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USINGAMODELHYBRIDBASEDONANN‐MLPANDTHESPIINDEXFORDROUGHTPREDICTIONCASEOFINAOUENBASIN(NORTHERNMOROCCO)

1BOUDADB.,2SAHBIH.,3MANSSOURII.,1MANSSOURIT.

1Researchstudent,DepartmentofGeology,FacultyofSciencesMoulayIsmailUniversity,Meknes,Morocco,Email:[email protected]:[email protected]

2Dean,DepartmentofGeology,FacultyofSciencesMoulayIsmailUniversity,Meknes,Morocco,Email:[email protected]

3Professor,LaboratoryofMechanics,MechatronicsandControl,ENSAMMoulayIsmailUniversity,Meknes,Morocco,Email:[email protected]

ABSTRACT

Thispaperdescribesanapproach forpredictingdroughts inthebasin InaouenbyusingahybridmodelbasedonartificialneuralnetworkssuchMultilayerPerceptron(ANN‐MLP)andSPIindex(StandardizedPrecipitationIndex).

Duringthefirststep,thecalculationoftheSPIindexhasbeentaken.Thisisachievedbyadjustingthefrequencydistributionmonthlyrecordsprecipitation,toaprobabilitydensityfunction.

Inasecondstep, threemodelsofANNMLPwereconstructedusing, for inputsadatasetcontaining theSPIcalculated, thevaluesofmonthlyprecipitationandintroducingalsotheNAOindextoestimatetheeffectoftheNorthAtlanticOscillationonthedroughtintheregion.

The performance of the neural predictionmodel integrating the three variables as inputs (ANN‐MLP 3) are showing fargreaterthanthoseestablishedbyothermodelsconsideringonlyprecipitationand/orSPI.Thisoptimalmodel(ANN‐MLP3)wasapplied to thepredictionofdrought in the regionusingSPI3,SPI6,SPI9,SPI12andSPI24.TheseSPIvalueswerepredictedforonemonthahead.ThemodelshowsverygoodprecisionandwhichbecomegreaterwhenwemovefromSPI3toSPI24.

IndexTerms:PredictionofDrought,ArtificialNeuralNetwork,StandardizedPrecipitationIndex,modelhybrid

1. INTRODUCTION

Droughtisoneofthemajorphenomenaarisingfromthevariability and climate change in recent decades. Thewordmeteorologicaldroughtrefers toastateofariditycaused by lower than normal rainfall for an extendedperiod.Indirecteffectsofsuchmeteorologicaldroughtintime can have economic, agricultural, hydrological andsocial impacts.Tomitigate these effects, it is importantand interesting to have the ability to predict suchextremeweatherevents.

The Standardized Precipitation Index (SPI) originallyproposedbyMcKeeetal.(1993)[1]isusedasanindexofdroughtmonitoringby themajorityofrecentmodelsof drought prediction. Its use to predict droughts hasincreased the ability to compare results obtained indifferentregionsoftheworld.

In the literature, thereareseveralworksapplied to thepredictionprocess,whicharecitedasanexamplesomeworkbasedonneuralnetworks:

Mansouri et al. (2014) [2] initially develop a modelbased on neural of MLP (Multi‐Layer Perceptron) forpredictingindicatorsofgroundwaterqualityofthewaterSoussMassaMorocco.The choiceof the architectureoftheartificialneuralnetworkofMLP type isdetermined

bytheuseofdifferentstatisticaltestsofrobustnessandLevenbergMarquardtalgorithmsusedtofixweightsandbiases existing between the different layers of neuralnetwork. Secondly, a comparative study was madebetween theneuralpredictionmodelPMCtypeandtheclassical statistical models, namely, the total multiplelinear regression. The output of the neural modelexceedsbyfartheclassicalstatisticalmodels.

Mansouri et al. (2013) [3] give twomodelingmethodsused for thepredictionofmeteorologicalparameters ingeneral, and the humidity in particular. Initially, themethods are based on the study of artificial neuralnetworks type MLP applied for the prediction ofmoisture, region of Chefchaouen in Morocco. Secondlythe new architecture of neural networks type MLPproposed was compared with that of the model ofmultiple linear regression (MLR). The modelsestablished by the MLP neural network predictivemodelsaremoreefficientcomparedtothoseestablishedby multiple linear regression, the fact that goodcorrelation was obtained by the parameters from aneuralapproachwithaMeanSquareErrorof5%.

El‐ Shafie et al. (2011) [4] developed two models forpredicting annual and monthly precipitation forAlexandria in Egypt. The first is basedonANNand thesecond on themultiple linear regressionmodel (MLR).

BOUDAD B. et al.

Date of Publication: August 27, 2014

ISSN: 2348-4098

Volume 2 Issue 6 August 2014

International Journal of Science, Engineering and Technology- www.ijset.in 1301

The MLR model showed a modest performanceprediction. The linear character of estimators MLRmodelmakes it inadequate toprovidegoodpredictionsfor a highly nonlinear variable. On the other hand, theANN model developed as a tool for non‐linearrelationship, which is potentially more suitable forpredicting precipitation (nonlinear physical variable),hasbeensuccessfulprediction.

Somvanshi et al. (2006) [5] have applied twofundamentally different approaches, the statisticalmethodbasedon theAutoregressive IntegratedMovingAverage (ARIMA) and new computational techniquesbased on RNA. The approaches ANN and ARIMA areapplied to the average annual rainfall data to calculaterespectivelytheweightsandregressioncoefficients.ThestudyshowsthattheperformanceofANNmodelismoreappropriatetopredictprecipitationcomparedtoARIMAmodel.

