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Advances in Bioresearch Adv.Biores.,Vol6(1)January2015:31-36©2015SocietyofEducation,IndiaPrintISSN0976-4585;OnlineISSN2277-1573 Journal’sURL:http://www.soeagra.com/abr.htmlCODEN:ABRDC3ICV7.20[Poland]

OORRIIGGIINNAALL AARRTTIICCLLEE

Study of Summer Precipitation (rainy) Days Occurrence Probability in South Zagros using Markov Chain Model

Nosrat Farhadi *, Hoseinasakereh , Amir Gandomkar, Majid Montazeri

DepartmentofGeographyNajafabadBranch,IslamicAzadUniversity,Najafabad,Iran.DepartmentGeography,UniversityofZanjan,Iran

Departmentofgeography,NajafabadBranch,IslamicAzadUniversity,Najafabad,Iran.Assistantprofessor,DepartmentofClimatology,UniversityofIsfahan,Iran

Email:farhadi.nosrat@yahoo.com

ABSTRACT Precipitation shortfall and air drought especially in summer season are of the obvious features of Iranweather. However, identifying behavioral characteristics of precipitation occasionally occurring in some parts of south and south west of the country due to the impacts on the residents׳life is necessary. In this survey , the probability of occurring the days with summer precipitation in south Zagros was studied using the network data resulted from the interpolation of daily precipitation statistics of 540 stations at a 51- years statistical period long( 1961-2011) and markov chain technique . The mentioned statistics were arranged based on counting matrix of the mode change of precipitation days and the days with no precipitation and then the probability matrix of mode change calculated based on maximum likelihood method and through frequent orders of this matrix , the daily reliable probability of each drought mode and precipitation estimated . The summer precipitation occurrence probability over the zone of south Zagros has been estimated between 1 to 7 days. The reduction trend of area with increased precipitation occurrence probability and the centralized regions with more precipitations occurrence probability in south east of the zone have been paid attention so that from the east to the west of the zone , the probability of occurring rainy days is sharply reduced due to being far away from the focus of Iran summer monsoon and descended probability of having the outcomes resulted from their activity. Key words: summer precipitation, Markov chain, occurrence probability, south Zagros. Received02/09/2014Accepted24/12/2014©2015SocietyofEducation,India

How to cite this article: NosratF,Hoseinasak,AmirG,MajidM.StudyofSummerPrecipitation(rainy)DaysOccurrenceProbabilityinSouthZagros using Markov Chain Model. Adv. Biores., Vol 6 [1] January 2015: 31-36. DOI: 10.15515/abr.0976-4585.6.1.3136

INTRODUCTION TheshortfallofrainydaysisconsideredasoneoftheintrinsicfeaturesofIranweather.Beingfarawaythe path of moving western winds systems due to the extension of subtropical high pressure, beinglocated of Iran on dry climatic belt , being neighbors with the world׳s vast deserts and special localpositionregardinglowgeographicallatitudeandincreasedangleofthesunradiationandreceivingmoreheatinthesummercausetheatmosphericprecipitationinthisseasonespeciallyinmorewesternpartsofthecountry.However,theoccasionalsummerprecipitationinsouthandsouthwestofthecountrycausesthedamagestotheresidentsandleavesinappropriateeffects.Forthisreason,studyingrainydaysinthesummerandcalculatingtheprobability percentofoccurring thisphenomenon insouthZagros aszonal isnecessaryfromtheviewofrecognizingtheclimatefeaturesofthesummerprecipitationinthiszone,identifyingtheexistent potential ( from the view of precipitation ) and planning to use resources resulted from theseprecipitationsoptimallyandpreventingtheirpossibledamagesandharms.Among the probability – statistical methods, Markov chain model has been seriously considered inatmosphericsciencesovertherecentyear.Markovchainhasmadethesolutionofprobabilityrelatedtothe processes easy using mathematical simple method such as matrices multiplication. Markov chainmodelhasbeenextensivelyappliedindifferentsciencessuchasmeteorology,climatology,economicandindustry. Cent Hiulan et al. [1] have calculated the possibility of weekly precipitation occurrence using

