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Raindrop size distribution in warm rain as measured in HawaiiBy MIYUKI FUJIWARA, Meteorological Research I nstitute, Tokyo, J apan

(Manuscript received February 13, 1967)ABSTRACT

On the eastern slopeof the Island of Hawaii, raindrop size distributions were sampledsimultaneously at 5 stations. From the data analyses, it was established that eachsequenceof data from one station represents the distributionof drops at various devel-opment stages. Then the representative data were inspected under the light of theauthor's previous paper (19656) which concerns the classification for 4 processes, (1)coalescence between precipitable drops, (2) mixing of different groups, (3) accretionof cloud water, and (4 ) sortingof drops. The results show that most of the cases duringthe project have small values of A and b, where these parameters are defined by theradar reflectivity ( 2 )equation,z =A R ~ , =rainfall rate.

This indicates that the mean diameters are smaller but that numbers are greatercompared with continental showers. The analyses imply that the initial concentrationo precipitable drops is very effective in determining the rainfall rates, especially inorographic rains.

1. IntroductionA great number of raindrop measurements

have been made in Hawaii by Blanchard (1953),and Blanchard& Spencer (1957). The analysisof the drop size characteristics has been givenin conjunction with data on sea salt nuclei byWoodcock & Blanchard (1955).

The author has studied the variation of theraindrop size distributions between storms(1965~)nd their significant changes with pre-cipitation mechanism (1965b). I n the presentproject, it wag intended to apply the conclusionsobtained in these papers to the study of themechanisms responsible for Hawaiian rainfall.

2. ObservationsFive filter-paper raindrop recorders were

placed along the saddle road at intervals ofabout 2 km. These stations are called E, B, C,D, A, beginning with that at the lowest eleva-tion. (Sse Fig. 1and Table 1.) Station B is theso called 9-mile site. One roll of filter paper is12cm wide, 270 m long and 0.1 mm thick. It isdriven at approximately 1.5 cm/sec and lastsfor about 5 hours. A rotating shutter waamounted above the opening of the device inorder to reduce the sampling volume by a

ratio 1/8 and to avoid the overlaping of flecksin the case of a heavy rain.All 5 instruments were operated by one switchat the 9-mile base through a power line. Timemarks were printed on the filter paper. Theshutter is closed whenever the motor stops inorder to prevent the recording paper frombeing damaged.4% - _ _ ,r 2 - .--3: Observed2-R characteristics

Since the radar reflectivety of the raindropsis defined as

z =xDO (1)a relationship between Z (mmo/mB) nd therainfall intensity R (mm/hr) is a characteristicof the raindrop size distribution. A and b aredetermined empirically from the drop size dataand using the equation

Z = A P . (2)Many empirical values for A and b have beenpublished since radar was first used in meteor-ology. After L.Battan (1956),A ranges from 17to 600, whereas b ranges from 1.24 to 2.87.Since the values range widely, an understandingof the variation is very important not only for

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RAINDROP SI ZE DISTRIBUTION 393

0 5HILESPig. 1. Topography around the raindrop stations.Five raindrop Stations,A, D, C, B, and E areshownalong the sadle road of the eastern slope of theIsland of Hawaii. The airport and the radar sitearealso illustrated.

rainfall measurement but also in interpretingechoes. The values for Hawaiianrainsareat theextreme of the range according to Blanchard(1953).

