Microwave propagation in dust stormsa review

S.O. Bashirand N.J. McEwan

Indexing term: Radiowave propagation (microwave)

Abstract: A review is given of the literature covering the effects of dust storms on microwave links. Mostauthors have calculated the effects of absorption of energy, revealing that it is not very significant unless veryhigh suspended dust densities are assumed. A few papers indicate the possibility of more significant cross polar-isation. Air refractive effects associated with dust storms have been relatively neglected but are strongly indi-cated by observations.

1 Introduction

With continued growth of satellite and terrestrial micro-wave systems and use of ever-higher frequencies, interesthas been expressed in the possible impact of dust stormson microwave link performance.

The intention of this survey is to summarise the presentknowledge of such effects. The possible impairments are:

(a) extinction of signal energy by flying dust particles(b) cross polarisation by flying particles(c) superrefraction, subrefraction and multipath effects

in some way associated with dust storms(d) effects of dust accretion on reflector antennas.

Most authors have concentrated on the first of theseeffects.

This paper simply reviews the existing microwave liter-ature on this subject. It is intended as the first of severalpapers in which we shall describe some further investiga-tions and conclude with an attempt to give the best practi-cal estimate of the severity of the effects that can beobtained without large-scale propagation measurements.Such experiments are unlikely to be performed in the nearfuture.

2 Direct and indirect methods

The only certain way of assessing the magnitudes and sta-tistical frequency of propagation impairments on radiolinks is by direct observation, i.e. by recording data on reallinks. Such a link may be an operational one or may be setup specially as a propagation experiment.

All other approaches to the problem are indirect andsemi-empirical. They are based on calculations but alwaysrely on some empirical inputs such as particle shapes, par-ticle dielectric constant, particle chemical composition etc.This is a familiar situation in connection with the micro-wave effects of rain.

2.1 Direct observationsWhereas hydrometeor effects have been extensively investi-gated by direct measurement, systematic observations ofdust storm effects on real links are very scarce. Only onestudy is known to the authors: Al-Hafid et al. [1, 2, 3]studied the direct influence of dust storms on the Nasiriya-Daraji (45 km) and Nasiriya-Sugal-Shiyki 11 GHz micro-wave links near Baghdad, Iraq. The authors concludedfrom these field measurements that dust storms attenuatedthe received signal to fade depths of typically 10 to 15 dBfor tens of minutes at a time. A 10 dB fade lasting 150

Paper 4573H, (Ell), received 12th August 1985

The authors are with the School of Electrical & Electronic Engineering, Universityof Bradford, Bradford, West Yorkshire BD7 1DP, United Kingdom

IEE PROCEEDINGS, Vol. 133, Pt. H, No. 3, JUNE 1986

minutes and a 26 dB fade lasting 40 minutes wereobserved. These experimental results showed much greaterattenuation than the authors predicted by an indirectmethod which was based on simple extinction, asdescribed later. The high attenuations are especially sur-prising as the optical visibilities quoted were in the range6-10 km, which appears to indicate very light dust stormsor dust haze [4].

2.2 Indirect methods: attenuationThe earliest work (1941) which discusses the microwavescattering properties of dust storms is believed to be thatof J.W. Ryde [5]. This report only deals with the radarreflectivity of dust storms, which is found to be negligibleexcept possibly for frequencies greater than 30 GHz andvery dense storms.

It is interesting to observe how the important issues inthe assessment of dust storm microwave effects have beenrecognised in this early work, and the uncertainties whichpervade it are made evident. Ryde draws the distinctionbetween the sandstorm, which contains particles mainlygreater than 75 micron radius and rises to at most 2 mabove the surface, and a dust storm containing small par-ticles and reaching much greater heights. Lacking a knowl-edge of precise particle sizes in the dust storm, Ryde givescalculations for specimen radii ranging from 1 micron to25 microns. To calculate a suspended mass density, Rydehas assumed that a 1 cm thick surface layer is simplyraised into a cloud of 300 m height, which implies a massdensity of about 7 x 10~5 gm cm"3. (Later work showsthis to be an extreme estimate of density). Finally, the dustparticle permittivity was taken to be that of quartz; theloss tangent was only known to be very small although itwas suggested that the presence of some iron in the dustmight raise it. Because of this uncertainty, Ryde has onlycalculated radar reflectivity and not attenuation.

Ahmed [6], at the University of Newcastle upon Tyne,performed a series of 10 GHz measurements of thecomplex permittivity of both bulk and dispersed sand andclay. The main features of these experiments can be sum-marised as follows:

(a) The 10 GHz permittivities of low density dispersions(10~6 to 10"2 gm cm"3) of sand and clay dust in air weremeasured by observing their effect on the resonant fre-quency and Q-factor of a large open resonator. The mea-surement gives directly the apparent macroscopicrefractive index of the dispersed particles, equivalent to thespecific attenuation and phase shift that this particledensity would cause on a microwave link. However, atthese low densities, the permittivity of the solid materialcan also be inferred with little uncertainty because (i) theRayleigh scattering approximation (assuming sphericalparticles) works well for single-particle scattering at these

241

particle sizes, and (ii) the low density of the air dispersionmeans that 'multiple scattering' or interaction of particlesis negligible.

