JointModelingofPrecipitationandTemperatureUsingCopula ... · 2019. 7. 30. · Extreme Value...

Research ArticleJoint Modeling of Precipitation and Temperature Using CopulaTheory for Current and Future Prediction under Climate ChangeScenarios in Arid Lands (Case Study Kerman Province Iran)

T Mesbahzadeh 1 M M Miglietta 2 M Mirakbari3 F Soleimani Sardoo4

and M Abdolhoseini5

1Assistant Professor Department of Reclamation of Arid and Mountain Regions Faculty of Natural ResourcesUniversity of Tehran Tehran Iran2Institute of Atmospheric Sciences and Climate of the Italian National Research Council (ISAC-CNR)Corso Stati Uniti 4 Padova Italy3PhD Faculty of Natural Resources University of Tehran Tehran Iran4Academic Staff Department of Natural Engineering University of JiroftKerman and PhD Student in Faculty of Natural Resources University of Tehran Tehran Iran5MSc Faculty of Natural Resources University of Tehran Tehran Iran

Correspondence should be addressed to T Mesbahzadeh tmesbahutacir

Received 5 January 2019 Accepted 21 April 2019 Published 19 June 2019

Academic Editor Nir Y Krakauer

Copyright copy 2019 T Mesbahzadeh et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Precipitation and temperature are very important climatic parameters as their changes may affect life conditions ereforepredicting temporal trends of precipitation and temperature is very useful for societal and urban planning In this research inorder to study the future trends in precipitation and temperature we have applied scenarios of the fifth assessment report of IPCCe results suggest that both parameters will be increasing in the studied area (Iran) in future Since there is interdependencebetween these two climatic parameters the independent analysis of the two fields will generate errors in the interpretation ofmodel simulations erefore in this study copula theory was used for joint modeling of precipitation and temperature underclimate change scenarios By the joint distribution we can find the structure of interdependence of precipitation and temperaturein current and future under climate change conditions which can assist in the risk assessment of extreme hydrological andmeteorological events Based on the results of goodness of fit test the Frank copula function was selected for modeling of recordedand constructed data under RCP26 scenario and the Gaussian copula function was used for joint modeling of the constructed dataunder the RCP45 and RCP85 scenarios

1 Introduction

Climate change has become a concern for the scientificcommunity over the past two decades due to its seriouseffects on humans societies and the environment It is theresult of changes in external forces such as fluctuation insolar cycle volcanic eruption or increase of greenhousegases caused by human activities and land-use changeAccording to studies conducted over the past decadesglobal warming has caused climate change at local

regional and global levels [1] Global warming evidencereveals that the Earth climate has undergone significantchanges between 1906 and 2005 meanwhile the temper-ature increased by about 074degC [2] and it is expected thatby the end of the 21st century global temperatures willincrease on average between 181degC and 4degC [3] esechanges and their impacts on the ecosystems and lands maycause changes in global water cycle sea level rise dryingout of lakes penetration and mixing of saline and freshwater and migration of species

HindawiAdvances in MeteorologyVolume 2019 Article ID 6848049 15 pageshttpsdoiorg10115520196848049

e results of various climate change models have beenpresented to now in the framework of the 1st AssessmentReport (TAR) of the 2nd Report (FAR) of the 3rd Report(TAR) of the 4th Report AR4 (CMIP3) and finally of the5th Report AR5 (CMIP5) of the Intergovernmental Panel onClimate Change

Unlike previous ones the fifth report models emphasizethe socioeconomic aspects of climate change and its role insustainable development and risk management and itsoverall framework focuses on reducing greenhouse gasesand adaptation approaches to climate change e fifthassessment report includes three working group reports anda synthesis report e first working grouprsquos report wasreleased in 2013 and the rest of the reports were completedin 2014 In the preparation of the fifth report which wasgradually released from 2013 to 2014 the output of CMIP5series models was used ese models use new emissionscenarios called ldquoRCPrdquo [4] ese scenarios have fourpathways namely RCP26 RCP45 RCP6 and RCP85which are named according to their radiative forcing in 2100[5] Different atmospheric general circulation model runsinclude all or some of these scenarios

Recently a majority of researchers around the worldhave used the 5th assessment report to study climatechange under new scenarios of emission in different re-gions [6ndash8] e fifth report models have higher resolutionand use newer scenarios than previous ones In the fifthreport roughly half of the models have a spatial resolutionof less than 13deg while previous reports models had a lowerspatial resolution e main difference between old andnew emission scenarios is that in new ones the radiativeforcing pathway resulted from increase in greenhouse gasesin the atmosphere at 2100 are measured in Wattsm2 whilein the old emission scenarios [9] just concentrationpathway of greenhouse gases is specified Climate changestudies in arid and semiarid regions that are more sus-ceptible to this phenomenon are essential to be undertakenwith higher-resolution models and under new scenarios asthese models provide a better understanding compared toprevious models (third and fourth reports)

e general circulation models which are the mostappropriate means for predicting future climate changeat global scales [10] have a coarse spatial resolutionOutputs of these models have a high spatial resolution(250ndash600 km) [11] erefore the direct application ofthese models is not suitable for a regional or local scalethus their output is not proper to be used for studying thehydrological and environmental impacts of climatechange at regional level [12] e most important andsuitable tool for connection between the localregionalscale and GCM large-scale is downscaling ere arevarious downscaling models In general two statisticaland dynamic methods are here presented for this pur-pose In the dynamic method a numerical model withhigh spatial resolution or regional climatic model withgrid spacing of about 5 to 50 km is coupled to the generalcirculation model In statistical downscaling method anempiricalstatistical relationship is set between large-scale and local variables Using the statistical methods

global scale climatic variables such as the mean pressureat sea level regional wind temperature and geopotentialheight are matched to localregional scale variables [13]Statistical methods are generally based on regressionrelationship Among statistical downscaling methodsSDSM has been widely used for downscaling of climaticvariables throughout the world [14] SDSM combines twomethods of linear multiple regression and statisticalproductive climate regression [11 15]

e most important parameters in climate changestudies are temperature and precipitation which also play acrucial role in meteorological and hydrological phenomenasuch as droughts and floods Furthermore they are con-sidered the most effective climate variables impacting ag-ricultural productivity [16ndash18] so that the temperatureaffects the length of the growing season and the precipitationaffects the yield [19 20] Many studies have been carried outon the impacts of precipitation and temperature on agri-cultural products [21ndash24]

All of these studies found that precipitation and tem-perature are two factors affecting the productivity of agri-cultural crops Precipitation and temperature are twoclimatic parameters and the knowledge about their futuretrend is essential for planning natural ecosystems e studyof the pattern of temperature and precipitation changes iscrucial due to climate change [25ndash27] Knowing the tem-poral variation of temperature and its relationship withother climate variables is very important for climate plan-ning [28] e precipitation and temperature have very hightemporal variations [29 30] e dependence of pre-cipitation to temperature causes its high variation over thetime [27] e dependence between the two parameters oftemperature and precipitation [27] makes their analysisproblematic when they are treated as independent of eachother since it creates errors in results of calculations

In climate change condition determining the in-terdependence relationship between two parameters oftemperature and precipitation can help the assessment of therisk of extreme hydrological and meteorological phenom-ena however determining the interdependence of theseparameters is difficult due to complicated dependence be-tween them

To determine the interdependence between precipitationand temperature it is necessary to set the joint distributionof these two variables In order to survey the in-terdependence between temperature and precipitation de-termining the joint distribution of two parameters isessential e conventional methods of calculating jointprobability distribution functions of random variables havethe limitation of the selection of the marginal function typewhich causes error in analysis Copula theory is a methodwhich does not suffer from the limitations typical of mul-tivariable distribution functions It can be used for modelingdistribution functions coupled with random variableswithout limitations of marginal distribution functions [31]e copula function can be used for determining de-pendence between temperature and precipitation in a waythat correlation calculated by this method is higher than forother methods

2 Advances in Meteorology

e joint modeling of precipitation and temperature canbe used for providing solutions aimed at reducing the risk ofextreme hydrological and meteorological events in the caseof climate change in future

Till now there has not been a single study on thestructure of interdependence between precipitation andtemperature under climate change condition e existingstudies have examined the joint distribution and in-terdependence structure between two parameters (pre-cipitation and temperature) in current period Aghakouchaket al [31] used two copula functions of Elliptical group (t andGaussian) for two-variable analysis of temperature andprecipitation ey found that fitness of t copula is betterthan Gaussian for extreme amounts Cong and Brady [25]specified 5 copula functions including Gumbel T NormalClayton and Frank as the best functions for determiningdependence structure between temperature and pre-cipitation distributions