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this method in order to plan the agriculture issues in Uttar Pradesh province in India and divided theweeksinwetanddryperiods.Dash[2]studiedthedailyprecipitationdatafrom2001to2010inOdishaby first order Markov chain and calculated wet and dry days in order to manage agricultural waterresources.Asakreh[3]studiedthefrequencyandcontinuousofrainydaysinTabrizthroughutilizingMarkovchaintechnique and using daily precipitation statistic from 1951 to 2005 and estimated the probability ofprecipitationoccurrenceateachdaytobe%22.6andtheprobabilityofitsnon-occurrence,%77.93andalsoconsideredthehighestprobabilityofrainydaysoccurrenceduringthespringseasonespeciallyMay.Alijanietal.[4]studiedthecontinuationofthefrostdaysinIranbyusingMaekovchainmodelfora15-yearperiod(1991-2005)fromOctobertoMayin58stationsofthecountryandconcludedthatthefrostdays occurrence in Iran involves the feature of Markov chain except the north and south areas of thecountry ,meaningthatthe continuationofthefrostdays isnotrandombuttheoccurrenceofthefrostday ( days ) depends on the climate conditions of the past days. Moreover, Asakreh [5] analyzed theprobability of frequency and continuation of early and late frosts of Zanjan utilizing the statistics ofminimummeandailytemperatureinJanuaryandAugustandusingMarkovchainmodelandobtainedthefrostoccurrenceprobabilityperdayforJanuarytobe%3519andforAugust,%375.Asakreh&Mazini[6]calculatedtheprobabilityofthedayswithprecipitationandalsothedayswithprecipitationlowerthan1mminGolestanprovinceandfoundthatthelocalchangesofdrydaysprobabilityisnotsignificantandwithincreasingtherainfall,theprobabilityofdrydayoccurrenceisreducedthanthattheareaswithlessrainsandwithrespecttotheincreasedprecipitationinsouthregionsofthisprovincetoitsnorthregionstheprobabilityofdrydayscontinuationinhigh-rainsouthregionsistoolowthanthatthesimilardaysinlow-rainnorthregions.YazdanPanahetal.[7]intheirresearchestimatedtheoccurrenceprobabilityof1to 9 heat wave periods at the stations of Kerman province using Markov chain model and 20-yearstatistics of maximum daily temperature .Fooladmand [8] used Markov chain model to select suitableplacesofdryfarminginFarsprovinceandregardingthattheprobabilityofprecipitationoccurrenceandregressionperiodofdifferentdroughtperiodsinNovembertoJanuaryarelowinthesouthFarsprovinceandare increasedtowardthenorthandnorth westof theprovince ,thenorthandnorth westzonesofFarsprovincearesuitablezonesfordryfarmingespeciallywheat.Lee[9]usedMarkovchaintechniqueinorder to forecast the summer seasonal precipitation in south east of U.S.A. Osman Yousef et al. [10]estimatedtherelationshipbetweenprecipitationandtherateofgrowingtheproductsinMinafarmsinNigeria so that based on this model , the government may prepare a long- term plan for the farmers.Edmasoetal.[11]usedMarkovchainmodelinordertoanalyzedryandwetweeksandanalyzedweeklyprecipitationinthecentralvalleyregionofEgyptforplanningagriculture. DATA AND METHODS Thezoneunderstudy(Fig .1) involvessomepartsofsouthandsouthwestofIranateasternlongitudefrom40˚47΄to56˚30΄andnorthernlatitudefrom26΄30΄to33˚includingKoosestan,KohgiluyehandBoyer-Ahmad,Fars,BushehrprovincesandsomepartsofHormozgntothenorthofHormozstraitwithanareaaround264208km2.Fromtheviewofroughness,thesouthwestandsouthrangesofZagroshavebeenspreadinthiszoneextendedfromthenorthtoZagrosandfromthewesttoIraqandfromthesouthside also extended from Koosestan plain and coasts of Persian Gulf to the north of Hormoz strait. ThedesiredzoneisbenefitedfromthehumidityresultedfromthesehydrologicalzonemonsoonactivitiesandsometimesutilizedfromprecipitationduetovicinitytoPersianGulf,sothatforadetailedstudyoftheseprecipitationsinthispartofIran,wehavecalleditsouthZagros.

