ADAO081 4 1 4ASL.TR-0049 Reports Control Symbol

OSD 1366

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ATMOSPHERIC EFFECTS ON MILLIMETER RADIO WAVES

JANUARY 1980 T

" * B y

• H.K. KOBAYASHI A

Approved for public retlease; distribution unlimited

liii US Army Electronics Research and Development CommandATMOSPHERIC SCIENCES LABORATORYWhite Sands Missile Range, NM 88002

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4. TITLE (and Subtitle) 5. TY E F Po!!T&~9pEE

ON~R&D Tehncl_( ATMOSPHERIC EFFECTS ONMILLIMETER RADIO _WAVES~ , Tcni6.PERFORMING ORO. REPOHT NUMNFR

S.HR~)8 CONrRACT CRra)

9-PEFOMIG RGNIAIO NMEAN ADRSS1. PRZOR ESTPRECTASK

Atmospheric Sciences LaboratoryWhite Sands Missile Range, NM 88002 DA Task I L162111AH7

I I CONTROLLING OFFICE NAME AND ADDRE.SS o T 1__US Army~ Electr onics ResearchJa

and Development Command NME FPCEdAdeRl h. MP 20783 ____ ________

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IS. SUPPLEMENTARY NOTED

IS. KEY WORDS (Continue an reverse aide if necessary and identify by block number)

Atmospheric effects Attenuation by rainMillimeter waves Backscatter by rainRain Raindrop-size diltributionHydrometeor3 Turbulence at millimeter wavelengths

U0 AStrRAcr Iesartie m ~vro utsshbF neeweaty md IdentiUO by block number~)

't;This report is a short survey intended to present the atmosphere's effect onmillimeter waves. The emphasis is on rain and raindrop-size distributions. :This emphasis is appropriate because rain (the most common nongaseous con-stituent of' the lower atmosphere) also has the greatest effect on millimeter

K waves, and raindrop-size distribution is needed to compute the theoretical andmeasured extinction of radio waves.,--..

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69CU.ITV CLA.ISIPICATbON OF THIS PACK(f-un D.Paid Ent.r.d

20. ABSTRACT (cont)

"-The pressing need to acquire short-time data on raindrop-size distribution,particularly in the smallest size classes, is emphasized. Likewise, theacquisition of data on atmospheric fluctuations will determine how wellmillimeter-wave propagation through turbulence will be understood.

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PREFACE

The author gratefully acknowledges the aid of Drs. Donald E. Sniderand Douglas R. Brown of the US Army Atmospheric Sciences Laboratory,White Sands Missile Range, New Mexico, and the staff of the EngineeringExperiment Station, Georgia Institute of Technology, Atlanta, Georgia,in the preparation of this survey.

A s ii11 or

D",'01 TAB.nnounoed FJ

SA -v,- .l.•t andior

Dis sp~ecial

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CONTENTS

INTRODUCTION 7

.RAIN 8

RAINDirect Measurement of Raindrop Sizes 9

Attenuation by Rain, the aRb Relation 14

Backscatter from Rain, Z ARb 26

FOGS AND CLOUDS 29

* TURBULENCE 31

CONCLUSIONS 31

REFERENCES 33

SELECTED BIBLIOGRAPHY 38

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INTRODUCTION

Electromagnetic waves traveling through the atmosphere are absorbed, scat-tered, and refracted by gases, hydromteors, and particulate matter.'

The gases that affect millimeter waves are mainly oxygen and water vaporthat have pronounced resonant absorption lines at 22, 60, 118, and 183GHz. 2 Nonresonant absorption also occurs within the transoarent"windows" centered at 35, 94, 140, and 220 GHz, but to a much lesserdegree; hence, most research reported to date is at or near thesewindows,

Hydrometeors are terms for the liquid and solid forms o* 'recipthted"atmospheric water vapor. Liquid water is known to scatLer electro-magnetic waves more strongly than ice because of its larger dielectricconstant. In addition, it will attenuate waves strongly because of itshigher dielectric loss and thermal dissipation. 3 Consequently, thereis general agreement In the literature from theory and observationthat-rain, the most frequently encountered hydrometeor of the loweratmosphere, is of paramount-importance in millimeter wave propagation.,' 5

Therefore, this report will focus initially on absorption and scat-tering by rain, and a brief account of fog and clouds will follow. Theliterature on melting hydrosols and their effect on millimeter waves isvirtually nonexistent, although nascent laboratory work has begun. 6

Particulate matter (smoke, dust, etc.) has a small dielectric constantcompared to water and is not considered as Important as the hydro- 'meteors.' Moreover, it has been poorly studied at millimeter

IF. B. Dyer and N. C. Currie, 1978, "Environmental Effects on Millimeter

Radar Performance," EPP Symposium, Neubiberg bei MUnchen, Germany2J. M. Waters, 1976, "Absorption and Emission by Atmospheric Gases,"Methods of Experimental Physics, 12(B):1423K. L. S. Gunn and T. W. R. East, 1954, "The Microwave Properties ofPrecipitation Particles," Quart I Roy Meteorol Soc, 80:522

1K. Fischer, 1978, "Atmospheric Influences on the Millimeter and Sub-millimeter Wave Propagation," EPP Symposium, Neuhiberg bei MUnchen,Germany

5J. H. Rainwater, 1977, "Weather Affects MM Wave Missile GuidanceSystems," Microwaves, September, p. 62

6D. L. Bryant and L. J. Auchterlonie, 1979, "Measurement of the Extinc-tion Cross-sections of Dry and Wet Ice Spheres at 35 GHz," ElectronicsLetters, 15:52

7

wavelengths, 5 , 7 and adequate discussion at this time is difficult.

Turbulence and its effect on refracting millimeter waves have beenstudied very little, but are potentially important atmospheric fea-tures. These aspects will be discussed at the close of this survey.

RAIN

Beginning at the turn of the century with Gustav Mie, the theoreticaleffect of particles on electromagnetic waves has been studied con-tinually, notably in cases where particles are assumed spherical, ornearly so, and their diameters are considered small compared to thewavelength of the incident radiation. This report will show that diffi-culties in understanding this effect are not in the theoretical com-putations, which are becoming more tractable yearly with rapid advancesin computer technology, but in the paucity and unreliability of meteo-rological data regarding the spatial and temporal distribution ofraindrop-size classes.

Collectively, scattering (S) and absorption (A) by a single particleare termed extinction (E) or alternatively, attenuation. Then by theusual radar definition of target cross section (u), we get aE =A +This nomenclature and the usage of Q for corresponding normalized crosssections, where Q - u t nD2/4 (D = drop diameter), have been fairlyconsistent as papers written in 1;54,3 1966,8 and 19777 will attest.Mie calculations of a involve the index of refraction for water (m),which is complex at millimeter wavelengths, difficult to assess ex-perimentally, and very temperature dependent. Mitchell has tabulatedvalues for m from wavelengths x - I to 100 mm for 0, 10, 18, and 200 C.8

Some idea of how the cross sections vary with 0 and x can be obtainedfrom figures I and 2, The values for m are at 180C. Note how the totalattenuation a increases as the millimeter frequency increases, and how

small raindrops, typically less than 1 mm diameter, become important inbackscatter aBS as frequency increases. Theoretical calculations sum

up the effect of every particle in a volume, and therefore depend onreliable field data of drop-size distribution.

5 j. H. Rainwater, 1977, "Weather Affects MM Wave Missile GuidanceSystems," Microwaves, September, p. 62

7W. L. Gamble and T. D. Hodgens, 1977, "Propagation of Millimeter andSubmillimeter Waves," US Army MIRADCOM Technical Report TE-77-14,

AD B023622

3K. L. S. Gunn and T. W. R. East, 1954, "The Microwave Properties ofPrecipitation Particles," Quart J Roy Meteorol Soc, 80:522

8R. L. Mitchell, 1966, "Radar Meteorology at Millimeter Wavelengths,"Aerospace Corporation, Report TR-669(6230-46)-9, AD 488085

8

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Direct Measurement of Raindrop Sizes

There are apparently four general techniques for obtaining drop-sizeclasses at one site:

1. Physical capture of drops by an absorbing agent with a knownsurface area9 , 0,119 ,2

2. Photographing drops within a known volume 10 ,12,13,14

",~~..... Vpr ///.4)m t ic . -,,

DIAMETER OF WATER SPHERE D (mm)Figure 1. Absorption, scattering, and total attenuation cross sections of water

spheres (ref 8).

9 L. J. Anderson, J. P. Day, C, H. Freres, and A. P. D. Stokes, 1947,"Attenuatiun of 1.26-Centimeter Radiation Through Rain," Proc IRE,35:35410J. Joss and A. Waldvogel, 1969, "Raindrop Size Distribution andSampling Size Errors," J Atmos Sc., 26:566

11J. 0. Laws and D. A. Parsons, 1943, "The Relation of Raindrup Sizeto Intensity," Trans Am Geophys Union, 24:452

12S. Ugai, K. Kato, M. Nishijima, T. Kan, and K. Tazakl, 1977, "FineStructure of Rainfall," Ann des Telecom, 32:4221 3M. A. Jones, 1959, "The Shape of Raindrops," J Meteorol, 16:50414R. Cataneo and G. E. Stout, 1968, "Raindrop-Size Distributions inHumid Continental Climates, and Associated Rainfall Rate-Radar Reflec-tivity Relationships," J Apl Meteorol, 7:901

9

3. Electromechanically by translating drop momenta to electricanalogst5,16

4. Electrostatically by measuring inherent or induced chargesof raindropsl7,1 8 ,19,2 0

4 r: 1 m mm, H61-I,885sL A~jk:1mtin m:r;3.411 I. I ,):7z: 0mm,m#5. 5,817.869

TE'M1' IS"('

k 2

- ..- ,

j :mlmm"

0) 2 4 6

I)AMETER OF WATER SPHERE D (mnm)

Figure 2. Backscatter cross section of water spheres (ref 8).

15A. Waldvogel, 1974, "The No Jump of Raindrop Spectra," J Atmos Sci,31 :1007

16L. J. Bruer and R. K. Kreuels, 1977, "Rainfall Drop Spectra Inten-sities and Fine Structures on Different Time Bases," Ann des Telecom,32:430

'IS. G. Bradley and C. D. Stow, 1974, "The Measurement of Charge andSize of Raindrops: Part I. The Disdrometer," JA Meteorol, 13:11418U. H. W. Lammers, 1969, "Electrostatic Analysis of Raindrop Distri-butions," J_ p Meteorol, 8:330

19M. M. Kharadly, J. D. McNicol, and J. B. Peters, 1978, "Measurementof Attenuation Due To Rain at 74 GHz," EPP Symposium, Neubiberg beiM~nchen, Germany

20W. P. Winn, 1969, "A Device for Measuring the Radii of Raindrops,"8J pp Meteorol, 8:335

10

1., V .V.k.