Pandey et al [27] determined the dependence betweentemperature parameters (Minimum Maximum Mean) andmonthly precipitation using 5 copula functions includingGumbel Frank T Clayton and Normal of which Normaldistribution showed the best fit so it was used for jointmodeling of temperature and precipitation variables Otherstudies on the two parameters of precipitation and tem-perature were also carried out by Favre et al [32] Serinaldi[33] Scholzel and Friederichs [34] and Laux et al [35]

In this study changes of temperature and precipitationas two key climatic parameters influencing natural ecosys-tems in future in the Kerman Province (southeast Iran) areinvestigated in the framework of general circulation modelsunder the 3rd and 5th report scenarios e general cir-culation models applied include CanESM2 of the 5th as-sessment report and HadCM3 of 3rd assessment reportFinally to study interdependence between precipitation andtemperature in future under climate change conditionstructure of their dependency is determined under copulatheory which lacks the limitations of multivariable distri-bution functions in using marginal functions Copula theorydetermines joint distribution of temperature and pre-cipitation to identify interdependence of two parametersResults of this study can be used for developing strategies inorder to reduce the risk of climatic and hydrological phe-nomena in future

2 Study Area

Kerman Province with a total area of 181716 km2 is locatedin southeast of Iran (Figure 1) According to Domartenclimatic classification it is considered as arid zone eprovince is at the conjunction of Zagros Chain Mountainand central Iran mountains with 160 km length is con-junction has created a unique environment and a specificnatural status Mean annual precipitation exceeds 1438mmmaximum monthly temperature 287degC minimum monthlytemperature 69degC and mean annual temperature 157degCTables 1 and 2 present the statistical characteristics ofprecipitation and temperature in the area in an historicalperiod between 1961 and 2005 In order to find changes in

temperature and precipitation and their future trends thestudies conducted on the climate change in the area have justused the data of 3rd report and HadCM3 model e studiessuggest that in future increased precipitation in winter andspring and increased temperature in the summer and fall willoccur However no studies have been carried out to de-termine the structure of the interdependency betweentemperature and precipitation affected by the climate changeusing copula theory in the area yet

3 Methodology

e data used in this study includes precipitation and meandaily temperature in Kerman synoptic station with geo-graphical eastern longitude of 56deg56prime and northern latitudeof 30deg25prime and data period of 1961 to 2005 in addition toreanalysis atmospheric data (NCEP) and data belonging totwo models of HadCM3 and CanESM2 Daily data are titledas predictand and NCEP predictor variables and data ofgeneral circulation model as large-scale predictor which areavailable in base periods of 1961 to 2001 for the model of 3rdreport and 1961 to 2005 for the model of 5th report and2006ndash2100 for future runs of the 5th report and 2002 to 2099for the 3rd report

31 Downscaling of GCM Data Using SDSM In order toreview the future trend of temperature and precipitationdata of 2 models of HadCM3 and CanESM2 are converted totiny-scale exponential data using statistical downscalingmethodSDSM In this method a quantitative relationship isset between large-scale atmospheric variables and localsurface variables such as temperature and precipitation [36]e relationship is as follows [37]

Y f(x) (1)

where Y is the predictor variable X is the predictand var-iable and F is the function of transfer which is experi-mentally estimated from observational data

Model of HadCM3 is one of the models of the 3rdevaluation report of intergovernmental panel on climatechange which has been developed by the Hadley center inEngland HadCM3 model is a ocean-atmospheric system(AOGCM) whose simulations include 2 scenarios A2 andB2 e Atmospheric part of this model also includes 19levels with spatial resolution of 25deg lat and 375deg long whilethe oceanic part includes 20 levels with spatial resolution of125deg lat and 125deg long [38 39] e model of CanESM2comes from the 5th Assessment Report of IntergovernmentalPanel on Climate Change (IPCC) which includes 3 sce-narios namely RCPP26 RCP45 and RCP85

CanESM2 is an improved version of the general circu-lation model developed by CCCma which is called ESMEffort has been made to include most of the land factorsaffecting the climate in the ESM modeling structureDownscaling of the small-scale data of HadCM3 model forperiod of 1961ndash2001 and future period since 2002 to 2009 isconducted by predictor variables Data of CanESM2 modelin the base period of 1961 to 2005 and future period of 2006

Advances in Meteorology 3

to 2100 are converted to small-scale data using predictorvariables and SDSM is method has 4 key steps whichincludes determining predictor variable of NCEP modelcalibration model veri cation and simulation of data re-lating mean temperature and precipitation under old andnew emission scenarios

32 Copulaeory In order to identify the interdependencestructure between temperature and precipitation the jointdistribution of two variables is determined using copulatheory e theory was presented for multivariable proba-bility modeling by Sklar (1959) [40] Copula function pro-vides the opportunity to combine several single-variabledistributions in various families of one two or multivariabledistributions considering the interdependence of the vari-ables In other words copula function C(u1 u2 uN) is aconjunctive function to link random variable distributionfunctions of X1 X2 XN with marginal functions ofFx1(X1) Fx2(X2) FXN(XN) [41] According copula the-ory joint distribution of two variables of mean temperature(X) and precipitation (Y) is as follows

F x1 x2 xN( ) Cθ FX1x1( ) FX2

x2( ) FXNXN( )[ ]

(2)

Copula functions are multivariate distributions withuniform marginal functions which model interdependencebetween several variables [41] e most important ad-vantage of using copula functions is that the structure ofdependency between variables can be de ned even if mar-ginal functions are dierent this means that in order to set(de ne) a joint distribution function having equal marginalfunctions for each variable is not necessary Other types ofprobability distributions carry out the modeling of in-terdependence of variable structures assuming that func-tions of marginal functions are equal but this assumptioncauses error in multivariable analysis By copula theorymarginal functions are selected for setting multivariablefunctions as well as de ning nonlinear and asymmetricrelationship between variables Copula function includes avariety of families such as Elliptical (t copula Normal)Archimedean (Gumbel Clayton Frank Ali- Mikhail-Haq)Extreme Value (Husler-Reiss Galambos Tawn and t-EV

Table 1 Statistical characteristics of monthly precipitation (1961ndash2005)

Month Jan Feb Mar Apr May June July Aug Sept Oct Nov DecMinimum 06 03 34 0 0 0 0 0 0 0 0 0Maximum 975 1084 731 98 65 78 113 74 6 239 31 942Mean 2910 2843 3117 1791 924 068 051 054 037 169 467 1983Standard deviation 1959 2411 1872 1452 168 177 15 114 46 406 804 2232

Table 2 Statistical characteristics of monthly temperature (1961ndash2005)

Month Jan Feb Mar Apr May June July Aug Sept Oct Nov DecMinimum minus312 151 816 1331 1823 2315 2357 2194 179 1167 55 12Maximum 691 1015 1437 18 2448 2741 2918 2761 2338 1766 1279 97Mean 425 693 1107 1611 2102 2539 2656 2438 2076 1558 974 585Standard deviation 193 171 147 148 124 104 143 141 154 147 152 177

Kerman synoptic station

High 4473

Low 100

Height

0 35 70 140 210 280km

N

W

S

E

27

28

29

30

31

32

27

28

29

30

31

32

5554 57 58 59 6056

54 55 56 57 58 59 6046 49 53 57 60 64

25

28

30

33

36

38

41

53 5749 60 6446

25

28

30

33

36

38

41

Figure 1 Location map of study area in the southeast of Iran


Gumbel) and other families namely Plackett and Farlie-Gumbel-Morgenstern [42] Families of Archimedean andElliptical are used mostly [43] Archimedean family has twosymmetric and asymmetric forms which respectively haveone parameter andmore than 2 parameters Elliptical familyunlike Archimedean family does not follow a specific shapebut its advantage is the dependence between upper andlower tails

Interdependence structure of random variables de-termines the type of copula function used for joint modelingAccording to Huang et al [44] interdependence of tem-perature and precipitation during the various months isnegative or positive en joint modeling of temperatureand precipitation is different depending on the structure ofinterdependency between variables As a result in the casethat interdependence is positive various families of func-tions such as Archimedean Elliptical and other types ofcopula functions can be used Unlikely for negative in-terdependence values a minor number of functions areusable In this research due to negative relationship betweenprecipitation and mean temperature data symmetricArchimedean functions such as Rotated Clayton RotatedJoe Frank Rotated Gamble and also Elliptical of Gaussianare used for joint modeling (Table 3)