(b) Mean permittivities of compressed samples of thesame materials were measured by various techniques, e.g.by packing them into a short-circuited waveguide andmaking reflection measurements. The major problem inusing these results is that the samples are far from solidand a mixing formula must be used to infer the permit-tivity of the solid material from that of the air-mineralmixture. Unfortunately, no precise theory exists for suchmixing when the particles' spacing is comparable with orsmaller than their size. These theories usually providemaximum and minimum limits which the effective permit-tivity can reach. The non-precision is in the magnitude ofthe average electric field within the particles of the mixture.It is known that the effective permittivity of the mixture isrelated to the above electric field average. Uncertainty inits value is caused by the indefinite mutual interactionbetween the polarisation fields of the particles, which inturn depends upon their relative orientations if they are

non-spherical. Various formulas based on different theo-retical approximations have been proposed. An importantaim of Ahmed's work was to establish a workable formulaby comparing the compressed sample and open resonatormeasurements.

Ahmed applied several mixing formulas to the bulk(waveguide) measurements, where the fractional volume ofmineral in the sample ranged from 0.57 to 0.72, to infer thesolid particle permittivity.

Three mixing formulas, due to Bruggeman [7], Bottcher[8] and Looyenga [9], all gave a prediction of the permit-tivity of sand which agreed well with the already knownlow frequency permittivity for fused silica. No independentvalue for clay was known but the success achieved withsand implied that these formulas would be usable.

Ahmed also derived estimates for the solid permittivitiesof clay and sand by simply extrapolating to unity volumefraction on log-log plots of real refractive index and tan <5against mixture density. These plots included pointsobtained from both the open resonator and waveguide

Table 1: Particle permittivities quoted in the literature

Author Frequency, PermittivityGHz

Remarks

sand % H2O clay or dust H20

Ahmed [6], [11] 10

10

3.8 +y"0.038

3.94+y0.042

5.1 +y0.24

4.48 +y0.18

Goldhirsh [20]

Al-Hafid era/. [2]

Chu [13]

Ghobrial [15]

Ghobrial [17]

Ansari andEvans [18]

Sharief andGhobrial [21]

Al-Bader andDawoud [23]

Haddad et al. [24]

10

10

11

9.4

X-band

10

37

8.6

10

9.35

3.35 +y0.042

3.7 +y0.001

2.5 +y0.02510 +yo.i

2.53 +y0.01

3.6 +y0.432

Pure powdered SiO2

Pure powdered AI203

Pure powdered Fe2O3

Pure powdered CaCO3

Pure powdered KCIPure powdered NaCI

?

00

0

3.88

7.42 +/1.119

4.62 +y0.1825.68 y0.378

5.34 +y0.1855.66 +y0.325

2.515+y0.074

2.88 +yO.O353

4.90 +y0.1306.10 +y"0.524.52 +;0.1055.03 +y"0.3825.23 +y0.26

4.38 +y0.05312.52 +/1.41016.38 +;1.080

8.2 +/0.124.7 +;0.055.7 +y0.09

2.5 +yO.O72(5.33 +y0.285)

1.8 +;0.171.907+y0.3642.634 + /0.734

?

04.3

0

5

oc

oo

co

o

oo

oo

oo

;

03

10

Values obtained by simple extrapolation, tosolid material, of e versus density plot.

Alternative values for solid material obtained[6] from bulk (waveguide) measurements usingBruggeman's mixing formula. Samples are Britishsand and clay. Measurements presumed at roomhumidity.

Value calculated by Goldhirsh for solid materialusing Rayleigh scattering, from open resonatormeasurements of Ahmed and Auchterlonie [10].

Open resonator measurements.

Chu assumes these values as probable upper andlower limits for desert conditions.

t Dry and moist values for one sample.t Results for two other samples similar.

t Values are given for six samples and are allt similar. Those with the smallest and largest

imaginary part are shown here.

* 'Sandy soil' at two water contents, originalmeasurements Von Hippel [32]

** 'Sandy clay loam' at two water contents,

original measurements Geiger and Williams [33]* Values for other frequencies and water

contents also collated.

First sample out of four

Third sample our of four

Mean of 9 dehydrated dust samples

Bracketed value derived by present authorsfrom previous one, for solid material, usingBruggeman's mixing formula.

One sample at several water contents. Valuesfor 5, 7% H20 also given.

242

t Values of real part in original paper have been increased by 1 (Ghobrial, private communication)* Raw bulk powder measurement values (not converted to solid material). Solid values would be considerably larger.