From the beginning, many investigators encountered problems. Drop sizescould vary unpredictably during a single shower 9 as well as from stormto storm. 1 Figure 3 taken from Lammers 18 is typical of results obtainedby meteorologist. during intervals of a few minutes. Direct criticismsinclude the geiurally poor statistical handling of field data 22 , 23 andthe sampliri size being an order of magnitude too small for valid esti-mations.I

V-

40RAINFALI, RATE' R,

Smm/hr 20

L.40 0

NUMBER Of DROPS 2M It, minper min 20/0 2 6, , _

DIAMETER D, mm 1

2 3SIZE RANGES

Figure 3. Drop sizes measured during a heavy shower (ref 18). ,'

9L. J, Anderson, J. P. Day, C. H. Freres, and A, P. D. Stokes, 1947,"Attenuation of 1.25-Centimeter Radiation Through Rain," Proc IRE,35:354

21Miyuki Fujiwara, 1965, "Raindrop-size Distribution from IndividualStorms," J Atmos Sci, 22:585

18U. H. W. Lammers, 1969, "Electrostatic Analysis of Raindrop Distri-butions," J_ u Meteorol, 8:330

22P. L. Smith and C. P. Laco, 1978, "Techniques for Fitting Size Dis-tribution Functions to Observed Particle Size Data," Am Meteorol Soc,18th Conference on Radar Meteorology, 28-31 March 1978, Atlanta, GA

23,C. P Laco, 1978, "A Technique for Fitting Fxponential Functions toPrecipitation Particle Size Data," Institute of Atmospheric Sciences,Report 78-3, S. Dakota School of Mines and Technology, Rapid City, SD57701

1oj. Joss and A. Waldvogel, 1969, "Raindrop Size Distribution andSampling Size Errors," J Atmos Sc., 26:566

Sd...:,4 "-,tan

One criticism worth discussing separately is the scarcity of data onraindrops smaller than 0.5 mm. It will be recalled from the previouspage that the smaller drops contribute more to attenuation and back-scatter at the shorter millimeter wavelengths. Uagi et a1 12 showedthat many drops exist in the 0.05 and 0.5 mm range which they claim hadnot been previously measured. Their claim is not entirely valid sincethe widely used Joss and Waldvogel disdrometer employing the thirdtechnique listed above has a lower limit of 0.3 mm.

The drop-size distributions of Laws and Parsons 1' and Marshall andPalmer 24 of the 1940's are still the most widely quoted today.Marshall and Palmer found that their data and those of Laws and Parsonsempirically fitted the curve A

AD 0NDa=NO e" . (1)

where D = diameter mm, N * 0.08 cm"", A 4.1 R 0 2 1 cm", and R *rainfall rate mm/hr. 0

Figure 4 taken from Marshall and Palmer's paper superimposes equation (1)and the data from both papers for three rainfall rates. Note that theMarshall-Palmer relation has more drops in the small sizes than the Laws-Parson data. Examples of Ugal et al in figure 5 have even greater num-bers of drops in the small range.

The Joss and Waldvogel drop-size distribution based on equation (1) isthe third most quoted distribution. The usefulness of this distributionlies in the introduction of another dimension by changing N and A andcharacterizing a rain event as a drizzle, widespread, or thunderstorm. 1 sWidespread rainfall has the "average" condition N = 0.07 and

A u 4.1 R-° 2 1 , and a comparison with equation (1) shows that it isvery similar to the Marshall-Palmer relation.

To find the drop-size frequency distribution in a volume (which is neededto find the attenuation usually expressed in decibels per kilometer), thesurface drop distribution and the fall velocity of drop-size classes mustbe known. For the latter, the careful work of Gunn and Kinzer on the

12S. Ugai, K. Kato, M. Nishijima, T. Kan, and K. Tazaki, 1977, "FineStructure of Rainfall," Ann des Telecom, 32:422

11J. 0. Laws and D. A. Parsons, 1943, "The Relation of Raindrop-sizeto Intensity," Trans Am Geophys Union, 24:452

24J. S. Marshall and W. McK. Palmer, 1948, "The Distribution of Rain-drops with Size," J Meteorol, 5:165

15A. Waldvogel, 1974, "The N Jump of Raindrop Spectra," J Atmos Sci,31:1067 0

12

410

3 \ 13R RAINFALL RATE (mm hr-1 )

'mi

3

10~'10

- 4A

100 %

10-1

0 1 2 3 4 5

DROP DIAMETER D (mm)Solid line-equation 1 (ref 24)Dashed line-Laws-Parsons (ref 11)Dotted-Marshall-Palmer (ref 24)

Figure 4. Distribution of raindrops solid line-equation 1 (ref 24).

13

6 z , M i, WUm lam U AJ 1 2 .,U

terminal velocity of water droplets 25 has been almost universally ac-cepted for the past 30 years. Some attempts have been made to refinetheir values; 26 , 2 7 however, recent work on photographing falling rain-drops is still in fair agreement with the original work.12

Keizer et a1 2 8 reviewed the calculations required to find the distri-bution in a volume from original or theoretical measurements. An ex-ample of this type of computation is figure 5 featuring data ranginginto sizes smal1er than 0.5 mm which are rarely available. It isapparent that for any given drop size, the number of drops increasesuniformly with Increasing rainfall Intensity, This result is very dif-ferent from any previous Investigations and needs verification.

Attenuation by Rain, the aRb Relation

In their review paper of 1954, Gunn and East credit J. W. Ryde as theone who first realized the importance of rain attenuation and back-scatter at radar frequencies. Ryde's paper of 1946 offered the

r '

25R. Gunn and G. D. Kinzer, 1949, "The Terminal Velocity of Fall forWater Droplets in Stagnant Air," J Meteorol, 6:2432 6A. N. Dingle and Y. Lee, 1972, "Terminal Fallspeeds of Raindrops,"J Apl Meteoro1, 11:87727E. X. Berry and M. R. Pranger, 1974, "Equations for Calculating theTerminal Velocities of Water Drops," 3 6a Meteorol, 13:108

12S. Ugai, K. Kato, M. Nishijima, T. Kan, and K. Tazaki, 1977, "FineStructure of Rainfall," Ann des Telecom, 32-422

28W. P. M. N. Keizer, J. Snieder, and C. D. de Haan, 1978, "RainAttenuation Measurements at 94 GHz: Comparison of Theory and Experi-ment," EPP Symposium, Neubiberg bei M Unchen, Germany3K. L. S. Gunn and T. W. R. East, 1954, "The Microwave Properties ofPrecipitation Particles," Q JRoy Meteorol Soc, 80:522

14

.. ... . . . . . .. . . .. ..

101

RAINFALL INTENSITY (mm.h'~-R.- 46.4

---a---R: 32.2-0- R: 5.6-7.1

ti R-:- :3.643.6-- o----R: 0.8-1.1

S102

10

~10 t

10 1 2 3

RAINFALL DIAMETER (mm)*Figure 5. Some examples of density of the distribution in space by calculation

using -che falling velocity of Gunn and Ki~nzer (ref 12).

15

... - .. .... ............. .....-.

following linear expression (in his notation) for the average attenuation

along a path in decibels per kilomater: 29

dB/km = kp (2)

where k depends on wavelength and temperature, and p "varies widely"with ralifall Intensity and geographical area,

Ryde fully realized the importance of path length, droo-size distributionand wavelength, although his expressions did not include these variables.Early investigators soon realized that attenuation could be better repre- V

sented in the form:

A- aRb (3)

where

A a attenuation in decibels per kilometer,R rainfall rate in millimeters per hour, and

a and b are frequency and temperature dependent.

In practice, simultaneous values of A and R are plotted and a curve ofthe form of equation (3) fitted to the points. The rainfall rate R is

X found from the drop-size distribution if a disdrometer or an equivalent Iinstrument is available, or by means of the more standprd tipping bucketrain gauge. The widely scattered points corresponding to pairs of A-Rvalues in figures 6 and 7 reveal the difficulty In computing a least-

square, or any other kind of fit, to the data, Highly scattered pointsalso indicate that drop sizes will vary tremendously during the courqeof a single rain event. This was seen as early as 1954 when Gunn andEast listed ten values for the "constants" a and b of equation (3) basedon original size data taken in various parts of the world by severalworkers. 3 Numbers ranged from 127 to 505 for a and from 1.041 to2.29 for b, Indicating that attenuation could vary as much as 2 or 3either way from an average value of aRb for a given rainfall rate (i.e.,a and b given by average values).

29j. W. Ryde, 1946, "The Attenuation of Centimeter Radio Waves andthe Echo Intensities Resulting from Atmospheric Phenomena," JIEE, Vol93, Part ILIA, No. I, p. 1013K. L. S. Gunn and T. W. R. East, 1954, "The Microwave Properties ofPrecipitation Particles," Quart I Roy Meteorol Soc, 80:522

16

.... . . .. . . . . .. .. ............. . . . . .. . . . .. . . .•,W'

iI25

20,.'

10

4 S6 GHZ

(0 0 20 40 60 8o 100 120

RAINFALL RATE, mm h*1

40 ,,

30 7 I.

0191~20

10 110 GHZ

2 0 40 60 so 100 120

RAINFALL RATE, mmh-

Theoretical values Laws and Parsonsfor different drop - thunderstorm'sine distributions: - -widespread' JON. It aW.

- -- 'drimic' J

Figure 6. Variation of attenuation with rainfall rate (ref 38).

17

.. ...... ....... ......... .. -.. *.. U

Conflicting and widely varying results from field measurements in thetwo decades following World War II prompted Medhurst to write his fre-quently cited comprehensive survey of 1965.30 He reviewed, tabulated,and graphed the then extant rainfall attenuation data spanningx - 4 to 32 mm, and in each experiment employed from 1 to 13 raingauges. A few even took raindrop-size distribution, which yields rain-fall rate when the fall velocity of raindrops is accounted for (see,for example, Anderson et al9 who used both rain gauges and drop counts).Medhurst found that in practically all 15 cases there was a tendencyfor measured attenuation to be higher than the maximum theoreticallyattainable. He concluded that possible errors may be due to:

1. Inadequacy of the theory to account for multiple-scatteringalong the path, and

2. " , . . The rain structure being more complex than has beenassumed."

In fairness to Medhurst because of the criticism from Crane and others(Crane 31 and his later papers, Olsen et al, 32 and Watson33 ), his papershould be judged in the light of information available to him at thattime. He explained in detail why Ryde's application of Mie theory seemedinadequate to him and tried to show this graphically with each of the 15cases he studied. Also, he analyzed and tabulated his remarks on thetaking of rainfall rate and thought only the technique of Anderson et alwas above criticism. He deemed Mie theory inadequate, not inappropriate,and appeared to give poor meteorological instrumentation and interpre-tation at least equal fault for inconsistent results.

In 1971 Crane argued that Mie theory was appropriate and that experimentsover a short path with closely spaced rain gauges would show that thefault lay with the inadequate meteorological data. 3 1 From his work with

30R. G. Medhurst, 1965, "Rainfall Attenuation of Centimeter Waves:Comparison of Theory and Measurement," IEEE Trans Antennas P,AP-13:550

9L. J. Anderson, J. P. Day, C. H. Freres, and A. P, D. Stokes, 1947,"Attenuation of 1.2b-Centimeter Radiation Through Rain," Proc IRE,35:354

3 1R. K. Crane, 1971, "Propagation Phenomena Affecting Satellite Com-munication System Operating in the Centimeter and Millimeter WavelengthBands," Proc IEEE, 59:173

32R. L. Olsen, D. V. kogers, and D. B. Hodge, 1978, "The aRb Relation inthe Calculation of Rain Attenuation," 1978, iEEE Trans Antennas Propagat,AP-26:3183 3M. Watson, 1976, "Survey of Measurements of Attenuation by Rain and

other Hydrometeors," Proc IEEE, 123:863

18

lAll

L-band radar backscatter from New England showers, 34,35 Crane believedthat a large area of light rain contains many small intense showers andbetter spatial resolution of rainfall rate is needed to predict atten-uation. In 1974 Crane reported the results of his well-known experimentusing simulated rain of known drop-size distribution. 36 He concludedthat the field measurements and the theoretical calculations based onMie single-scattering theory for water spheres were in agreement at34 GHz, and the discrepancies noted by Medhurst and a few later workersare due to inadequate meteorological characterization.

