632 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 4~

Distributions of Raindrop Sizes and Fall Velocities in a Semiarid Plateau Climate:Convective versus Stratiform Rains

SI-JENGJIE NIU AND XING CAN JIA

Key Lahort/tory of Meteorological Disaster (K LME), Miflislry oj EdIlClIl;OIl. School oJ Atmospheric Physics,Nalljill8 Vllil'crs;,.\' of lnformntiOlI Science and Tet:!lI/o!ogy. Ntmji/lg, Chil/(I

JIANREN SANG

Ningxia /lIstillftC oJ Mereorologicl/l Science, Yillcllllm/, Chill(l

XIAOLI LJu AND CI-lUNSONG LvKey Ll/bortltory of Meteorological Dismilc:r (K LME), Minislry of Educatiun, School of AUlJospheric Physics.

NflJlji"B University of IIl/urmmiOlI Science IIlftl Tcc:llllo{ogy. NUI/jillg. Chil/a

YANGANG LJu

Brookhat1en NmioJla/ Labomtory. Upto", Nelli York

(Manuscript received 3 March 2009, in finlll form 11 November 2009)

ABSTRACT

Joint size and fall velocity distributions of raindrops were measured with a Particle Size and Velocity(PARSIVEL) precipitation particle disdromcterin a field experiment conducted during July and August 2007at a semiarid continental site located in Guyuan, Ningxia Province, China (36"N, l06"16'E). Dil\a from bothstratiform and convective clouds arc analyzed. Comparison of the observed rnindrop size distributions showsthat the increase of convective min rates arises from the increases of both drop concentration and dropdiamctcr while the increasc of the rain mte in the str3tiform clouds is mainly due to the increase of median andlarge drop concentration. Another striking contrast between the stratiform and convective rains is that thesize distributions from the strntiform (convective) rains tend to narrow (broadcn) with increasing rain rntes.Statistical analysis of the dislribution pattern shows that the observed size distributions from both rain typescan be well described by the gamma distribution. Examination of the raindrop fall velocity reveals thnt thedifference in air density leads to l.l systematic change in the drop fall velocity while organized air mOlions(updrafts and downdrafts), turbulence, drop breakUp, and coalescence likely cause the large spread of dropfall velocity, along with additional systematic deviation from terminal velocity al certain raindrop diameters.Small (large) drops tend to have superterminal (SUbterminal) velocitics statistically, with the positive de­viation from the terminal velocity of small drops being much larger than the negative deviation of large drops.

1. Introduction

As a key component of the hydrologic cycle, pre­cipitation is critical [or understanding the earth's climateand predicting climate change as a resull of human ac­tivities, such as emission of greenhouse gases and aerosolparticles into the atmosphere (Chahine 1992; Entekhabi

Corresponding ali/hoI' address: Prof. Shcngjie Niu, Key Labo­ratory of Metcorological Disaster(KLME), Ministry of Education.School of Atmospheric Physics, Nanjing University of InformalionScience and Technology (NUISn, Nanjing, China.E-mail: niusj@nuisl.edu.cn

DOl: 10.1 I75/2009JAMC2208. I

© 2010 American Meteorological Society

et aJ. 1999). Precipitation processes need to be parame­lerized in global climate models because these processesoccur over scales smaller than typical model grid sizes.Over Ihe lasl few decades, increasing errorl has beendevoted 10 improving global satellite remote sensingor precipitalion (Tokay and Shorl 1996) and parame­lerization of precipitalion processes in global climatemodels (Rotstayn 1997), and great progress has beenmade in bOlh areas as a resulL. Despile the great prog­ress, precipitation measurement and parameterizationstill suffer from large uncertainties, and much remains tobe done.

APRIL 2010 NIU ET AL. 633

As probably the most fundamental microphysical prop­erty of precipitation, knowledge of the raindrop size dis­tribution (RSD) is essential for further improving remotesensing and parameterization of precipitation processes.Accurate knowledge of the RSD is important in tele­communications, precipitation scavenging of aerosolparticles, soil erosion, and understanding precipitationphysics as well (Uijlenhoet el al. 2003; Uijlenhoet andTorres 2006). In particular, recent development in re­mote sensing techniques permits long-term retrievalsof more RSD parameters and their vertical profiles overlarge areas (Bringi et al. 2003; Kirankumar el al. 2008).Such progress enhances our abilily to monitor precipi­tation and provides powerful tools to investigate rain­fall microphysics, and at the same time, calls for moreaccurate assumptions regarding the spectral shape ofRSDs. For example, studies have shown that RSDs varyboth spatially and temporally, not only within a climaticregime but also within a specific rain type (Nzeukou et al.2004). The wide RSD variability represents a majorsource of inaccuracy in rainfall estimation by remotesensing, and this is especially true for drops smaller thanaboul 1.5 mm because of the limited sensitivity andaccuracy of available remote sensing techniques (Williamsel al. 2000). Our understanding of the RSD variation,especially, with different precipitation types is still far[rom complete, and more analyses of in situ measurementsunder a wide variety of climatic regimes are needed.

Raindrop fall velocity is an equally important quantityand closely related to the measurements of RSDs andvarious integral quantities such as rain rate. Use of theterminal velocity measured in stagnant air (e.g., Gunnand Kinzer 1949), which exhibits a one-to-one relation­ship with drop sizes, has been a common practice in rain­related studies such as numerical simulation and remotesensing (Pruppacher and Klell 1998; COllon and Anthes1989). However, raindrop fall velocity is affected by manyother faclors in addition to drop sizes. For example,rainfaU is often associated with various air motions (e.g.,updrafts and downdrafts) in and below clouds (Balian1964); drops of the same sizes in updrafts and downdraftsare expected to have different fall velocities. Recent studieshave indicated that turbulence (Pinsky and Khain 1996)and raindrop breakup/coalescence (Montero-Martinezet al. 2009) can exert substantial influences on the rain­drop fall velocity as well. The complex effects of airmotions and other factors on raindrop fan velocity havenot been adequately addressed, especially in the con­text of RSD measurements.

