GEOPHYSICAL RESEARCH LETTERS, VOL. 27, NO.12, PAGES 1763-1766, JUNE 15, 2000

Comparison of Simultaneous Rain Drop Size Distributions

Estimated from Two Surface Disdrometers and a UHF Profiler

Christopher R. Williams, 1.2 Anton Kruger,3 Kenneth S. Gage,2 Ali Tokay,4.S

Robert Cifelli,s.6 Witold F. Krajewski3 and Christian Kummerows

Abstract. In support of the NASA Tropical Rainfall Measur-ing Mission (TRMM) Ground Validation Program, a suite ofsurface instruments and vertical pointing Doppler radarprofilers were deployed in central Florida to quantify thenumber and size of the rain drops reaching the surface.Analyzing 276 minutes of simultaneous observations from twosurface disdrometers and one profiler revealed good agreementamong the instruments for drop sizes > 1.5 mm diameter butpoor agreement for smaller drop sizes. The magnitude of thedifference in small drop estimation was proportional to thereflectivity (and rainrate). At reflectivities greater than 40dBZ, the differences in the estimation of the number of smalldrops yielded differences in estimates of mass-weighteddiameter of > 13% and of rainrate > 25%. The combinedeffect of these uncertainties impact the interpretation of theprecipitation processes and the development and validation ofspace-based precipitation retrieval algorithms.

These instruments were deployed in the TRMM GroundValidation Field Campaigns to quantify the rain drop sizedistribution near the surface.

Equipment DescriptionJoss- Waldvogel Disdrometer

The Joss-Waldvogel disdrometer (JWD) (Joss andWaldvogel 1967) is manufactured by Distromet II'1c. TheJWD's durability and accuracy in measuring integral DSDparameters like rainrate and reflectivity has made it thestandard instrument for surface precipitation measurements forthe last 30 years. The JWD estimates the diameter or thedrops by sensing the voltage induced from the downwarddisplacement of a 50 cm2 styrofoam cone. The output voltagerelates to the diameter of the raindrop falling at terminalvelocity (Joss and WaldvogeI1977).

This disdrometer has a dead-time associated with therecovery time of the transducer immediately following theimpact of a rain drop. No rain drops are detected during thisdead-time. An analytic correction has been proposed by themanufacturer to account for the drops missed during the dead-time and has also been reported by Sheppard and Joe (1994)and Sauvageot and Lacaux (1995):

(I)

where Nj is the number of drops with diameter Dj withoutcorrection, N: is the number of drops with diameter Dj withcorrection, and T is the sampling time in seconds (seeSauvageot and Lacaux (1995) for more details). The JWDobservations used in this study were corrected for theinstrument dead time using (I). The JWD was calibrated bythe factory on 6 Apri11998.

Introduction

The Tropical Rainfall Measuring Mission (TRMM) satellitecombines passive and active remote sensors to estimatemonthly rainfall over 5 degree latitude by 5 degree longitudeboxes with an accuracy greater than I mm/day or 10% inheavy precipitation (Chang et al. 1999). To achieve thisaccuracy, the algorithms that convert the observed quantitiesinto rainfall estimates must account for the variations in theprecipitation processes over the different geographic regionsof the tropics. An important quantity thought to vary over thedifferent life cycles of the precipitation processes is the raindrop size distribution (DSD). ,

During the second phase of the TRMM Ground ValidationProgram TExas -FLorida UNderflight Experiment (TEFLUN-B), a Joss-Waldvogel disdrometer (JWD), a two-dimensionalvideo disdrometer (2DVD), and a vertically pointing profileroperating at 915 MHz were deployed on Triple-N-Ranchapproximately 40 kIn west of Melbourne, Florida. Allinstruments were within 20 meters of each other and wereoperational for the months of August and September 1998.

Two-Dimensional Video Disdrometer

With the advance of optical electronics and video signalprocessing, Joanneum Research, Graz, Austria, developed anew device called a two-Dimensional Video Disdrometer(2DVD). As a raindrop passes through a 10 cm wide sheet oflight, a fast line-scanning camera detects the projected s\1~dowand records the two-dimensional shape of the raindrop. Atapproximately 6 mm below the flfSt sheet of light lies a secondsheet of light projecting in the orthoginal plane. Videoprocessing of the two images removes beam blockage effectsfrom multiple drops not resolved from a single view angle.For this study, the nominal diameter resolution was a constant0.2 mm with a minimum diameter centered on 0.5 mm. Thelargest observed drop was 6.3 mm.

lCooperative Institute for Research in Environmental Science,University of Colorado, Boulder.