In table 1, rain attenuation investigations along a one-way path at about30 GHz or higher are listed in chronological order. Two-way paths as inradar backscatter will be discussed in the next section. Table I andthe tables in the summary paper by Watson3 3 comprise most of the openliterature on the subject. Not listed are several theoretical studies,notably by the Soviets, described by Richard et a1 37 who use the dis-tribution of Marshbll and Palmer and other Western investigators as wellas their own. Table I experiments express the aRb relation with compara-tive plots of measured and theoretical attenuation versus rainfall rate.The rate in turn is derived from original drop distributions and/or con-ventional rain gauge data modified in the later experiments for fastsampling, and/or from known distributions such as the Marshall-Palmer.Some who wished to bracket their scattered data points also includeJoss's distributions for the extremes of "thunderstorm" and "drizzle" 38

A reading of these references will reveal that there is general agree-ment between measured and theoretical attenuations, particularly below50 GHz, and thus Crane's criticism of Medhurst appears Justified.

At this time then, simultaneous measurements--one below 50 GHz and oneabove--through the same rain path are valuable for comparative purposes.Figure 6 from Zavody and Harden 38 contrasts such a pair of frequencies:

34R. K. Crane, 1968, "Simultaneous Radar and Radiometer Measurementsof Rain Shower Structure," Lincoln Lab MIT Technical Note 1968-33,AD 67807935R, K. Crane, 1966, "Microwave Scattering Parameters for New EnglandRain," Lincoln Lab MIT Technical Report 426, AD 647798

36R. K. Crane, 1974, "The Rain Range Experiment-Propagation Through ASimulated Rain Environment," IEEE Trans Antennas Propagat, AP-22:321"33M. Watson, 1976, "Survey of Measurements of Attenuation by Rain andOther Hydrometeors," Proc IEEE, 123:86337V, W. Richard, J. E. Kammerer, and R. G. Reitz, 1977, "140-GHz Atten-uation and Optical Visibility Measurements of Fog, Rain and Snow,"Ballistic Research Labordtory, Memo Report ABRL-MR-2800, Aberdeen ProvingGround, MD 2100b38A. M. Zavody and B. N. Harden, 1976, "Attenuation/Rain-rate Relation-ships at 36 and 110 GHz," Electronics Letters, 12:422

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36 and 110 GHz. Despite the compressed ordinate scale of the llO-GHzattenuation, the sensitivity to smaller drop sizes is evident in themore divergent theoretical curves and the greater scattering of measureddata points. The authors appeared satisfied with the results at 35 GHz.Two plausible explanations were offered for the wide scattering of pointsat 110 GHz. The first was that drops 0.5 mm or less were not counteddue to equipment limitations, and there was no way to check the originalagainst the theoretical drop-size distributions. The second is an errordue to the sensitivity of small drops to updrafts and downdrafts. ThisI Is a serious problem since the number reaching the disdrometer and thefall velocity would change unpredictably. No longer would the Gunn andKinzer estimates for the small drops apply because these were done instagnant air. 25 On anotner point, the authors comment that their cal-.culations show that whether a raindrop is modeled as a sphere or aspheroid is significantly less important to attenuation at 110 GHz thanat 36 GHz, They based their calculations on Oguchi 39 who extended Mietheory to aspherical drops and their effect on centimeter and millimeterwaves. One explanation of this insensitivity put forth by others is thatat higher millimeter wavelengths, small drops cortribute more to atten-uation and deform very little during their fall through space. 37 ,4 0

At lower frequencies, shape is unimportant since small drops contributelittle to attenuation,

Another distinct advantage of dual frequency experiments exploited byZavody and Harden 38 and Ho et al"4 is the elimination of rainfall ratednd any attendant measurement errors by plotting attenuation at the twofrequencies against each other. Theoretical attenuation curves fromoriginal or known drop-size distributions can be superimposed on theplot for comparison. Both papers report good agreement with Laws-Parsonsor Joss distributions.

25R. Gunn and G. D. Kinzer, 1949, "rhe Terminal Velocity of Fall forWater Droplets in Stagnant Air," J Meteorol, 6:243

39T. Oguchi, 1973, "Attenuation and Phase Rotation of Radio WavesDue to Rain: Calculations at 19.3 and 34.8 GHz," Radio Sc, 8:3137V. W. Richard, J. E. Kammerer, and R. G. Reitz, 1977, "149-GHzAttenuation and Optical Visibility Measurements of Fog, Rain and Snow,"Ballistic Research Laboratory, Memo Report ABRL-MR-2800, Aberdeen ProvingGround, MD 21005

40j. Sander, 1975, "Rain Attenuation of Millimeter Waves atX 5.77, 3.3, and 2mm," IEEE Trans Antennas Propagat, AP-23:21338A. M. Zavody and B. N. Harden, 1976, "Attenuation/Rain-rate Relation-ships at 36 and 110 GHz," Electronics Letters, 12:4224 1K. i. Ho, N. D. Mavrokoukoulakis, and R. S, Cole, 1978, "Rain-inducedAttenuation at 36 GHz and 110 GHz," IEEE Trans Antennas Propagat,AP-26:873

21

h. .. . .. . . .. . .

The recent work by Keizer et al in 197828 at 94 GHz merits separate dis-cussion for its clarity of presentation and attention to important de-tails. It includes a thorough explanation of how drop-size distributionis obtained by the incorporation of drop-size class data into densityand rainfall rate expressions. Sources of error are discussed with care.For instance, the results of a wetting test on the antenna are presentedin a table listing wetting condition versus loss in decibels. Fluc-tuations of 5.8 dB or over for a wet antenna or radome are believed un-acceptable for short paths by the authors. The results of their experl-ment are seen in figures 7 and 8. Satisfactory agreement betweenmeasured and calculated attenuations at most rainfall rates is evident.But at low rates, there is a tendency for measured attenuation to behigher. According to the authors, a plausible cause is the inabilityof the disdrometer to record drops smaller than 0.3 mm diameter. Thisseems reasonable since the attenuation calculated from their disdrometerdata would underestimate attenuation at this high millimeter frequency.It is worth noting that this calculated attenuation (shown as + infigure 7) agrees very well with the theoretical curves, thus bringingu the possibility that the number of small drops is underestimatedwhen data are extrapolated to diameters below 0.3 mm. Extra olationhas been the rule for the Laws-Parsons with diameters less than 0.5 mmMarshall-Palmer less than 1.0 mm, and Joss et al less than 0.3 mm.10,t1,+2The data of figure 5 of Ugal et al need to be verified because of theimportance of small drop sizes at the shorter millimeter wavelength.

Arecent imortant paper on the aRb relation is that of Olsen, Rogers,and Hodge.3 2 In their introduction, the authors state that Medhurst'sdoubts on theoretical calculations 30 have been repudiated in recentyears with improved rain rate sampling techniques and that a more theo-retical approach to this empirical relation is due. First, the authors

show A = aRb (equation (3)) to be an approximation to an infinite series

28W. P. M. N. Kelzer, J. Snieder, and C. D. de Haan, 1978, "Rain Atten-uation Measurements at 94 GHz: Comparison of Theory and EUperiment,"OPP Symposium, Neubiberg bel Munchen, Germany

10 J. Joss and A. Waldvogel, 1969, "Raindrop Size Distribution andSampling Size Errors," J Atmos Sc_, 26:566

11J. 0. Laws and D. A. Parsons, 1943, "The Relation of Raindrbp Sizeto Intensity," Trans Am Geophys Union, 24:452

24J. S. Marshall and W. McK. Palmer, 1948, "The Distribution of Rain-drops with Size," J Meteorol, 5:165

32 R. L. Olsen, D. V. Rogers, and 0. B. Hodge, 1978, "The aRb Relationin the Calculation of Rain Attenuation," 1978, IEEE Trans AntennasPropagat, AP-26:31830R. G. Medhurst, 1965, "Rainfall Attenuation of Centimeter Waves:Comparison of Theory and Measurement," IEEE Trans Antennas Propagat,AP-13:550

22

• .

t0.00 THEORETICAL CURVES FOR VARIOUS IDROP SIZE I)IHTHIBUTIONNI -JOSS4 KT Al.. DRIZZLE 1 915 42 -2MARSIHALL AND PALMER *,J f 3.

*3 LAWS AND PARSONS / :4 - JOSS IT Al. TIILINDERSTORM

M.00 • - JOHS FT AL,. WII)DE SPItRAI)D

M.00

7.,•00

4.00hA /

0,00)

6.112 1 31 05

RAINFALL RATE IN HM/HRA ME;AHUIRED ATTENUATrION+. CAL~tUIATED:I ATTE•NUATION DE•RIVE'D PROM MEASIURED RtAINDRIOP SIZ.E D)ISTRIBUTION

Figure 7. Measured and calculated rainfall attenuation versus ralnfall rate .at 94 GHz (ref 28). :-

4 A

1.0 -

C

A~~ ~ kid . 6

0,2 0! 1 2 150 20) 50RAINFALL RATE IN MM/HI

Figure 7. Difference of measured and calculated rainnafl attenuation vref 2r).

232.0

~ 00 0 , 0~ ..... _,___,_

0

relation which includes the effect of froquency, rain temperature, anddrop-size distribution parameters in the higher order terms. The drop-size distribution, in turn, is shown to be an approximation of a modifiedgamma function. Next, to facilitate calculations at single frequenciesfor workers wanting to obtain attenuation directly, three tables cor-responding to 200C, O°C, and -10'C were generated from Mie computationsfor spherical drops. Values for a and b for 41 frequencies between 1and 1000 GHz for Five drop-size distributions are listed in each table.The authors' comments on the drop-size distributions and their choiceof two distributions to characterize the Laws-Parsons values are worthreading carefully. Finally, Olsen et al derive analytic expressionsfor a and b from rigorous Mie calculations which are more amenable tocomputer generation of multiple-frequency curves. The frequency bandof 1 to IOCO GHz is divided into four segments, each with four powerlaw relatiotiships of the form A - aRb. Two conclusions by the authorsare considered here:

The results show the parameters a and b to be leastsensitive to drop-size distribution in the frequency range 10 - 30 GHz.This is also the range where the relation A - aRb is most accurate."

2. Above 10 GHz, the tabulated values of the Laws-Parsons dis-tribution at 0C is recommended. A "high" rain rate or a "low" rainrate value may be chosen for a frequency.

A summary of what has been presented so far in this section shows thatagreement between measured and theoretical attenuation has been bettersince Medhurst's time. This better agreement is due, at least partly,to improved rain sampling by increased usage of fast-response disdro-meters and rain gauges. There Is an awareness of the importance ofsampling periodically at faster rates rather than relying on cumulativedata. Watson33 reports that a rain gauge with a response slower than15 s will underestimate rainfall intensity at a site and will result ina prediction of low attenuation as reported by Medhurst and other workers10 years ago.