IEE PROCEEDINGS, Vol. 133, Pt. H, No. 3, JUNE 1986

measurements. His results are shown at line 1 of Table 1.Line 2 of the table shows alternative values he obtained bya mixing formula from the waveguide measurement.

Finally, the permittivities of the solid materials, derivedfrom the high density measurements, were used to predictthe low-density permittivities to be observed in the openresonator. Reasonable agreements were obtained for sand,but the predicted permittivities for clay were noticeablyless than those observed, especially for the imaginary part.

An interesting point is that the Bruggeman and Bott-cher formulas must be correct in the limit of a low densityof small spherical particles because they agree in this limitwith the results of the Rayleigh scattering approximation.This is not true of Looyenga's formula which, nevertheless,seems satisfactory at the high densities.

The open resonator results were also published byAhmed and Auchterlonie [10], giving the effective permit-tivities of the low density clay or sand in air. This paperhas been referenced by several later authors.

Finally, Ahmed, in his thesis [6] and a later paper [11],estimates the 10 GHz attenuation which could occur in areal dust storm. He derived the values: 0.1 dB/km forsand; 0.4 dB/km for clay (applicable to a true dust storm),these values being based on a density of 10 ~5 gm cm~3

which he considered an upper limit. The Newcastle workrepresents a pioneering attack on the dust problem and isincomplete mainly in not fully investigating the effect ofwater uptake and chemical composition. (The sand andclay samples used were British).

Another early attempt to predict attenuation was givenby Ghobrial et al. [12]. At this stage assumptions had tobe made about the permittivity, which was taken to be3.7 +7I.O at its most lossy, and the suspended dust den-sities. 106 particles m~3 were assumed. However, a mea-sured particle size distribution for a Khartoum sand stormwas presented, showing an upper limit radius of 150microns. Below this limit the distribution of radius a couldbe roughly approximated as exponential

N(a) = — ea0

-a/ao

with a mean radius a0 of about 8 microns. The worst cal-culated X-band attenuation was about 10"3 dB/km.

The paper by Al-Hafid et al. [2] in addition to describ-ing fades on an operational link, also describes some mea-surements of particle permittivity made using an openresonator. Their measured loss tangent of 0.00024 is sur-prisingly low (Table 1, line 4) even though the particlesused are described as 'sand' which is expected to be lesslossy than dust. In consequence the predicted attenuationsare much lower still than Ahmed's.

A significant advance is made in the paper by Chu [13]which makes clear the connection between optical visibil-ity and dust density. Using the Rayleigh approximation forsmall particles, and noting that scatter cross sections arealso negligible, Chu points out that the microwave absorp-tion is proportional to

1.N(a)a3 da

where a denotes particle radius, and N(a) is the number ofparticles per m3 per unit radius range.

Thus attenuation is proportional to the suspendedmass, as all dusts have roughly the same density. Opticalextinction is derived as proportional to

I.N(a)a2 da

i.e. it is a cross-sectional area effect. Thus for monodispersedust, the attenuation is directly proportional to particlesize for a given visibility. Chu presents specimen calcu-lations of 11 GHz attenuation per km against optical visi-bility for monodisperse particles of radii 0.01 and 0.1 mmand for specimen solid permittivities of 2.5 + jO.025 and10 + jOA (Table 1).

The lower value is a quoted one for dry soil and mustbe an underestimate because soil is an air-mineral mixture.The upper value appears to be the approximate upperlimit of quoted values for likely (solid) minerals.

The assumed loss tangent of 0.01 is a similar upper limitfor dry minerals, i.e. desert conditions are assumed for thestorm.

Chu also used his assumed permittivities, with Rayleighscattering, to predict the apparent permittivity of a low-density air-dust mixture, as would be observed in an openresonator. A direct comparison with Ahmed and Auchter-lonie's results [10] then showed fair agreement except thatthe loss tangent of clay dust was greatly under-estimated.A similar discrepancy was already evident in Ahmed's owninternal comparisons, as noted before. Chu commentedthat the water content of Ahmed's dust was not known.

The largest specific attenuation, based on the lower losstangent, predicted by Chu was 0.03 dB/km for 0.1 mmradius particles and 100 m visibility. (Following Middleton[14], the visibility distance was taken to correspond to15 dB of optical extinction.) Chu commented on the pos-sible effect of antenna height in reducing the attenuation.

At this stage of development it was evident that therewas still uncertainty about the permittivities of dust stormparticles, and particularly the effect of moisture content. In1980 Ghobrial [15] described measurements on three dustsamples collected in Khartoum. A conventional resonantcavity method was used, giving permittivities for com-pacted dust which were extrapolated to the solid materialusing Mandel's mixing formula [16]. Table 1 shows hisresults. It is interesting that 4.3% of water can raise theloss tangent to 0.068, but it is also noteworthy that thedehydrated material had a loss tangent of 0.039 which issubstantially larger than Chu assumed.