These issues regarding RSD and raindrop fall velocitystand out especially with precipitation over the semiaridplateau in western China because of the scarcity of ob­servational sites. To overcome these deficiencies, a field

experiment measuring rainfall in the semiarid plateau cli­mate was conducted at Guyuan (36°N,106°16'E), NingxiaProvince, China, to simultaneously measure RSDs andraindrop fall velocities with a PARSNEL disdrometer (seesection 2b for details about the PARSNEL disdrometer).This paper examines the measurements collected dur­ing this experiment, with three foci: 1) characteristiccomparison-eontrast of the spectral shapes of RSDs fromstratiform and convective rains and their variation withrain rates; 2) the analytical expression for describing theRSDs; and 3) raindrop fall velocity and the variousfactors that affect it. The rest of the paper is organizedas follows: section 2 describes the field experiment. Sec­tion 3 presents RSD analyses. Section 4 examines themeasurement of raindrop fall velocities. The major find­ings are summarized in section 5.

2, Experiment description

a. Location

The field experiment was conducted at Guyuan (Fig. 1).The site is located in a hilly-gully area of the Loess Pla­teau near the upper YeUow River; and is in the semiaridtemperate continental climatic regime with mean annualtemperatures of 4.4°-7.J°C, cumulative rainfall of478 mOl,and evaporation of 1100--2000 mm.

b. PARSIVEL disdromeler and daln-quality issues

RSDs were measured with a PARSrVEL precipitationparticle disdrometer manufactured by OTI Messtechnik,Germany. Laffler-Mang and Joss (2000) and Yuter et al.(2006) provided a detailed description of this instrument.Briefly, the PARSNEL probe is a laser-based opticaldisdrometer that can simultaneously measure both sizesand fall velocities of precipitation particles. The core el­ement of the instrumen t is an optical sensor that producesa horizontal sheet of light (180 mm long, 30 mm wide,and 1 mm high). The particle passing through the lightsheet causes a decrease of signal due to extinction. Theamplitude of the signal deviation is a measure of particlesize, and the duration of lhe signal allows an estimate ofparticle fall velocity. Particles with diameters between 0.2and 25 mm and fall velocities between 0.2 and 20 m S-1

are detectable by the instrument. The parlicle size andvelocity are each categorized into 32 size and velocitybins, respectively, with different bin widths.

The instrument was placed about 1.8 m above theground. Calibration before the experiment was per­formed, along with daily maintenance. Continuous mea­surements were taken from 17 July to 26 August 2007to cover the rainy season (from early July to late Sep­tember). The lime interval of each RSD measurement

I

634

37°N

36°N

35°N

JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY

~Kmo 30 60 120

-0

'.(1''.r .....~. ,,

, ....... ,t ..,,'

l <,-~':

!05°E lO6°E 1f17°E lO8°E

Elevation(m)~

jOb' 998 038 1871 2·/79 3;/71 ·JtiYS

VOLUME 49

FIG. I. (left) The topographic distribution of the experiment site and radar site. The elevation of the CINRAD site is2853 m. (right) Mainland China. with the square rcpreseming the domain shown in the left panel.

was 10 s. A total of 15 895 instant RSD samples wascollected from 29 precipitation events.

The PARSIVEL disdrometer has been known to sufferfrom some potential instrumental errors. For example, itcannol distinguish drop sizes within a given size interval,which may cause some measurement errors, in particularfor drops larger than 10 mm in diameter because of largesize intervals (;;,,2 mm). There may be some so-calledmargin fallers that are not totally within the light sheetand thus appear to be smaller and fall faster than otherdrops of the same sizes (Yuter et al. 2006). Krajewskiel al. (2006) suggested that drop splashing on the hous­ing and subsequent fragmentation might produce un­realistically low fall velocities. Furthennore, small dropswith diameter <1 mOl may not be accurately measuredbecause of poor signal quality and very short signals(Leimer-Mang and Joss 2000). To minimize these po­tential instrumental artifacts, the following criteria areused in choosing data for analysis: I) raindrops in Lhetwo smallest-sized bins «0.25 mm) are discarded; 2) thetotal drop concentration of an RSD is over 10 (counts ofeach IO-s sample); 3) the maximum raindrop diameterof ao RSD is larger than I mm (avoiding sand effect);and 4) the velocity-size relationship (Gunn-Kinzer ve­locity adjusted to local air density) is used Lo identify

potentially erroneous data using 30 criteria, that is, dis­carding the raindrops of any diameter with velocities3 tin'es the standard deviation of velocity calculated fromevery 60 consecutive samples at the correspondingdiameters.

3. Raindrop size distributions

a. Comparison of RSDs ill slratiform alld cOllvecliverains

Precipitation is generally considered to be divided intotwo distinct types: slratifonn and convective. Identifica­tion of RSD features with these two precipitation typesis useful and important for numerous applications, forexample, in the calculation of heating profiles (Langet al. 2003), development of rainfall retrieval algorithm,precipitation parameterization ror use in atmosphericmodels, and deciphering microphysical processes (Tokayand Short 1996; ROistayn 1997). In general terms, ver­tical air velocities within clouds exhibit a strong dis­tinction between the two types of precipitation. withstratifonn (convective) clouds having weaker (sLronger)vertical motions. Houghton (1968) showed that the mi­crophysical difference between stratiform and convec­tive precipitation depended on the magnitude of the

APRIL 2010 NIU ET AL. 635

in-cloud vertical air motion and the time scale of theprecipitation processes. However. observations of verti­cal air motions are often unavailable, and other featureshave been used 10 idenlify differenl rain Iypes. Oneuseful quantity is the radar reflectivity. For example,stratiform rains are generally more uniform than con­vective rains. Existence of the bright band of radar re­flectivity is thought to be associated with stratiformprecipitation. Steiner et aJ. (1995) pointed out that amelhod that identifies only the brightband regions asstratiform and classifies the remainder of the precipitationas convective tends to underestimate the stratiformtype but overestimate the convective parL. They furtherproposed an approach that firsl identifies the convec­tive type based on the intensity and peakedness of theradar reflectivity.