I n Fig. 2, Blanchard's data (after Blanchard,1953) are plotted with the author's which are

0 Biawhard DataHawall al t ar Fujiwara

X Shower VI Japan

X

01 1 1 1 1 1 1 1 1 1 11.0 1. 1 1.2 1.3 1.4 1.5 I.$ 1.7 10 1.9 2.0 2b

Fig. 2. A , b values (for the relationshipZ =ARb)observed in showers. The dotted region is afterFujiwara (1965a), which is determined with morecontinental data. Blanchard data is after Blanchard(1953).TelluaXIX (1967), 3

Table 1Elevation fromStation Sea level (m)

A 1030D 888C 798B 715E 651

Table 2. 2 - R relationships calculated for everystorm and stat i on

Obs. St. A b Remarks28 July, 1701-1812 A 45 1.07 A , b are de-

D 67 1.35 fined byZ=C 60 1.34 ARbB 113 1.34E 80 1.34Mean 73 1.29

31 July, 1647-1818 A 54 1.26D 59 1.33C 100 1.55B Not plottedE No data

Mean 71 1.3816Aug., 1613-1625 A (84) 1.47 ParenthesesD No rain mean the

C (114) 1.30 value isB 230 1.68 uncertain.E 99 1.35Mean 132 1.45

18Aug., 1826-1907 A (58) 1.33D (66) 1.39C 100 1.40B 100 1.33E 80 1.34Mean 81 1.36

21Aug., 1620-1657 A 73 1.45D (49) 1.10C 63 1.20B 91 1.45E 112 1.50

Mean 80 1.3423Aug., 1124-1147 A 47 1.36D No datac 47 1.19B 41 1.15E 39 1.10

Mean 43 1.20D 50 1.21C 50 1.13B (57) 1.17E (40) 1.10Mean 46 1.14

23Aug., 1343-1401 A 35 1.10

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394 MIY UKI FUJI WARA

II1.3-

1826 I& 1835 50 1855 1900Pig. 3. N , contour section with time on 18th August. Five small arrows show the peak concentrations.Other interpretation are given in Section 5 .

also given in Table 2. Data were classified ac-cording to stations and storms before A andbwere calculated. For comparison, the data ofshowers taken in J apan, where sometimes inSummer the prevailing air mas8 is maritimetropical, were plotted with symbols x . Theregion encircled by dots contains the valuesfor continental sources. The parameters for theweak Hawaiian showers are enclosed within anextreme region which extends down to A =35and b =1.1. One characteristic of this distribu-tion is that A increase with the exponent b, forwhicha brief explanation will be given in Sec.11.4. N Dcontour sections

Generally speaking, large raindrops aregenerated in thick and heavy clouds either byaccretion of cloud water droplets or by coales-cence between raindrops. Illustrations of rein-drop size distributions measured at the5stationsare given in Figs. 3 and 4. The vertical axisshows the drop diameters in mm. The horizontal

axis represents the sample number which maybe interpreted as time. The isopleths show theconcentrations of drops in the size intervals0.2mm per cubic meters. The period in whichthe outer contour reaches toward larger dropsizes suggestsa thicker or denser cloud, probablydue to increased convection. The peak around1830 (sample91) in Fig. 3 is in accordance withthe convective part of the rain as revealed by adoppler radar observation given by Rogers&J iusto (1966). The biggest drop size was 1.7mmin diameter. A t stations A and D, the dropswere smaller than 1.0mm and the size distribu-tion was stationary, implying that the cloud wasstratified.5. Interpretation of N Dcontour section byradar

Asa part of the joint program, oneM-333-cmradar was operated at the Hilo campus (See pa-per by Illinois group). Fig. 5 showsa rainband ofthe shower moving from northeast to southwest

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RAINDROP SI ZE DISTRIBUTION

1.71.3

396

- C-

D Aug. 21. 16h20m - 16h57m

D

E

@i, (a I I II 6 I I 16 21 26 DATA#3

(in 1.22min)Fig. 4 . N , contour section with time on 21st August. Convective part is heading at Stations A, B, andE.

FUII gain rm6 db down- - - - -____

I8: 23. 2 18127.3 18:32.0 18:39.5 18:43.418. Aua. 1965.HILO.