In future research, the parameters of existing drop-size distributionsneed to be reexamined. Although the Laws-Parsons distribution of 1943in particular has stood the test of time below 50 GHz, its underesti-mation of small drops in light rain should give values of attenuationwhich are too low at higher millimeter wavelengths according to Watson. 3 3

This has been the case with the results of Keizer et al. 28 Waldvogelreported that the proportion of small drops can be much higher in a

33M. Watson, 1976, "Survey of Measurements of Attenuation by Rain and

other Hydrometeors," Proc IEEE, 123:863

28W. P. M. N. Keizer, J. Snieder, and C. D. de Haan, 1978, "Rain Atten-uation Measurements at 94 GHz: Comparison of Theory and Experiment,"EPP Symposium, Neubiberg bei MUnchen, Germany

24

thunderstoiin than in a uniform widespread rain of similar rainfall. 15

As recently as 1978, Kharadly et al analyzed over 100 hr of rain activityand found several instances where the measured attenuation was outsidethe limits of Joss's distributions1 9 which enclose all values of theLaws-Parsons distribution. In the light of Keizer and Kharadly's find-ings, it may be instructive to examine Ugai et al 1977 work more closely.12

After noticing that their measured attenuation was two or three times thevalue predicted by the Laws-Parsons distribution, the authors measureddrops down to the 0.05 mm range by improvements in the first two tech-niques for directly measuring raindrop sizes listed on page 9. A com-parison of Ugal et al and the Marshall -Palmer/Laws-Parsons distributionscan be made with figures 4 and 5. Both are in the same units of number iof drops per volume and rainfall rate. Three points become evident:

1, There are more drops in the below 0.5 mm range than a simpleextrapolation of large diameter data would predict as in the Marshall-Palmer and Laws-Parsons distributions.

2. The proportion of drops in each size class remains about thesame regardless of the rainfall intensity. This is not the case i.nthe theoretical distributions where lighter rainfalls have propor-tionately more small raindrops.

S "4

3. At drop sizes 0.5 mm or larger all distributions are in agree-ment, a point made by the authors in their paper.

More data are needed in the size range below 0.3 mm to substantiate orrefute the findings of Waldvogel and Ugal et al. However, this sub-stantiation or refutation can be done only by improving or developingdisdrometers capable of counting in this range with response times ofless than a second. Also, more disdrometers need to be employed at onetime to delineate the microstructure of a rainfall event. Three disdro-meters appear to be the maximum number placed out for a millimeter ex-periment at this date, 4 C probably becruse disdrometers are electronicdevices and expensive compared to tipping bucket rain gauges. Oneingenious way to circumvent this problem is to find the path-averageddistribution of raindrops and rtin rate with a single instrument. Such

15 A. Waldvogel., 1974, "The NO Jump of Raindrop Spectra," J Atmos Sci,31:106719M. M. Kharadly, J. D. McNicol, and J. B. Peters, 1978, "Measurement ofAttenuation Due to Rain at 74 GHz," EPP Symposium, Neubiberg bel MUnchen,Germany12S. Ugai, K. Kato, M. NishijimaT. Kan, and K. Tazaki, 1977, "FineStructure of Rainfall," Ann des Teolecom, 32:422

'o0J. Sander, 1975, "Rain Attenuation of Millimeter Waves at x • 5.77,3,3, and 2mm," IEEE Trans Antennas Propagat, AP-23:213

25

Ij 'L ILI: U I I I I i w =

a device projecting a laser beam along the rain path has been developedby the National Oceanic and Atmospheric Administration at Boulder,Colorado.'12

Backscatter from Rain, Z = ARb

During World War II, several workers 3' 2 9 used Mie computations fortheoretical investigations of the potential of monostatic radar tolocate and characterize meteorological phenomena. Thus radar meteo-rology was born, a field which has been given a comprehensive treat-ment in the standard reference by Battan for frequencies up to about40 GHz.4 3 As In attenuation, a relation between equipment parameters A(in this case, radar) and rainfall rate Is needed for measurement pur-poses. This relation is the familiar Z-R relation, usually stated in I,the form:

Z ARb, (4)

where

Z * reflectivity factor in m2 /m3 (cross section/unit volume)

R - rainfall rate in millimeters per hour

A and b are dependent on frequency, temperature, etc.

In an extensive survey on radar rain backscatter before 1969, Stout andMueller reported differences of more than 500 percent for the same rain-fall among investigators,44 One source of error is the small areasampled by rain gauges or disdrometers compared to the area underlyinga radar resolution cell. Radar and a single tipping bucket rain gaugecan differ by a factor of two in estimating the amount of rain in a

42Ting-i Wang, K. B. Earnshaw, and R. S. Lawrence, 1979, "Path-averaged Measurements of Rain Rate and Raindrop Size DistributionUsing a Fast-response Optical Sensor," J Appl Meteorol (in print)3K. L. S. Gunn and T. W. R. East, 1954, "The Microwave Properties ofPrecipitation Particles," Qua3rt o a Meteorol Soc, 80:52229J, W. Ryde, 1946, "The Attenuation of Centimeter Radio Waves and theEcho Intensities Resulting from Atmospheric Phenomena," JIEE, Vol 93,Part ILIA, No. 1, p. 10143L. J. Batten, 1973, Radar Observation of the Atmosphere, Chicago:The University of Chicago Press44G. E. Stout and E. A. Mueller, 1968, "Survey of Relationships BetweenRainfall Rate and Radar Reflectivity in the Measurement of Precipitation,"J Appl Meteorol, 7:465

26

... .............. ........ 4.•. ,•..u .

cell.4a Even with seven tipping buckets, Desautels and Gunn foundthat if a single averaged relation Z - AR'" 6 derived from five stormswas used to find the amount of rainfall for one storm, errors rangingfrom -35 to +54 percent could result.46 On the other hand, Joss andWaldvogel in a paper presented at the same radar meteorology conferenceclaimed to double the accuracy of radar rain measurements by the useof the A-R relations corresponding to their drizzle, widespreaa, andthunderstorm conditions.• 7 Stout and Mueller also classified Z-Rrelations by general meteorological conditions. After examining44 pairs of A and b values by 13 investigators in their paper, theyconcluded that differences appear to be related primarily to geographic

11area, and secondarily to rain type (continuous, showers, thunderstorms)and synoptic class (fronts, occlusions, waves, etc.). 44

During the past decade, agreement between theory and measurement atIi centimeter radar frequencies has been generally good 48 .49 probably

with improvement in meteorological instrumentation. Another reasonfor good results is that centimeter radar operates in the Rayleighregion where raindrop diameter is small compared to wavelength anddrop shape is not important. The reflectivity factor Z becomes in-dependent of wavelength and can function as a method of comparing

•5M. C. Hodson, 1970, "Rainfall Rate Variation Within a Radar ResolutionCell," Am Meteorol Soc, 14th Radar Meteorol Conference Tucson, AZ,p. 241 Mo' 6G. Desautels and K. L. S. Gunn, 1970, "Comparison of Radar with Net-

work Gauges," 14th Radar Meteorol Conference, Tucson, AZ, p. 239

47j. Joss and A. Waldvogel, 1970, "A Method to Improve the Accuracy ofRadar Measured Amounts of Precipitation," J Atmos Sci, 26:56644G. E. Stout and E. A. Mueller, 1968, "Survey of Relationships BetweenRainfall Rate and Radar Reflectivity in the Measurement of Precipitation,"A 1 Meteorol, 7:465

"8N. C. Currie, F. B. Dyer, and R. D. Hayes, 1975, "Some Properties ofRadar Returns from Rain at 9.375, 35, 70, and 95 GHz," IEEE Inter-national Radar Conference, p. 215

"R9 K. Crane and H. K. Burke, 8,En n "The Evaluation of Models forAtmospheric Attenuation and Backscatter Characteristic Estimation at95 GHz," ERT Document No. P-3606, Environmental Research and Tech- 'nology, Inc., 696 Virginia Rd, Concord, MA 01742

27

711

backscatter at different wavelengths. 8 Generally at these low fre-quencies, Z, as well as attenuation, increases as the rain rate in-creases.4

8

At millimeter frequencies, the larger drops are comparable in sizeto the wavelength and frequency-dependent Mie scattering dominates,although very small drops may still be Rayleigh-scattered as in thc'case of fog droplets. For Mie-scattered waves, the actual drop-sizedistribution Is the most important factor to consider. 4 Theoreti-cal rain backscatter computations, often based on the Laws-Parsonsdistribution, have been extended into the millimeter region by severalworkers. 8 , 35 ,SC, 51 According to Richard and Kammerer, 52 the Soviets.have published extensively on theory--at times based on their owndistributions--but have done no measurements to verify their findings.

r ri

I• .,I

8R. L. Mitchell, 1966, "Radar Meteorology at Millimeter Wavelengths,"Aerospace Corporation, Report TR-669(6230-46)-9, AD 488085

"48 N. C. Currie, F. B. Dyer, and R. D. Hayes, 1975, "Some Propertiesof Radar Returns from• Rain at 9.375, 35, 70, and 95 GHz," IEEE Inter-national Radar Conference, p. 2153 5R. K. Crane, 1966, "Microwave Scattering Parameters for New EnglandRain," Lincoln Lab MIT Technical Report 426, AD 64779850A. Downs, 1975, "A Model for Predicting the Rain Backscatter fromA 70-GHz Radar," BRL Memorandum Report 2467, AD A009699

51D. E. Setzer, 1970, "Computed Transmission Through Rain at Micro-wave and Visible Frequencies," Bell System Tech J, 49:1873

52V. W. Richard and J. E. Kammerer. 1975, "Rain Backscatter Measure-ments and Theory at Millimeter Wavelengths," US Army Ballistic ResearchLaboratory, Report No. 1838, Aberdeen Proving Ground, MD 21005,AD B00817L

28

._ .. _ _ .. 4 ..... _ ...

Also in the West, millimeter measurements of backscatter are almostnonexistent except for the multiwave experiment to be discussed next.49

The multiwave backscatter experiment at 10, 35, 70 and 95 GHz at rainintensities from 1 to 100 mm/hr by Richard and Kammerer 52 is the mostthorough work to date on rain backscatter at millimeter wavelengths.Especially valuable is the ability to relate commonplace X-band (10 GHz)backscatter data (reportedly in good agreement with theory) to scatterat higher frequencies for the same rain condition. For meteorologicaldata, raindrop-size distributions for short periods were taken alongwith longer duration tipping bucket readings. The authors claimed goodagreement at all frequencies. They found only a 5 dB maximum differencebetween their measured backscatter and theoretical values based on soy-eral distributions. Particularly satisfying was the decrease in back- iscatter above 70 GHz predicted by theory. Although the authors andCrane who reviewed this experiment in 197849 believe that theory basedon known average drop-size distributions has been shown to be valid,they caution that not enough is known about drop-size distributions tocalculate reliable estimates of backscatter for any short-time event.11 It would be instructive to eliminate rainfall rate and errors associated

with Its computation by plotting simultaneous values for backscatter forpairs of frequencies as were done by British investigators for one-wayattenuation.. 8 ,41

In summary of the foregoing, backscatter, like attenuation, shows agree-ment between theory and measurement at millimeter wavelengths althoughCImeasurements are very meager at this time. There is also the same needto characterize the raindrop spectra in space and time.