According to these previous studies and the dataavailable to us, in this paper, the rainfall types are clas­sified based on a combination of Ihe brightband crite­rion, the method presented in Steiner et aJ. (1995), andthe meteorological observations at the surface. Rainfallwith a bright band of radar reflectivity is identified asstratiform. Considering that bright bands are only clearlyidentifiable in well-developed stratiform precipitationand thaI using only the brightband criterion may lead tooverlooking some stratiform events, we further appliedthe reflectivity-based method presented in Steiner et aJ.(1995). Briefly, this approach focuses firsl on identify­ing the convective type based on concepts of convectivecenter and peakedness. A region with reflectivity of30 dBZ or higher is identified as a convective cenler.Note that the value of 30 dBZ is lower than Steineret al.'s 40 dBZ and is chosen as the convective centerthreshold reflectivity because precipitating systems arenormally weaker in the semiarid continental climateregime (Zhang and Du 2000,314-329). The convectivecenler is then supplemented using the peakedness cri­terion that identifies additional points as convective ifthe corresponding reflectivities exceed the mean intensityaveraged over the background (an ll-km-radius circlecentered on the grid points) by at least the reflectivity dif­ference (t.Z = 10 - ZI,/180, 0 dBZ '" Z1>. '" 42.43 dBZ;t.Z = 0, Zb. < 0 dBZ; Zh. is background reflectivity)used by Steiner et aJ. (J 995). The points that surroundthe convective centers and subcenters within a convectiveradius determined by the mean background reflectivityare also considered convective areas. The remainingpoints of nonzero reflectivity are classified as a stratiformregion. A rainfall event is then classified as the convectivetype if 80% of radar data during the rainfall period be­long to convective points. Surface observations of pre­cipitating clouds and thunder characteristics are used asadditional references. For example. the stratiform rains

are often associated with nimbostratus or altostratusopacus whereas the convective rains are mainly con­comitant with thunder, cumulonimbus capillatus. andcumulus congestus. FurthemlOre, about 67% of convec­tive rains (mostly showers) happened in the afternoonbecause of local thermal instability. As an example, Fig. 2contrasts two images of the plan position indicator (PPf)of the radar reflectivity factor (dBZ): (i) a stratiform rainsystem at 2019 local time [Beijing lime (B1T)] 19 July2007 and (ii) a typical convective cell observed at1700 BJT 12 August 2007. The radar renectivity data wereobtained using the China Weather Radar (CINRAD/CD)near Guyuan. CINRAD/CD is a 5-cm-wavelength, volume­scanning Doppler radar with 10 half-power beamwidthand O.3-km horizontal resolution. Each volume scan takes6 min to complete.

According to this type of classification, there were 11individual cases of stratifonn rains and 18 cases of con­vective rains during this field experiment (Table I), pro­viding us a unique opportunity to examine the differencesbetween individual events of stratiform and convectiverains in a rnidlatitude semiarid climate. Figure 3 com­pares the RSDs from the stratifoml and convective rainsobtained by averaging all the instant RSDs for each raintype sampled during the en lire experimental period.Notably. on average, the convective rain tends to havemore raindrops than the stratiform counterpart acrossmost drop sizes (i.e .. 0.8 mm < D < 7.5 mm). But, thestratiform rain has more small raindrops with D <0.8 mm. The mean diameters for the straliform andconvective rains averaged over all the events are 0.52 and0.91 mm, respectively. In comparison, much larger meanraindrop diameters for stratiform rains were observed inChangchun (0.72 mm) and Yitong (0.74 mm) in 2008,both of which belong to tbe temperate continental mon­soon ctimale. The orographic effect and high evaporationrate may be responsible for the smaller mean diameterobserved al Guyuan. For example, previous studies haveshowed that orographic lifting can create a large numberof small raindrops by supplying enough condensates, re­sulting in RSDs witll very small mean diameters (Rosenfeldand Ulbrich 2003). Furthermore, the convective RSD ismuch broader than the stratiform RSD, with the maxi­mum raindrop diameters being 7.5 and 3.8 mm for theconvective and stratiform rain, respectively.

b. RSD variatioll lVith the raill rate

To furlher discern the difference between the con­vective and stratiform rains, Ihe observed RSDs of eachrain type are Eurther stratified into six or seven classesaccording to their rain rates (mm h-'): R '" 2, 2 < R '" 4,4 < R '" 6, 6 < R '" 10, 10 < R '" 20,20 < R '" 40, and40 < R (Table 2). Figures 4a and 4b show the averaged

636 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 4~

NW+, ~-.I IKm0 20 40 80

s dBZ

{J II " III 1:1 :!f1 2;; :<0 :6 -Ill 'I:i :i0 ;;;; (1lJ ;(lO

FIG. 2. PPI displays of radar rcncctivity factor (dBZ): (a) stratiform rain casc al 2019 BJT 19 JuI2007; (b) convective rain case at 1700 BJT12 Aug 2007 observed in Guyuan.