Pig.5. The PPI echoes observed byM33,3-cmradar, at the Cloud Physical Observatory,Hilo campus. Thecontours wer e made from the photographs according to favour of M r. G. Stout, I llinois Water Survey.Interpretation is given in Section 6.Tellus X I X (1967), 326- 72899

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396 M I Y U K I FUJ IWARAwith the speed about 15km/hr past the 5 rain-drop stations, shown by x .The axis of the bandwas tilted slightly to the west of north. Theecho had started to become diffusea few mileseast of the 9-mile site, and evidently continuedto spread out and to weaken during the periodfrom 18:23.2 to 18:43.4.

The three cells I , 11, and 111, passed thestations during the 50 minute period from18:20 to 19:lO. Although there are some dif-ferences of intensity between cells, roughlyspeaking, the difference was mom remarkablebetween observed times. The times correspond-ing to the echoes shown in Fig. 5 are shown inFig. 3 by four broken lines. The raindrop datataken in the rainband are those illustratedbetween two slant lines in Fig. 3. Therefore, thescheme of major chronological development ofthe raindrop size distribution will be representedby the contours in a series in the directionshown by the open arrow. At any given time,the northern cell was more diffused than thesouthern ones. Combining this information withthe movement of showers, the time section atany station shown in Fig. 3 will be in part theexpression of changes in an order of cells I , 11,and111.

6. Data selectionValues of the parameters A and b given inTable 2 show, commonly, larger differences

between storms than between stations. Forinstance, the values of A and b determined fromStationE or B and those from D or A, on the18th, August, are rather similar in spite of thevery different stage of development of thoclouds as revealed in Fig. 5. It is therefore,concluded that the A and b values determinedfrom the data from one station are significantand representative for the rain system. Thusto choose representative samples of the dropsize spectrum the proximity of the2 -R pointto the 2 -R regression line will serve as anadequate criterion. The ensemble of ND curvesso selected is regarded asan expression of cloudstates in different stages of development duringa common weather circumstance. I n Figs. 6-13the families of the representative NDcurves areshown.

7. Basic processes for formation of a rain-drop spectrum

The theory which is applied in the presentpaper has been discussed in the previous paper(1965b). There are four main processes for thedevelopment of raindrop size distributions.These are: (1) coalescence between precipitabledrops, (2)mixing of raindrop groups which haveindividually different histories, (3) accretion ofcloud droplets, involving change in concentrationof the initial precipitation particles, and (4)gravitational sorting, which is a result of differ-ent fall velocities.Process 1, coalescence between raindrops,

decreases the total number of drops as rainfallintensity is increased. The raindrop size distri-bution resulting from this process is a mono-modal spectrum. Here, the process is not af-fected by the way in which the initial precipi-table drops are generated. If the collisions andcoalescences are assumed to occur without re-gard to the size of the partner drops, the processis called random coalescence. The effect of thisprocess on the size distribution is calculated inthe previous paper (1961). Thus the relationshipbetween radar reflectivity, 2 ,and rainfall rate,R, is given as a function of the coalescence pa-rameters, T (m3)andN (m3)by

Z =3.88 x lo3 x R1.718 To.718 (mm6/m3) ( 3)for a constant rate of collision, T. This case willbe referred to as process l a and in this case2is proportional toR to the 1.7th power. For pro-cess l b , an initial constant concentration ofdrops, N , is assumed. This yields

(4)=11.66x 108" x N-5R6.That is2 is proportional to R to the 6th power.Although the assumption of random coalescenceseems extreme, the remarkable difference in theexponent between the processes l a and l b ,which in initial conditions is surprising.Process 2, mixing of raindrop groups. Frompast data analyses (1965a), it was concludedthat the drop size distribution becomes aMarshall-Palmer typeas the mixing takes place.The radar reflectivity 2 is then proportional toR to the 1.6th power.

Process3, accretionof cloud droplets. For accre-tion of cloud droplets which are not counted onthe ground, two conditions are considered.