Another 1980 paper by Ghobrial [17] gives permit-tivities, obtained by the same methods, for other samples(Table 1). Here the effect of water is not discussed, but par-ticle size distributions are given for four of the samples. Itwas again found that no particles had radii greater than0.15 mm and that typically 70% of particles (by number)had radii between 50 and 0.5 microns. The calculationsshowed that 108 particles m" 3 could produce 1 dB/km ofabsorption at X-band but this very high density was notrelated to a visibility.

The 1982 paper by Ansari and Evans [18] is notable inextending calculations of attenuation up to 37 GHz. Acareful attempt was made to deduce from the literature thenecessary particle permittivities over a wide range of fre-quency and water contents. It was necessary for them touse published bulk permittivities for soils, mostly mea-sured with a view to remote sensing of the earth's surface.This can be criticised in that they have not scaled thesepermittivities of air-water-particle mixtures, to the permit-tivity of the particle material, and so will have underesti-mated the permittivities. However, some useful generalconclusions are drawn:

(a) Both real and imaginary parts of the bulk permit-tivity of dry soils are nearly frequency independent.

(b) Moisture content dominates the imaginary partincreasing it by an amount which has a complex frequencydependence, but which increases between 1 and 24 GHz.

IEE PROCEEDINGS, Vol. 133, Pt. H, No. 3, JUNE 1986 243

(c) Moisture also increases the real part by an amountwhich is constant up to about 8 GHz and then decreasesup to 24 GHz.

(d) Cihlar and Ulaby [19] are quoted to the effect thatchemical composition of dry soils has little effect on dielec-tric constant except where metallic or magnetic mineralsare present.

A careful treatment was given of attenuation/optical visi-bility relations, using the size distributions from Ghobrialet al. [12]. For 15 m visibility, predicted specific attenu-ations were 0.25 dB/km and 1.35 dB/km, for 14 and 37GHz, respectively, and dry particles. Corresponding valuesfor particles with 10% water were 3.6 and 15.1 dB/km. Weshall return to this paper in the context of cross polarisa-tion.

Goldhirsh [20] presented a review of work up to 1982.In reviewing permittivity measurements he applied Chu'sprocedure in reverse to Ahmed and Auchterlonie's [10]results, converting them to the inferred solid permittivitiesshown in Table 1. Again, the high tan <5 of clay is observed.In the context of visibility and suspended mass density,Goldhirsh shows that Ghobrial's assumed 108 particles perm3 corresponds to visibilities of only 4 to 5 metres and asuspended mass of order 4 x 10"5 gm cm"3 to 6 x 10"5

gm cm"3. He concluded that these conditions would give44 dB of 2-way attenuation on an X-band radar observinga target at 20 km range, but he recognised these conditionsas being both very extreme and very unlikely to exist overmany kilometres of path. His conclusion thus effectivelyconfirms that of other authors that absorption is not verysignificant in practice. An interesting feature of Goldhirsh'spaper is a prediction of the radar reflectivity of dust, whichis found not to be a significant source of clutter (though itmay be detectable).

Sharief and Ghobrial [21] investigated in more detailthe effects of moisture content and chemical compositionon dust permittivity. Permittivities were measured bycavity and transmission line techniques for compressedsamples taken from Khartoum dust storms; values wereextrapolated to those for solid material by Looyenga'smixing formula [9]. For four samples, curves of e versuswater content (up to about 5% by mass) varied consider-ably in shape but all showed a marked increase in bothparts of e. The imaginary part could be increased fromabout 0.2 to about 0.9.

Chemical compositions were given for two samples,showing (by mass) about 61% silica, 12.5% alumina andabout 8.5% ferric oxide. There was about 4.2% calciumcarbonate and small amounts of magnesium, sodium andpotassium oxides. Permittivities were determined for puresamples of alumina, silica, ferric oxide and three other sub-stances (Table 1), and it was shown that the Looyengaformula would accurately predict the permittivity of a syn-thetic dust mixture of these 5 compounds. It could then beshown that for the typical compositions observed in realsamples, silica would be the dominant factor in the realpart of e and alumina could dominate the imaginary part.

Two interesting features are revealed in this work. Thefirst, noted by the authors themselves, was that the mean £of nine samples of dehydrated real dust was 5.23 +J0.26whereas a representative mixture of silica, alumina andferric oxide would give a predicted e of 5.54 +7O.I6. Theauthors comment that 'the discrepancy in the imaginarypart is easily explained. The computed dielectric constantignores many compounds the dielectric constant of whichhas not been determined yet. . . . Preliminary measure-ments of the permittivity of manganese oxide indicate that

this compound is very lossy. The percentage by weight ofthis compound in dust is about 0.07'. This explanationdoes not seem entirely convincing as the authors' ownmeasurements would indicate that all the unknown lossyconstituents would only constitute at most 2% of thesample mass.