2National Oceanic and Atmospheric Administration, AeronomyLaboratory, Boulder, Colorado.

~e Iowa Institute of Hydraulic Research, The University of Iowa,Iowa City.

4National Aeronautical Space Administration, Goddard SpaceFli§ht Center, Maryland.

Joint Center for Earth Systems Technology, University ofMaryland at Baltimore County.

6Atmospheric Science Department, Colorado State University, FortCollins.

:opyright 2000 by the American Geophysical Union.

Paper number 1999GLO11100.

0094-8276/00/1999GLO11100$05.00

Vertical Pointing Doppler Profiler

The vertically pointing profiler observes the Dopplervelocity of the air motion or hydrometeors directly overhead

763

WILLIAMS et at.: COMPARISON OF SIMULTANEOUS DROP SIZE DISTRmUTIONS

(Gage et al. 1994; Carter et al. 1995). Operating at 915 MHz,the profiler detects backscattered energy from gradients in therefractive index in clear-air (Bragg scattering) and fromhydrometeors (Rayleigh scattering) (Gage et al. 1999). Theprofiler estimates the rain drop size distribution from thespectrum of raindrop terminal fallspeeds. Therefore, theobserved Doppler velocity spectra of the hydrometeor motionsmust be shifted by the mean air motion to obtain the terminalfallspeed spectra. A multiple peak picking routine separatesthe air motion and hydrometeor motion portions of theDoppler spectra. After shifting the hydrometeor portion of thespectra by the mean air motion, the discrete rain drop sizedistribution is estimated using the formulation (Atlas et al.1973):

a. Reflectivit;y

~60 ~50

~.-40>.~~ 30

c::"~ 20 ., ...,. .

b. Rain Rate

.~:~::I::!::1~:i:~~:j::j~:1::f::

I:~I ~: : : i. .

~

, , , , , , ,..

~! ! ~! !! !1:t!~! j! j!i! j!! j! ! !:! ! !: :! !!i:!!1!

~

'.:=

!£~=.~~

100;

lU,

1,

6.~~ ~.

~4.i ~

:~::c. Joss~Waldvo2el DisdrometerNumber Concentration

log(N(D))

l ~

O

log(N(D))4

3

2

1

O

log(N(D))

I ~

1

O

~ (2)N(D) =

I" ,U I; i i; ;

.d. .Io~a 2-D, V.id~o .Di.sd!,ol:11e~er.N:u/1:1be:r t;:011C~n\l'a!ion .

D6dD

where S(v) is the reflectivity at each Doppler velocity spectralpoint v. dv is the Doppler velocity resolution, D is the diameterin mm, and dD is the diameter resolution associated with eachD. The observed Qoppler velocities are converted intodiameters using the relation (Atlas et al. 1973):

Vt(D) = 9.65 -.lO.3exp[ -0.6D] (3)

a).!4..."..,

~0where V1(D) is the terminal fallspeed in ms-1 of the drop of

diameter D expressed in mm. For this study, the profilerobservations at the range gate centered at 307 meters above thesurface were compared with the surface observations.

Observed Rain Drop Size Distributions

On 17 September 1998, a precipitation event passed overthe instrument site generating 276 minutes of simultaneousobservations. This event produced the total rainfallaccumulation of 76 mm mainly due to heavy convectiveprecipitation, with corresponding reflectivities greater than 50dBZ.

01 ..; ;i i i i i i i. ii i ;ie. Profiler Number Concentration

6 I.' .: :' ; ~~' ~~' '~~ ~~~ ~~: ~ : ;'t;'...I54.11 3.

.,j~.0 1.

O I; : ; ; i : ..;18:00 19:00 20:00 21:00 22:00 23:00 24:00

Hour of Day (UT)

Figure I. Reflectivity (a) and rainrate (b) calculated from thesurface Joss-Waldvogel disdrometer (blue), the surface two-dimensional video disdrometer (red), and the 915 MHzprofi1er (green) at 327 meters above the ground. Drop sizedistribution number concentration, N(D), estimated from theJoss-Waldvogel disdrometer (c), the two-dimensional videodisdrometer (d), and the 915 MHz profiler (e). The solid linein (c), (d), and (e) indicates the mass weighted mean diameter,

Dm.