33EstimationofParameters ofCopulaFunction In order toestimate the parameters of copula function both theparametric and nonparametric methods are used Inparametric method relationship between generatorfunction of each copula and Kendall coefficient (equation(3)) is used [45] (Table 3) In this equation c and d are thenumber of pairs of concordant and discordant variablesand n is number of observations Two pairs of variables (XiYi) and (Xj Yj) are concordant if Xj gtXi and Yj gtYi orXi gtXj and Yi gtYj ey are also considered discordantwhen Xi gtXj and Yj gtYi or Xj gtXi and Yi gt Yj Alterna-tively if (Xi minusXj) (Yi minusYj) gt 0 variables are concordantand if (Xi minusXj) (Yi minusYj) lt 0 variables are discordant In theparametric method using the maximum log-likelihoodfunction (equation (4)) parameter of θ is estimated[32] Log-likelihood function estimates parameter of θusing density copula function If dependent randomvariables are as x1k x2k xpk (k 1 n) with copulafunction of Fθ(x1k xpk) Cθ(F1(X1k) Fp(Xpk)) log-likelihood function is defined as follows [32]

τ (cminusd)

n

21113888 1113889

(3)

L(θ) 1113944n

k1log cθ F1 x1k( 1113857 Fp xpk1113872 11138731113966 11139671113960 1113961 (4)

where cθ is the copula density function F is the marginaldistribution function and x1k x2k xpk k 1 n arethe dependent random variables

34 Goodness of Fit Test for Copula Function Before mod-eling by copula functions the copula function having thebest fit is selected For selecting the best copula functionvalue of joint empirical probability of two variables ofprecipitation and temperature is calculated through em-pirical copula (equation (5)) and then is compared with thevalues resulted from copula functions (Archimedean andElliptical families) To compare empirical copula with eachcopula functions normalized root mean square error(NRMSE) and NashndashSutcliffe coefficient were selected(equations (6) and (7)) Also two criteria namely AkaikeInformation Criterion (AIC) and Bayesian InformationCriterion (BIC) (equations (8) and (9)) [46 47] are used Inthese equations the empirical probability of precipitationandmean temperature is v and u Pei is the value of empiricalcopula Pi is the value of copula theory K is the modelparameter n is the number of observations and L is thevalue of maximum log-likelihood function

Cn(u v) 1n

1113944

n

t11 Ut lt u Vt lt v( 1113857 (5)

NRMSE

1n

1113970

1113944

n

i1

Pei minusPi( 11138572

Peimax minusPeimin1113872 1113873 (6)

NSE 1minus1113936

Nn1 Pei minusPi( 1113857

2

1113936Nn11 Pei minusPei( 1113857

2 (7)

AIC 2kminus 2 ln(L) (8)

BIC 2n LogL + k Log(n) (9)

4 Results

41 Downscaling GCM Data After reviewing and con-trolling the quality of the observational data the NCEPpredictor variables which have the highest correlationwith each observational data were selected e numberof NCEP variables for temperature as an unconditionalparameter is less than that for precipitation which is aconditional variable (due to including zero-precipitationdays) (Table 4) NCEP variables have been estimated formodels of GCM for two periods of 1961ndash2001 and1961ndash2005 (Table 2)

e model calibration and verification steps were un-dertaken based on NCPE variables for both models in thebase period In order to increase the accuracy of the modelvarious values of variance inflation factor were selected fortemperature and precipitation parameters and bias correc-tion was applied for precipitation Later based on the resultsof the model verification exercise the best value of eachfactor was determined through statistical comparison Inthis way variance inflation factors of temperature andprecipitation and also bias correction factors of precipitationwere determined as 6 10 and 1 respectively Figure 2 showsefficiency of SDSMmodel for downscaling precipitation and


temperature data in two base periods of 1961ndash2001 and1961ndash2005 respectively for two models of HadCM3 andCanESM2 Generally because of consistency of temperaturedata this efficiency is higher for temperature in comparisonto precipitation Finally large-scale data of HadCM3 andCanESM2 were downscaled under SERA and RCP scenariosusing SDSM method for precipitation and mean tempera-ture in future (2017ndash2100)

42 Assessment of Efficiency and Uncertainty of ModelStatistical criteria of NashndashSutcliffe index and NRMSE werecalculated in order to assess downscaled values of pre-cipitation and mean temperature by NCEP variables andlarge-scale (HadCM3 and CanSM2) models for the period of1961ndash2001 and 1961ndash2005 (Table 5) e results display thatdownscaled values of mean temperature have a higher ac-curacy compared to precipitation in both GCM modelsGiven existence of so many zeroes in precipitation dataseries data do not follow normal distribution so accuracy ofmodeling precipitation decreases in comparison to tem-perature Furthermore values relating to the assessmentcriteria of precipitation data modeled by CanESM2 (5thReport) have further compliance with observed data incomparison to values estimated by HadCM3 e data ofmean temperature modeled by GCM have nearly equal

compliance with the observed data erefore in order tojoint modeling of precipitation and mean temperaturevalues calculated by CanESM2 are used

In order to study the trend of climatic parameters infuture period compared to the base period the Mann-Kendall test was applied for precipitation and mean tem-perature data modeled by CanESM2 (Table 6) Based on theMann-Kendall test observed and modeled precipitation donot follow any meaningful trend under RCP26 and RCP85scenarios However data produced by RCP45 scenarioshows a decreasing trend e results of the Mann-Kendalltest on mean temperature showed the series modeled byRCP scenarios and observed data have an increasing trendand the increase in the data modeled under scenario ofRCP85 is higher e results of modeling of precipitationdata under scenario of RCP showed that mean annualprecipitation in future based on RCP26 RCP45 andRCP85 scenarios will be 1572mm 1481mm 1902mmrespectively which in comparison with the observationperiod (1438mm) an increase would be seen in the studyarea (Figure 3) Also the results of modeling of mean tem-perature data under scenario of RCP showed mean annualtemperature in future based on RCP26 RCP45 and RCP85scenarios will be 169degC 174degC and 182degC respectivelywhich in comparison with the observation period (equal to156degC) an increase would be seen in the study area (Figure 3)

Table 4 NCEP variables for two periods (1961ndash2001 and 1961ndash2005)

Predictand NCEP variable

1961ndash2001 Precipitation

Ncepp5thas 500 hPa wind directionNcepr500as 500 hpa relative humidityNcepr850as 850 hpa relative humidityNceprhumas Near surface relative humidityNcepshumas Surface specific humidity

Temperature Ncepptemas Mean temperature at 2m


Ncepp500gl 500 hpa geopotentialNcepprcpgl Accumulated precipitationNceps500gl 500 hpa specific humidityNcepshumgl 1000 hpa specific humidity

Temperature Ncepptempgl Screen air temperature

Table 3 Different types of copula functions

Joint CDF θ Kendall τ

Archimedeanfamily

Frank C(u v θ) 1θ ln[1 + (eminusθu minus 1)(eminusθv minus 1)eminusθ minus 1] R 0 1minus (4θ)(1minusD1(θ))

Dk(x) kxk 1113938x

0tk(exp(t)minus 1)dt

Rotated Joe 1minus [1minus 1113937mi1(1minus (1minus ui)

θ)]1θ (minusinfinminus1) minus1minus 41113938 x log(x)(1minusx)minus2(1+θ)θmiddotdx

RotatedGumbel C(u v θ) u + vminus 1 + C(1minus u 1minus v) (minusinfinminus1) minus1minus (1θ)

RotatedClayton C(u v θ) u + vminus 1 + C(1minus u 1minus v) (minusinfin 0) θ(2minus θ)

Elliptical family Gaussian C(u v) 1113938u

0 Φ(Φminus1(v)minus ρxyΦminus1(t)1minus ρ2xy

1113968)dt (minus1 +1) (2π)arcsin(θ)


Figure 4 shows error bar of mean monthly precipitationdata Error data are used for displaying deviation of dataBased on RCP scenario mean precipitation in future in themonths Jan Feb Mar Apr and Dec would fall down and in

other months would go up e error bar of mean monthlytemperature shows an increase throughout the year eincrease rate in warm months of May to August will be

Historical (1961ndash2001)NCEP (1961ndash2001)HadCM3 (1961ndash2001)


Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecJanMonth


0

5

10

15

20

25

30

Mea

n m

onth

ly te

mpe

ratu

re

0

5

10

15

20

25

30

35M

ean

mon

thly

pre

cipi

tatio

n

(a)

Historical (1961ndash2005)NCEP (1961ndash2005)CanESM2 (1961ndash2005)




0

5

10

15

20

25

30

35

Mea

n m

onth

ly p

reci

pita

tion

0

5

10

15

20

25

30M

ean

mon

thly

tem

pera

ture

(b)

Figure 2 Comparison of downscaled data using predictor variables (NCEP and GCM models) with the historical precipitation andtemperature for (a) 1961ndash2001 (HadCM3) and (b) 1961ndash2005 (CanESM2)