Another, perhaps related, point is that the loss tangentsmeasured by the authors for powdered pure silica andalumina are very much higher than those quoted [22] forsolid fused silica and alumina ceramic. This may indicatethe effect of powdering on the dielectric loss mechanisms.

Al-Bader and Dawoud [23] measured the complex per-mittivity of several dust samples by a transmission methodwith the samples placed in a waveguide (withoutcompaction). Two samples were taken from the ground inAl Dhahran and in the Empty Quarter of Saudi Arabia. Athird sample of airborne particles was also collected from adust storm. It is interesting that the loss tangent appearedto decrease with particle size, which is what would beexpected for loss arising from adsorbed water on the outersurface of particles due to the increasing ratio of volume tosurface area. The real part of e also decreased somewhatfor larger particles, and increased slightly with frequencybetween 8.5 and 10.5 GHz. These authors made no deduc-tions about propagation effects, but it is useful to comparetheir permittivities with other measurements. The mostuseful measurement to quote here is that for the real air-borne sample which was described as 'mainly clay' withmaximum particle radii of 150 microns. The bracketedvalue shown in Table 1 has been converted to solidmaterial by applying Bruggeman's formula to the measure-ment (e = 2.5, tan S — 0.0286) given in the original paper.

Haddad, Salman and Jha [24] studied the permittivitiesand size distributions of four particle samples. One of thesesamples was collected from a dust storm in Iraq at aheight of 3 m. Two of the samples are described as sand,and presumably taken from the ground, while the fourth isa simulated sample obtained by mixing clay and threegrades of silt. The most useful results to mention here arethose for the real storm sample. The permittivities, mea-sured by a waveguide method [25], are shown in Table 1.These values, which have clearly not been scaled to thesolid material, again show the expected effect of wateruptake. The loss factor of the dry material appears sur-prisingly large. Another useful result is the size distributionof this sample, which shows 50%, 20% and 10% of themass contributed by particles with radii greater than 15, 50and 95 microns, respectively. Relating attenuation to visi-bility by Chu's method, typical predictions for 9.4 GHzand 100 m visibility are 0.3 dB/km for dry dust and 0.8dB/km for dust with 10% moisture.

A particularly interesting experiment is also described inthis paper. The simulated dust sample was suspended in alaboratory chamber and the 9.4 GHz attenuation acrossthis simulated dust storm was measured. Obviously theattenuations were very small but were claimed to be mea-surable. The surprising result is that they were found to beas much as 30 times larger than calculated from the mea-sured permittivity. For example, with a suspended densityof 6 x 10"5 gm cm"3, the measured attenuation was 0.034dB/m when the calculated value was 0.001 dB/m. Althoughthis remains unexplained, in our opinion it is not yet suffi-cient evidence to overthrow the conventional theory of theattenuation. Further investigation would be of great inter-est.

Finally, the little-known study by Rafuse [26] is worthyof special mention. This is the only work which expresses adefinite opinion as to a mechanism, alternative to absorp-

244 IEE PROCEEDINGS, Vol. 133, Pt. H, No. 3, JUNE 1986

tion, to account for the observed deep fades on terrestriallinks [1]. By methods similar to those already described,Rafuse reached a definite conclusion that absorptioneffects are insignificant up to 44 GHz. For a storm withvisibility 100-200 m, a specific attenuation of 0.085-0.2 dB/km for 44 GHz was predicted. He considers thatmost authors have tended to over-estimate the absorptionsthat will occur in practice, having sometimes assumed veryhigh dust densities acting over implausibly long distances(10 km or more).

Rafuse considers that the 'forgotten parameter' is thebulk refractivity change caused not by the dust but by theair mass containing it. Taking typical dust storm param-eters, he shows that the suspended dust could change theoverall refractivity by 0.2 N units. By contrast, the differen-tial temperature and humidity of the storm would changethe refractivity, compared with surrounding air, by 26 Nunits, possibly on a short distance scale. It is therefore sug-gested that there is every reason to expect severe multipathfading and ray bending effects, associated with dust stormson terrestrial links.

2.3 Indirect methods: cross polarisationThe first attempt to calculate cross polarisation in a duststorm was made by Bashir et al. [27] using the followingmodel:

(a) Particles were treated as oblate spheroids with anaxial ratio of approximately 0.95.

(b) Particle symmetry axes were assumed to be allaligned in the same direction, and this could exhibit acanting angle of 1, 3 or 6 degrees with respect to the verti-cal and horizontal polarisations of a terrestrial microwavelink.

(c) Specimen solid permittivities of 1.82 +J0A3 and7.16+;6.5 for dry and moist particles (11% H2O) wereused, derived from Stuchly [28].

{(I) A suspended mass density of 10"5 gm cm"3 wastaken following Ahmed [11].

