IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS, VOL. GE-17, NO. 4, OCTOBER 1979

Differential Reflectivity Measurements in Rain:First Experiments

THOMAS A. SELIGA, MEMBER, IEEE, V. N. BRINGI, MEMBER, IEEE, AND H. H. AL-KHATIB

Abstract-Results of the first measurements of differential reflectivity(ZDR) in rain are reported. ZDR = 10 log (ZH/ZV) dB involves copolarmeasurements of ZH and Zv, the radar reflectivity factors at horizontaland vertical polarizations, respectively. The data were obtained withthe University of Chicago-Illinois State Water Survey (CHILL) radarfacility in Oklahoma during Spring 1977 and confirmed theoreticalexpectations that ZDR should be positive, ranging between around0-4 dB. By combining ZDR measurements with ZH, it is shown howestimates of No and Do, the parameters of an exponential raindropsize distribution, can be obtained. These estimates were subsequentlyused to compute rainfall rates as a function of range along a radarray. These results illustrate that ZDR can have important applicationsin the quantitative, remote measurement of drop-size distributions andrainfall.

I. INTRODUCTION

THE POTENTIAL use of differential reflectivity measure-ments at linear, orthogonal polarizations for measuring

precipitation was first introduced by Seliga and Bringi [1].This paper presents the first measurements of differentialreflectivity (ZDR) using the 10-cm University of Chicago-Illinois State Water Survey (CHILL) radar facility. The mainpurpose of these experiments was to determine the feasibilityof measuring ZDR in rain. Further, combining ZDR measure-ments with absolute reflectivity at horizontal polarization (ZH)yields estimates of No and Do which are parameters of anexponential raindrop size distribution. Using these estimates,other size distribution related quantities such as rainfall rateand liquid water content can be computed. Because of limitedresources these first experiments were conducted withoutadequate ground truth observations; hence it is not possible tocompare radar derived estimates of rainrate to direct measure-ments in this paper.

II. REVIEW OF THEORY

The ZDR-technique has been discussed in detail by Seligaand Bringi [1], [2] ; hence only a brief outline of the theorywill be presented here.The shapes of falling raindrops in the atmosphere are usually

nonspherical, resulting in polarization-dependent scatteringproperties. Furthermore, many observations support thehypothesis that raindrops fall with preferred orientation, e.g.,

see Hendry and McCormick [3]. This combined effect ofnonsphericity and preferred orientation of raindrops when in-tegrated over a drop-size distribution results in differentialscattering between horizontally and vertically polarized waves.To apply the ZDR-technique, a truncated exponential rain-

drop-size distribution of the form

N(De) = No exp (-3.67 DeIDo), 0 < De <Dm (1)

is assumed where De is the equivolumic diameter of the non-spherical raindrops, No is the magnitude, Do is the medianvolume diameter, and Dm is the maximum drop-size diameter.Because of truncation in (1), Do loses its precise physicalsignificance for Do > 0.30 cm when Dm = 0.8 cm. Raindropsare assumed to be oblate spheroidal with vertically orientedaxes of symmetry. The a/b ratios as a function of De are givenin Pruppacher and Beard [4] or in simpler form by Green [5],where a and b are the semiminor and semimajor axes of theoblate spheroids, respectively.The average backscattered power from a common pulse

volume centered at range r, due to horizontally or verticallypolarized incident waves, may be expressed by

(PH(r)) = CZHIr2

(Pv(r)) = CZvIr2

(2a)

(2b)

where C is the radar constant and ZH,V are the horizontal andvertical radar reflectivity factors, given by

ZH,V = rrKD2J UH,v(De)NO exp (- 3.67 DelDo) dDe

(3)

X is the incident wavelength;K = (Er - l)/(er + 2), Er being therelative dielectric constant of water; and UH,V are the radarcross sections of the oblate spheroidal drops at horizontal(aligned along the major axes) and vertical (aligned along theminor axes) polarizations. Details of such radar cross sectioncalculations are given in Seliga and Bringi [2]. Differentialreflectivity is defined by

ZDR = 10 log (ZHIZV). (4)Manuscript received May 9, 1979; revised August 16, 1979. This

work was supported by the Atmospheric Research Section of theNational Science Foundation through Research Grants ATM-7683648and ATM-790866.The authors are with the Atmospheric Sciences Program and the

Department of Electrical Engineering, Ohio State University, Colum-bus, OH 43210.