RSDs of the different rain-rate classes for the stratiformand convective rains, respeclively. For the convectiverains, both their maximum drop diameters and thenumber concentrations across all the diameter bins in­crease when rain rates increase, suggesting that increasingrain rates of the convective rains arise from the combinedincreases of the drop concentration and raindrop di­ameters. The RSD variation with the rain rate for thestratiform rains is markedly different from that of theconvective rains. The number concentration in the strati­form rains increases with increasing rain rates only whenD > 1.3 mm; for the small drops with D < J mm, theconcentration decreases significantly with increasingrain rates (R > 10 mm h-'). Also, unlike the convec­tive rains, no increase in the maximum drop diameter isdetected for the stratiform rains. These results indicatethat the increase in the rain rate of the stratiform rainsstems mainly from the increase in the concentration ofraindrops with D > 1.3 mm.

The differences between the convective and strati­form RSDs can be further seen from the relationships ofthe rain rate to the drop concentration, mean volumediameter, and relative dispersion of the RSD (defined asthe ratio of the standard deviation to the mean diameterof the raindrop population). As shown in Figs. 5a-5c, atthe same rain rate, the convective rains have values ofvolume-mean diameter and relative dispersion larger thanthose of the stratifonn rains whereas the strati[onn rainstend to assume relatively higher raindrop concentrations,consistent with what is shown in Fig. 4. Furthermore,for the convective rains, raindrop concentration, volume­mean diameter, and relative dispersion all increase asthe rain rate increases. But, for the stratiform rains,although the volume-mean diameter tends to increasewith increasing rain rates, the relative dispersion tendsto decrease. The distinct Z-R relationships (Z ~ aR")between the convective and stratiform rains are givenin Fig. 5d, wherein the radar reflectivity factor Z and

APRIL 2010 NIU ET AL. 637

rain rale R are calculated from RSDs using the fol­lowing equations:

(4)

(3)

--stratifonn"" convective

•

•

••

N(D) = N" exp(-AD),

••

IODO

10. •

~

10EE

'7 1-5>: •.,

0.01

1[,,'

1£-1• 4 5Ditlmclcr(mm)

FIG. 3. Average RSDs for (he stratiform and convective rains fromthe entire dataset.

many areas. For example, the well-known exponentialraindrop size distribution is defined as

where N" and A are two empirical coeWcienls. By ana­lyzing previous measurements, Marshall and Palmer(1948) found thai N" is a constant but A varies with therain rale. Since then the exponential distribution hasbecome a milestone assumption in remote sensing ofrainfall (Ailas et al. 1973) and precipitation parame­terizalion in almospheric models (Kessler 1969). Lalerstudies showed thai although the exponential distribu­tion tends 10 describe large-sample, averaged, raindropsize distributions well, instant spectra often deviate fromit, and the gamma dislribution has been proposed asa first-order generalization (Ulbrich 1983; Liu 1992,1993; Tokay and Short 1996):

(1)

(2)R = r' N(D)V(D)D3 dD,."

z = J' N(D)D" dD and

"

TABLE 1. Summary of observed rainfall evenlS (H is the cumulativerainfall measured by surface station).

No. of REvents samples H(mm) Rain type (mm 11- 1)

17 lui a 35622.4

Convective 6.1617 lui b 1527 Convective 4.9318 Jul a 197

0.5Stratiform 0.90

18 lui b 100 Stratiform 0.4719 lui 2116 4.1 Stratiform 0.9420 lui 2956 5.6 Stratiform 0.8721 lui 217 0.6 Convective 1.4922 Jul 29 0.0 Convective 1.2824 lui a 27

0.4Convective 1.15

24 lui b 76 Convective 1.8326 lui, 140

1.5Convective 1.07

26 lui b 45 Convective 7.6927 lui a 425

2Convective 1.80

27 lui b 64 Stratiform 0.2929 lui 95 0.2 Convective 0.9131 lui a 35

0.0Slratifoml 0.33

31 lui b 14 Stratifoml 0.453 Aug 45 0.7 Convective 3.894 Aug 286 1.2 Convective 1.795 Aug 7 0.0 Convective 1.836 Aug a 109

6.1Convective 23.30

6 Aug b 16 Convective 0.348 Aug 1979 16.7 Convective 3.629Aug 64 0.7 Stratifoml 0.06

12 Aug 74 1.4 Convective 9.8325 Aug 644 11.9 Convective 7.9026 Aug a 375 Stratiform 0.6326 Aug b 3863 8.4 Stratiform 0.8526 Aug c 14 Stratiform 0.18

where N(D) is Ihe number of raindrops per unit volumeper unit diameler interval (mm-' m-3

), V(D) is theraindrop velocity (m s-'), and D is the equivalent spher­ical diameler (mm). The coefficient a for the stratiformrains is smaller than thai for convective rains whereas theOpposile holds true for the power b. This resull differsfrom thai reponed in Nzeukou et al. (2004).

c. Analytical fllllctioll for describing RSDs

Over Ihe last few decades, greal efforl has been de­voted to finding the appropriate analytical expressionfor describing the RSD because of its wide utilities in

where the speclral parameler J.I. is introduced to quantifythe devialion of the spectral shape from Ihe exponentialdistribution; the gamma distribution reduces 10 the ex­ponential distribulion when J.I. equals O. The gamma sizedistribution has become a new standard assumption toreplace the classic exponential distribution in manyapplications such as advanced remote sensing of pre­cipitation (Ulbrich and Atlas 1998) and multimomenlparameterization of precipitation (Ferrier et al. 1995).

Most previous studies on analytical RSDs have beenbased on empirical curve fillings 10 individual measuredRSDs. Since RSD is the end results of many complexprocesses that can be considered to be stochastic in

638 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 49

where D, is the central diameter of the ith bin, N, is thenumber concentration of the ith bin, and N, is the totalnumber concentration. For the gamma distribution givenby Eq. (4), it can be shown that

;

(8)

(7a)

(7b)

1 J <ldial1lClcrtllllll)

1C=C=--, , 1+1'

"

I.U

10.(1

10U.0 -

z

z

FIG. 4. RSDs averaged according 10 different min rates for the(n) strntiform and (b) convective rains.