Propagation parameters were then calculated (by a pointmatching method) for 9.4 GHz. Predicted absolute and dif-ferential attenuations were small, as expected, but a differ-ential phase shift of typically 1.5 degrees/km was predicted.Over 1 km of path this would produce a cross polar dis-crimination of 51 dB. Although not specifically stated inthe paper, the assumed axial ratio was based (Bashir,private communication) on microscopic measurements ona small sample of real particles. Later measurementssuggest much higher eccentricity. However, this paperdraws attention to the possibility of significant cross pol-arisation due to differential phase shift, even thoughabsorption is small.

Cross polarisation was also treated by Ansari andEvans [18], where frequencies up to 37 GHz were con-sidered. These authors noted the lack of information onthe shape or alignment of dust particles, and therefore con-sidered a range of possibilities. Particles were consideredas spheroids with axis ratios varying up to 5 :1 in bothoblate and prolate senses. Assuming that the particles aresystematically aligned, lower and upper limits on crosspolarisation were given by assuming that the mean align-ment direction could make an angle between 1° and 45°with the linear polarisation of a microwave link. The 45°value would also apply for circular polarisation. It wasconsidered that the mean alignment direction of the sym-metry axes would probably be at most around 1° fromvertical (cf. the 'canting angle' of rain). Thus in a terrestriallink, which would usually use vertical-horizontal polarisa-tions, cross polarisation would be small.

The plotted results showed cross polar discriminations(XPD) that were reduced by about 10 dB when the watercontent was increased from 0 to 20%. Increasing the axialratio from 1.1:1 to 2 :1 reduced the discrimination byabout 20 dB, but a further increase to 5 :1 only reduced itby about another 8 dB. Table 2 shows some specimenvalues of XPD from this paper. The authors' qualitativeconclusions are that 'linear cross polarisation values in dryregions will not be significant even where visibilities reduceto 15 m and particles are very eccentric. The same will betrue for high humidity areas up to about 20 GHz . . . ,circular polarisation would prove to be unsuitable even indry regions with storm visibilities around 100 m'.

Uncertainties concerning particle shape and alignmentwere addressed by McEwan and Bashir [29]. Twomethods were used to quantify shapes of particles takenfrom a Khartoum sandstorm. In the first 2-dimensionalmethod, ellipses were fitted by eye to the outlines of photo-micrographic images of particles. The mean axis ratio was0.55. The second method, being three dimensional, allowedparticles to be modelled as ellipsoids rather than spher-oids. A rotatable graticule was used to measure theextreme widths and lengths of the particle outlines as seenthrough a microscope, the graticule being aligned paralleland normal to an axis chosen as a perceived best-fit longaxis of the particle. The third dimension of height wasobtained by focussing the microscope on the top of theparticle and then on the supporting slide. Mean axis ratioswere b/a = 0.76 and c/a = 0.53.

A theoretical investigation was then given of the ques-tion of whether storm particles would exhibit any non-random orientation. Forces disrupting alignment wereidentified as turbulence and, less importantly, Brownianmotion. Systematic alignment would tend to be generated

Table 2: Cross polarisation factors predicted by different authors

Author

Bashir et al.[27]

Ansari et al.[18]

McEwan et al.[29]

Frequency

9.4

10

37

10

10

XPD for1 km path, dB

moist drydust dust

50 77.5

14.7

4.6

19.4

16.1

Condition

10-5 gm/cm-3

suspendedmass (-v15mvisibility)15 mvisibility15 mvisibility10~5 gm cm"3

suspendedmass (-v. 15 mvisibility)

Polarisation

vertical

circularor 45°circularor 45°circularor 45°

circularor 45°

Remarks

Particles' measured eccentricity was verylow (see text)Particles 'canting angle' assumed as 6

16.8% H20

20% H2O

4.3% H2O

Particle model is prolatespheroids with eccentricity 2 :1and long axes vertical. Sizedistribution exponential withmean radius a = 0.01 mm.

IEE PROCEEDINGS, Vol. 133, Pt. H, No. 3, JUNE 1986 245

by electrostatic forces and an inertial torque of air flowround the particle. Another 'asymmetry' torque was identi-fied due to particles having a more asymmetric shape thanan ellipsoid, e.g. an 'egg' or 'pear' shape. This was harderto quantify but was also thought to produce non-randomalignment. The general conclusion was that particles ofequivolumic radii greater than about 50 microns wouldnormally be systematically aligned by the inertial torque,with the shortest length vertical. Electrostatic fields ofthunderstorm strength could also have a large influence onalignment.

Having affirmed the probable existence of non-randomalignment, cross polarisation could be calculated. Speci-men values for a suspended mass of 10"5 gm cm"3 aregiven in Table 2. This predicts potentially severe cross pol-arisation on slant paths where circular polarisation or anon-vertical linear polarisation might be used. The ques-tion of the 'canting angle', and of a possible preferred long-axis azimuth of particles falling with their shortest axisvertical, have not yet been treated. We hope to return tothese points in a later paper.

3 Effects of dust on antennas

This topic has received little attention and it appears thatonly the case of accretion on the surface of an unprotectedreflector antenna has been treated.

