Size distribution of Raindrops-Part -VI

Abstract

A.C. Best has fo1lnd an empirical formula for the size distribution of raindrops. If F (x) is the fraction of liquid water in the air comprised by drops of diameter less than x, 1 -F = exp [-(x/a)ⁿ ], where a and n are constants for any particular rainfall. Contrary to the general supposition that the above formula, applies to the average size distribution of a number of samples of rain, it has boon found that the formula holds for individual samples, in 90 out of 104 cases of general monsoon rains and in 134 out of 169 cases of thundersturm rains recorded at Poona. The formula fails where the liquid water distribution is multimodal (generally bimodal) or is J-shaped.

       The parameters a and n are found to be independent for general rains but are connected by the average relation a n = 7.1 mm for thunderstorm rains. There is also a correlation between the intensity of precipitation I and the parameter n For general rains the average rell1,tioll found is I = 6.9 exp [-0.14 (n-5.5)²] and that fur thundorsturm rains is I = 975 exp (-n).

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1. Introduction and Results ;,~; identIcal value of the intensity of precipitation,

..' viz., 3.3 mm/hr, having very different diameter

Best(1950)ha8s~own.tha.t m?st ?i,the avaIlable spectra of liquid water. The averttge values for

dt,l.tt~ on t~e ,ili'op-s1Ze dlBtnbutIonIs 111 aGGordance these two 8amples were calculated and a similar ::.:

wIth the formulae --graph was plotted. It was found that the graph :':

1-1!' = exp [ -(xla)n ] and a = AlP was a str.aig~t line for each of the individu~1

I sample8 WIth Its own valnes of a and n ~s shown ill

where F is the fraction of liquid water in the air Figs. l(a) and l(b). For the average values, how-

comprised by drop8 of diallleter less than x; a aud ever, the plot showed a sharp kink so that two

1t are constants for a particular rainfall. I!~rom the straight lines with different slopes were obtall1ed as

first of these equations it follows that- shown in Fig. l(c). Realising that the individual

I samples wcre more suitable and that there was a

log loglo [l,(l-F)] = -0.36 + n (loglox-Ioglo(t) danger in calCulating averages of such heteroge-

and that log log~o [lj(~-F») plotted against loglox neou~ ~aterial (very di~erent diame.te~ 8~c~tr~ ),

should be a straIght Ime wIth 810pe rt. The value Bcst s Imes were plotted 1o1;' all the 1~9 1U~IVIdu,ll

of a can be calculated from the intercept. sa1Uple8. It was foUlld that a straIght line was

..obtained for 134 samples, showing that Best's

Followillg the usual practIce, the whole of the formula holds for individual samples. It was further

data.on thu!l~erstor.m rains consisting of 169 sam- found that the 35 samples -for which the formula

pies was dI':'lded mto 1~ groups a!ld aver~ge does not apply, could be divided into three cate-

values obtamed. On usmg these for plottmg gories aB follows -

log ~lO [lj(l-F)] against logloX' it was foUlld that

in 9 cases a straight line was obtained, in 7 (;ases (a) Two straight line8 with the second line

two strt\ight lines were obtained and in one case haying a higher slope were obtained in 21 cases.

three straight lines were obtall1ed. Suspecting An exactly similar result was obtall1ed by Best

.that this non-agreement was due to averaging of (1950) for the East -Hill data which he has atLribut-

such heterogeneous ma~rial, Best's lines were ed to the small amount of data Gorresponding to

plotted for :tw~ individual samples of raiu with that line.