FOGS AND CLOUDS

The small particle sizes of fogs and clouds permit the use of Rayleighapproximations at millimeter frequencies; 3 therefore, attenuation is

49 R. K. Crane and H. K. Burke, 1978, "The Evaluation of Models forAtmospheric Attenuation and Backscatter Characteristic Estimation at95 GHz," ERT Document No. P-3606, Environmental Research and Tech..nology, Inc., 696 Virginia Rd, Concord, MA 0174252V. W. Richard and J. E. Kammerer, 1975, "Rain Backscatter Measure-ments and Theory at Millimeter Wavelengths," US Army Ballistic ResearchLaboratory, Report No. 1838, Aberdeen Proving Ground, MD 21005,AD B00817L38A. M. Zavody and B. N. Harden, 1976, "Attenuation/Rain-rate Relation-ships at 36 and 110 GHz," Electronics Letters, 12:422"41 K. I. Ho, N. D. Mavrokoukoulakls, and R. S. Cole, 1978, "Rain-inducedAttenuation at 36 GHz and 110 GHz," IEEE Trans Antennas Propagat,AP-26:8733K. L. S. Gunn and T. W. R. East, 1954, "The Microwave Properties ofPrecipitation Particles," Quart _J Roy Meteorol Soc, 80:522

29

independent of particle size distribution7 and consists almost entirely :,of molecular absorption.53 Attenuation Is very dependent on liquid (

water content and temperature.8 Theoretical calculations by Koesterand Kosowsky 5 4, 5 5 at millimeter wavelengths reveal that a low-temperature fog may more than double the attenuation raused by a trop-ical fog for the same liquid water content.

Dpite the strong temperature dependency, fog droplets attenuatemil11meter waves about one order of magnitude less than raindrops,This difference is seen by the following range of values taken fromRainwaters for 35 and 95 GHz:

Fog 0.034 - 0.47 dB/km

Rain 0.24 - 4 dB/km

Rain appears to be more significant in affecting millimeter waves thanfog or clouds. However, confirmation is needed in cold advective fogswhich theory predicts as the worst-case condition.

7W. L, Gamble and T. 0. Hodgens, 1977, "Propagation of Millimeter andSubmillimeter Waves," US Army MIRADCOM Technical Report TE-77-14,AD B02362253R. D. Etcheverry, G. R. Heidbreder, and W. A. Johnson, 1967. "Measure-ments of Spatial Coherence in 3.2mm Horizontal Transmission," IEEETrans Antennas Propagat, AP-15:136 A

8R. L. Mitchell, 1966, "Radar Meteorology at Millimeter Wavelengths,"Aerospace Corporation, Report TR-669(6230-45)-9, AD 488085

51K. L. Koester and L. H. Kosowsky, 1970, "Attenuation of MillimeterWaves in Fog," Amer Meteorol Soc, 14th Radar Meteorol Conference,Tucson, AZ, p.55K. L. Kuester and L. H. Kosowsky, 1971, "Millimeter Wave Propagationin Fog," IEEE Antennas and Propagation Symposium, Los Angeles, CA,p. 329

5J. H. Rainwater, 1977, "Weather Affects HiM Wave Missile GuidanceSystems," Microwaves, September, p. 62

30

TURBULENCE

Small-scale fluctuations at centimeter and millimeter frequencies, par-ticularly of atmospheric water vapor, are known to cause local changesin the refractive index. It follows then that limitations may be im-posed on instruments relying on the spatial and temporal coherence ofwavefront$ such as radio interferometers and pencil beam trackingradars. Field experiments in Hawaii,s 6 ,'5 the British Isles,.s86and the Soviet Union62,63 strongly suggest that Tatarski's theory of op-tical wave propagation through a turbulent medium6 4 as further developedby Clifford and Strohbehn 6 s and Ishimaru66 may be useful in gauging themagnitude of scintillations experienced by millimet,r waves in the loweratmosphere.

In England, Mavrokoukoulakis et al found that the frequency spectra ofamplitude fluctuations at 36 GHz and 110 GHz followed Tatarski's -8/3power law, and the ratio of the fluctuations followed Ishimaru's for-mulas for comparing two radio frequencles. 6 1 The authors also foundgood agreement with the experimental work in Hawaii which compared 9.6to 34.5 GHz. 56

To apply Tatarski's theory, an estimate of the physical length of theouter scale of turbulence is needed. One indirect way is to derive itfrom the variances computed for the phase or amplitude fluctuations attwo frequencies. 60 The most direct way pertinent to millimeter andcentimeter wavelengths is to obtain the spectral density of water vaporfluctuations C2 during the experiment. However C2 is a difficult measure-

P Pment to obtain, and it is customarily found indirectly through valuesof the outer scale of the refractive Index or the temperature fluc-tuations, C2 or C2, respectively. 5 9,6 0 The scintillation and temperature

experiment of Ho et a159 is a straightforward example of how an estimateof C2 is used to independently verify that the signal scintillations are

within the limitations imposed by the conditions of Tatarski's theory,The authors found an outer scale of about 25 m.

In summary of turbulence at millimeter wavelengths, millimeter-wavescintillations may be explainable by an extension of Tatarski's theoryfrom optical wavelengths. However, there is need to measure the outerscale of turbulence during millimeter-wave experiments because thisscale is needed to apply Tatarski's theorems, and data are virtuallynonexistent at this date.

CONCLUSIONS

No lengthy conclusion is included here since this report is a survey in-tended to present the atmosphere's effect on millimeter waves. Instead,

*See reference section for references cited on this page.

31

the reader is referred to the summaries at the end of the major break-downs of the report. Most of this review is on rain and raindrop-sizedistributions. This is appropriate because rain, the most common non-gaseous constituent of the lower atmosphere, also has the greatest effecton millimeter waves, and raindrop-size distributions are needed to com-pute the actual and theoretical effect of rain on radio wave propagation.The common thread running through this review is the still pressing needto acquire short-time data on raindrop-size distributions, particularlyin the smallest size classes. Similarly, data on atmospheric fluctua-tions are needed to study the behavior of millimeter waves in turbulence.

32

32?

II'i

REFERENCES

Important references are starred(*).

1. Dyer, F. B., and N. C, Currie, 1978, "Environmental Effects onMillimeter Radar Performance," EPP Symposium, Neubiberg bet MUnchen,Germany.

2. Waters, J. M. 1976, "Absorption and Emission by Atmospheric Gases,"Methods of Experimental Physics, 12(B):142.

*3, Gunn, K. L. S., and T. W. R. East, 1954, "The Microwave Propertiesof Precipitation Particles," urt J Roy Meteorol Soc, 80:522.

4. Fischer, K., 1978, "Atmospheric Influences on the Millimeter andSubmillimeter Wave Propagation," EPP Symposium, Neubiberg bet MUnchen,Germany.

5. Rainwater, J. H., 1977, "Weather Affects MM Wave Missile GuidanceSystems," Microwaves, September, p. 62.

6. Bryant, D. L., and L, J. Auchterlonie, 1979, "Measurement of theExtinction Cross-sections of Dry and Wet Ice Spheres at 35 GHz,"'Electronics Letters, 15:52.

7. Gamble, W. L., and T. D. Hodgens, 1977, "Propatgation of Millimeterand Submillimeter Waves," US Army MIRADCOM Technical Report TE-77-14,AD B023622.

8. Mitchell, R. L., 1966, "Radar Meteorology at Millimeter Wavelengths,"Aerospace Corporation, Report TR-669(6230-46)-9, AD 488085.

9. Anderson, L. J., J. P. Day, C. H. Freres, and A. P. D. Stokes, 1947,"Attenuation of 1.25-Centimeter Radiation Through Rain," Proc IRE,35:354.

10. Joss, J., and A. Waldvogel, 1969, "Raindrop Size Distribution andSampling Size Errors," J Atmos Sci, 26:566.

*11. Laws. J. 0., and D. A. Parsons, 1943, "The Relation of Raindrop-size to Intensity," Trans Am Geophys Union, 24:452.

12. Ugai, S., K. Kato, M. Nishijima, T. Kan, and K. Tazaki, 1977,"Fine Structure of Rainfall," Ann des Telecom, 32:422.

13. Jones, M. A., 1959, "The Shape of Raindrops," JMeteorol, 16:504.

14. Cataneo, R., and G. E. Stout, 1968, "Raindrop-Size Distributionsin Humid Continental Climates, and Associated Rainfall Rate-RadarReflectivity Relationships," J Appi Meteorol, 7:901.

S.. 33

15. Waldvogel, A., 1974, "The N Jump of Raindrop Spectra," JAtmos Sci, 31:1067,

16. Bruer, L. J., and R, K, Kreuels, 1977, "Rainfall Drop SpectraIntensities and Fine Structures on Different Time Bases," Ann desTilicom, 32:430.

17. Bradley, S. a., and C. D. Stow, 1974, "The Measurement of Chargeand Size of Raindrops: Part I. The Disdrometer," J A&p~p Meteorol,13:114.

18. Lammers, U. H, W., 1969, "Electrostatic Analysis of Raindrop Distri-butions," J_ Al Meteorol, 8:330.

19. Kharadly, M. M., J. D. McNicol, and J. B. Peters, 1978, "Measurementof Attenuation Due To Rain at 74 GHz," EPP Symposium, Neubiberg beiMUnchen, Germany.

20. Winn, W. P., 1969, "A Device for Measuring the Radii of Raindrops,"J_ Ap. Meteorol, 8:335.

21. Fujiwara, Miyuki, 1965, "Raindrop-size Distribution from IndividualStorms ," J Atmos Sci, 22:585. " n f F g

22. Smith, P. L., and C, P. Laco, 1978, "Techniques for Fitting Size

Distribution Functions to Observed Particle Size Data," Am MeteorolSoc, 18th Conference on Radar Meteorology, 28-31 March 1978, Atlanta, GA.

23. Laco, C. P., 1978, "A Technique for Fitting Exponential Functionsto Precipitation Particle Size Data," Institute of Atmospheric Sciences,Report 78-3, S. Dakota School of Mines And Technology, Rapid City, SD57701.

*24. Marshall, J. S., and W. McK. Palmer, 1948. "The Distribution ofRaindrops with Size," J Meteorol, 5:169.

*25. Gunn, R.. and G. D. Kinzer, 1949, "The Terminal Velocity of FallFor Water Droplets in Stagnant Air," J Mptan.rn•, 6:243.

26. Dingle, A. N., and Y. Lee, 1972, "Terminal Fallspeeds uo Raindrops,"JAPI Meteorol, 11:877.

27. Berry, E. X., and M. R. Pranger, 1974, "Equations For Calculatingthe Terminal Velocities of Water Drops," J Appl Meteorol, 13:108.

28. Keizer, W. P. M. N., J. Snieder, and C. D. de Haan, 1978, "RainAttenuation Measurements at 94 GHz: Comparison of Theory and Experi-ment," EPP Symposium, Neubiberg bel MUnchen, Germany.

S34

29 ; Ryde, J. W,p 194;, "The Attenuation of Centimeter Radio Waves and

he Echo Intensitiu, : 'multing from Atmospheric Phenomena," JIE.E, VolPart ILIA, No. 1, p., 101.