Table 5 Evaluation criteria of downscaled data for HadCM3 andCanESM2 models

Predicted Predictor NSE NRMSE Correlation

PrecipitationNCEP 0946 00259 099

CanESM2 0551 0057 084HadCM3 0458 00829 067

TemperatureNCEP 09824 00094 09923

CanESM2 0984 00053 0998HadCM3 0964 00133 0991

Table 6 e results of Mann-Kendall test for historical andmodeled data under RCP scenarios

Parameter Z value P value

Precipitation

Historical minus0988 0323RCP26 0341 0733RCP45 minus2476 0013RCP85 137 0169

Temperature

Historical 477 0000RCP26 246 0014RCP45 94 0000RCP85 1187 0000


higher than in other months On the contrary the increaserate will be less between October and December (Figure 4)

43Determining Interdependence Structure of PrecipitationandMean Temperature in Two Historical and Future Periods

431 Marginal Functions of Temperature and PrecipitationIn order to provide a joint modeling of temperature andprecipitation correlation between the variables was esti-mated using the Kendall rank correlation coefficient Ken-dall correlation was selected because the data do not follow anormal distribution Table 7 displays the Kendall correlationcoefficient of monthly precipitation and mean temperature

for the historical period and the future e Kendall cor-relation coefficient amounts show that the relationshipbetween precipitation and temperature is different in variousmonths so in the historical period there is a meaningfulnegative correlation in March April May and Septembere meaningful relationship between temperature andprecipitation under RCP26 and RCP45 scenarios in Apriland May is negative and in other months there is nomeaningful relationship Meanwhile there is a negativemeaningful relationship in April and May and a meaningfulpositive relationship in August between precipitation andtemperature in future under RCP85 en the amounts ofprecipitation and temperature in April which show thehighest correlation were selected for joint modeling in the

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

0

100

200

300

400

500

600

700

800Pr

ecip

itatio

n

(a)

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

14

15

16

17

18

19

20

21

22

Tem

pera

ture

(b)

Figure 3 Comparison of precipitation (a) and temperature (b) observed and modeled under RCP scenarios during the period 1961ndash2100

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash20

ndash10

0

10

20

30

40

50

Prec

ipita

tion

(a)

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash5

0

5

10

20

15

30

25

35

40

Tem

pera

ture

(b)

Figure 4 Error bar of mean monthly precipitation (a) and temperature (b) in historical and future periods


historical and the future periodemarginal distribution ofprecipitation and temperature was determined throughfitting 20 univariate distribution based on KolmogorovndashSmirnov and chi-square tests Based on statistical testsWakeby distribution was selected for precipitation data inhistorical period and under RCP45 and RCP85 andJohnson SB distribution for the modeled data under RCP26Also Wakeby distribution was selected for temperature datain historical period and under RCP26 and RCP85 scenariosand Beta distribution for the data under RCP45 scenario(Table 8)

44 Selecting the Best Copula for Joint Modeling of Temper-ature and Precipitation in Historical and Future PeriodsIn order to fit copula functions to precipitation and tem-perature variables the parameters of copulas were estimatedusing parametric and nonparametric methods for historicaland future periods (Table 9) Parameters of copula functionpresent structure of dependency between temperature andprecipitation variables Based on the results of the selectioncriteria of the best fit of copula function for precipitation andtemperature in historical and future climate among 5copulas Frank copula function was selected for jointmodeling in historical and future periods under scenario ofRCP26 and Gaussian copula function under scenarios ofRCP45 and RCP85 (Table 9) Figure 5 shows Q-Q plots ofFrank and Gaussian copula functions for historical data andthe modeled under RCP scenarios High correlation betweentheoretical and empirical copula suggests fitness of Frankand Gaussian functions for joint modeling of temperatureand precipitation Figure 6 shows the values of probabilitydensity of Gaussian and Frank copula functions in historicaland the future period e values of joint probability densityof precipitation and temperature show these variables havesymmetric correlation in upper and lower tails this is one ofthe specifications of Frank and Gaussian copula functions

[48] In other words random variables which follow Frankand Gaussian copula functions lack correlation in upper andlower tails e structure of dependence between pre-cipitation and temperature in historical and future periodsunder RCP26 scenario is equale structure of dependenceof these variables under RCP45 and RCP85 is equal as well

45 Joint Probability of Precipitation and Temperature forTwo Historical and Future Periods Joint probability ofprecipitation and mean temperature is very important formanagement and assessment of the risk imposed by extrememeteorological and hydrological events as well as manage-ment of productivity of agricultural products Joint prob-ability is defined as the probability when precipitation andtemperature simultaneously exceed a certain value which isshown as (P(Uge u Vge v)) Awareness of this probability canbe useful in establishment of an early warning system forextreme events such as flood and drought Joint probabilityof precipitation and mean temperature based on copulatheory is defined as follows [49]

P(Uge u Vge v) 1minusFU(u)minusFV(v) + C FU(u) FV(v)( 1113857

(10)

Awareness that the probability of precipitation andtemperature simultaneously exceeds a certain value is alsouseful for improving water resources systems underclimate change condition in future For example prob-ability that simultaneously precipitation exceeds itsmaximum value (Pr(U ge 98)) and temperature exceedsthe temperature corresponding to maximum pre-cipitation (Pr(V ge 18)) is 0007 (Figure 7(a)) Also theprobability that simultaneously temperature exceeds itsmaximum value (Pr(U ge 1955)) and precipitation ex-ceeds the precipitation corresponding to maximumtemperature (Pr(V ge 0)) is 0004 (Figure 7(a)) According

Table 7 Kendall correlation coefficient (τ) and P value for mean temperature and precipitation in historical and future periods

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

Historical τ minus012 minus003 minus021 minus043 minus043 minus015 016 002 023 minus009 002 minus008P value 022 074 003 0000 0000 019 017 082 004 042 082 042

RCP26 τ 002 002 minus007 minus044 minus027 minus009 minus006 minus0005 007 012 008 minus004P value 073 078 028 0000 0000 022 036 094 035 007 023 05

RCP45 τ 002 minus005 minus007 minus034 minus022 minus008 007 minus007 minus0004 minus0001 minus0003 minus002P value 072 047 031 0000 0001 03 032 031 096 098 095 072

RCP85 τ minus003 minus002 minus008 minus031 minus027 minus009 007 022 008 009 minus003 013P value 058 069 02 0000 0000 021 028 0005 026 021 064 006

Table 8 Marginal distribution functions and selection of the best copula for joint modeling of temperature and precipitation in historicaland future periods

Precipitation TemperatureDistribution Parameters Distribution Parameters

Historical Wakeby α 2199 β 01191 c 0 δ 0 ξ minus1734 Weibul α 1282 β 1667RCP26 Johnson SB c 091 δ 050 λ 386 ζ minus242 Wakeby α 121 β 535 c 148 δ minus021 ξ 141RCP45 Wakeby α 859 β 0177 c 169 δ 038 ξ minus0706 Beta α1 674 α2 417 a 988 b 226RCP85 Wakeby α 1293 β 0082 c 0 δ 0 ξ minus129 Wakeby α 5586 β 243 c 544 δ minus089 ξ 1305


Table 9 Selection criteria of the best fit of copula functions for historical and future periods

Copula functionsParametric Nonparametric

AIC BIC NRMSE NSE Parameter AIC BIC NRMSE NSE Parameter

Historical

Gaussian minus171 minus153 0039 093 minus0589 minus17 minus152 0038 091 minus0597Frank minus188 minus177 0038 094 minus484 minus188 minus17 0037 093 minus4613

Rotated Clayton minus106 minus887 0041 092 minus0918 minus737 minus557 0043 090 minus1518Rotated Gumbel minus149 minus131 0039 093 minus161 minus143 minus125 0038 091 minus1759Rotated Joe minus105 minus873 0043 092 minus174 minus595 minus441 0045 089 minus2395

RCP26


Rotated Clayton minus325 minus301 0043 095 minus0992 minus215 minus198 0048 091 minus129Rotated Gumbel minus379 minus354 0044 095 minus156 minus368 minus331 005 090 minus164Rotated Joe minus269 minus231 0069 092 1674 minus177 minus156 0078 091 minus218

RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF

02 04 06 080Empirical CDF

(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

02 04 06 08 10Empirical CDF

(d)

Figure 5 Q-Q plot for (a) historical data (b) modeled data under RCP26 (c) modeled data under RCP45 and (d) modeled data underRCP85


110805 0604020 0

Temperature Rainfall010203040506070809

Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

10

Join

t PD

F

(c)

1108Temperature

05 06

Rainfall04020 0

010203040506070809

Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

1012

Join

t PD

F

(d)

Figure 6 e joint PDF and corresponding contour lines for (a) historical period (b) RCP26 (c) RCP45 and (d) RCP85


020

0204

18 100

P (U

geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)