Equation (8) indicates that in the C.,-C, diagram, thegeneral gamma distribution with varying I' satisfies thediagonally straight line, and the point (I, I) representsthe exponential distribution as a special gamma functionwith I' = O.

Figure 6 shows the scatterplot of C., and C, calculatedfrom the observed RSDs from the stratiform and con­vective rains. A rew points are evident. First, despitesome occasional departures, most or the points fromboth the convective and stratiform rains fall near thediagonal straight line of the gamma distribution, con­firming that the RSD patterns from both types of cloudsfollow well the gamma distribution statistically, withthe correlation coefficients being 89.8% and 94.6% for

It is obvious that for the gamma distribution we have

(6a)

(Sa)

(5b)

(6b)

23671710827474451217

51

and

8959629116503113o

Sample numbers

Stratifonn Convective

J(D, _15)3~ dD

[J (D, - 15)' Ni~~') dDrJ(D, _15)4 N'i:,J dD

I 1 - 3,

[J (D, - 15)' N,~,J dDr

S=

K=

TABLE 2. Sample numbers aI each min·rate category.

R '522 < R s64<Rs66<Rsto

10 < R s 2020<Rs4040 < R

nature, such as collision and coalescence (Jaw 1966).statistical approaches that are applicable to a large numberof individual RSDs are more desirable. Liu (1992, 1993)proposed such a simple stalistical method based on therelationship between the skewness (S) and kurtosis (K) ofthe RSD to identify the statistical RSD pallem. Liu andLiu (1994) and Liu et al. (1995) further applied a similarapproach to study aerosol and cloud droplet size distri­butions. Here we apply this approach to investigate if thestatislical pallern of the I-min RSDs follows the gammadistribution, and if there are any pallern differences be­tween the stratiform and convective RSDs.

Briefly, skewness and kurtosis of an RSD are definedby the following two equations:

S = 2 dan~

K=_6_.1+1'

Equations (6a) and (6b) indicate thai S = 2 and K = 6for the commonly used exponenlial distribution withI' = O. With the classical exponential distribution as areference, the skewness and kurtosis deviation coe[ficients(c:, and C,) are introduced such that

FIG. 5. Relmionships of Ihe rain ralc 10 (a) drop concenlralion, (b) volume-mean diameter. (c) relative dispersion, and(d) radar reflectivity for the stmtifoml (squares) and convective (crosses) mins. The equations arc the cUI"e·fining results.

the stratiform and convective rains, respectively. Sec­ond, the I-min averaged pairs of (, and Ck do notelusteraround poinl (1, 1), suggesting that the exponentialdistribution is not suitable for describing most RSDs.This finding is consistent with many previous studies(e.g., Liu 1992). Finally, the spectral shope varies sub­stantially from one RSD to another, and the convectivemins tend to have more RSDs with larger values of C"and Ck compared to the stmtiform rains. Note that wehave also examined I O-s RSDs, and found similar results.

To examine the dependence of the spectral shape on therain mle, Fig. 7 furlher displays the scalterplot of C" and Ck

calculated from Ole RSDs avemged according to the min­mte classes shown in Fig. 4. Clearly, the mte-stratifiedRSDs of both min types tend to statislically follow thegamma distribution (C, = Ck ) as well, which is especiallytrue when the min mles are high (R > 6 mm h-I). The re­markable contrast between the stratiform and convectiverains in the variations of (Cs , Ck ) with the rain rate is

noteworthy: when the rain rate increases, Cs and Ck

decrease away from the exponential point (1, 1) for thestratiform rains, but increase toward the exponentialpoint (1, 1) for the convective mins. This contmst is ingeneral agreement wilh that of the variation of the rel­ative dispersion with the rain rate shown in Fig_ 5. Alsonoteworthy is that the stratiform rains have two pointswith relatively large deviations from the C.. = Ck line.More research and data are needed to address whatcauses such relatively large deviation.

4. Raindrop fall velocity

a. Gelleral teall/fe

In addition to drop sizes, the PARSIVEL disdrometermeasures drop fall velocities (UHller-Mang and Joss2000). Figures 80 and 8b show the observed mean numberconcentration as a function of the drop diameter and the

640 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOI.UME 49

slrntifonn minsconvcclivc rains

..

FIG. 6. The C.-C" scatlcrplol of the I-min-averaged RSDs forthe stratiform (squares) and convective (crosses) rains. Each pointrepresents onc I-mill-averaged RSD. The sirnighilinc presents lhr.:C,-C" relation of the gamma function.

1.0

cUl!\'ecl i\'c rains

l..' sirmifonn r::Ilns

0.1) ......

c.

-0.2 '::-_~=---_~~_~:-__~__---l0.0 0.2 IIA O.r. O.~

FIG. 7. The C~-Ck scauerplol for the RSDs 'Iveraged accordingto differenl rain rates. The squares and circles denote lhe convcc·live and slratifonn rOlios, respectively; the size reflects the rain rate,wilh Ihe smallest square or circle corresponding 10 the lowest ruinrate.

4lC,

..

•

where m, A, and D are the mass. area. and maximumdimension of the particle, respectively; (x, /3, y, and fT are

atmospheric conditions at sea level, with the air densityof 1.23 kg m-J However, the air properties at Guyuanduring the observational period are markedly different,with an altitude of 1753 m above sea level, mean pres­sure of 819.3 hPa, and mean air density of 0.97 kg m-3. Itis expected that the lower air density at Guyuan will re­sult in a terminal velocity larger than the correspondingGunn-Kinzer terminal velocity, other things being thesame (Pruppacher and Klett 1998).