*30. Medhurst, R. G., 1965, "Rainfall Attenuation of Centimeter Waves:Comparison of Theory and Measurement," IEEE Trans Antennas Propagat,AP-13:550.

31. Crane, R. K., 1971, "Propagation Phenomena Affecting SatelliteCommunication System Operating in the Centimeter and Millimeter Wave-length Bands," Proc IEEE, 59:173.

*32. Olsen, R. L., D. V. Rogers, and D. B. Hodge, 1978, "The aRb Relationin the Calculation of Rain Attenuation," 1978, IEEE Trans AntennasPropagat, AP-26:318.

33. Watson, M., 1976, "Survey of Measurements of Attenuation by Rainand Other Hydrometeors," Proc IEE, 123:863.

34. Crane, R. K., 1968, "Simultaneous Radar and Radiometer Measurementsof Rain Shower Structure," Lincoln Lab MIT Technical Note 1968-33,

AD 678079.

35. Crane, R. K., 1966, "Microwave Scattering Parameters for New EnglandRain," Lincoln Lab MIT Technical Report 426, AD 647798.

*36. Crane, R. K., 1974, "The Rain Range Experiment-Propagation ThroughA S1mulated Rain Environment," IEEE Trans Antennas Propauat, AP-22:321.

37. Richard, V. W., J. E. Kammerer, and R. G. Reitz, 1977, "140-GHzAttenuation and Optical Visibility Measurements of Fog, Rain and Snow,"Ballistic Research Laboratory, Memo Report ABRL-MR-2800, Aberdeen ProvingGround, MD 21005.

38. Zavody, A. M., and B. N. Harden, 1976, "Attenuation/Rain-rate"110 GHz, Electronics Letters, 12:422.

39. Oguchi, T., 1973, "Attenuation and Phase Rotation of Radio WavesDue to Rain: Calculations at 19.3 and 34.8 GHz," Radio Sc., 8:31.

40. Sander, J., 1975, "Rain Attenuation of Millimeter Waves atX 5.77, 3.3, and 2 mm," IEEE Trans Antennas Propagat, AP-23:213.

41. Ho, K. I., N. D. Mavrokoukoulakis, and R. S. Cole, 1978, "Rain-induced Attenuation at 36 GHz and 110 GHz," IEEE Trans AntennasPropagat, AP-26:873.

42. Wang, Ting-i, K. B. Earnshaw, and R. S. Lawrence, 1979, "Path-averaged Measurements of Rain Rate and Raindrop Size DistributionUsing a Fast-response Optical Sensor," J Appl Meteorol (in print).

35 I

43. Battan, L. J, 1973, Radar Observation of the Atmosphere,Chicago: The University o0TniTciagOPress.

44. Stout, G. E., and E. A. Mueller, 1968, "Survey of RelationshipsBetween Rainfall Rate and Radar Reflectivity in the Measurement ofPrecipitation," J Appl Meteorol, 7:465.

45. Hodson, M. C., 1970, "Rainfall Rate Variation Within a RadarResolution Cell," Am Meteorol Soc, 14th Radar Meteorol Conference,Tucson, AZ, p. 2417

46. Desautels, G., and K. L. S. Gunn, 1970, "Comparison of Radar withNetwork Gauges," 14th Radar Meteorol Conference, Tucson, AZ, p. 239.

47. Joss, J., and A. Waldvogel, 1970, "A Method to Improve the Accuracyof Radar Measured Amounts of Precipitation," J Atmos Sc., 26:566.

48. Currie, N. C., F. B. Dyer, and R. D. Hayes, 1975, "Some Propertiesof Radar Returns from Rain at 9.375, 35, 70, and 95 GHz," IEEE Inter-national Radar Conference, p. 215.

49, Crane, R. K., and H. K. Burke. 1978, "The Evaluation of Models forAtmospheric Attenuation and Backscatter Characteristic Estimation at95 GHz," ERT Document No. P-3606, Environmental Research and Tech-nology, Inc., 696 Virginia Rd, Concord, MA 01742.

50. Downs, A., 1975, "A Model for Predicting the Rain Backscatter fromA 70-GHz Radar," BRL Memorandum Report 2467, AD A009699.

51. Setzer, D. E., 1970, "Computer Transmission Through Rain at Micro-wave and Visible Frequencies," Bell System Tech J, 49:1873.

*52. Richard, V. W., and J. E. Kammerer, 1975, "Rain Backscatter Measure-ments and Theory at Millimeter Wavelengths," US Army Ballistic ResearchLaboratory, Report No. 1838, Aberdeen Proving Ground, MD 21005,AD B00817L.

53. Etcheverry, R. D., G. R. Heidbreder, and W. A. Johnson, 1967, "Measure-ments of Spatial Coherence In 3.2-mm Horizontal Transmission," IEEETrans Antennas Propagat, AP-15:136.

54. Koester, K. L., and L. H. Kosowsky, 1970, "Attenuation of Milli-meter Waves in Fog," Amer Meteorol Soc, 14th Radar Meteorol Conference,Tucson, AZ, p. 231.

55. Koester, K. L., and L. H. Kosowsky, 1971, "Millimeter Wave Prop-agation in Fog," IEEE Antennas and Propagation Symposium, Los Angeles,CA, p. 329.

36

' I

56. Janes, H. B., M. C. Thompson, Jr., D, Smith, and A, W. Kirkpatrick,1970, "Comparison of Simultaneous Line-of-Sight Signals at 9.6 and34.5 GHz," IEEE Trans Antennas Propagat, AP-18;447.

57. Thompson, M. C., L. E. Wood, and H. B. Janes, 1975, "Phase andAmplitude Scintillations in the 10 to 40 GI1z Band," IEEE Trans AntennasPropagat, AP-23:792.

58. Mavrokoukoulakis, N. D., K. L. Ho, and R. S. Cole, 1977, "Obser-vation of Millimetre-Wave Amplitude Scintillations in a Town Environ-ment," Electronics Letters, 13:391.

59. Ho, K. L., N. D. Mavrokoukoulakis, and R. S. Cole, 1977, "WavelengthDependence of Scintillation Fading at 110 and 36 GHz," ElectronicsLttters, 13:181.

60. Matthews, P. A., 1977, "Scintillation on Millimetre Wave RadioLinks and the Structure of the Atmosphere," Inst. Radtoengineering &Electronics, Anglo-Soviet Seminar on Atmospheric Propagation at Milli-metre and Submillimetre Wavelengths, Moscow, USSR, p. Hl.

61. Mavrokoukoulakis, N. D., K. L. Ho, and R. S. Cole, 1977, "TemporalSpectra of Atmospheric Amplitude Scintillations at 110 GHz and 36 GHz,"IEEE Trans Antennas Propagat, AP-26:875.

62. Gurvich, A. S,, 1968, "Effect of Absorption on the Fluctuation inSignal Level During Atmospheric Propagation," Radio Engineering andElectronic Ph sscs, 13:1687.

63. Armand, N. A., A. 0. Izyumov, and A. V. Sokolov, 1971, "Fluctuationsof Submil.limeter Waves in a Turbulent Atmosphere," Radio Engineeringand Electronic Physics, 16:1259.

"*64 Tatarski V. I., 1961, Wave Propagation in a Turbulent Medium(translatlon3 , New York: Dover Bo-o s.

65. Clifford, S. F., and J. W. Strohbehn, 1970, "The Theory of Micro-wave Line-of-Sight Propagation Through a Turbulent Atmosphere," IEEETrans Antennas Propagat, AP-18:264.

*66. Ishimaru, A., 1972, "Temporal Frequency Spectra of MultifrequencyWaves in Turbulent Atmosphere, IEEE Trans Antennas Propagat, AP-20:0.

37

SELECTED BIBLIOGRAPHY

Downs, A. R,, 1976, "A Review of Atmospheric Transmission Information inthe Optical and Microwave Spectral Regions," BRL Memorandum Report No.2710.

Harden, B. N., D. T. Llewellyn-Jones, and A. M. Zavody, 1975, "Investigationsof Attenuation by Rainfall at 110 GHz in South-east England," Proc. IEE,122:600. - -

Semplak, R. A., 1970, "The Influence of Heavy Rainfall on Attenuationat 18.5 and 30.9 GHz," IEEE Trans Antennas Propagat, AP-18:507,

Valantin, R., 1977?, "Attenuation Caused by Rain at Frequencies Above 10GHz," Ann des Telecomm, 32:465.

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Comma nder CommanderUS Army Night Vision US Army Training & Doctrine Command

& Electro-Optics Lab Fort Monroe, VA 23651ATTN: DELNV-VI (Richard Bergemarin)Fort Belvoir, VA 22060 Commander

US Army Training & Doctrine CommandCommander ATTN: ATCD-IE-R (Mr. Dave Ingram)US Army Night Vision Fort Monroe, VA 23651

& Electro-Optics Lab ,

ATTN: DELNV-VI (Dr. John Ratches) CommanderFort Belvoir, VA 22060 US Army Training & Doctrine Command

ATTN: ATCD-STECommander Fort Monroe, VA 23651US Army Night Vision

& Electro-Optics Lab CommanderATTN: DELNV-FIR (Fred Petito) US Armiy Training & Doctrine CommandFort Belvoir, VA 22060 ATTN: ATCD-CF (Chris O'Conner)

Fort Monroe, VA 23651CommanderUS Army Engineering Topographic Lab CommanderATTN: ETL-TD-MB US Army Training & Doctrine Command ,,Fort Belvoir, VA 22060 ATTN: ATCD-AN-TD (Seymour Goldbert)

Fort Monroe, VA 23651US Army Engineer SchoolATTN: ATSE-CD CommanderFort Belvoir, VA 22060 US Army Trainin & Doctrine CommandATTN: ATCD-TA (M. P. Pastel)Commandant Fort Monroe, VA 23651 "US Army Engineering Center & School

Directorate of Combat Developments CommanderFort Belvoir, VA 22060 US Army Training & Doctrine CommandATTN: Tech Library

Commander Fort Monroe, VA 23651US Army Mobility Equip R&D CommandATTN: DRDME-RT (Mr. Fred Kezer) Department of the Air ForceFort Belvoir, VA 22060 5WW/DN

Langley AFB, VA 23665DirectorApplied Technology Laboratory CommanderATTN: DAVDL-EU-TSD (Tech Library) US Army INSCOM/QRCFort Eustis, VA 23604 6845 Elm Street - $407McLean, VA 22101Department of the Air Force

OL-C, ,WW MITRE CorporationFort Monroe, VA 23651 ATTN: Rcbert Finkelstein

1820 Dolly Madison BlvdCommander McLean, VA 22101HQ, TRADOCATTN: A'rCD-PM Science Apylications, Inc.tort Monroe, VA 23651 13400 Westpark Drive

ATTN: Dr. John E. CockayneMcLean, VA 22101

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Director General Research CorporationDevelopment Center MCDEC ATTN: Dr. Ralph ZirkindATTN: Firepower Division 7655 Old Springhouse RoadQuantico, VA 22134 McLean, VA 22101

US Army Nuclear & Chemical Agency Commander 14ATTN: MONA-WE (Dr. Jack Berbereb) MIRADCOM7500 Backlick Road ATTN: DRDMI-TE (Mr. W. J, Lindberg)Springfield, VA 22150 Huntsville, AL 35807