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RAINDROP SIZE DISTRIBUTION 397These are; 3acases in which only changes in theeffective thickness of cloud layer occur and 3 bcases in which the number of precipitable par-ticles entering the cloud layer change. On thefirst condition calculations with a very narrowinitial size distributions show that the exponentsb, is about 1.7.With broader initial spectra, b isa little larger. But in the second condition, b isapproximately unity, that is, 2 is proportionalto R. This case produces the lowest value of bof all the processes. The process 3a causes thedrop diameter to shift evenly to larger sizes.Therefore, the mode of the NDcurve is shiftedto larger values without a remarkable decreasein the peak height.Process 4, gravitational sorting increases theindex b considerably in almost every case,sometimes up to 2.0 or even more, dependingon the original size distribution and wind shearof the fall depth.The effect of evaporation on the 2 22 rela-tionships is similar to process 1b. However, inthe present analyses this will not be consideredsince the raindrops were sampled near cloudbases. Generally, when b

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398 MIY UKI FUJIWARA

I I IU 05 1.0

16 Aug 1965Data 8 R "" /h8 I - 0391

2 . aim95 -----om

I : im

I I05 10 D 15mmFig. 7. Families of the representative N , curveson 16th August. The low concentration and widespectrumare the characteristic of this storm.

The feature of this rain situation is that theconcentrations of raindrops are rather lowwhen rather large drops are involved, as isstrikingly evident from Station B, where thevalue b is rather high. This feature suggests ahigh coalescence factor, T,which is very com-mon in thunderstorms. Although the peakheight is low, it decreases with remarkablebroadening of the spectrum, implying that themajor process contributing to the developmentis the process l a.(c) Rainfall on the 18thAugustSome interpretation for this rain is given inSection 4 to 6. I n Figs. 3, sand 9theN, contoursections and N, families are illustrated, re-spectively. The showers were observed in arainband as illustrated in Fig. 5. The mostremarkable differehce between stations is thata N, curve taken at Station A has a high peakconcentration, about 13,500 drops/mm. ma,while at other stations the corresponding peakww about 2500 drops/mm. m3.It is interestingto compare the NDpattern with each other inFigs. 8 and 9. Although the drawing of thecurve is subjective in detail, the curves at

I0nEEN0

4

-lo:0z16

ION

-Rmm/hr8 Aug. \ 965

AX 3 3-27332 - - - - _ _ _ _ _.14431 ----- 009928 006925 ____ 0023

I I Iv 05 10 D 1.5mmFig . 8.Familiesof the representative curves on 18thAugust at Station A. The narrow but high peakspectrum is the characteristic of the storm ofStationA .

IdI E'-Ey0lo:

elo:

10

R mm/h6 1 8-.97069l - - -____.C8 9 040D 22 0 IID 7 5- 029I S Aug. 1965

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RAINDROP SIZE DISTRIBUTION 399

I

I0 I S Aug . 1965

Station A are evidently monomodal. Thepeak heights increased with slight increase inthe width. From the categories presented inSection 7, this more or less steady rain wasformed by the processes l a combined with 3b.This conclusion is based on the characteristicsof N , curves and the intermediate value of b.I n Figs. 8 and 9, the development characteris-tics show that asthe rainfall intensity increasesprocess 2 becomes effective. Curve E l showsby the larger mode size about 0.5 mm theappreciable effect of the process 3a probablycaused by updrafts.( d ) Rainfall on the 21st August

I n'Fig. 4, two remarkable convective activi-ties are shown at Stations A and B, in front ofthe stratified rain. It can be seen that the con-centrations of drops are relatively low. Thespeed of the leading edge of storm was about700 m/min. In Figs. 11 and 12 the representa-tive N, families were plotted. It was noticedthat the N, curves were developed by processl a combined with 3b until the rainfall intensityreached 0.3mm/hr, and then mixing with largerTellus X I X (1967), 3

Data I t mm/hr21 Bug . 1965 A I3 -.+- 5. 79I I - - - . - - 3. 4314 2. 2616- . 9517 -0.1518 0.039

I I I05 1.0 D 15m

Fi g. 11. Families of the representative N, curveson 2lst August at Station A . Data were taken afterthe rainfall maximum.