Many studies have been attempted to extrapolate theGunn-Kinzer measurements to other atmospheric con­ditions, and to quantify the effect of air density on thedrop terminal velocity (Battan 1964; Foote and DuToit1969; Atlas et al. 1973; Beard 1976). In particular, Mitchell(1996) presented a general, semitheoretical frameworkby coupling the Abraham (1970) conceptual model to thepower-law relationship between the Reynolds numberand Best number. The Mitchell formulation not onlyaccounts for the effect of air density but also is easy tograsp mathematically and physically. In view of theseadvantages of the Mitchell formulation, below we applythis formulation to evaluate the contribution of the airdensity difference to the systematic discrepancy betweenthe ohserved drop fall velocity and the Gunn-Kinzerterminal velocity.

Briefly, the mass- and area-dimensional relationshipscan be descrihed by power laws such that

fall velocity for the stratiform and convective rains, re­spectively. Also shown as a reference (black solid curve)are the laboratory measurements by Gunn and Kinzer(1949) of the terminal velocities under the standard at­mospheric conditions at sea level (air pressure of lOB hPa,temperature of 20°C, and relative humidity of 50%).Consistent with the RSDs shown in Fig. 3, raindropsin the stratiform rain concentrate in the fall velocitiesranging 2-4 m S-I and then decrease sharply with in­creasing fall velocities while the raindrops in the con­vective rain peak at higher velocities (4-6 m s-') anddecrease with increasing velocities much more slowly.Besides these differences, the stratiform and convec­tive rains share some similarities too. First, on average,the observed drop fall velocities for both rain typestend to be higher than the corresponding Gunn-Kiozerterminal velocities obtained under the standard sea levelconditions. Second, there are large spreads in the dropfall velocities at virtually all the drop diameters, withthe convective rains having an even larger spread thanstratiform rains. Similar features have been previouslyreported in rare studies of in situ measurements of dropfall velocities (Donnadieu 1980; Hosking and Stow 1991;Ltifner-Mang and Joss 2000). In the next two subsections,the physical mechanisms underlying the large spread inthe measured fall velocities, and the systematic dis­crepancy between the measured fall velocities and theGuon-Kinzer terminal velocities, will be examined indetail.

b. Air density effect

The classical Guon-Kinzer measurement of the dropterminal velocity was conducted under the standard

111 = (XD~ and

A =yD",

(9)

(10)

72 3 ~ 5 6Drop dinmclcr (mm)

(b) for conw:t:live rains in GUYUUll

234Drop diameler (mm)

(a) for slf3tifonn l1Iins in Guyuan

APRIL 2010 NIU ET AL. 641

" I< , ,.....

'0

:- R :-"

oS

'" '".;:; 6 'g0.. ~>

l~

4e0

30.0114.0118,016.010.01 1:!.OINtm·l )

FIG. 8. Number conccntration distribution (colors) as a function of the drop diameter andraindrop fall velocity for the (a) stratiform and (b) convcctive rains. The black curve (Vn) in (a)and (b) shows the empirical relationship between diameter and velocity of Atlas et a!. (1973)after the measurements from Guno and Kinzer (1949): Vn = (9.65-1 O.3)e-ll.fiD . The blue curvesarc the simulation of Mitchell's terminal velocity considering the air density effect in Guyuan.The red curves arc the simulation of Beard's (1976) terminal velocity considering the air densityeffect in Guyuan.

the empirical parameters depending on particle shapes.The Reynolds and Best numbers are given by ~ )""V = V Pa

, no

(14)

Under the assumption that the parameters a, /3,1', and'7 are independent or the air density or simply a constant,Eq. (13) can be simplified as

where the empirical coefficients a and b depend on therange or X. A combination of Eqs. (11) and (lZ) leads tothe general expression ror the terminal velocity,

where g is the gravitational constant, 71 is the air dynamicviscosity, and Pn is the air density. Over a certain rangeor x, the relationship between R, and X can be ap­proximated by a power-law expression (Knight andHeymsfield 1983; Heymsfield and Kajikawa 1987):

P DIIR = _0__' and, '7

2agp D(J+2-rrX= IJ

1''7'

R ::=.aX", '

II = "26(Zag)" h"D"lJl+'-u).11 aT1 y PII .

(lla)

(Ilb)

(lZ)

(13)

where Vo represents the terminal velocity in the stan­dard atmosphere at the sea level, say, the Gunn-Kinzerterminal velocity. Equation (14) reveals that the effectof air density is determined by the value or b. For con­venience, Table 3 summarizes the values of b for the tworanges of X applicable to the rain drops encounteredduring the field experiment. Tbe values of b = 0.6 and0.5 lead to tbe correction ractors or (p,,/Pn)-O.4 and(P",Pn)-n.5 ror 585 < X :5 1.56 X 10" and 1.56 X la' <X:5 108

, respectively. It is interesting to note thallhesesemitheoretical correction factors are very close to theempirical ones suggested in Foote and DuToit [1969;(Po/Pn)-n,4] and Atlas et al. [1973; (P'/Pll)-O.S], revealingthaI these two previous correction ractors actually holdover different ranges of X or drop diameters.

Using Eq. (14) with the proper values of b, air densi­ties, and lin, we calculated the theoretical dependenceof the terminal velocity on the drop diameter correctedror the efrect or air density at Guyuan. The result isshown as the red solid curve in Fig. 8. It is evident thatcompared to the Gunn-Kinzer terminal velocity, thecorrection for the effect of air density brings the terminalvelocities much closer to the observed drop fall velocities.

642 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 49

TARLE 3. Summary of Icmlinal velocity expressions, where I) isthe empirical coefficient of the power law of R~ and X, p" is the airdensity, and Po is the air density at the standard sea level.