Kumar [30] considered a uniform layer of thickness taccreted on a sector subtending an angle 0S at the vertexof an axisymmetric antenna. His theoretical modelassumes that the aperture plane field over that sector ismodified by a formula derived from plane wave transmis-sion through a plane sand-metal structure; for lossless dustthe effect is just an aperture phase error. Integrating themodified field over the aperture gives boresight gainreduction as a function of (f)s, and curves for 7 GHz with(j)s = 180° and 360° are shown. Experimental points aregiven which agree with these curves although the measure-ments are not described in detail. The 'full-dish' curve pre-dicts 25 dB gain loss when t = 8.5 mm, and about 4 dB ispredicted for the 'half dish' case at the same thickness.

Bashir and McEwan [31] attempted to verify Kumar'stheory by directly measuring the phase modification of theaperture plane fields produced by a sand layer on a testantenna. The results supported Kumar's formulation.However these authors disagreed with his deduction of alarger gain reduction for the completely covered dish; theypredicted a larger reduction, due to phase cancellation, forthe <f)s = 180° case. A first attempt to consider enhancedcross polarisation was also given. Much further work ispossible.

4 Discussion

From this review of the literature, the existing state ofknowledge on microwave effects of dust storms can besummarised as follows:

First, virtually all the work points to the conclusionthat attenuation due to absorption and scatter is negligiblein practical terms at least up to 30 GHz. Secondly, thereare clear indications that terrestrial links do experiencefading associated with dust storms. One author has givenan explanation of this in terms of the refractivity changesin the air mass suspending the dust. However, there existsno detailed model for the effect and certainly no means ofpredicting its severity at any location. Finally, thereappears to be a strong possibility of significant cross pol-arisation, due mainly to differential phase shift, on circu-

larly polarised links and linearly polarised links (e.g. tosatellites) when the polarisations are not vertical/horizontal.

Although there will probably be no definitive propaga-tion experiments in the near future, there are several waysin which the present picture can be consolidated. Bettermodels of the water uptake of particles and its effect onpermittivity may be useful, as this has some bearing oncross polarisation, and may be essential if attenuationabove 30 GHz is to be considered. An apparent anomalyin the measured loss tangent of dry materials remains ofindirect interest. To date no author has considered theparticle-water system as an inhomogeneous structure,which is undoubtedly very difficult.

Some attempt might be made to model the supposedair-refractivity effects in more detail, but this again is verydifficult.

Cross polarisation may prove to be the most significanteffect for satellite-earth paths, and estimates of its severitymay be improved by a more careful consideration of therelations between dust density and visibility, and the waythe dust density decays with height. Particle shape mea-surements could be extended, possibly to include somemeasure of the asymmetry. The existence of cross polarisa-tion hinges on the theoretical prediction that particles havesome preferred orientation. Laboratory tests of this predic-tion could be made, especially concerning the effect onalignment of shape asymmetry. The theory itself can beextended to deal with the already mentioned question ofthe 'canting angle' and of preferred particle long-axis azi-muths.

Finally, it would be of general value to compile avail-able geographical and morphological data on dust stormsto obtain, if possible, better estimates of the occurrence fre-quencies of various visibilities in the storms.

We hope, in later papers, to contribute some additionalknowledge in the areas suggested.

5 Acknowledgment

The above work was funded in part by Intelsat. The viewsexpressed, however, are not necessarily those of Intelsat.

6 References

1 AL-HAFID, H.T., GUPTA, S.C., and BUNI, K.: 'Effect of adversesand-storm media on microwave propagation', Proc. National RadioScience Meeting, URSI F.8, 1979, p. 256

2 AL-HAFID, H.T., GUPTA, S.C., and AL-MASHHADANI, M., andBUNI, K.: 'Study of microwave propagation under adverse duststorm conditions', 3rd World Telecom. Forum, 1979, pp. 2.3.7.1-2.3.7.3

3 AL-HAFID, H.T., GUPTA, S.C., and IBRAHIM, M.: 'Propagationof microwaves under adverse sand storm conditions of Iraq', Proc.North American Radio Science Meeting, URSI F.5, AP-S, 1980, p.274

4 MORALES, C. (Ed.): 'Saharan Dust' (John Wiley & Sons, 1977)5 RYDE, J.W.: 'Echo intensities and attenuation due to clouds, rain,

hail, sand and dust storms at centimetre wavelengths', Report 7831,Research Laboratories of General Electric Company Ltd., 1941, pp.22-24

6 AHMED, I.Y.: 'Microwave propagation through sand and duststorms', PhD Thesis, University of Newcastle Upon Tyne, UK, 1976

7 BRUGGEMAN, D.A.C.: 'Berechnung Verschiedener PhysikalischerKonstanten von Heterogenen Substanzen', Ann. Phys., 1935, 24

8 BOTTCHER, C.J.F.: 'Theory of dielectric polarization' (Elsevier,9 LOOYENGA, H.: 'Dielectric constants of heterogeneous mixtures',