It follows directly from (3) and (4) that ZDR depends on Doalone and is independent of No and radar constants for equalsystem response at both polarizations. Hence it should bepossible to determine ZDR through relative power measure-ments, yielding Do directly. ZDR may also be combined with

0018-9413/79/1000-0240$00.75 © 1979 IEEE

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SELIGA et al.: DIFFERENTIAL REFLECTIVITY MEASUREMENTS IN RAIN

-30

DO / -5u I0z

I Log (Z /NZ45 - -60 N

m/ 0

40 - -70 o

N3.5 -80

_30 90

s 25 -/_ o100 o

5) ~~~~~~~~~~~~020 -110

15 -120 E0

10 _ - -130

05 - -140

0 -1500 005 0.10 015 020 025 030 035 040

Medion Drop Size Diameter Do (cm)

Fig. 1. Differential reflectivity ZnR and normalized horizontal reflec-tivity 10 log (ZHINo) as a function of the equal volume median drop-size diameter Do.

ZH measurements to give NO and, therefore, radar derivedrainfall rates (R). The theoretically calculated values of ZDRand 10 log (ZH/No) as a function ofDo are indicated in Fig. 1.These calculations were based onDm = 0.8 cm, X = 10 cm, anda water temperature of 50C with a/b ratios as a function ofDegiven by Green [5]. Rainfall rate, R mm h-1, is given by

JDmR=0.61r D v(De)No exp (-3.67 DefDo)dDe (5)e 5

where v(De) is the terminal velocity (m * s-1) given by Gunnand Kinzer [6]. This expression may be approximated by apower law relationship of the form Do = 1.053 (R/No)0 22

where Do is in cm, R in mm h-1, and No in m-3 cm-l .The procedure for estimating No and Do from combined

ZDR - ZH measurements is now clear. For a given ZDR mea-surement, Do is obtained from the curve marked ZDR inFig. 1. Corresponding to the value ofDo obtained from ZDR,the theoretical value of 10 log (ZHINo) can be obtained fromthe second curve. By combining this with the radar measure-ment of ZH, NO can be estimated. This procedure yields bothparameters NO and Do of the assumed exponential raindropsize spectra. Calculation of rainfall rate using (5) is thenstraightforward. Sensitivity of the distribution parameters toradar inaccuracies has been examined in [11 .This ZDR -ZH concept for rainfall rate measurement is

similar in philosophy to the rain parameter diagram method ofUlbrich and Atlas [7] where other types of radar observablesare combined and used to estimate No and Do. It can also beshown that ZDR is simply related to the circular polarizationcorrelation technique used by McCormick and Hendry [8].

r= 4S b

V ViH Switch

K 2Ss 2s

|f| On | f | On ft | Transmitter

ZE L 1Z3 Pulses

Est ima ted210 210 | 210 Independent

Pulses

V H H H V V V Hl l l IiI I | Ref lectivity11111111 ~~~~~Record

JjJJ ~~~Sequence

Fig. 2. Polarization switching sequence of CHILL radar, indicatingtransmitter on-off times, number of pulses per polarization, estimatednumber of independent pulses per polarization and the reflectivityrecording events at a single range gate.

III. EXPERIMENTAL METHOD

The 10-cm CHILL radar facility was used for obtaining ZDRand ZH measurements when the radar was located in Okla-homa in the Spring of 1977 and operated by the Illinois StateWater Survey by Dr. Mueller. Certain unique characteristics ofthe radar system are described in [14]. Suitable modificationswere made on the radar to automatically activate a waveguideswitch which switches between horizontal and vertical polari-zations. The switching sequence consisted ofan approximately4-s period divided into two 2-s intervals as illustrated in Fig. 2.Each of these 2-s intervals were devoted to a single polariza-tion and contained four half-second intervals. The shadedinitial half-second intervals correspond to transmitter off timeto enable switching of the polarizations. In each of the threesucceeding half-second intervals the average values of (PH) or

(Pv) over 512 pulses were recorded. This corresponds to tak-ing an average over about 70 independent pulses during eachhalf-second interval [9]. In this manner a sequence of (PH>,(Pv) measurements could be recorded over 4-s periods. Fromthese measurements reflectivity factors ZH and Zv and differ-ential reflectivity ZDR could be found for each range gate.The experimental scheme described here gives ZDR as

10 log [(PH)I(Pv)] where (PH) and (Pv) are measured overdifferent time intervals. This "slow" switching procedure willgive good representative measurements of ZDR only when themean characteristics of the rain do not change significantlyover times on the order of a few seconds. A preferable ap-proach would be to switch polarizations very rapidly on apulse-to-pulse basis. This method has been implemented atthe Chilbolton radar facility by the Appleton Laboratory inthe United Kingdom. Such a "fast" polarization switchutilizes the high degree of correlation between the horizontallyand vertically polarized returns to reduce considerably thestatistical errors in ZDR and enables the measurement to bemade more accurately and rapidly [10]. A switching system

241

IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS, VOL. GE-17, NO. 4, OCTOBER 1979

c

12 4:2E 288.7 1.3H .IGHT 1KM)

go_.90 1.21 1.52 1.83 2.13 2.44 Z.§

_. _ ~. I.