Figure 7 e joint probability Pr(Uge u Vge v) of precipitation and temperature for historical (a) and future (b) RCP26 (c) RCP45 and(d) RCP85


to the modeled data under RCP26 scenario probabilitythat simultaneously precipitation exceeds its maximumvalue (Pr (U ge 3586)) and temperature exceeds thetemperature corresponding to maximum precipitation(Pr(V ge 1576)) is 0006 Also probability that pre-cipitation (Pr(U ge 64)) and temperature (Pr(V ge 2092))simultaneously exceeding the maximum temperature andits corresponding precipitation is 0004 (Figure 7(b))Based on the amounts modeled under RCP45 scenarioprobability that precipitation (Pr(U ge 4875)) and tem-perature (Pr(V ge 1536)) simultaneously exceeding max-imum precipitation and its corresponding temperature is00034 Also probability that precipitation and temperaturesimultaneously exceeding the maximum temperature (Pr(Vge2161)) and its corresponding precipitation (Pr(Uge 233)) is00005 (Figure 7(c)) Based on the modeled data underRCP85 probability that precipitation and temperature si-multaneously exceeding maximum precipitation (Pr(U ge 55))and its corresponding temperature (Pr(Vge 1561)) is 0002Also probability that precipitation and temperature simul-taneously exceeding the maximum temperature(Pr(Vge 2255)) and its corresponding precipitation (Pr(Uge 0)) is 00002 (Figure 7(d)) According to this probabilitythat precipitation and temperature simultaneously exceedingmaximum precipitation and its corresponding temperature inhistorical period is higher than the future period Further-more probability that precipitation and temperature ex-ceeding the maximum temperature and its correspondingprecipitation in historical period is higher than in the futureperiod under climate change condition

5 Conclusion

In this study copula theory was used for joint modeling ofprecipitation and temperature which are two main climaticfactors impacting agricultural production and meteorolog-ical and hydrological phenomena such as flood and droughtin climate change condition Increase or decrease of climaticparameters such as precipitation and temperature impactson extreme events Knowing the pattern of temporal changeof temperature and its relationship with other climaticparameters is essential for climatic planning for futureGlobal warming in recent years has been reported usingclimate change models by many researchers e fifth as-sessment report issued by IPCC despite the former reportshas focused on socioeconomic aspects of climate change andits impact on sustainable development and risk managementwhen its general framework underlines greenhouse re-duction and adaptation with the climate change esemodels have higher resolution and use new emission sce-narios in comparison to the older reports In this study inorder to compare the 5th report with the former ones twomodels of HadCM3 and CanESM2 were used for reviewingthe trends of precipitation and temperature change in futureunder new and old scenarios e results of the modeledprecipitation and temperature show that CanESM2 hasmore compliance with the observed data which is because ofhigher resolution of the 5th report models Based on the

modeled data under RCP scenarios the study area showstemperature and precipitation will increase in future

Interdependence between temperature and precipitationis such that their independent analysis will cause errors inestimations Dependence of precipitation to temperaturecauses its significant change over the time In climate changecondition determining the relationship of interdependencebetween precipitation and temperature can help assessingrisk associated with extreme hydrological and meteorolog-ical phenomena Aiming at finding the interdependence ofprecipitation and temperature it is needed to determine thejoint distribution of these variables For this purpose copulatheory has been used for joint modeling of temperature andprecipitation in climate change condition According to theresults of applying selection criteria of the best fit Frankcopula function for historical and modeled data underRCP26 scenario and Gaussian copula function for modeleddata under RCP45 and RCP85 scenarios were selected forjoint analyzing temperature and precipitatione presentedresults of joint modeling are in line with previously pub-lished research For instance Cong and Brady [25] Keer-thirathne and Perera [18] and [50] indicated two Frank andGaussian copulas for joint modeling of precipitation andtemperature [48]

Frank and Gaussian copula functions show that data inthe historical and future periods have symmetric de-pendence in upper and lower tails Frank and Gaussiancopula functions were used for joint modeling in thehistorical and future periods Awareness that precipitationand temperature simultaneously exceed a certain value isvery useful for improving water resources systems underclimate change condition in future e joint probabilityvalues showed that the probability of simultaneously ex-ceeding temperature and precipitation with respect to themaximum precipitation and its corresponding tempera-ture is higher in historical period than that in the futureperiod under climate change In addition the probabilitythat precipitation and temperature exceed the maximumtemperature and its corresponding precipitation in his-torical period is higher than that in future under climatechange condition As a whole joint modeling of pre-cipitation and temperature for future under climatechange condition can be used towards providing riskreduction strategies for extreme meteorological and hy-drological events

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] R-l Li and S Geng ldquoImpacts of climate change on agricultureand adaptive strategies in Chinardquo Journal of Integrative Ag-riculture vol 12 no 8 pp 1402ndash1408 2013


[2] H Tabari S Marofi A Aeini P H Talaee andK Mohammadi ldquoTrend analysis of reference evapotranspi-ration in the western half of Iranrdquo Agricultural and ForestMeteorology vol 151 no 2 pp 128ndash136 2011

[3] Z Wang D L Ficklin Y Zhang and M Zhang ldquoImpact ofclimate change on streamflow in the arid Shiyang River Basinof northwest Chinardquo Hydrological Processes vol 26 no 18pp 2733ndash2744 2012

[4] R H Moss J A Edmonds K A Hibbard et al ldquoe nextgeneration of scenarios for climate change research and as-sessmentrdquo Nature vol 463 no 7282 pp 747ndash756 2010

[5] D P Van Vuuren J Edmonds M Kainuma et al ldquoerepresentative concentration pathways an overviewrdquo Cli-matic Change vol 109 no 1 pp 5ndash31 2011

[6] R Chadwick I Boutle and G Martin ldquoSpatial patterns ofprecipitation change in CMIP5 why the rich do not get richerin the tropicsrdquo Journal of Climate vol 26 no 11 pp 3803ndash3822 2013

[7] V V Kharin F W Zwiers X Zhang and M WehnerldquoChanges in temperature and precipitation extremes in theCMIP5 ensemblerdquo Climatic Change vol 119 no 2pp 345ndash357 2013

[8] P Kumar Bal A Ramachandran R Geetha et al ldquoClimatechange projections for Tamil Nadu India deriving high-resolution climate data by a downscaling approach usingPRECISrdquo 2eoretical Applied and Climatology vol 123no 3-4 pp 523ndash535 2016

[9] C H Xu and Y Xu ldquoe projection of temperature andprecipitation over China under RCP scenarios using a CMIP5multi-model ensemblerdquo Atmospheric and Oceanic ScienceLetters vol 5 no 6 pp 527ndash533 2012

[10] C Miao Q Duan Q Sun and J Li ldquoEvaluation and ap-plication of Bayesian multi-model estimation in temperaturesimulationsrdquo Progress in Physical Geography Earth and En-vironment vol 37 no 6 pp 727ndash744 2013

[11] S Y B Gebremeskel L F de Smedt L Hoffmann andL Pfister ldquoAnalysing the effect of climate changes on streamflow using statistically downscaled GCM scenariosrdquo In-ternational Journal River Basin Management vol 2 no 4pp 271ndash280 2005

[12] L E Hay R L Wilby and G H Leavesley ldquoA comparison ofdelta change and downscaled Gcm scenarios for threemountainous basins in the United States1rdquo JAWRA Journal ofthe American Water Resources Association vol 36 no 2pp 387ndash397 2000

[13] F AWetterhall D Bardossy S H Chen and C Y Xu ldquoDailyprecipitation downscaling techniques in three Chinese re-gionsrdquo Water Resources Research vol 42 article W114232006

[14] J Huang J Zhang Z Zhang C Xu B Wang and J YaoldquoEstimation of future precipitation change in the YangtzeRiver basin by using statistical downscaling methodrdquo Sto-chastic Environmental Research and Risk Assessment vol 25no 6 pp 781ndash792 2011

[15] R L Wilby P G Whitehead A J Wade D ButterfieldR J Davis and G Watts ldquoIntegrated modelling of climatechange impacts on water resources and quality in a lowlandcatchment River Kennet UKrdquo Journal of Hydrology vol 330no 1-2 pp 204ndash220 2006

[16] L Chen V P Singh S Guo A K Mishra and J GuoldquoDrought analysis using copulasrdquo Journal of Hydrologic En-gineering vol 18 no 7 pp 797ndash808 2013

[17] D J Dupuis ldquoUsing copulas in hydrology benefits cautionsand issuesrdquo Journal of Hydrologic Engineering vol 12 no 4pp 381ndash393 2007

[18] D G T C Keerthirathne and K Perera ldquoJoint Distribution ofrainfall and temperature in Anuradhapura Srilanka usingcopulasrdquo in Proceedings of the International Research Sym-posium on Engineering Advancements (RSEA 2015) SAITMMalabe Sri Lanka 2015