Director Teledyne Brown EngineeringUS Army Signals Warfare Laboratory ATTN: Bruce Tully, Mail Stop 19ATTN: DELSW-OS (Dr. R. Burkhardt) Cummings Research ParkVint Hill Farms Station Huntsville, AL 35B07Warrenton, VA 22186

Applied Physics LaboratoryCommander John Hopkins UniversityUS Army Cold Regions Test Center ATTN: Dr. Michael LunATTN: STECR-OP-PM John Hopkins Road AAPO Seattle, WA 98733 Laurell, MD 20810

Effects Technology Inc.ATTN: Jack Carlyle5383 Hollister AvenueSanta Barbara, CA 93111 1Raytheon CompanyElectro-Optics DepartmentATTN: Dr. Charles M. SonnenscheinBoston Post RoadWayland, MA 01778

Norden SystemsATTN: Estelle Thurman, LibrarianNorwalk, CT 06856

MIT Lincoln LaboratoryATTN: Dr, T. Goblick, D-447PO Box 73Lexington, MA 02173

Commander/Di rectorUS Army Combat Surveillance & Target

Acquisition LaboratoryATTN: DELCS-R (Mr, David Longinotti)Fort Monmouth, NJ 07703

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A 7MOSPIIARi(' S( 'IENC.(S RESEA RCU! PA PERS

1. Lindberg, J,D,, "An Improvement to a Method for Measuring the Absorption Coef.ficient of Atmospheric Dust and other Strongly Absorbing Powders,ECOM-5565, July 1975,

2. Avara, Elton, PK, "Mesoscale Wind Shears Derived from Thermal Winds," ECOM.5566,July 1975.

3. Gomez, Richard B,, and Joseph 11, Pierluissi, "Incomplete Gamma Function Approxi.mation for King's Strong.Line Transmittance Model," ECOM.5567, July 1975,

4. Blanco, A,J., and BF, Engebos, "Ballistic Wind Weighting Functions for TankProjectiles," ECOM.5568, August 1975,

5. Taylor, Frodrick J,, Jack Smith, and Thomas H., Pries, "Crosswind MeasurementsLhrc,.ugh Pattern Recognition Techniques," ECOM-5569, July 1975,

6. Walters, D,],, "Crosswind Weighting Functions for Direct.Fire Projectiles," ECOM.5670, Augiust 1975,

7. Duncan, Louis D., "Ail Improved Algorithm for the Iterated Minimal InformationSolution for Remote Sounding of''Temperature," ECOM.5571, August 1975,

8. Robbiani, Raymond L,, 'Tactical Field Demonstration of Mobile Weather Radar SetAN/TPS.41 alt Fort Rucker, Alabama," ECOM-5572, August 1975,

9, Miers, B., G, Blackman, D, Langer, and N, Lorlimler, "Analysis of SMS/GOES FilmData," ECOM.5573, September 1975,

10, Manquoro, Carlos, Louis Duncan, and Rufus Bruce, "'An Indication from SatelliteMoasurements of Atmospheric C,02 Variability," 1,COM.5574, September1975.

11, l'etracca, Carmine, and James D, Lindberg, "Installation and Operation of an Atmo.spheric Particulate Collector," ECOM.5575, September 1975,

12. Avara, Elton P., and George Alexander, "Empirical Investigation of Three IterativeMethods for Inverting the Radiative Transfer Equation," ECOM.5576,October 1975,

13, Alex.ander, George D,, "A Digital Data Acquisition Interface for the SMS DirectReadout Ground Station - Concept and Preliminary Design," ECOM.5577, October 1975,

14. Cantor, Isra•el, "Enhaneemeant of Point Source Thermal Radiation Under Clouds ina Nonattenuating Medium," ECOM.5578, October 1975,

15, Norton, Colburn, and Glenn Hloldale, "The Diurnal Variation of Mixing Height byMonth over White Sandis Missile Rang~e, NM," ECOM.5579, November 1975,

16, Avara, Elton P., "On tie Spectrum Analysis of Binary Data," ECOM-5580, November1975.

17, Taylor, Frvdrick J,, Thomas 11, Pries, and Chao.Huan Huang, "Optinmal Wind VelocityEstiimation," ECOM-5581, December 1975,

18, Avara, Elton P,, "home Effects of Autocorrelated and Cross-Correlated Noise on theAnalysis of Variancep, " l'COM.5582, December 1975,

19. Gillespie, Patti S,, R,L, Armstrong, and Kenneth 0, White, "The Spectral Character.istics and Atmospheric C02 Absorption of the Ho', YLF Laser at 2.05mil,"ECOM.5583, December 1975,

20, Novlan, David J, "An Empirical Method of Forecasting Thunderstorms for the WhiteSands Misfile Rang•," ECOM.5584, February 1976,

21, Avara, Elton P., 'Randomization Effects in Hypothesis Testing with .utocorrelatedNoise," iCOM.5585, February 1976,

22, Watkins, Wendoll R., "Improvements in Long Path Absorption Cell Measuremlent,"ECOM.5586, March 1976,

23. Thomas, ,Joe, George I). Alexander, and Marvin Dubbin, ''SATTIL -- An ArmyDedicated Mleteorouogical 'rehnietry Syste m,' ECOM.i5587, March 1976.

2.1. Kentn'dy, Bruce W., and Delbert Bynum, "Army User Test lProgroni or the liD'l&E,.XM-75 Mereorologicai locket," ECOM-5588, April 1976.

J ..... .... ....... . . .. .............'-1ft .tf l4, IV.... . • • m '

II25, Barnett, Kenneth M,, "A Description of the Artillery Meteorological Comparisons at

White Sands Missh, Range, October 1974 December 1974 ('PASS' •Prototype Artillery IMeteorological] Subsystem)," ECOM.5589, April 1976.

26, Miller, Walter B., "Preliminary Analysis of Fall-of-Shot From Project 'PASS'," ECOM-5590, April 1976.

27. Avara, Elton P., "Error Analysis of Minimum Information and Smith's Direct Methodsfor Inverting the Radiative Transfer Equation," ECOM.5591, April 1976.

28. Yee, Young P,, James D. Horn, and George Alexander, "Synoptic Thermal Wind Cal-culations from Radiosonde Observations Over the Southwestern UnitedStates," ECOM.5592, May 1976,

29. Duncan, Louis D,, and Mary Ann Seagraves, "Applications of Empirical Corrections toNOAA.4 VTPR Observations," ECOM.5593, May 1976,

30, Miers, Bruce 1,, and Steve Weaver, "Applications of Meterological Satellite Data toWeather Sensitive Army Operatlons,"ECOM-5594, May 1976.

31. Sharenow, Muses, "Redesign and Improvement of Balloon ML.566," ECOM.5595,June, 1976,

32, Hansen, Frank V,, "The Depth of the Surface Boundary Layer," ECOM.5596, June1976.

33, Pinnick, R.G., and E,B. Stenmark, "Response Calculations for a Commercial Light.Scattering Aerosol Counter," ECOM.5597, July 1976.

34, Mason, J,, and GB, Hoidale, "Visibility as an Estimator of Infrared Transmittance,"

ECOM.5598, July 1976,35, Bruce, Rufus ,., Louis D, Duncan, and Joseph H. Pierluissi, "Experimental Study of 1

the Relationship Between Radiosonde Temperatures and Radiometric-AreaV Temperatures," ECOM-5599, August 1976,

36, Duncan, Louis D,, "Stratospheric Wind Shear Computed from Satellite ThermalSounder Measurements," ECOM.5800, September 1976.

37, Taylor, F., P, Mohan, P. Joseph and T, Pries, "An All Digital Automated WindMeasurement System," ECOM.5801, September 1976,.38, Bruce, Charles, "Development of Spectrophones for CW and Pulsed Radiation Soturces,"

ECOM.5802, September 1976,39, Duncan, Louis D,, and Mary Ann Seagraves,"Another Method for Estimating Clear

Column Radiances," ECOM.5803, October 1976,40, Blanco, Abel J,, and Larry E, Taylor, "Artillery Meteorological Analysis of Project Pass,"

ECOM-5804, October 1976,41. Miller, Walter, and Bernard Engebos," A Mathematical Structure for Refinement of '3

Sound Ranging Estimates," ECOM.5806, November, 1976,42, Gillespie, James B,, and James D. Lindberg, "A Method to Obtain Diffuse Reflectance

Measurements from 1,0 to 3,0 pm Using a Cary 171 Spectrophotometer,"ECOM-S806, November 1976,

43, Rublo, Roberto, and Robert 0. Olsen,"A Study of the Effects of TemperatureVariations on Radio Wave Absorption,"ECOM.5807, November 1976,

44, Ballard, Harold N,, "Temperature Measurements in the Stratosphere from Balloon.Borne Instrument Platforms, 1968.1975," ECOM.5808, December 1976,

45, Monahan, H.H,, "An Approach to the Short-Range Prediction of Early MorningRadiation Fog," ECOM.5809, January 1977,

46, Engebos, Bernard Francis, "Introduction to Multiple State Multiple Action DecisionTheory and Its Relation to Mixing Structures," ECOM.5810, January 1977, N

47, Low, Richard D.H,,"Effeets of Cloud Particles on Remote Sensing from Space in the10-Micrometer Infrared Region," ECOM-5811, January 1977,

48. Bonner, Robert S., and R, Newton, "Application of the AN/GVS.5 Lager Rangefinderto Cloud Base Height Measurements," ECOM.5812, February 1977, I

49. Rubio, Roberto, "Lidar Detection of Subvisible Rec.ntry Vehicle Erosive AtmosphericMaterial," ECOM-5813, March 1977.

50. Low, Richard 'D.H,, and J.D, Horn, "Mesoscale Determination of Cloud.Top Height:Problems and Solutions," ECOM-5814, March 1977.

51. Duncan, Louis D),, und Mary Ann Svagraves,"I',valuat~ion of the NOAA-4 VITR T1hermnalWinds for Nucloar Fallout Prvdictions,' ECOM-5815, March 1977.

52, Randhawa, .Jagir S,, M. lz~quierdo, Carios Mcl~onald aid Xvl Salpett'r, ''Stratospheric(kowe liensity ais NleaSUred by U C'hemi LluineQscent SeNSOr IDuring theStratcom VI. A Flight,," IX ( )M.5816(, April 1 977,

53. Rubio, Roberto, and Mlk 10I:ýquivrdo, "M visu rerenits of' Not Atmioqpheric Irrad iancioin the 0.7- to 2. 8-M icroiw'ter hIr rareýd H egion,'' lCOM -15817, May 1977.

54, Ballard, Harold N,, Jose MI, Serna, and Frank P., Hudson Consultant for ChemicalKinetics, "Calculation of Selected Atmospheric Composition Parametersfor thv Mid -Latitude, Septembher Stratosphere,' ECOM -5818, May 1977.

55, Mitchell, J.D., R.S, Sagar, and R.O. Olsen, "Positive Ions in the Middle AtmosphereDuring Sunrise Conditions," KCOM-13819, May 1977.

