.85 -3.00 -2.34 -1.69 -1.03 -0.36Moan -1.4 -4.2 4.6 -3.5 -3.3 -3.1 -2.9 -2.7 -2.4,^Standard Ow. 3.9 2.2 1.98 1.96 1.99 _^2.07 2.20 2.36^_ 2.56• Predicted interference levels minus measured levels. Values in parentheses include rough correction for melting layer.ReferencesReferences 1. Awaka, J. [March, 1978] Estimation of rain scatter interference in the case of mediumscale broadcasting satellite for experimental purposes (BSE). Journal of the RadioResearch Laboratories, Vol. 25, No. 116, 23-48.2. Awaka, J. [March 1989] A three-dimensional rain cell model for the study of inter-ference due to hydrometeor scattering. Journal of the Radio Research Laboratories,Vol. 36, No. 147, 13-44.3. Capsoni, C., Fedi, F., Magistroni, A., Paraboni, A., and Pawlina, A. [May-June1987] Data and theory for a new model of the horizontal structure of rain cells forpropagation applications. Radio Science. Vol. 22, No. 3, 395-404.4. CCIR Document 12-3/29 (Rev. 1) [January 1992] Effect of the Melting Layer onHydrometeor Interference and Coordination Distance, Canada submission.5. CCIR Revision Rep. 452-4 [December, 1991] Prediction Procedure for the Eval-uation of Microwave Interference between Stations on the Surface of the Earth atFrequencies above 0.7 GHz, Doc. 5/14(Add.1)6. CCIR Rep. 569-3 [1986] The evaluation of propagation factors in interferenceproblems between stations on the surface of the Earth at frequencies above about0.5 GHz. Document 5/1051—E.7. COST Project 210 [1991] Influence of the atmosphere on interference between RadioCommunications Systems at Frequencies above 1 GHz. Final Report of COST210 Management Committee, EUR 12407, ISBN 92-826-2400-5, Commission ofEuropean Communities, Luxembourg.153References8. Crane, R.K. [March, 1974] Bistatic scatter from rain. IEEE Trans. Ant. Prop., Vol.AP-22, 2, 312-320.9. Gibson, C., Kochtubajda, B. and Bergwall, F. [March 1991] Feasibility study forthe extraction of melting layer statistics from archived Alberta S-Band weather radarobservations. Final report; Environmental Research and Engineering Department,Alberta Research Council, Edmonton, Alberta.10. Kharadly, M. and Choi, Angela S.-V. [February, 1988] A Simplified Approach to theEvaluation of EMW Propagation Characteristics in Rain and Melting Snow. IEEETrans. Ant. Prop., Vol. 36, No. 2, 282-295.11. Kharadly, M. [September, 1990] A Model for evaluating the bistatic scattering crosssections of the melting snow. Final report: CRC 36100-9-0247—/01—ST, Departmentof Electrical Engineering, University of British Columbia, Vancouver, Canada.12. Kharadly, M. and Kishk, A. [1992, in preparation] Models for estimating meltinglayer attenuation. Manuscript in preparation, Department of Electrical Engineering,University of British Columbia, Vancouver, Canada.13. Klassen, W. [1988] Radar observations and simulation of the melting layer ofprecipitation, J. Atmos. Sci., Vol. 45, No. 24, 3741-3753.14. Medhurst, R. [July, 1965] Rainfall Attenuation of Centimeter Waves: Comparison ofTheory and Measurement. IEEE Trans. Ant. Prop., Vol. AP-13, 550-564.15. Oguchi, T. [September, 1983] Electromagnetic propagation and scattering in rain andother hydrometeors. Proc. IEEE, Vol. 71, No. 9, 1029-1078.16. Olsen, R., Rogers, D.V., and Hodge, D.B. [March, 1978] The aRb Relation in theCalculation of Rain Attenuation. IEEE Trans. Ant. Prop., Vol. AP-26, No. 2,318-329.154References17. Persson, 0., and P. Lundgren [1986] Reduction of melting level effects on radarrain rate estimates. Promis Report no. 5, Swedish Meteorological and HydrologicalInstitute. 28 pp.18. Ray, P.S. [August, 1972] Broadband complex refractive indices of ice and water.Appl. Opt., Vol. 11, 1836-1844.19. Rogers, R. R. [1979] A short course in cloud physics. Pergamon Press, Toronto, Ont.155

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