mathematical distribution ofrainfall in arid and semi-arid zones...

l Hdi(Jn J. Mel. Geophy, . (1972). 23,2,153·100

551.577

Mathematical distribution of rainfall in arid andsemi-arid zones of Rajasthan

A. KlUSHNAN and R. S. KUSIIW,UIA

Department oj Mat1lematics.

University oj Jodhpu" Jodhpur

(Recei<-ed 11 February 19'11)

ADSTRA (JI.'. Tho mnthemetica l dlstribntion of a(,Mlm\llllt t'u rainfall fur 2!)('utaw. 4 pent ads • . •. •. 20 JK'n t~d.A

ccmmoncing from tbe onse t of monsoon bas 1.1(.'(\11 flt mlilod in n'tlptO(·t of a typica l arid ZOllO ste tion, nz. dodhpurend scmt-nrld 8llttionll. namely , .Ialpu r in Ra jesthen. 1Ill'Il~U of -Iaipur, distribution beyond ll. month is norma ! whilefor -Iodhpur, all accumulated pentads including tho ent ire t10asn ll i~ nut norma l at all, Probability chart. usingthese tboorctical distributions havu ~n lI1111Jllrod and their utility discussed.

1. Introduotlon

Rajasthan reveals a variety of climatic zonesranging from extremely arid zone in J ai sal mcrdistrict to humid zone in Sirohi distr ict, Delinea­tion of various climatic zones in Rajas tha n am]their variation have been discussed by Krishnan(1968). Major portion of tho area ill tho State,however, falls under arid and semi-arid zones,the respective coverage to the total area of theState being 58 and 36 per cent respectively. IIIthese hot and dry regions, the rainfall is hy furthe most important factor limiting crop produc• .tion, An interesting feature in the seasonaldistribution of rainfall in these regions is that85 to 95 per cent of the annual rainfall occursduring southwest monsoon season which com­mences in the semi-arid zone by the end of Juneand in the arid zone by the Iirst week of July.The withdr..wal of the monsoon occurs by thesecond or third week of September. Thus, theKharif season (J uly to October) is the main crop­ping season with Baj ra, Til ami pulses like J!OOllg,.noth and gua, etc as predominant crops in aridzone and Jawor in the semi-arid zone. Areaswith irrigation ure very limited. In view ofthese factors, .. knowledge of the distribu tion ofrainfall during the crop season ami evaluationof drought hnzanls at various periods by com­puting probabilities of ditTerent amounts of rain­fall during the growing season arc extrenrelyhelpful for agricultural operations. The objectof this jlllper is, therefore, to study in deta il thedistr ibution of the rainfall in different periodsfrom thc commencement of rainy season in aridand semi-arid zones, viz., Jodhpur and Jaipur

rea

respect ively, Attempt is also made to constructa probability chart for rainfall.

2. Review of literature

Pramanik and J"!,'llnnathall (1953) studied therainfall distribution of a number of stations inIudiu and showed that the skewness is smallexcept in the arid region of Rajasthen and thosemi-arid regions of the Deccan.

On the basis of assumption of normality indi stribution, Sreeni vssainh and Yegnanarayaunu(1959) produced rnaps showing probability ofoccurrence of different amounts of rainfall durinzthe year as well as dur ing the monsoon season.The percentage frequencies of daily rainfallexceeding specified intensities in Rajasthanhave been shown to be , successive terms oflogari thmic series by J agannathan and Ragha.vcndra (1964). ~[al1ik and Godbole- (\966) pro­sented merely weekly frequency distributionof rainfall in west Rajasthan during the mon­soon without any attempt to study their theore­tical distribution.

3. Data ullllsed

The daily rainfall data for sixty years (1901­19(0) in respect of J()(lhpur and Jaipur wereuti lised in this study. The rainfall totals foreach pentad (five-day period) in the rainy season(June to September) were worked out. Theserial numbering of pentads commences fromI January and thus 31st pentad correspond,to 31 Muy to 4 June, 54th pentad correspondsto 2:1 to 27 September and so on.