1-0

9J_

1-I

9

Fig. 3. Real time PPI display of the storm at 2700 azimuth with respectto the NSSL WSR-57 radar in Norman, OK. (Courtesy of Dr. P. S.Ray, National Severe Storms Laboratory.)

0.90

I

9

FaLMWS

a,

Ioso

92-

12 4:23 288.7 1.3HEIGHT (KM)

1.21 1.52 1.83 2.13 2.44 I

3.00 45.00 55.00 65.00 75.00 85.00 85.00

RANGE IKM)Fig. 4. Sample plot of horizontal reflectivity ZH(dBZ) versus radarrange. Local time, azimuth and elevation angles and geometric heightabove a spherical earth are also indicated.

of this type was not available for this work and this limitationis not considered serious for the experiments reported here,since only semiquantitative verification of the ZDR conceptwas sought.

IV. RESULTSThe first measurements of ZDR were performed during a

storm of June 12, 1977, at approximately noon local time.Fig. 3 shows the real time PPI display observed with the Na-tional Severe Storms Laboratory WSR-57 radar. The CHILLradar was located southwest of Norman near Anadarko, OK.The storm, located about 150 kmn west of Norman, OK, devel-oped near the Clinton-Sherman AFB (CSM). Observations atCSM indicated that this storm system produced two smalltornadoes. In addition, radiosonde soundings at CSM madeat 1305 CST indicated a stability index of -60C indicatingsevere storms and the possibility of tornadoes. The freezinglevel was at a local elevation of 3.9 km. The results presentedhere are limited to times when the antenna elevation anglewas low enough to ensure that the beam was well below thisfreezing level.

o

IaII

0 .90 1.21 1.52 1.83 2.13 2.44 . 75HE I GHT (KM)

Fig. 5. Differential reflectivity ZDR versus radar range correspondingto reflectivity profiles shown in Fig. 4.

A representative sample of horizontal reflectivity ZH withradar range is shown in Fig. 4. ZH was averaged in range overthree consecutive range gates and for a period of 12 s (12 :04:11-12:04:23 CST) in order to reduce the standard error ofZDR. The azimuth and elevation angles were held constant at1.30 and 288.70, respectively. This representative sample isone data set out of 144 recorded over a period of around 10min and is typical of the low-elevation angle observations.Three distinct cells with peak reflectivity greater than 40dBZare observed at ranges of 48, 55, and 76 km from the radar.The corresponding ZDR values were obtained by comparing

ZH and Zv during the same time period and are given in Fig. 5.This averaging gives approximately a ±0.3dB uncertainty inZDR at the 80-percent confidence level, assuming steady-staterainfall and excluding any calibration errors. There were noopportunities for calibrating ZDR in Oklahoma. Therefore,the calibration of ZDR which was performed in subsequentexperiments at Muskegon, MI, under misty rain conditions,and at Chicago, IL, with the radar pointing vertically duringrainfall was applied to the Oklahoma data. These calibrationswere obtained by Al-Khatib et al. [111 and are used to correctthe ZDR data reported here by subtracting 0.32 dB from Zv.It should be noted that this ZDR calibration may be inappro-priate to the Oklahoma experiments, but is nevertheless usedhere in lieu of other data.

Fig. 5 shows that ZDR is positive and lies within the rangeof about 0 <ZDR < 4.5 dB. The majority of ZDR values liewithin the expected range of 0.35 dB (Fig. 1). The resultsalso show that significant errors in interpreting radar reflec-tivity factors, using the spherical drop shape approximation,are possible. That is, ZH and Zv measurements in rain willtend to overestimate and underestimate the equivalent spheri-cal drop reflectivity, respectively. The important point is thatpolarization effects can significantly affect any interpretationof quantitative radar rainfall measurements when made interms of spherical raindrop shapes.A scatter plot of ZDR versus ZH for these data is shown in

Fig. 6. No obvious relationship between ZDR and ZH isevident, in agreement with the theory that ZDR depends onlyon Do while ZH is a function- of both No and Do in the ex-

i.00 45.00 55.00 65.00 75.00 85.00RANGE (KM)

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243SELIGA et al.: DIFFERENTIAL REFLECTIVITY MEASUREMENTS IN RAIN

12 4:23 288.7 L.310.00 20.00 30.00 40.00 so 00

I~~~~~

o *'

01 ('E ".tw .o ''~~~~~~~~~~~~~~~~~~~~~~~~~~~~1

CDo

CD0 _

CS 00.1o0o. 00 2c.0n 30. 00 40. 00 50.00 6ZH (De)

0.00 10.00 20.00 30.00 t!0.00 50.00

Fig. 6. Scatter plot ofZDR (dB) and ZH(dBZ).