[19] P Cantelaube and J-M Terres ldquoSeasonal weather forecastsfor crop yield modelling in Europerdquo Tellus A DynamicMeteorology and Oceanography vol 57 no 3 pp 476ndash4872005

[20] J E Olesen and M Bindi ldquoConsequences of climate changefor European agricultural productivity land use and policyrdquoEuropean Journal of Agronomy vol 16 no 4 pp 239ndash2622002

[21] P Cooper J Dimes K Rao B Shapiro B Shiferaw andS Twomlow ldquoCoping better with current climatic variabilityin the rain-fed farming systems of sub-Saharan Africa anessential first step in adapting to future climate changerdquoAgriculture Ecosystems and Environment vol 126 no 1-2pp 24ndash35 2008

[22] W Erskine and F El Ashkar ldquoRainfall and temperature effectson lentil (Lens culinaris) seed yield in Mediterranean envi-ronmentsffects on lentil (Lens culinaris) seed yield in Med-iterranean environmentsrdquo Journal of Agricultural Sciencevol 121 no 3 pp 347ndash354 1993

[23] D Lobell and C Field ldquoGlobal scale climate-crop yield re-lationships and the impacts of recent warmingrdquo Environ-mental Research Letters vol 2 no 1 article 014002 2007

[24] R Muchow T Sinclair and M Bennett ldquoTemperature andsolar-radiation effects on potential maize yield across loca-tionsrdquo Agronomy Journal vol 82 no 2 pp 338ndash343 1999

[25] R-G Cong and M Brady ldquoe interdependence betweenrainfall and temperature copula analysesrdquo Scientific WorldJournal vol 2012 pp 1ndash11 2012

[26] J Kreyling and C Beier ldquoComplexity in climate changemanipulation experimentsrdquo Bioscience vol 63 no 9pp 763ndash767 2013

[27] P K Pandey L Das D Jhajharia and V Pandey ldquoModellingof interdependence between rainfall and temperature usingcopulardquo Modeling Earth Systems and Environment vol 4no 2 pp 867ndash879 2018

[28] S Balyani Y Khosravi F Ghadami M Naghavi andA Bayat ldquoModeling the spatial structure of annual temper-ature in Iranrdquo Modeling Earth Systems and Environmentvol 3 no 2 pp 581ndash593 2017

[29] L F Buba N U Kura and J B Dakagan ldquoSpatiotemporaltrend analysis of changing rainfall characteristics in GuineaSavanna of Nigeriardquo Modeling Earth Systems and Environ-ment vol 3 no 3 pp 1081ndash1090 2017

[30] R Sethi B K Pandey R Krishan D Khare and P C NayakldquoPerformance evaluation and hydrological trend detection ofa reservoir under climate change conditionrdquo Modeling EarthSystems and Environment vol 1 no 4 2015

[31] A AghaKouchak A B Bardossy and E Habib ldquoCopula-based uncertainty modelling application to multisensorprecipitation estimatesrdquo Hydrological Processes vol 24no 15 pp 2111ndash2124 2010

[32] A C Favre S E Adlouni L Perreault N iemonge andB Bernard ldquoMultivariate hydrological frequency analysisusing copulasrdquo Water Resources Research vol 40 no 1pp 1ndash12 2004


[33] F Serinaldi ldquoAnalysis of inter-gauge dependence by KendallrsquosτK upper tail dependence coefficient and 2-copulas withapplication to rainfall fieldsrdquo Stochastic Environmental Re-search and Risk Assessment vol 22 no 6 pp 671ndash688 2008

[34] C Scholzel and P Friederichs ldquoMultivariate non-normallydistributed random variables in climate research ampampndash introduction to the copula approachrdquo NonlinearProcesses in Geophysics vol 15 no 5 pp 761ndash772 2008

[35] P Laux S Vogl W Qiu H R Knoche and H KunstmannldquoCopula-based statistical refinement of precipitation in RCMsimulations over complex terrainrdquo Hydrology and EarthSystem Sciences vol 15 no 7 pp 2401ndash2419 2011

[36] R L Wilby C W Dawson and E M Barrow ldquoSDSMndashAdecision support tool for the assessment of regional climatechange impactsrdquo Journal of Environmental Modeling andSoftware vol 17 no 2 pp 147ndash159 2002

[37] Y B Dibike and P Coulibaly ldquoHydrologic impact of climatechange in the Saguenay watershed comparison of down-scaling methods and hydrologic modelsrdquo Hydrology vol 307no 1ndash4 pp 145ndash163 2005

[38] C Gordon C Cooper C A Senior et al ldquoe simulation ofSST sea ice extents and ocean heat transports in a version ofthe Hadley Centre coupled model without flux adjust-mentsflux adjustmentsrdquo Climate Dynamics vol 16 no 2-3pp 147ndash168 2000

[39] V D Pope M L Gallani P R Rowntree and R A Strattonldquoe impact of new physical parameterizations in the HadleyCentre climate model HadAM3rdquo Climate Dynamic vol 16no 2-3 pp 123ndash146 2000

[40] A Sklar Fonctions deracuteepartition ` a n dimensionset leursmargesPublications de lrsquoInstitut de Statistique de lrsquoUniversitacutee de Parisvol 8 pp 229ndash231 1959

[41] R B Nelsen An Introduction to Copulas Springer New YorkNY USA 2006

[42] J Yan ldquoEnjoy the joy of copulas with a package copulardquoStatistical Software vol 21 no 4 pp 1ndash21 2007

[43] S Madadgar and H Moradkhani ldquoDrought analysis underclimate change using copulardquo Journal of Hydrologic Engi-neering vol 18 no 7 pp 746ndash759 2013

[44] Y Huang J Cai H Yin and M Cai ldquoCorrelation of pre-cipitation to temperature variation in the Huanghe river(yellow river) basin during 1957ndash2006rdquo Journal of Hydrologyvol 372 no 1ndash4 pp 1ndash8 2009

[45] C Genest and L-P Rivest ldquoStatistical inference proceduresfor bivariate archimedean copulasrdquo Journal of the AmericanStatistical Association vol 88 no 423 pp 1034ndash1043 1993

[46] H Akaike ldquoA new look at the statistical model identificationrdquoIEEE Transactions on Automatic Control vol 19 no 6pp 716ndash723 1974

[47] H Bozdogan ldquoAkaikersquos information criterion and recentdevelopments in information complexityrdquo Journal of Math-ematical Psychology vol 44 no 1 pp 62ndash91 2000

[48] P K Mohammadi and D M Zimmer ldquoCopula modeling anintroduction for practitionersrdquo Foundations and Trends inEconometrics vol 1 no 1 pp 1ndash111 2005

[49] J T Shiau ldquoFitting drought duration and severity with two-dimensional copulasrdquo Water Resources Management vol 20no 5 pp 795ndash815 2006

[50] N Bezak K Zabre and M Sraj ldquoApplication of copulafunctions for rainfall interception modellingrdquo Journal ofWater vol 10 no 8 pp 1ndash17 2018


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Submit your manuscripts atwwwhindawicom

e results of various climate change models have beenpresented to now in the framework of the 1st AssessmentReport (TAR) of the 2nd Report (FAR) of the 3rd Report(TAR) of the 4th Report AR4 (CMIP3) and finally of the5th Report AR5 (CMIP5) of the Intergovernmental Panel onClimate Change

Unlike previous ones the fifth report models emphasizethe socioeconomic aspects of climate change and its role insustainable development and risk management and itsoverall framework focuses on reducing greenhouse gasesand adaptation approaches to climate change e fifthassessment report includes three working group reports anda synthesis report e first working grouprsquos report wasreleased in 2013 and the rest of the reports were completedin 2014 In the preparation of the fifth report which wasgradually released from 2013 to 2014 the output of CMIP5series models was used ese models use new emissionscenarios called ldquoRCPrdquo [4] ese scenarios have fourpathways namely RCP26 RCP45 RCP6 and RCP85which are named according to their radiative forcing in 2100[5] Different atmospheric general circulation model runsinclude all or some of these scenarios