The improved agreement suggests that the lower airdensity at Guyuan is (at least partly) responsible for thesystematic discrepancy between the terminal velocitiesand the PARSIVEL-measured drop fall velocities. Thedifference between the air densities at Guyuan and atthe standard sea level leads to a percent difference of10%-12% in the terminal velocity, depending on thevalue of b (0.6 or 0.4).

c. Otl,er illfluellcillg [actors

The difference in air density can explain away (some)systematic deviation of the PARSlVEL-measured fallvelocity from the Gunn-Kinzer terminal velocity, but itleaves unresolved the large spread in the measurementof the instant drop fall velocity. It has long been rec­ognized that complex air motions (e.g., updrafts anddowndrafts) often accompany natural rainfall, causingdeviations in the shape, velocity, and trajectory of fallingraindrops from Ihose in still air where the dependenceof terminal velocity on raindrop diameter is developed(Kinnell 1976; Donnadieu 1980). For example, in theinvestigation of the PARSIVEL-measured drop veloci­ties, Lamer-Mang and Joss (2000) found similar spreadsin their measured relationship between the drop fall ve­locity and terminal velocity, and attributed the spread toair turbulence and instrumental errors. However, thelimited previous studies have been largely qualitative,lacking rigorous investigation. Here we will furtherthe previous studies to examine the issue of spread andthe potential factors that influence measurements of thedrop fall velocity in a more detailed way.

Without loss of generality, the fall velocity (V) ofa raindrop measured by the PARSIVEL probe can beregarded as a combination of the terminal velocity instill air (V,) and a component V' that results from all theother potential influencing factors (e.g., turbulence, or­ganized air motions, breakup, and measurement errors):

(17)

(16)

t.V ~ V' = O.

t.V=V-V =V'.,

Equation (17) also indicates that a perfect random dis­tribution of V' will result in the average of manyinstantaneous measurements being equal to the corre­sponding terminal velocity corrected for the effect of airdensity. To examine if Eq. (17) holds or if there are anysystematic differences between the drop fall velocity andthe terminal velocity in addition to that caused by thedifference in air density discussed in section 4b, Fig. 9shows the mean t.V against the drop diameter for thestratiform and convective rains in Guyuan. Obviously,the mean deviation velocities are not zero, suggestingmore systematic bias in addition 10 that caused by theair density difference. The deviation is positive forsmall drops with diameters <1.4 mm, indicating that thePARSlVEL-measured fall velocities are higher than thecorresponding terminal velocities. The overestimationreaches a maximum for small raindrops, and decreasessharply when the drop diameter increases from 0.2 to1.4 mm. On the contrary, the mean deviation velocitiesare negative for large drops. Physically, the positivedeviation could stem from the coexistence of strongdowndrafts and small and median drops whereas thenegative velocity deviation could stem from the co­existence of strong updrafts and large drops.

Figure 10 further shows relative velocity deviationdefined as the root-mean-square velocity deviationnormalized by the corresponding terminal velocity. The

If the total of the other influencing factors was com­pletely random, the mean V' over an ensemble of sam­ples would lead to

AI qualitative glance, clouds are known to be areas ofenhanced turbulence and rainfall that are associatedwith a complex mixture of upward and downward airmotions of various scales. The large spread of the mea­surements at both sides of the terminal velocity curvesshown in Fig. 8 seems compatible with the notion ofnearly random collections of downdrafts and updraftsfor the stratiform and convective rains examined. Awider spread for the convective rains implies a widerrange of variation in vertical motions compared to theirstratiform counterparts, which seems consistent with ourgeneral understanding of both rain types.

More quantitative information can be obtained byinspecting the velocity deviation, which is the differencebetween the PARSIVEL-measured fall velocity and thecorresponding terminal velocity and measures the totaleffect of other factors:

(J5)

x

1.56 X 1O-~ < X:=s; 10"

585 < X:::;; 1.56 X l(t~

0.499

0.638

b

V= V, + V'.

Terminal velocity (\I,)

APRIL 2010 NIU ET At.. 643

--- stl'll.tirOntl ruinsconvective Dins

"

14.

§ 120

FIG. 10. Dependence of thc mean relalive velocity deviation 011

the raindrop diameter for the stratiform (squares) and convective(triangles) rains.

- • - slnltifonn ruins

convective ruins

\ .. /\! .-, /'

\

\"......

•

-,

'.

4 5Diamclcr(mm)

FIG. 9. Dependence of the mean vclocity deviation on the rain­drop diameler for the stralifonn (squares) and convective (tri­angles) rains.

PARSIVEL probe can overestimate the terminal ve­locity by up to 150% for small drops ofO.3-mm diameter;the overestimation then decreases sharply with increasingdrop diameters, to 10% at I-mm diameter, and staysapproximately at the 10% level after that.

The particularly large mean relative velocity deviationfor small raindrops is noteworthy. Loffter-Mang and Joss(2000) regarded instrumental limitations such as quanti­zation, threshold, and drop splashing on the housing asthe likely reasons for it. On the other hand, Pinsky andKhain (1996) demonstrated through numerical simula­tions that wind shear of turbulent flows and the inertialacceleration of particles in atmospheric turbulence canresult in substantial drop velocity deviations from theair velocity. Furthermore, the result shown in Fig. 10appears to qualitatively resemble the variation of therelative turbulence-induced velocity deviation with thedrop diameter shown in Fig. 17 of Pinsky and Khain(1996). These results qualitatively agree with Pinsky andKhain's (1996) model simulation results. Therefore, wecannot totally rule out the possibility of atmosphericturbulence inducing some vertical velocity for smalldrops, although the measurement error in small raindropsis 25%.