Fig1.ThepositionofunderstudyzoneinIran

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Tostudytheprobabilityofoccurringthedayswithsummerprecipitation,thedataofdailyprecipitationinsummer season( July ,August ,September)of540stationswithvariousstatisticalperiodlongandmaximallyfor51yearswasextractedandoneT-shapedmatrixat540×93perparedandregardedforthestationswithnovacancydata.Therefore,51datamatriceswereobtainedfrom1961to2011.Sincethestatisticalshortagesmayberesolvedbytheaidofinterpolationmethods,amapwitharesolutionof7000monLambertconformalconic imagesystemwasprovidedusingKriging interpolationperdayonthetotal4743summerdaysofthestatisticalperiod.Theresultofthispracticewastofill thestatisticalgapsofthestationswithstatisticaldefect.Ontheotherhand,thenetworkdataofsummerprecipitationwithacommonstatisticalperiodlonganddimensionsof5392×4743withT-shapedarrays(theplaceon the lines and the time on the columns ) were provided and used as the database for this survey. Inaddition, to minimize the errors resulted from interpolating; the values of %5 mm and less have beenignored.Aphenomenaincludingdrought,flood,precipitationwithadefiniteamount,snowfallataspecialtimethattheiroutcomesmaynotbedeterminedbeforetheiroccurringcertainlyarecalledrandomprocesses.Since theoccurrence of the mentioned eventsdepends ona varietyof factors,smallchanges ineachofthesefactorsmaychangeitsnaturetoahighrateorevenpreventitsoccurrence,Therefore,indifferentobservationsoftheseeventsandeachsimilarevent,variousoutcomesareresultedthattheiroutcomescan’t be determined definitely before their occurring . Based on the probability rules , some randomphenomenahavemorechancestobeoccurredbutthechanceofoccurringsomeoftheotherphenomenaislower.Markovchainisamathematicalmethodformodelingrandomphenomena[3].Anyoutcomeofrandom processes depending only on the outcome immediately before it is called random process orMarkovfeature.Accordingly,arandomprocessthatistrueinMarkovfeatureiscalledprocessorMarkovchain. The chain indicates this fact that outcome is related to its immediate event before itself and notrelated to a prior event. In fact, in this trend , the possibility of occurring a climatic mode at time tdependsonitsconditionat thepriortime,thatis ,t-1 . Ifaprocessisonlyrelatedtoaprocesspriortoitself, it will be called the first approximation of Markova chain and if any process is related to two orthreeprocessesbeforethemselves,itwillbesaidthesecondandthirdapproximationofMarkovchain.Inmanyoftherandomprocesses,theestablishmentofMarkovchinfeaturemaybenotdetermined.Inthiscases,Markovfeatureisconsideredasanassumption.TouseMarkovchaininthissurvey,thefollowingphaseshavebeenadopted,respectively:1. The desired observations should be arranged as Markov chain and based on threshold ≤0.5 mm(withoutprecipitation)and>0.5(thedayswithrainfall).2. At the second step, the frequency arrays of observations should be formed that it itself is a base oftransfer probability array (the probability of change mode) .In frequency array of observations , thenumber of the modes are identified . Markov chains in this research follow a two – mode algorithm(occurrenceandnon-occurrence),sotheprobabilityofoccurringaneventornon-occurringaneventareconsidered.

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Theabovefrequencyarrayofconditionchangingfromadrydaytoadryday(D→D)isshownwithn11,fromadrydaytoarainyday(D→W)withn12,fromawetdaytoadrydaywithn21andfromarainydaytoarainyday(W→W)withn22.3. At the next step , based on the information resulted from phase 2 , the transfer probability array iscreated .Thewayofperformingthisphaseisrelatedtotheresearchers׳view.Forthispurpose, inthissurvey the maximum likelihood method has been applied as the most simplest method on probabilityestimation.