Recently a majority of researchers around the worldhave used the 5th assessment report to study climatechange under new scenarios of emission in different re-gions [6ndash8] e fifth report models have higher resolutionand use newer scenarios than previous ones In the fifthreport roughly half of the models have a spatial resolutionof less than 13deg while previous reports models had a lowerspatial resolution e main difference between old andnew emission scenarios is that in new ones the radiativeforcing pathway resulted from increase in greenhouse gasesin the atmosphere at 2100 are measured in Wattsm2 whilein the old emission scenarios [9] just concentrationpathway of greenhouse gases is specified Climate changestudies in arid and semiarid regions that are more sus-ceptible to this phenomenon are essential to be undertakenwith higher-resolution models and under new scenarios asthese models provide a better understanding compared toprevious models (third and fourth reports)

e general circulation models which are the mostappropriate means for predicting future climate changeat global scales [10] have a coarse spatial resolutionOutputs of these models have a high spatial resolution(250ndash600 km) [11] erefore the direct application ofthese models is not suitable for a regional or local scalethus their output is not proper to be used for studying thehydrological and environmental impacts of climatechange at regional level [12] e most important andsuitable tool for connection between the localregionalscale and GCM large-scale is downscaling ere arevarious downscaling models In general two statisticaland dynamic methods are here presented for this pur-pose In the dynamic method a numerical model withhigh spatial resolution or regional climatic model withgrid spacing of about 5 to 50 km is coupled to the generalcirculation model In statistical downscaling method anempiricalstatistical relationship is set between large-scale and local variables Using the statistical methods

global scale climatic variables such as the mean pressureat sea level regional wind temperature and geopotentialheight are matched to localregional scale variables [13]Statistical methods are generally based on regressionrelationship Among statistical downscaling methodsSDSM has been widely used for downscaling of climaticvariables throughout the world [14] SDSM combines twomethods of linear multiple regression and statisticalproductive climate regression [11 15]

e most important parameters in climate changestudies are temperature and precipitation which also play acrucial role in meteorological and hydrological phenomenasuch as droughts and floods Furthermore they are con-sidered the most effective climate variables impacting ag-ricultural productivity [16ndash18] so that the temperatureaffects the length of the growing season and the precipitationaffects the yield [19 20] Many studies have been carried outon the impacts of precipitation and temperature on agri-cultural products [21ndash24]

All of these studies found that precipitation and tem-perature are two factors affecting the productivity of agri-cultural crops Precipitation and temperature are twoclimatic parameters and the knowledge about their futuretrend is essential for planning natural ecosystems e studyof the pattern of temperature and precipitation changes iscrucial due to climate change [25ndash27] Knowing the tem-poral variation of temperature and its relationship withother climate variables is very important for climate plan-ning [28] e precipitation and temperature have very hightemporal variations [29 30] e dependence of pre-cipitation to temperature causes its high variation over thetime [27] e dependence between the two parameters oftemperature and precipitation [27] makes their analysisproblematic when they are treated as independent of eachother since it creates errors in results of calculations

In climate change condition determining the in-terdependence relationship between two parameters oftemperature and precipitation can help the assessment of therisk of extreme hydrological and meteorological phenom-ena however determining the interdependence of theseparameters is difficult due to complicated dependence be-tween them

To determine the interdependence between precipitationand temperature it is necessary to set the joint distributionof these two variables In order to survey the in-terdependence between temperature and precipitation de-termining the joint distribution of two parameters isessential e conventional methods of calculating jointprobability distribution functions of random variables havethe limitation of the selection of the marginal function typewhich causes error in analysis Copula theory is a methodwhich does not suffer from the limitations typical of mul-tivariable distribution functions It can be used for modelingdistribution functions coupled with random variableswithout limitations of marginal distribution functions [31]e copula function can be used for determining de-pendence between temperature and precipitation in a waythat correlation calculated by this method is higher than forother methods






2 Study Area



3 Methodology



Y f(x) (1)








x2( ) FXNXN( )[ ]

(2)







High 4473

Low 100

Height

0 35 70 140 210 280km

N

W

S

E

27

28

29

30

31

32

27

28

29

30

31

32

5554 57 58 59 6056

54 55 56 57 58 59 6046 49 53 57 60 64

25

28

30

33

36

38

41

53 5749 60 6446

25

28

30

33

36

38

41






τ (cminusd)

n

21113888 1113889

(3)

L(θ) 1113944n

k1log cθ F1 x1k( 1113857 Fp xpk1113872 11138731113966 11139671113960 1113961 (4)



Cn(u v) 1n

1113944

n

t11 Ut lt u Vt lt v( 1113857 (5)

NRMSE

1n

1113970

1113944

n

i1



NSE 1minus1113936


2

1113936Nn11 Pei minusPei( 1113857

2 (7)



4 Results


















Archimedeanfamily


Dk(x) kxk 1113938x
















0

5

10

15

20

25

30

Mea

n m

onth

ly te

mpe

ratu

re

0

5

10

15

20

25

30

35M

ean

mon

thly

pre

cipi

tatio

n

(a)





0

5

10

15

20

25

30

35

Mea

n m

onth

ly p

reci

pita

tion

0

5

10

15

20

25

30M

ean

mon

thly

tem

pera

ture

(b)





CanESM2 0551 0057 084HadCM3 0458 00829 067


CanESM2 0984 00053 0998HadCM3 0964 00133 0991



Precipitation


Temperature







HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

0

100

200

300

400

500

600

700

800Pr

ecip

itatio

n

(a)

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

14

15

16

17

18

19

20

21

22

Tem

pera

ture

(b)


RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash20

ndash10

0

10

20

30

40

50

Prec

ipita

tion

(a)

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash5

0

5

10

20

15

30

25

35

40

Tem

pera

ture

(b)








(10)















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

10

Join

t PD

F

(c)

1108Temperature

05 06

Rainfall04020 0

010203040506070809

Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

1012

Join

t PD

F

(d)



020

0204

18 100

P (U

geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy



















2 Study Area



3 Methodology



Y f(x) (1)








x2( ) FXNXN( )[ ]

(2)







High 4473

Low 100

Height

0 35 70 140 210 280km

N

W

S

E

27

28

29

30

31

32

27

28

29

30

31

32

5554 57 58 59 6056

54 55 56 57 58 59 6046 49 53 57 60 64

25

28

30

33

36

38

41

53 5749 60 6446

25

28

30

33

36

38

41






τ (cminusd)

n

21113888 1113889

(3)

L(θ) 1113944n

k1log cθ F1 x1k( 1113857 Fp xpk1113872 11138731113966 11139671113960 1113961 (4)



Cn(u v) 1n

1113944

n

t11 Ut lt u Vt lt v( 1113857 (5)

NRMSE

1n

1113970

1113944

n

i1



NSE 1minus1113936


2

1113936Nn11 Pei minusPei( 1113857

2 (7)



4 Results


















Archimedeanfamily


Dk(x) kxk 1113938x
















0

5

10

15

20

25

30

Mea

n m

onth

ly te

mpe

ratu

re

0

5

10

15

20

25

30

35M

ean

mon

thly

pre

cipi

tatio

n

(a)





0

5

10

15

20

25

30

35

Mea

n m

onth

ly p

reci

pita

tion

0

5

10

15

20

25

30M

ean

mon

thly

tem

pera

ture

(b)





CanESM2 0551 0057 084HadCM3 0458 00829 067


CanESM2 0984 00053 0998HadCM3 0964 00133 0991



Precipitation


Temperature







HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

0

100

200

300

400

500

600

700

800Pr

ecip

itatio

n

(a)

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

14

15

16

17

18

19

20

21

22

Tem

pera

ture

(b)


RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash20

ndash10

0

10

20

30

40

50

Prec

ipita

tion

(a)

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash5

0

5

10

20

15

30

25

35

40

Tem

pera

ture

(b)








(10)















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

10

Join

t PD

F

(c)

1108Temperature

05 06

Rainfall04020 0

010203040506070809

Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

1012

Join

t PD

F

(d)



020

0204

18 100

P (U

geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy


















x2( ) FXNXN( )[ ]

(2)







High 4473

Low 100

Height

0 35 70 140 210 280km

N

W

S

E

27

28

29

30

31

32

27

28

29

30

31

32

5554 57 58 59 6056

54 55 56 57 58 59 6046 49 53 57 60 64

25

28

30

33

36

38

41

53 5749 60 6446

25

28

30

33

36

38

41






τ (cminusd)

n

21113888 1113889

(3)

L(θ) 1113944n

k1log cθ F1 x1k( 1113857 Fp xpk1113872 11138731113966 11139671113960 1113961 (4)



Cn(u v) 1n

1113944

n

t11 Ut lt u Vt lt v( 1113857 (5)

NRMSE

1n

1113970

1113944

n

i1



NSE 1minus1113936


2

1113936Nn11 Pei minusPei( 1113857

2 (7)



4 Results


















Archimedeanfamily


Dk(x) kxk 1113938x
















0

5

10

15

20

25

30

Mea

n m

onth

ly te

mpe

ratu

re

0

5

10

15

20

25

30

35M

ean

mon

thly

pre

cipi

tatio

n

(a)





0

5

10

15

20

25

30

35

Mea

n m

onth

ly p

reci

pita

tion

0

5

10

15

20

25

30M

ean

mon

thly

tem

pera

ture

(b)