The behavior of the velocity deviation seems consis­tent with a hypothesis recently proposed by Montero­Martinez et al. (2009) as well. They argued that whentwo drops coalesce, it will result in a bigger drop thatfalls nearly at the same speed as the larger one of the twOcoalescing drops. Therefore, coalescence will lead to aterminal velocity slightly smaller than the correspond­ing terminal velocity of that diameter. On the contrary,a drop breakup leads to many smaller fragments, allmoving at the same speed as the parent bigger drop,

resulting in the small fragment drops falling much fasterthan their temlinal velocities. According to this theory,the balance of drop breakup and coalescence would leadto a "higher-than-terminal velocity" fall velocity (super­terminal velocity in their terminology) for small drops but"Iower-than-terminal velocity" fall velocity (subterminalvelocity) for large drops. They also analyzed data ob­served at calm conditions with an average horizontalwind speed of only 0.6 m S-I and bounded by 2 m S-I,

and found a similar asymmetrical pattern of velocitydeviation. This hypothesis is further reinforced by a re­cent study that emphasizes the importance of drop breakupin shaping RSDs (Villermaux and Bossa 2009).

It is worth noting that the processes of drop breakupand coalescence are closely related to air motion, es~

pecially turbulence. It is expected that strong turbulenceenhances the breakup-coalescence processes; a com­bined effect would induce larger deviation of the dropfall velocity from the terminal velocity. The potentialeffect offalling raindrops on turbulence, air motion, andbreakup adds another layer of complexity to this issue,and more research is needed to ultimately resolve it

5. Conclusions

A field experiment was conducted at a site located in aregion of semiarid, temperate, plaleau climate. A totalof 29 rainfall events was sampled and classified into IIstratiform and 18 convective rains. A total of 15 895joint raindrop size and fall velocity distributions mea­sured with a PARSIVEL disdrometer is analyzed todiscern the similarity and difference between stratifonnand convective rains, to determine the statistical patternof the raindrop size distribution, and to examine the

644 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 49

mechanisms that affect raindrop fall velocities. Com­parison of the type-averaged raindrop size distributionsshows that the convective rains have more raindropswith diameters larger than 0.8 mm than the stratiformrains whereas the opposite is true for raindrops smallerthan 0.8 mOl. The convective raindrop size distributionis also broader than the stratiform raindrop size distri­bution. Further comparison of the raindrop size distri­butions stratified according to rain rale reveals that forthe convective rains the increase of rain rate arises [romthe combined increases of drop concentration and maxi­mum diameter while for the stratifonn rains rain rate in­creases are mainly due to the increase of median and largedrop concentration.

It is shown by use of an approach based on the re­lationship between the deviation coefficients of skew­ness and kurtosis that the 1-min averaged raindrop sizedistributions from both the convective and stratiformrains can be well described statistically by the gammadistribution. Application of the same approach to theraindrop size distributions averaged according to rainrate further reveals that this fInding is true, especially forthose with high rates. A contrast of the variation ofspectral shape with the rain rate between the stratiformand convective rains is that the stratiform and convectiveraindrop size distributions tend to narrow and broadenwith increasing rate rates, respectively.

Three characteristic Ceatures oC the PARSIVEL­measured raindrop fall velocities are found: (i) on average,it is systematically larger than the classical Gunn-Kinzerterminal velocity obtained at the standard sea level;(ii) there is substantial spread in the instantaneousPARSIVEL-measured raindrop Call velocities across allthe raindrop sizes; and (iii) the spread for the convectiverain appears wider than that for the stratiform rain. Theeffects of air density and other factors on raindrop fallvelocities are examined rigorously as plausible reasons.II is shown that the measurement site assumes an airdensity lower than that of the standard sea level. Byusing the Mitchell semitheoretical formulation for theterminal velocity, the expression that accounts for theeffect of air density is derived. Application of this ex­pression to the air density at the experiment site suggeststhat the lower air density results in a terminal velocityabout 10% larger systematically than the Gunn-Kinzerterminal velocity measured at the standard sea level.Correction for this air density effect moves the terminalvelocity much closer to the mean PARSIVEL-measuredraindrop Call velocity.

Analysis of the dependence of the relative velocitydeviation on the raindrop diameter further suggests thatthe PARSIVEL probe can overestimate the terminalvelocity by up to 150% for small drops of 0.3-mm

diameter; the overestimation then decreases sharplywith increasing drop diameters, to 10% at 1-0101 diam­eter, and stays approximately at the 10% level aCter that.Evaluation of the relative contributions to the drop fallvelocity indicates that the average effect of unknownfactors (e.g., turbulence/organized air motions, breakup/coalescence, instrumental errors, or their combination)is about 2 times larger than that of the air density.

A few points are noteworthy. First, the conclusion onthe effect of other potential factors that influence rain­drop fall velocity is not definitive, and more compre­hensive research is needed to further discern and separatethese factors. Second, this study is mainly concernedwith the precipitation types classifIed on the basis ofindividual rainfall events and limited datasets. It is wellknown that periods/portions of stratiform and convec­tive types exist even during an individual rainfall event(ALIas et al. 1999). More research is needed to determinesuch effects on the results presented here. Third, thespecifIc form of an individual raindrop size distribution isoften dependent on the scale over which the distributionis averaged/sampled because of inherent fluctuations andsampling errors (Joss and Gnri 1978; Uu 1993; Smithet al. 1993). Further investigation of all these issues isbeyond the scope of this paper, bUI will be pursued in thefuture.

Acklloll'/edgmellCs. This study is mainly supported bythe Chinese National Science Foundation under Grant40537034-"Observational Study 011 Rainfall PhysicalProcesses and Seeding ECfect of Stratifornl Cloud"-andby the Ministry of Science and Technology of Chinaunder Grant 2006BACI2BOO-0I-0I-07-"Critical Tech­nology and Equipment Development in Weather Modifi­cation." Author Y. Uu is supported by the ARM Programof the U.S. Department of Energy. The authors thankDrs. Mitchell at DRI and Heymsfield at NCAR fortheir stimulating suggestions. The authors also thanktheir colleagues at the Laboratory for AtmosphericPhysics and Environment of the China MeteorologicalAdministration and Ningxia Institute of MeteorologicalScience Cor their support during the field experiment.

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