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Theabovematricesarerandommatricesbecauseeachoftheirarrayisnon-negativeanditstotalarraysperrowis1 ,sothat thearraysofthesematricesarecorrespondedwiththeprobabilityofone–phasemodechange.

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4. All of the orders of probability matrix are also random and from a value onward by increasing theorder, no change is made in probability matrix . In this mode , it is said that matrix has reached thestationary ( reliability ) . The probability of reliable mode shows that how much is the probability ofoccurringarainyordrydaywithinalongtime.Therefore,inthisphase,theprobabilityofreliabilityforprecipitationoccurrenceinsummerseasonofsouthZagroswillbecalculated.5.Preparation , interpretation and analysis of the maps are related to the summer precipitationoccurrenceprobabilityinsouthZagros. RESULT AND DISCUSSION InthissurveyaimingatdetectingtheprobabilityofthesummerprecipitationoccurrenceinsouthZagros, first order Markov chain technique has been applied . As seen in Fig.2, the probability of the summerprecipitation occurrence has been estimated to be between 1 to 7 percent in different regions so thatgray-colored cores show the maximum probability of 7% precipitation occurrence in south east and iscorresponded with Hormozgan heights and the eastern regions of Fars province , while toward northwest and coastal strip , the probability of precipitation occurrence is intensively decreased. Theimportantpointsinthisfigurearethereductiontrendofareawithincreasedprobabilityofprecipitationoccurrenceaswellasreducedprecipitationslopefromthesoutheasthalftowardthenorthwestsothattheconcentrationofareaswithmoreprobabilityofprecipitationoccurrenceisinthesoutheasthalfandattached to the northern heights of Hormoz strait . This important matter indicates more utilization ofthis part of the zone from the summer precipitation of the south eastof Iran resulted from the vicinitywithmonsoonsrangebeyondthestraitofHormozandwhateverthedistancefromthemonsoonareasisincreased , the probability of reaching the monsoons and involving the outcomes resulted from theiractivitiesthat is thesummerprecipitationwillbedecreased. Insum ,basedonTab.1 , in49.4%ofthezone area located mainly on coastal strip and from low height parts of Bushehr to north west partslocatedinKoozestanprovince,only1to2percentofprecipitationoccurrenceprobabilityareinvolved.In21.2%of thezone, theprobability is from2 to3percent, in13.6%of theareasfrom3 to4percent , in11.6% from 4 to 5 percent and only in 4% of the zones , there is 5 to 6 percent of the precipitationprobability.Finally,thehighestprobabilityaround6to7percentisalsoseenin0.2%ofthezone.

TabLE.1.TheprobabilitydistributionofprecipitationoccurrenceonthezoneofsouthZagros

Probabilityofoccurrence(percent)

1-2 2-3 3-4 4-5 5-6 6-7

Theareaofeachperiod(percent)

summer 49.4 21.2 13.6 11.6 4 0.2July 67.6 14.8 12.9 4.5 0.3 --august 40.8 25.3 12.2 11.3 10.4 --September 53 24.6 13.6 8.8 --- --

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Fig.11-4.LocaldistributionoftheprobabilitypercentofsummerprecipitationoccurrenceinsouthZagrosduringthesummerseason:(1)July,(2)August,(3)September.