DSD Number Conceutratiou for each Minute

Figure I shows the time etolution of the surfaceprecipitation. Panels la and lb show the total reflectivity andrainrate for all three instruments. Panels lc, Id, and le showthe rain drop size distributions obtained from all three instru-ments. The number concentration, N( D ), in units of numberof drops per cubic meter per diameter interval, accounts for thedifferent sampling volumes of the three instruments. Superim-posed on the number concentration panels (lc, Id, and le) arethe calculated mass weighted mean diameters, Dm:

D"",

J N(D)D4dD

two disdrometers, discrepancies exist in the small diameterregime. The JWD appears to be underestimating the numberof small drops relative to the 2DVD. The underestimationoccurs throughout the event.

The bottom panel of Figure I shows the 915 MHz.ptofilerderived rain drop number concentration. The largest diameterdetected in the profiler DSD parallels the largest di~mete..J.detected by the JWD and 2DVD, indicating that these.instru-ments observe the same general features of this precipitationevent. The profiler derived DSD does not have a decrease innumber concentration at diameters less than I mm as observedby the JWD. Instead, the number concentration increases withdecreasing diameters, consistent with the 2DVD observations.The ability of the multiple peak picking algorithm to separatethe air motion and hydrometeor motion in the Doppler velocityspectra determines the smallest resolved diameter in theprofiler observations. Overlapping Bragg and Rayleighportions of the spectra increases the minimum resolveddiameter.

Dmin (4)Dm = ~

N(D)D3dD

Dmin

Comparing number concentrations from the two surface

disdrometers, both similarly resolve the maximum diameter

for each minute observation. The JWD maximum resolved

diameter of 5.25 mm (based on hardware constraints) is

reached during the convective rain near 19:15 UTC. The

consistency in the envelope of maximum diameter between the

two instruments suggests their similar sensitivity to the large

diameter region of the drop size spectra. As opposed to the

consistency of the maximum resolved diameter between the

WILLIAMS et al.: COMPARISON OF SIMULTANEOUS DROP SIZE DISTRIBUTIONS [765

--a. Number Concentration

~10000; "2(3O- 35), n= 632(40-45), n= 372(5O-55), n= 8

~

:k\",.

.8

~=O

.=tUb=4)u=o

U

~8:)

Z

1000

100

10

Mean Number Concentration

In order to more clearly illustrate the effect ofunderestimat-ing the small drop region in the retrieved size distribution, themean drop size distributions, the mass weighted mean diame-ters, and rainrate are calculated for each instrument. Figure 2shows these mean quantities for the reflectivity intervals 30-35, 40-45, and 50-55 'dBZ.

The mean number concentrations shown in Panel 2a can beanalyzed over three different diameter ranges: small drops(less than 1.5 mm), medium drops (between 1.5 and 3 mm),and large drops (greater than 3 mm). Of these three diameterregions, the best agreement between the three instrumentsoccurs in the medium drop regime. For the small diameterregion, the JWD underestimates the number concentration forall quartiles relative to the 2DVD and profiler. The amount ofdisagreement between the JWD and the other two instrumentsincreases with reflectivity.

Panels 2b and 2c show the mass weighted mean diameter,Dm, and mean rainrate for each 5 dBZ reflectivity interval forthe surface disdrometers. These panels illustrate the diversionof the calculated values for these two instruments at and abovethe 30-35 dBZ reflectivity interval. The diversion is caused bythe underestimation of the small drops in the DSD. Fiftypercent of the observations in this precipitation event had2DVD reflectivities greater than 34 dBZ. Thus, the diversionin the calculated values effects approximately 50% of theobservations in this case study.

Z(50-;.S5)

..., ....' , , ..

..:.Z(30.:..35'. ..:.1

0 1 2 3 4 5 6Diameter (mrn)

-e b. Mass Weighted Mean Diameter9 3.0 I. I..

v~ 2.5~02.0~~ 1.

"31.0.:Qbl)~ 0.5

~ ocu .

