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

lHdi(J n J. Mel. Geophy, . (1972). 23,2,153·100 551.577 Mathematical distribution of rainfall in arid and semi-arid zones of Rajasthan A. KlUSHNAN and R. S. KUSIIW,UIA Department oj Mat1le matics. University oj J odhpu" J odhp ur ( Recei<-ed 11 February 19'11) ADSTRA (JI. '. Tho mnthemetical dlstribntion of a(,Mlm\lllltt' u rainfall fur 2!)('ut aw. 4 pentads • . •. •. 20 ccmmoncing from tbe onse t of monsoon bas 1 .1(.' (\ 11 flt mlilod in n 'tlpt O(·t of a typical arid ZOllO ste tio n, nz. dodhpur end scmt-nrld 8llttionll. namely, .Ialpu r in Rajesthen. of -Iaipur, dis tribution beyond ll. month is norma ! while for -Iodhpur, all accumulated p entads including tho entire t10asn ll nut norma l at all, Probability chart. using these tboorctical distributions havu and their utility discussed. 1. Int roduotlon Rajasthan reveals a variety of climatic zones ranging from extremely arid zone in J ai sal mcr district to humid zone in Sirohi district, Delinea- tion of various climatic zones in Rajasthan 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 the State being 58 and 36 per cent respectively. III these hot and dry regions, the rainfall is hy fur the most impo rtant factor limiting crop produc• . tion, An interesting feature in the seasonal distribution of rainfall in these regions is that 85 to 95 per cent of the annual rainfall occurs during southwest monsoon season which commences in the semi-arid zone by the end of June and in the arid zone by the Iirst week of Jul y. The withdr..wal of the monsoon occurs by the second or third week of September. Thus, the Kharif 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 arid zone and Jawor in the semi-arid zone. Areas with irrigation ure very limited. In view of these factors, .. knowledge of the distribu tion of rainfall during the crop season ami evaluation of drought hnzanl s at various periods by computing probabilities of ditTerent amount s of rainfall during the g rowing season arc extrenrely helpful for agricultural operations. The object of this jlllper is, therefore, to study in detail the distribution of the rainfall in different periods from thc commencement of rainy season in arid and semi-arid zones, viz., Jodhpur and Jaipur rea respectively, Attempt is also made to constr uct a probability chart for rainfall. 2. Review of literature Pramanik and J"!,'ll nnathall (195 3) studied the rainfall distribution of a number of stations in Iudiu and showed th at the skewness is small except in the arid region of Rajasthen and tho semi-arid regions of the Deccan. On the basis of assumption of normality in distribution, Sr eeni vssainh and Yegnanaray aunu (1959) produced rnaps showing probability of occurrence of different amounts of rainfall durinz the year as well as during the monsoon season. The percentage frequencies of daily rainfall exceeding specified intensities in Rajasthan have been shown to be , successive terms of logarithmic series by Jaga nnathan and Ragha. vcndra (1964) . and Godbol e- (\966) prosented merely weekly frequency di stribution of 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 (1901- 19(0) in respect of J()(lhpur and J aipur were utilised in this study. The rainfall totals for each pentad (five-day period) in the rainy season (June to September) were worked out. The serial numbering of pentads commences from I January and thus 31st pentad correspond , to 31 Muy to 4 June, 54th pentad corresponds to 2:1 to 27 September and so on.

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Page 1: Mathematical distribution ofrainfall in arid and semi-arid zones …metnet.imd.gov.in/mausamdocs/52323.pdf · Mathematical distribution ofrainfall in arid and semi-arid zones of Rajasthan

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.