Physica, 1965, 31, pp. 401-40610 AHMED, I.Y. and AUCHTERLONIE, L.J.: 'Microwave measur-

ments on dust, using an open resonator', Electron. Lett., 1976, 12, p.445

246 IEE PROCEEDINGS, Vol. 133, Pt. H, No. 3, JUNE 1986

11 AHMED, I.Y.: 'The effects of sand and dust storms on microwavepropagation', Arab States Broadcast. Union Tech. Rev., 1977, 1, pp.23-29

12 GHOBRIAL, S.I., ALI, I.A., and HUSSEIN, H.M.: 'Microwaveattenuation in sand storms', Proc. Int. Symp. Antennas and Propaga-tion, Sendai, Japan, 1978, pp. 447-450

13 CHU, T.S.: 'Effects of sandstorms on microwave propagation', BellSyst. Tech. J., 1979, 58, pp. 549-555

14 MIDDLETON, W.E.K.: 'Vision through the atmosphere' (Universityof Toronto Press, Toronto, 1952) p. 220

15 GHOBRIAL, S.I.: 'Effect of hygroscopic water on dielectric constantof dust at X-band', Electron. Lett., 1980,16, pp, 393-394

16 MANDEL, M.: 'The dielectric constant and Maxwell-Wagner disper-sion of suspensions of oriented prolate spheroids', Physica, 1961, 27, p.827-840

17 GHOBRIAL, S.I.: 'Effect of sandstorms on microwave propagation',IEEE National Telecomms. Conf., Houston, Texas, 1980, pp. 43.5.1-43.5.4

18 ANSARI, A.J., and EVANS, B.G.: 'Microwave propagation in sandand dust storms', IEE Proc. F, Commun., Radar & Signal Process.,1982,129, pp. 315-322

19 CIHLAR, J., and ULABY, F.T.: 'Dielectric properties of soils as afunction of moisture content', RSL Technical Report 177-47, Uni-versity of Kansas Centre for Research, Lawrence, NASA, CR-141868,1974

20 GOLDHIRSH, J.: 'A parameter review and assessment of attenuationand backscatter properties associated with dust storms over desertregions in the frequency range of 1 to 10 GHz', IEEE Trans., 1982,AP-30, pp. 1121-1127

21 SHARIEF, S.M., and GHOBRIAL, S.I.: 'X-band measurements of thedielectric constant of dust', Proc. URSI Commission F Symposium,Louvain-la-Neuve, Belgium, 1983, ESA publication SP-194, pp.143-147

22 'ITT reference data for radio engineers' 6th Edition (Howard W. Sams& Co. Inc., Indianapolis, USA, 1981)

23 AL BADER, S.J., and DAWOUD, M.M.: 'Measurements of thecomplex refractive index of soils and airborne particles', Proc. URSICommission F Symposium, Louvain-la-Neuve, Belgium, 1983, ESApublication SP-194, pp. 149-152

24 HADDAD, S., SALMAN, M.J.H., and JHA, R.K.: 'Effects of dust/sandstorms on some aspects of microwave propagation', ibid., pp.153-161

25 SUCHER, M., and FOX, J.: 'Handbook of microwave measurements,Vol. II', (Polytechnic Institute of Brooklyn Press, 1963) 3rd Edn., pp.495-518

26 RAFUSE, R.P.: 'Effects of sandstorms and explosion-generated atmo-spheric dust on radio propagation', MIT, Lincoln Lab, Lexington,1981, Project Report DCA-16, ESD-TR-81-290

27 BASHIR, S.O., DISSANAYAKE, A.W., and MCEWAN, N.J.: 'Pre-diction of forward scattering and crosspolarisation due to dry andmoist 'Haboob' and sand storms in Sudan in the 9.4 GHz Band', ITUTelecomm. J., 1980, 47, pp. 462-467

28 STUCHLY, S.S.: 'Dielectric properties of some granular solids con-taining water', J. Microwave Power, 1970, 5, pp. 62-68

29 MCEWAN, N.J., and BASHIR, S.O.: 'Microwave propagation insand and dust storms: the theoretical basis of particle alignment', IEEConf. Publ. 219, 1983, pp. 40-44

30 KUMAR, A.: 'Attenuation due to accretion of dust and sand onreflector antennas at microwave frequencies', IEE Conf. Publ., 155,1981, pp. 518-521

31 BASHIR, S.O., and MCEWAN, N.J.: 'Crosspolarisation and gainreduction due to sand or dust on microwave reflector antennas', Elec-tron. Lett., 1985, 21, pp. 379-380

32 VON HIPPEL, A.R.: 'Dielectric materials and applications' (MITPress, 1954) p. 314

33 GEIGER, F.E., and WILLIAMS, D.: 'Dielectric constants of soils atmicrowave frequencies', NASA-TM-X-65987

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