~

~:,

.r

5

20 25 30 35 40 45 50 55Reflectivity (dBZe)

Discussion

The loss-Waldvogel impact disdrometer, designed tomeasure the total integrated rainrate and radar reflectivityfactor of the surface rain in order to improve scanning radarestimates of rainfall (loss and Waldvogel 1977), has gainedfavor as the reference surface disdrometer due to its durabilityand accuracy. Although not designed for detailed studies ofthe rain drop size distribution, many researchers have success-fully used the JWD to investigate the DSD to improve under-standing of the cloud processes associated with precipitation(see for example, Waldvogel 1974; Ulbrich 1983; Feingoldand Levin 1986; McFarquhar and List 1993). Two limitationsof the JWD for detailed rain drop size distribution analysishave been documented in previous studies. First, the mini-mum resolved diameter is variable and greater than 0.3 mmdepending on the ambient noise and the rain intensity (lossand Gori 1976; Sauvageot and Lacaux 1995; McFarquhar et al.1996). Second, the total calibration is accurate for integratedreflectivity estimates but the diameter-to-diameter calibrationis not adequate for identifying multiple peak distributions(Sheppard 1990).

The analysis presented in this work is consistent with thefirst documented limitation. Namely, the minimum resolveddiameter is variable and sensitive to noise in the enviroqIpent.In this study, the insensitivity of the JWD may extend to 1.5mm diameter during heavy rainrates (greater than 40 dBZ)when the effects of noise in the environment and noiseproduced by the rain itself are combined.Figure 2. Mean drop size distribution (a) for reflectivity

intervals 30-35, 40-45, and 50-55 dBZ, JWD (blue), 2DVD(red), and 915 MHz profiler (green). Mass weighted meandiameter (b) and mean rainrate (c) for 5 dBZ reflectivityintervals. The squares indicate the JWD and circles the2DVD. Number of samples in each 5 dBZ interval: 10, 73,63,61, 37,23, and 8.

Conclusion

During TEFLUN-B, a precipitation event on 17 September1998 yielded 276 minutes of simultaneous measurements fromcollocated JWD, 2DVD, and profiler instruments. Analysis of

WILLIAMS et al.: COMPARISON OF SIMUL' 'ANEOUS DROP SIZE DISTRIBUnONS766

the resulting drop spectra showed that while there was generalagreement among the instruments for larger drop sizes (greaterthan 1.5 mm diameter), there was poor agreement among theinstruments for smaller drop sizes. The JWD measuredsignificantly fewer drops at sizes < 1.5 mm diameter incomparison to the other instruments. At reflectivities greaterthan 40 dBZ, the differences in the estimation of the numberof small drops by the JWD compared to the 2DVD yielddifferences in estimates of mass-weighted diameter of morethan 13% and ofrainrate of more than 25%.

From this work, one should not conclude that rain drop sizedistributions are best analytically described with exponentialfunctions. At low intensity rainrates, the one-minute DSDsobtained from the 2DVD and profiler had curvature substan-tially different from exponential (not shown in this work). Theanalysis presented in this work does not refute the curvature ofthe DSDs, but it demonstrates that the JWD observations mayoveremphasize the convexity of the drop size distribution.This increased curvature in the DSD increases the calculatedmass weighted mean diameter, Dm. and decreases the calcu-lated rainrate.

It is very difficult to estimate the small drop regime of theDSD particularly at high rainrates using anyone of the threeretrieval technologies presented. Using computational fluidmechanic methods, the 2DVD underestimates the number ofsmall drops during windy conditions (Nespor et al. 2000). Notincluding the turbulent air motions in the profiler retrievaloverestimates the number of smaller drops. The agreementamong the three instruments at diameters greater than 1.5 mmindicates that the three retrieval technologies are complimen-tary in this size range and should be deployed together toexploit their inherent strengths. Further analyzes of theprofiler. JWD, and 2DVD derived-DSD and comparisons totipping bucket rain gauges and in situ aircraft data must beperformed to understand the causes and to quantify theuncertainties between the different DSD measurement technol-

ogies.The main ramification for TRMM physical validation

studies incorporating DSD measurements is that the uncertain-ties associated with DSDs have. in addition to sample sizedependence, afunctional dependence on drop size that islikely different among the profiler, 2DVD, and JWD instru-ments. The combined effect of these uncertainties impact th~interpretation of the precipitation processes and the develop-ment and validation of space-based precipitation retrieval

algorithms.

References

Atlas, D., R. C. Srivastava and R. S. Sekhon, 1973: Doppler radarcharacteristics of precipitation at vertical incidence, Rev.Geophys. Space Phys., II, 1-35.