21 Aug. 1965 Data S R mnyh

I I I05 1.0 D 1 5 mFi g. 12. Families of the representative N , curveson 2lst August at StationA . Data were taken beforethe rainfall maximum.

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400 MIY UKI FUJ IWARAI0 23 Aug. 1965 Data R mm/hr

3 - - - - - - 0. 904 I . 05A X I-

- 7 0. 65I S- . 24I 2-.168I 7- . 13314 -&--A- 0.095ID3-2Id-

Id-

I1 I I0 0 5 lo 15mmFig. 1.3. Families of the representativeN, curvesin the forenoon of 23rd August at Station A. Thespectrum is narrow and the mean size changeincreases with the rainfall rate without appreciablechangein thepeak height.

drop groups accompanied the further increaseof rainfall intensity. The families shown inFigs. 12 and 11 are the time before and thetime after the mature rainfall at Station A,respectively.It isnoticed that, at the beginning of rainfall,a monomodal spectrum whose peak height isincreasing is combined with a group of verylarge and sparsely distributed drops, whereas inthe diminishing stageasshown in Fig. 11, dropsarelost from larger sizes.(e)Rainjall on the 23rd August

From the ND contour sections it was foundthat, in the forenoon, the mode size of raindropsat Station A was decreasing, and the rainfallwas light and continuous. The size of the largestdrops was less than 1.1 mm in diameters. Thetwo parameters A and b are less than 50 and1.36, respectively. As shown in Fig. 13 the NDcurves show fairly constant mode height. Theeffective processes would be types l b and 3a.I n the afternoon, the rainfall at the mountainslope became slightly convective. The N, pat-

terns became to have unique variation, whichimply that more seeding had occurred with anaccompanying increase in the effective thicknessof the cloud layer. This seems to be consistentwith one of the particular models of warm rainproposed by Komabayasi (1957), because thecloud thickness and the sea salt seeding will in-crease when the trade wind prevails.9. Summary

I n most cases raindrop spectra develop byprocess 1 followed by 3 until the rainfallintensity reaches a certain value, though thiscritical value may change from day to day,for example it is 0.39, 0.19, and 0.34 mm/rhon the 31st July, 18th and 21st, August re-spectively. Further development is accompa-nied by theN curves becoming a multimodalor a widely skewed spectrum. This is result ofthe mixing process 2 with groups of well-deve-loped large drops, which in turn probably de-velop by process 3. The primary stage consistsof processes 1and 3 and appears alone in thecase of weakened convection and stratifiedclouds. The process 4 was hardly effective be-cause the height of cloud base was low.10. Analyses of b value

I n Fig. 14, the vertical axis is in log 2 andhorizontal, in log R. Two of the regression linesfor the 18th and 23rd, August,areshown on the2 -R diagram (Fujiwara, 1961). n this diagramthe steepest lines are for N =constant and themoderately steep lines are for T =constant,whereN and T are the parameters of the ran-dom coalescence process. Accretion of cloudwater with constant seeding concentration isshown by N(acc) =constant. The dotted lineswith a slope 1.0 are lines of constant drop dia-meters. The three processes, constant coales-cence 1a, constant seeding concentration 3 b,and mixing 2 have the same slope of 1.6-1.7.

Consider the two points P and Q on thefigure. These points represent a 2 -R relation-ship for the process3b of accretion with chang-ing numbers of initial seeds. This process cor-responds well to the hypothesis that the saltnuclei concentration along with favorable accre-tion conditions are responsible for the rain. NOWif this rain is considered to undergo furthertransformation by accretion or by coalecence,

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RAINDROP SIZE DISTRIBUTION 401

R (mm/hr)F ig. 14.2-R diagram which interprets the processesfor the rainfall development.the points move fromP toP andQ toQ. Theselective growth at higher rates of Q to Q isconsidered to be by coalescence. The points Pand Q represent the August 23 case which wasfrom a stratified orographic warm rain.