July month Fig.2clearlyshowsthatinJuly,firstlytheprobabilityofprecipitationoccurrencehasbeenestimatedtobe6% and secondly the maximum probability of precipitation occurrence between 5and 6 percent arelocated in smaller parts in Hormozgan and Fars covering about 0.3% of the zone area and the regionswithlowprobabilityofprecipitationoccurrenceareseeninasmallerzoneonlyinFars,HormozganandKohgiluyehandBoyer-Ahmad.Forexample,basedonTab.1,themostareasinvolvingabout67.8%ofthezoneholds1-2percentoftheprobabilityforreceivingtheprecipitationand14.8%between2-3percentandtheprobabilityof3-4percentofprecipitationat12.9%and4-5percentofprobabilityforrainydaysalsomaybeseenat4.5%ofsouthZagrosextension.Insum,theprecipitationwithlowprobabilityandwithasmallerextensioninthismonththantheothermonthsofthesummerseasonandmorezoneshaveaweakerprobability.August month In August based on Fig.2 and Tab.1, about 40.8% of the least probability (1-2% ) is seen so that theminimum probability observed at a smaller areas than the other months indicating the occurrence ofmore precipitations in a wider parts of the zone. As seen in the figure , the probability of moreoccurrencesisextendedtowardcoastalstripalongtheZagrosmountainrangetotheeastofKoozestan.Ingeneral , at one fourth of the zone , there is the probability of 2-3% precipitations and at 12.2% , 4-5percentofprecipitationsandfinallytheprecipitationwith5-6%probabilityoccursin10.4%ofthezones.Insum,inthismonththemaximumprobabilityoccursatmoreextensionsandtheminimumprobabilityatasmallerzonethantheothermonths.September month InSeptemberasseeninFig.2,themaximumcoresareseenagaininsoutheastofthezonethatisthewestHormozganand eastFars.But ,moving towardthesouthandwestof maximumcoresof precipitationoccurrenceprobability is followed due to the more regressions of subtropical scanning high and itsapproximated departure from the south west borders of the country would provide a ground of risingabundant humidity resulted from evaporation of south coastal warm watersand also cause theprecipitation occurrence probability as small but with a large extension.With respect to Tab.1 , in thefinalmonthofthesummer,afewmorethanhalfareasofthezone(53%),1-2%rainydayshavebeenestimatedandaroundonefourthoftheextension(24.6%),around2-3%andat13.6%also3-4%andthehighestprobabilitythatis4-5%isseenat8.8%ofsouthZagros. CONCLUSION Inthissurvey,Markovchainmodelwasappliedtostudytheprobabilityofoccurrencethesummerrainydays in south Zagros and the calculations carried out on the generated zonal data of the dailyprecipitation with a 50-year period long. Based on the findings of this survey , at the heights ofHormozgan province and some parts of the east and south of Fars the probability of occurrence thesummerrainydays ishigher thantheotherparts.This important matter is due tomore benefitof thispart from the south east monsoon precipitation of Iran resulted from vicinity with monsoon rangebeyondtheHormozstrait.Whateverthedistancefromthemonsoonregionsisincreased,theprobabilityofreachingthemonsoonsandutilizingtheoutcomesresultedfromtheiractivitywillbedecreased.InJuly

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,theprecipitationwithlessprobabilityandatasmallextensionthantheothermonthsofthesummerisseen.InAugust,theoccurrenceofmoreprecipitationandoveramorewiderpartsofthezoneisoccurredandtheprobabilityofmoreoccurrenceswithleft-sidedmovementisextendedtowardthecoastalstripaswell as across the range of Zagros mountain to east Koozestan. In September, the maximum cores areseeninthenorthofwesternhalfofHormozganandeastFars.Duetomoreregressionsoftropicalhighpressuresystemanditsapproximateddeparturefromthewesternbordersofthecountry,thegroundofrisingabundanthumidityresultedfromevaporationofsouthcoastalwarmwaters isprovidedandalsocauses the precipitation occurrence probability as small but with a large extension. However, theprecipitation occurrence probability is much higher in the south east parts than the North West. It isrecommendedthatthefindingsofsuchthissurveytobepaidattentioninplanningregardingtheintenseshortageoffreshwaterinthispartofthecountryinordertomakemorebenefitfromthewaterresourcesresulted from these precipitations and on the other hand, through identifying and forecasting theconditionscoincidedwiththeseprecipitations,theincidenceofthepossibledamagescanbeprevented. REFERENCES 1. Senthilvelan.A, Ganesh.A, Banukumar.K (2012) Markov Chain Model for probability of weekly rainfall in

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