56. White, Kennath 0,, Wondell It, Watkins, Stuart A. Schk'usenier, and Ronald L. Johnson,"Solid-State Laser Wavelength Identification Using a Reference Absorber,"

EC'OM-5824, Junie 1977,

61, r~ub Cell Re oadoutrouend stm Digital2 Video 1977, ncs"ECM585 Jn

582, Millor, W.Dai, and B. gbo, MasPelmnar "Analysis of Obevewoi Sound RaningurAlgorithso " ReletaceM5," July52 1977, 977

59, Dencned, Bruie 1), and Jamey Ani Suearavs, "Balluti PhredTechinius CormpueaurinmSatompelierice Parietes," ECOM -6527, July 1977..

64 Sunidan, Luis, D,,. "Zenith, Angl Vucari adW Wlim, Ivsiation of StlieTemlSudrMaue6b,-liwd Enanncnd mnfrtse ECOM-682, Augsiont 1977SERET

Frank V.4, "The Cr19l77h, snNmbr"EO-52,Speme 9766, Dballar, Marold N,1, and Dranknis Hudlon (lComilrs),U "Steratospica Compllite iren

BealdoonBrornd SExperimnDgt, l Video830 Elctrobers, 1977.2 un67, Barlr, WlimC, and Brngeold CA Peterioia"WindaMeaiuringTAccuracyTestiof

MAleorologmsal Systms52," July53, eme 1977.

68.Ethidg, A. andFV aen"Amspheric Paiffusion: Similarity Jhuor and7.64, Duncan mpirisal "ZerivhAgeVrations for Uaelet inema Soundar a er Mifiio rbeas,"e

ments58," NCovm ber8ugs 1977.69. Lanow, Fricark V,, "The Cinternal Rcladoud RdtiNuFieldan aCM599 Sehiqembor Det7r,

10,Wak~n, inigllo udBon Exlackmnet," ECOM-5830, O~ctober 1977.67.Bar, WlJame C. LindArnodg, " eesn,"idMeasurimnnt Reuiedfu redctio ofs Hig

MneterolgyiLale Trastmisso," ECOM-5834, Deember 1977,

71.RuloRoEmprta " Dnertivations fofArup UsecresBoundAtmospherDfuioall Probleatmsr"

minir nrgyCodBlcns," ECOM-5835 , Decemberr 1977.

72, Monahan, 1-1,1, and R,M, Cionco, "An Interpretative Review of Existing Capabilitiesfor Measuring and Forecasting Selected Weather Variables (EmiphasizingIRemote Means)," ASL.-TR-0OO1, January 1978,

73. Heaps, Melvin (It., "The 1979 Solar Eclipse and Validation of U-Region Models," ASL-'lR.0002. March 1918.

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74. Jeonings, S.,G, and J.B. Gillespie, "MI.i, Theory Sensitivity Studies The Effectsof Aerosol Complex Refractive Indlex and Size Distribution Variationson Extinction and Absorption Coefficients Part It: Analysis of theComputational Results," ASL.TR.0003, March 1978,

75. ,11hite, Kenneth 0. et al, "Water Vapor Continuum Absorption in the 3.4im to 4,UipmRegion," ASL*TR-0004, March 1978.

76, Olsen, Robert 0., and Bruce W. Kennedy, "ABRES Pretest Atmospheric Measure-ments," ASL.TR.0005, April 1978.

77. Ballard, Harold N., Jose M. Serna, and Frank P. Hudson, 'Calculation of AtmosphericComposition in the High Latitude September Stratosphere," ASL-TR-00O6,May 1978.,9

78, Wottkins, Wendell R. et al, "Water Vapor Absorption Coefficients at HF Laser Wave-lengths," ASL-TR.O007, May 1978.

79. Hansen, F'rank V., "The Growth and Prediction of Nocturnal Inversiens," ASL-TR-0008, May 1978,

Y80. Samuel, Christine, Charles Bruce, and Ralph Brewer, "Spectrophone Analysis of GasSamples Obtained at Field Site," ASL-TR-0009, June 19~78,

81. Plnnick, R.G. et al., "Vertical Structure iii Atmospheric Fog and Haze and its Effectson JR Extinction," ASL.TR-0010, July 1978.

82. Low, Richard D.H,, Louis D. Duncan, and Richard B, Gomnez, "The MicrophysicalIBasis of Fog Optical Characterization," ASL.TR-0011, August 1978,

83. Heaps, Melvin G,, "The Effect of a Solar Proton Event on the Minor Neutral84. Constituents of the Sumnmer Polar Mesosphere," ASL-TR..001 2, August 1978.

8.Mason, James B., "Light Attenuation in Falling Snow," ASL-TR-0013, August 1978.85, Blanco, Abel J., "Long.Range Artillery Sound Ranging: "PASS" Meteorological Appli-

cation," ASL-TR.0014, September 1978,86. Heaps, M.G,, and FE, Niles, "Modeling the Ion Chemistry of the D.Reglon: A case

Study Rased Upon the 1906 Total Solar Eclipse," ASL-TR-0015, September1978,

87. .Jennings, S.G., and R,G. Pinnick, "Effects of Particulate Complex Refractive Indexand Particle Size Distribution Variations on Atmospheric Extinction andAbsorption for Visible Through Middle-Infrared Wavelengths," AS L-TR-0016,September 1978,

8 8. Watkins, Wendell R., Kenneth 0. White, Lanny R. Bower, and Brian Z. Sojka, " Pres.sure Dependence of the Water Vapor Continuum Absorption in the 3.5- to4 ,0-Micrometer Region," ASL.-TI{0017, September 1978.

89. Miller, W,B,, and B.F. Engebos, "Behavior of Four Sound Ranging Techniques in anIdealized Physical Enviromnent," .*SL I'R-0018, September 1978,

90, Gomez, Richard G., "Effectiveness Studies of the CBU-88/B Bomb, Cluster, SmokeWeapun" (1.), CONFIDENTIAL ASL-TR-0019, September 1978.

91. Miller, August, Richard ý'. Shirkey, and Mary Ann Seagraves, "Calculation of ThermalEmission from Aerosols Using the Doubling Technique," ASL-TR.0020,November, 1978,

92. Lindberg, James D, et al ., "Measured Effects of Battlefield Dust and Smoke on Visible,Infrared, anid Millimeter Wavelengths Propagation: A Preliminary ReportAonl Dusty Infrared Tvgt.l (l)IRT-l)," ASL-TR-0021, January 1979.

93, Kennedy, B~ruce W., Arthur Kinghorn, and B.R. flixon, "Engineering Flight Testsof Range Meteorological So~inding Systemn Radiosonde," ASL.TR.0022, *

94. Rubio, Roberto, and Don Hoock, "Microwave Effective Eaith Radius Factor Vari-ability at Wiesbaden and Balboa," ASL.TR.0023, February 1979.

95. Low, Richard D.H,, "A Theoretical Investigation of Cloud/Fog Optical Propertiesand Their Spectral Correlations," ASL.TR.0024, February 1979.

..... ..... ..

96. Pinnick, RU,., and H.~J. Auve-.iiann, "Response Characteristics of Knol!enberg Light.Scatte-ring Aerosol Counters," ASL.TR.0025, February 1979.

97. !-leaps, Melvin C., Robert 0. Olsen, and Warren W, Berning, "Solar Eclipse 1979, At-inosplieric Sciences Laboratory Progr-am Overview," ASL-TR-0026 February1979.

*98, BlancoL, Abel J,, "Long-Range Artillery Sound Ranging: 'PASS' GR.8 Sound RangingData," ASL-TrR.0027, March 1979.

99. Kennedy, Bruce W., and Jose M. Serna, "Meteorological Rocket Network SystemReliability," ASL.TR.0028, March 1979,

100. Swingle, 1)c nald M,, "Effects of Arrival Time Errors in Weighted R~ange Equation Solutionsfor Linear Base Sound Ranging," ASL-TR-0029, April 1979,

101. Umstead, Robert K., Ricardo Penn, and Frank V. Hansen, "KWIK: An Algorithm forCalculating Munition Expenditures for Smoke Screening/Obscuration in Tac-tical Situations," ASL.TR.0030, April 1979.

102, D'Arcy, Edward M., "Accuracy Validation of the Modified Niki, Hercules Radar," ASL.TR.00:31, May 1979.

10:1. Rodriguez, Ruben, "Evaluation of the Passive Remote Crosswhid Sensor," ASL.TR.0O32,May 1979.ofNa-uae

104, Barber, 1',L,, and R, Rodgrlquez, "Transit Time Lidar MeasurementofNa-uacWinds In the Atmosphere," ASL.TR.0033, May 1979,II105. Low, Richard D.H., Louis D, Duncan, and Y.Y, Roger R, Hsiao, "Microphysical and Optical

106. odriuezProperties of California Coastal Fogs at Fort Ord," ASL.TR.0034, June 1979.106 RorigezRuben, and William J. Vechione, "Evaluation of the Saturation Resistant Cross.

wind Sensor," ASL-Trt-003, July ing.107. Ohnmtadle, William D., "The Dynamics of Mat(-iial Layerg," ASL-TR-0036, July 1979.108, Pinnick, RG,, S.,G Jennings, Petr Chylek, and HJ, Auvernmann "Relationships between IR

Extinction, Absorption, and Liquid Water Content of Fogs," ASL.TR-0037,10~i Rodri u st, Rube 9,

109.Rodrgue, Ruenand Williamu J, Vechione, "Performance Evaluation of the Optica~l Cross.wind Profiler," ASL-'1R-0038, August 1979. "

10, Mlers, Bruce T,, "Precipitation Estimation Using Satellite Data" ASL-TR-0039, September1979.

111. Dickson, David H., and Charles M. Sonnenschein, "Helicopter Remote Wind SensorSystem Description," ASL-TR-0040, September 1979,

112, Heaps, Melvin, G,, and Joseph M. Heimerl, "Validation of the Dairchemn Code, 1: QuietM idlatitude Conditions," ASL-TR--0041, September 1979.

113I. Bonner, Robert S., and William .1. Lentz, "The Visiocellometer: A Portable Cloud Heightand Visibility Indicator," ASL-.TH-0042, October 1979.

114. C'ohn, Stephen L., "The Role of Atmospheric Sulfates in Battlefield Obscurations," ASL-TR-0o4:3, October 1979,

115. Faw.iU'4h, EdJ, et al, "Characterization of Atmospheric Conditions at the High Energy LaserSystem 'rest Facility (HEI-STF), White Sands~ Missile Rarige, New Mexico, Part1, 24 March to 8 April 1977," ASL-TR-0044, N"uvember 1979

116. B~arb~er, Ted L,, "Short-Time Mass Variation In Natural Atmospheric Dust,"ASL-'rR-0045, November 1979

117. l~ow, Richord DI-l,, "Fog Evolution in the Vimlib and Infrared Spectral Regions and itsMeaning in Optical Modeling," ASL-'l >-0046, December 1979I

118. I111Unco, L~ouis 1). et mil, "The Rlectro-Optical Systemns Atmospheric Effects Library,VoIlume 1: Tlechnical D~ocumentation, ASL-TR-0047, Dueember 1979,

119, Shirkey, R. (", 0' al, "Interinm E-0 SAEL, Volume 11, Users Manual," ASL-TR-0048,IDe)cembel~r 1979,

12), lKohomvnshimi, lN k, -At o.pheric F~fects on N ill) meter Radio WAves,'' ASI-LA'R-0049,1IIL~y1980.

U) S LUOVý INMFN t 'FIINtING 01OI'F Oi1980 611. 11I 5