90.90 1.21enS0O0

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0

aU-o

Z O

a:

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II

6000

HEIGHT (KM)°0.90 1.21 1.52 1.83 2.13 2.44 2.'Lo I _ 1_ _ I____ _I __LIJo

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* *I* * *

*A %*

: ** * it

*. .*

o-1 ---I r Ir--- O

35.00 45.00 50.00 65.00 75.00 85.00 95.00RfNGE 1KM)

Fig. 7. Radar derived values of Do corresponding to ZDR profiles ofFig. 5.

o HE I GHT (KM)50.90 1.21 1.52 1.83 2. 13o { _ __ 1_

2.44L

12 4:23 288.7 1.3

Marshall - Palmer N0

O_*

o * _35.00 45.00 55.00 65.00 75.00 85.00

RRNGE (KM)95.00

Fig. 8. Radar derived values of No corresponding to ZH and ZDRprofiles of Figs. 4 and 5.

HE I GHT (KM) 01.52 1.83 2.13 2.44 2.15

I_ _

12 11:23 288.7 1. 3

;SAP.

35.00 45.00 55.00 65.00 75.00 85.00 95.00FIRNGE (KM)

Fig. 9. Radar derived rainfall rates computed from (Do, No) profilesof Figs 7 and 8.

ponential raindrop size spectrum. Nevertheless, there is atendency for ZDR to increase with ZH up to around 30 dBZ.Beyond this level ZDR appears to level off and possibly evendecrease. This behavior, although unconfirmed, is consistentwith a raindrop spectral model in which larger drops in moreintense rainfall break up into smaller drops due to collisionsas in the model of List and Gillespie [12] .Calculated values of Do and No as a function of range are

derived from the data of Figs. 4 and 5 using Dm = 0.8 cmand are shown in Figs. 7 and 8, respectively. These resultsclearly show that the drop-size distribution varies with range.Note that the majority ofDo values lie in the expected range0 <Do < 0.3 cm. The few large values ofDo correspond to thelarge ZDR values (> 3.5 dB) encountered in Fig. 5. Also, Noexhibits wide variability with range with most of the valueslying below the Marshall-Palmer level of 80 000 cm-1 m-3[13]. By combining the values of Do and No the rainfallrate profile can also be found from (5). The result is shownin Fig. 9. The accuracy of this inferred rainfall profile can-not be assessed due to the absence of any other supportingobservations.These Oklahoma results demonstrate that ZDR is a measur-

able parameter, that ZDR can be measured with the slow-switching CHILL radar and that measurements of ZDR inrainfall are in general agreement with theoretical predictions.

V. CONCLUSIONSThe first measurements of differential reflectivity (ZDR)

were made with the CHILL radar facility on June 12, 1977, inOklahoma under thunderstorm conditions. The results tendto confirm earlier theoretical predictions by Seliga and Bringi[1] that ZDR would be of the order of 0-4 dB in rainfall.Sample data sets were presented showing ZDR and ZH, atfixed elevation and azimuth, versus range. Sample profilesof DO, No, and R with range were presented to illustrate theradar technique.A number of further investigations of the ZDR concept

have been initiated. Additional experiments have been per-

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IEEE TRANSACTIONS ON GEOSCIENCE ELECTRONICS, VOL. GE-17, NO. 4, OCTOBER 1979

formed using the CHILL radar through the cooperation ofthe Universities of Chicago and Illinois, and are reported byAl-Khatib et al. [11]. A cooperative research program withthe Appleton Laboratory, England, using the Chilbolton10-cm radar facility has also been initiated to investigate thesignal properties of horizontally and vertically polarized wavesunder various switching conditions [101. These studies areexpected to provide additional insights on the technique andon the meteorological interpretation of data derived fromradars equipped to measure ZDR.

ACKNOWLEDGMENTThe authors are grateful to Dr. R. C. Srivastava of the Uni-

versity of Chicago, IL, and Dr. E. A. Mueller of the IllinoisState Water Survey for their encouragement and support in theuse of the CHILL Radar Facility.