CanESM2 0551 0057 084HadCM3 0458 00829 067


CanESM2 0984 00053 0998HadCM3 0964 00133 0991



Precipitation


Temperature







HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

0

100

200

300

400

500

600

700

800Pr

ecip

itatio

n

(a)

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

14

15

16

17

18

19

20

21

22

Tem

pera

ture

(b)


RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash20

ndash10

0

10

20

30

40

50

Prec

ipita

tion

(a)

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash5

0

5

10

20

15

30

25

35

40

Tem

pera

ture

(b)








(10)















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

10

Join

t PD

F

(c)

1108Temperature

05 06

Rainfall04020 0

010203040506070809

Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

1012

Join

t PD

F

(d)



020

0204

18 100

P (U

geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy


















τ (cminusd)

n

21113888 1113889

(3)

L(θ) 1113944n

k1log cθ F1 x1k( 1113857 Fp xpk1113872 11138731113966 11139671113960 1113961 (4)



Cn(u v) 1n

1113944

n

t11 Ut lt u Vt lt v( 1113857 (5)

NRMSE

1n

1113970

1113944

n

i1



NSE 1minus1113936


2

1113936Nn11 Pei minusPei( 1113857

2 (7)



4 Results


















Archimedeanfamily


Dk(x) kxk 1113938x
















0

5

10

15

20

25

30

Mea

n m

onth

ly te

mpe

ratu

re

0

5

10

15

20

25

30

35M

ean

mon

thly

pre

cipi

tatio

n

(a)





0

5

10

15

20

25

30

35

Mea

n m

onth

ly p

reci

pita

tion

0

5

10

15

20

25

30M

ean

mon

thly

tem

pera

ture

(b)





CanESM2 0551 0057 084HadCM3 0458 00829 067


CanESM2 0984 00053 0998HadCM3 0964 00133 0991



Precipitation


Temperature







HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

0

100

200

300

400

500

600

700

800Pr

ecip

itatio

n

(a)

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

14

15

16

17

18

19

20

21

22

Tem

pera

ture

(b)


RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash20

ndash10

0

10

20

30

40

50

Prec

ipita

tion

(a)

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash5

0

5

10

20

15

30

25

35

40

Tem

pera

ture

(b)








(10)















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

10

Join

t PD

F

(c)

1108Temperature

05 06

Rainfall04020 0

010203040506070809

Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

1012

Join

t PD

F

(d)



020

0204

18 100

P (U

geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy





























Archimedeanfamily


Dk(x) kxk 1113938x
















0

5

10

15

20

25

30

Mea

n m

onth

ly te

mpe

ratu

re

0

5

10

15

20

25

30

35M

ean

mon

thly

pre

cipi

tatio

n

(a)





0

5

10

15

20

25

30

35

Mea

n m

onth

ly p

reci

pita

tion

0

5

10

15

20

25

30M

ean

mon

thly

tem

pera

ture

(b)





CanESM2 0551 0057 084HadCM3 0458 00829 067


CanESM2 0984 00053 0998HadCM3 0964 00133 0991



Precipitation


Temperature







HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

0

100

200

300

400

500

600

700

800Pr

ecip

itatio

n

(a)

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

14

15

16

17

18

19

20

21

22

Tem

pera

ture

(b)


RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash20

ndash10

0

10

20

30

40

50

Prec

ipita

tion

(a)

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash5

0

5

10

20

15

30

25

35

40

Tem

pera

ture

(b)








(10)















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

10

Join

t PD

F

(c)

1108Temperature

05 06

Rainfall04020 0

010203040506070809

Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

1012

Join

t PD

F

(d)



020

0204

18 100

P (U

geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy





















0

5

10

15

20

25

30

Mea

n m

onth

ly te

mpe

ratu

re

0

5

10

15

20

25

30

35M

ean

mon

thly

pre

cipi

tatio

n

(a)





0

5

10

15

20

25

30

35

Mea

n m

onth

ly p

reci

pita

tion

0

5

10

15

20

25

30M

ean

mon

thly

tem

pera

ture

(b)





CanESM2 0551 0057 084HadCM3 0458 00829 067


CanESM2 0984 00053 0998HadCM3 0964 00133 0991



Precipitation


Temperature







HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

0

100

200

300

400

500

600

700

800Pr

ecip

itatio

n

(a)

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

14

15

16

17

18

19

20

21

22

Tem

pera

ture

(b)


RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash20

ndash10

0

10

20

30

40

50

Prec

ipita

tion

(a)

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash5

0

5

10

20

15

30

25

35

40

Tem

pera

ture

(b)








(10)















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

10

Join

t PD

F

(c)

1108Temperature

05 06

Rainfall04020 0

010203040506070809

Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

1012

Join

t PD

F

(d)



020

0204

18 100

P (U

geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy



















HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

0

100

200

300

400

500

600

700

800Pr

ecip

itatio

n

(a)

HistoricalRCP26

RCP45RCP85

1980 2000 2020 2040 2060 2080 21001960Year

14

15

16

17

18

19

20

21

22

Tem

pera

ture

(b)


RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash20

ndash10

0

10

20

30

40

50

Prec

ipita

tion

(a)

RCP26RCP45

RCP85Historical

2 4 6 8 10 12 140Month

ndash5

0

5

10

20

15

30

25

35

40

Tem

pera

ture

(b)








(10)















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


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pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

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t PD

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05 06

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02 03 04 05 06 07 08 0901Rainfall

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t PD

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(d)



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06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy




















(10)















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

Join

t PD

F

(b)

110805 0604020 0


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pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

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t PD

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(c)

1108Temperature

05 06

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pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

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t PD

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(d)



020

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18 100

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geuV

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06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

gev))

06

30Temperature

08

18

Rainfall

1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy


















Historical



RCP26



RCP45



RCP85



R2 = 09482

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(a)

R2 = 09784

0

01

02

03

04

05

06

07

08

Theo

retic

al C

DF


(b)

R2 = 09855

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF

05 10Empirical CDF

(c)

R2 = 09862

0

01

02

03

04

05

06

07

08

09

Theo

retic

al C

DF


(d)



110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

0

1

2

3

4

Join

t PD

F

(a)

110805 0604020 0


Tem

pera

ture

02 03 04 05 06 07 08 0901Rainfall

012345

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t PD

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(b)

110805 0604020 0


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pera

ture

02 03 04 05 06 07 08 0901Rainfall

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t PD

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(c)

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05 06

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pera

ture

02 03 04 05 06 07 08 0901Rainfall

02468

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t PD

F

(d)



020

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18 100

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geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

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geuV

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06

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08

18

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1

2016 1014 0

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01

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15

16

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18

19

20

Tem

pera

ture

(b)

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20

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08

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Rainfall

1

15 201010 0

01

01

02

02

03

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5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

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geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















110805 0604020 0


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pera

ture

02 03 04 05 06 07 08 0901Rainfall

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2

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(a)

110805 0604020 0


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02 03 04 05 06 07 08 0901Rainfall

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1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

Tem

pera

ture

(a)

022

0204

20 40

P (U

geuV

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06

30Temperature

08

18

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1

2016 1014 0

01

01

02

02030405060708

5 10 15 20 25 30 350Rainfall

15

16

17

18

19

20

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pera

ture

(b)

025

0204

50

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geuV

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20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

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20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















020

0204

18 100

P (U

geuV

gev))

06

80Temperature

08

16 60

Rainfall

1

4014 2012 0

01

01

02

0304050607

10 20 30 40 50 60 70 80 900Rainfall

14

15

16

17

18

19

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pera

ture

(a)

022

0204

20 40

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geuV

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06

30Temperature

08

18

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1

2016 1014 0

01

01

02

02030405060708

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15

16

17

18

19

20

Tem

pera

ture

(b)

025

0204

50

P (U

geuV

gev))

20

06

40Temperature

08

30

Rainfall

1

15 201010 0

01

01

02

02

03

030405060708

5 10 15 20 25 30 35 40 450Rainfall

13

14

15

16

17

18

19

20

21

Tem

pera

ture

(c)

025

0204

60

P (U

geuV

gev))

20

06

Temperature

08

40

Rainfall

1

15 2010 0

01

01

02

02

03

0405060708

5 10 15 20 25 30 35 40 45 50 550Rainfall

141516171819202122

Tem

pera

ture

(d)




5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy
















5 Conclusion





Data Availability




References























































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy



































































Journal of










Volume 2018





Geophysics


Journal of




Microbiology





Agronomy















JointModelingofPrecipitationandTemperatureUsingCopula ... · 2019. 7. 30. · Extreme Value...

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Transcript of JointModelingofPrecipitationandTemperatureUsingCopula ... · 2019. 7. 30. · Extreme Value...