Carter, D. A., K. S. Gage, W. L. Ecklund, W. M. Angevine, P. E.Johnston, A. C. Riddle, J. Wilson, and C. R. Williams, 1995:Developments in lower tropospheric wind profiling at theNOAA Aeronomy Laboratory. Radio Science, 30, 977-1001.

Chang, A. T. C., L. S. Chiu, C. Kummerow, J. Meng, and T. T.Wilheit, 1999: First results of the TRMM microwave imager(TMI) monthly oceanic rainrate: Comparison with SSM/I.Geophys. Res. Lett., 26,2379-2382.

Feingold, G., and Z. Levin, 1986: The lognormal fit to raindropspectra from frontal convective clouds in Israel. i. Climate andAppl. Meteor., 25, 1346-1363.

Gage, K. S., C. R. Williams, and W. L. Ecklund, 1994: UHF windprofi1ers: A new tool for diagnosing tropical convective cloudsystems. Bull. Amer. Meteorol. Soc., 75,2289-2294.

Gage, K. S., C. R. Williams, W. L. Ecklund, and P. E. Johnston,1999: Development and application of Doppler radar profi1ers toground validation of satellite precipitation measurements. Adv.Space Res., 24,931-934.

Joss, J., and A. Waldvogel, 1967: A raindrop spectrograph withautomatic analysis. Pure Appl. Geophys., 68,240-246.

Joss, J., and E. Gori, 1976: The parametrization of raindrop sizedistribution. Rivista ltaliana De Geofisica, 3, 275-283.

Joss, J., and A. Waldvogel, 1977: Comments on "Someobservations on the Joss-Waldvogel rainfall disdrometer." I.Appl. Meteor., 16,112-113.

McFarquhar, G. M., and R. List, 1993: The effect of curve fits forthe disdrometer calibration on raindrop spectra, rainfall rate, andradar reflectivity. I. App. Meteor., 32,774-782.

McFarquhar, G. M., R. List, D. R. Hudak, R. P. Nissen, J. S.Dobbie, N. P. Tung, and T. S. Kang, 1996: Flux measurementsof pulsating rain with a disdrometer and Doppler radar duringPhase II of the Joint Tropical Rain Experiment in Malaysia. i.Appl. Meteor., 35, 859-874.

Ne§por, V., W. F. Krajewski, and A. Kruger, 2000: Wind-inducederror of rain drop size distribution measurement using a two-dimensional video disdrometer, Journal of Atmospheric andOceanic Technology, submitted.

Sauvageot, H. and J-P. Lacaux, 1995: The shape of averaged dropsize distributions. i. Atmos. Sci., 52, 1070-1083.

Sheppard, B. E., 1990: Effect of irregularities in the diameterclassification of raindrops by the Joss-Waldvogel disdrometer. i.Atmos. Oceanic Technol.,7, 180-183.

Sheppard, B. E., and P. I. Joe, 1994: Comparison of raindrop sizedistribution measurements by a Joss-Waldvogel disdrometer, aPMS 2DG spectrometer, and a POSS Doppler radar. I. Atmos.Oceanic Technol., II, 874-887.

U1brich, C. W., 1983: Natural variations in the analytical form inthe raindrop size distribution. I. Climate and Appl. Meteor., 22,1764-1775.

Waldvogel, A., 1974: The No jump of raindrop spectra. I. Atmos.Sci.,31, 1067-1078.

Acknowledgments. Aeronomy Laboratory research for the TRMMField Campaigns has been supported, in part, by funding from NASAHeadquarters through the NASA TRMM Project Office. TheUniversity of Iowa research for the TRMM Field Campaigns has beensupported, in part. by NASA Grant NAG 6-2084. We thank ProfessorEd Zipser for supplying the Joss-Waldvogel disdrometer. We thankDr. Sandra Yuter for her comments placing the JWD results in contextwith previous work. We thank the Florida Fresh Water Fish andGame Department for making Triple-N-Ranch available of our useduring the TEFLUN-B campaign.

Christopher R. Williams, ClRES/NOAA Aeronomy LaboratoryMS R/AL3, 325 Broadway, Boulder, CO 80303-3328. (e-mail:cwilliams @ ai.noaa.gov )

(Received: September 20, 1999; revised: February 2, 2000accepted: Apri114, 2000)