REFERENCES

[1] T. A. Seliga, and V. N. Bringi, "Potential use of radar differentialreflectivity measurements at orthogonal polarizations for mea-suring precipitation," J. Appl. Meteor., vol. 15, pp. 69-76, 1976.

[2] -, "Differential reflectivity and differential phase shift: Appli-cations in radar meteorology," Radio Sci., vol. 13, pp. 271-275,1978.

[3] A. Hendry, and G. C. McCormick, "Polarization properties ofprecipitation particles related to storm structure," J. Rech.Atmos., vol. 8, pp. 189-200, 1974.

[4] H. R. Pruppacher, and K. V. Beard, "A wind tunnel investigation

of the internal circulation and shape of water drops falling atterminal velocity in air," Quart. J. Roy. Meteor. Soc., vol. 96,pp. 247-256, 1970.

[5] A. W. Green, "An approximation for the shapes of large rain-drops," J. Appl. Meteor., vol. 14, pp. 1578-1583, 1975.

[6] R. Gunn, and G. D. Kinzer, "The terminal velocity of fall forwater droplets in stagnant air," J. Meteor., vol. 6, pp. 243-248, 1949.

[7] C. W. Ulbrich, and D. Atlas, 'The rain parameter diagram:Methods and applications," J. Geophys. Res., vol. 83, pp. 1319-1325, 1978.

[81 G. C. McCormick, and A. Hendry, "Principles for the radar deter-mination of the polarization properties of precipitation," RadioSci., vol. 10, pp. 421-434, 1975.

[91 L. J. Battan, Radar Observation of the Atmosphere. Chicago,IL: Univ. Chicago Press, 1973, p. 324.

[101 V. N. Bringi, S. M. Cherry, M. P. M. Hall, and T. A. Seliga, "Anew accuracy in determining rainfall rates and attenuation dueto rain by means of dual-polarization radar measurements,"in Proc. IEE Int. Conf Antenna and Propagat., pp. 120-124,Nov. 1978.

[11] H. H. Al-Khatib, T. A. Seliga, and V. N. Bringi, "Differentialreflectivity and its use in the radar measurement of rainfall,"Atmos. Sci. Prog., Ohio State Univ., Columbus, Rep. AS-S-106,Apr. 1979.

[12] R. List, and J. R. Gillespie, "Evolution of raindrop spectra withcollision-induced breakup," J. Atmos. Sci., vol. 33, pp. 2007-2013, 1976.

[13] A. Waldvogel, 'The No jump of raindrop spectra," J. A tmos. Sc.,vol. 31, pp. 1067-1077, 1974.

[14] E. A. Mueller, and E. J. Silha, "Unique features of the CHILLradar," in Proc. 18th AMS Conf Radar Meteorology, Mar. 28-31,1978, Atlanta, GA, pp. 381-3 82, 1978.

A Model for the Microwave Emissivity of the Ocean'sSurface as a Function of Wind Speed

THOMAS T. WILHEIT, JR., SENIOR MEMBER, IEEE

Abstract-A quantitative model is presented, which describes theocean surface as an ensemble of flat facets with a normal distributionof slopes. The variance of the slope distribution is linearly related tofrequency up to 35 GHz and constant at higher frequencies. Thesefacets are partially covered with an absorbing nonpolarized foam layer.Experimental evidence is presented for this model.

I. INTRODUCTION

THE scanning multichannel microwave radiometer (SMMR)is a five-frequency (6.6, 10.7, 18, 21, and 37 GHz) dual-

polarized microwave radiometer which was carried aboard theNimbus-7 and Seasat satellites, both of which were launched

Manuscript received May 2, 1979;revised August 30, 1979.The author is with Goddard Space Flight Center, Greenbelt, MD

20771.

in 1978. The instrument has an 80-cm parabolic dish antenna,which scans its main beam 500 in azimuth along a conicalsurface with a 420C cone angle and a vertical axis. This pro-vides a constant incidence angle of approximately 50° at theearth's surface for the orbital altitudes of the two spacecraft(ca. 600 km Seasat, 800 km Nimbus). The spatial resolutionis proportional to wavelength and varies from approximately150 km at 6.6 GHz to 25 km at 37 GHz. The instrument hasbeen described in detail by Gloersen and Barath [1]. The pur-pose of this instrument is to measure sea surface temperatureand wind speed at the sea surface globally, even in the pres-ence of clouds and light rain.The SMMR, being a radiometer, measures the upwelling

thennal microwave radiation, the intensity of which is charac-terized by a brightness temperature. The physical significance

U.S. Government work not protected by U.S. copyright

244