Process3bis the only mechanism found whichproduces values of the slopeas low as 1.1 to 1.2which are very common in Hawaiian rai ns(see Table 2) .11. Conclusion

The results are compatible with the saltnuclei theory in the sense that the first stage ofrain growth appears to be process 3b for low

rainfall rates. This is clearly revealed by theexamples of orographic or stratified weak rains.The process 3 is an effective one in such rai ns;the effect of the change in N is also evident.Although, the present analyses are not able toexamine the way of growth of the initial raindrops from cloud droplets, the coalescencegrowth between precipitable drops, is veryevident.

I n Hawaiian rainshowers as shown in Fig. 2,the value b increases with A in the low b regionwhereas the upper part of the rainshower regionshows the opposite tendency. Since the value Ais responsive to the mean drop diameters, theformer tendency suggest that the effect of saltnuclei on the rainfall intensity through process3 b gradually diminishes asconvective activityis intensified. The latter tendency, though alooser correlation which was found in more orless continental data, is consistent if the rain-drops are considered to havegrownmore throughan ice-phase nuclei seeding process with moreconvective activity, where the seeding willeffectas the process 3b. More intense convectionwill cause to activate more ice nuclei becausemoisture will be transported to lower tempera-tures.

AcknowledgementsThe author wishes to express his hearty

thanks to all staff scientists and cooperatingmembers of the project for their warm andkind help through operation, discussion anddata exchange. Expecially to Dr. E.A. Muellerand Prof. R. L. Lavoie for their help in writingthis paper in English and for their helpfulsuggestions. The author is also appreciative ofthe encouragement and guidance for this projectgiven to him by Dr. K. Isono. For data reduc-tion and drawing, the author expresses histhanks to Mrs. T. Yanase and T. K oyama.

REFERENCESBattan, L. 1956. Radar meteorology. University of Fujiwara, M. 1965a. Raindrop-size distributionChicagoPress. from individual storms. J our. Atrnos. Sci. 22,Blanchard, D. C. 1953. Raindrop size distributionin Hawaiian rains. J our. Meteor. 10, 457-473. Fujiwara,M. 1965b. A proposed formulaof raindropBlanchard, D. C.& Spencer, A. T. 1957. Raindrop size distribution Proc. International Conf. onmeasurement during Project Shower. Tellus 9, Cloud Phys, pp. 265-270. Tokyo and Sapporo.641-562. Fujiwara,M. 1961. Raindrop size distributions with

585-591.

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402 MIYUKI FUJ IWARArainfall types and weather conditions. Res. Rep.No. 8, 111. State Water Survey, Contract No.DA-36-039 SC-87280.Fujiwara, M. 1967. An improved raindrop radio-sonde with filter paper. Tellus, 19, 403-407.

Komabayashi,M. 1957. Some aspect of rain forma-tion in warm cloud (l ), salinity of individualraindrops andother quantities concerning rainfall.J our. M et. SOC. apan 35, 205-220.

Rogers, R. R. & J iusto, J .E. 1966.A n investigationof rain on the island of Hawaii, 117 pp. Tech.Rep. CAL No. Vc-2049-p-1. Cornell AeronauticalLab. Inc., Corn. Univ., N. Y., U.S.A.Squires, P. &Warner, J . 1957. Some measurementsin the orographic cloud of the Island of Hawaiiand in trade wind cumuli. Tellus lo,, 475-494.Woodcock, A . H. & Blanchard, D. C. 1955. Teat ofthe salt-nuclei hypothesis of rain formation. Tellus7. 435-448.

P -YC I I PEAE J I EHME no P A3ME PAM KAn E J I M B TEn J IOM AOIKaE H A A OCT. I'ABAflI?

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