Inthiscontext,ourmainobjectiveinthisworkistobuilda hybrid model based on ANN Multilayer Perceptrontype and SPI developed byMcKee for the prediction ofdrought at different time scales on the basis of dataselectedstationslocatedwithinthewatershedInaouen.

2. APPLIEDMETHODS

2.1 The Standardized Precipitation Index(SPI)

The Standardized Precipitation Index (SPI) wasdevelopedbyMcKeeetal.(1993)[1]asawaytodefineandmonitordroughtevents. It isa simple index,basedsolely on rainfall data, and allows equally checking thewet periods / cycle’s and the dry periods / cycles. TheSPI compares precipitation over a certain period(normally 1‐24 months) to the average long‐termprecipitationobservedatthesamesite.[6]

TheSPIwasdesignedtoquantifytheprecipitationdeficitfor multiple time scales. These time scales reflect theimpactofdroughtontheavailabilityofdifferenttypesofwater resources. Ground moisture reacts relativelyquickly to rainfall anomalies in the short term, whilegroundwater, stream flowandwater volumes stored inreservoirs are sensitive to rainfall anomalies in thelongerterm.

TheSPIisdeterminedbyanormalizationofrainfallforagiven station, afterwhich there is a probability densityadjusted. The distribution that best represents theevolutionof sets of rain is theGammadistribution ([7]and [8]). This Gamma distribution is defined by itsprobabilitydensityrepresented,forx>0,by:

1Γ

Where:

αistheshapeparameter βisthescaleparameter xistheheightofthemonthlyprecipitation Γ represents the Gamma mathematical functiondefinedas:

Γ∞

The adjustment of the gamma distribution to datarequires therefore to determine α and β. They can beestimatedinthisway[7]:

α 1 1 ,βαwithA ln x

Σ

Where N is the size of the sample and is the mean ofobservations.

Theequationfortheprobabilitydensityfunctioncanbeintegrated to provide the cumulative function F(X) ofprobabilityforx>0:

F X f x dx1

βαΓ αxα e β dx

Butwenotethat,forthisdefinition,x>0,howeverthereare periods where x = 0. To take into account of theprobability of zero, the function of the cumulativeprobabilitydistributionofgammaismodifiedasfollows:

H X q 1 q F X

With q, the probability of each station to have a zeroprecipitationovertheentireperiod.

IfmisthenumberofzerosinaseriesofprecipitationofNvariable,qcanbeestimatedby[6]:

qmN

We therefore obtain for each x, a corresponding valueH(x). This finally allows to calculate the SPI, as follows[9]:

SPI Wc c W c W

1 d W d W d W

withW ln for0 0.5

SPI Wc c W c W

1 d W d W d W

withW ln for0.5 1

The constants are: c0 = 2.515517, c1 = 0.802853, c2 =0.010328,d1=1.432788,d2=0.189269,d3=0.001308.

NegativevaluescorrespondtoaSPIdeficitrainfallwhile,conversely positive values indicate higher than normalrains.Table1detailsaclassificationsystemthatdefinestheintensityofdroughtsbasedonthevalueoftheSPIforatimescalewhatsoever[1].

Table1:ClassificationofcategoriesofdroughtaccordingtothevaluesoftheSPI[1]

SPIValues Category2.0andmore Extremelyhumid

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1.5to1.99 Highly humid1.00to1.49 Moderatelyhumid‐0.99to0.99 Closetonormal‐1.0to‐1.49 Moderatelydry‐1.5to‐1.99 Highlydry‐2.0andless Extremelydry

2.2 Artificial Neural Networks (ANN):MultilayerPerceptron(MLP)

An artificial neural network is a computational modelwhose original inspiration was a biological model. ThemainstrengthofANNistheirabilitytoidentifycomplexand nonlinear relationship between input and outputdata setswithout theneed to understand thenatureofphenomena [10]. Multilayer Perceptron Type (MLP) isthe simplest andmost commonly neural network used.Themathematical representationofanartificialneuroncalledartificialneuronisshownschematically inFigure1[11].

Figure1:Structureofartificialneuralnetwork

Wecanthencharacterizeaformalneuronby:

A combination function or an added thatperformstheweightedsum.Theweightedsumisequalto:

A W X

WhereWijisthesynapticweightandXiistheinputvaluerelative to the variable i. This is the weighted sum ofactivation,whichconvergestotheneuronj;

An activation function (or transfer) f thatanimatestheneuronbydeterminingitsactivation; Anactivation,theequivalentofneuronoutput.Itisequalto:

Whereθ isthebiasoftheneuronj.

There are several activation functions (hyperbolictangent, Gaussian, sigmoid ...), but themost used is thesigmoid function ([12], [13], [14]). It is written asfollows:

11 exp

The configuration of the best MLP model and itsimplementation amounts to choosing the transferfunctions, to identifytherelevant inputs, thenumberofneurons in the hidden layer, to choose the learningalgorithmandthenoptimizeandtestthenetwork.

3. APPLICATION

3.1 Studyregionanddataused

This study focuses on the basin of Inaouen (Figure 2).Locatedbetween latitudes34°35’24’’Nand33°50’24’’N,and longitudes 4°49’48’’W and 3°48’36’’W, it covers anarea of 3648 km2 with an average altitude of 694 m.Located in the western part of the basin of Sebou, theInaouenregion profits from a Mediterranean climatewithoceanicinfluence[15].Thisclimateischaracterizedby strong seasonal contrasts and very irregular rainfall[16]. Geological domainof Inaouenbasin is divided intotwomainareas:thenorthernpartofthebasinbelongstothe Pre‐Rif area and the southern part of the basin isrelatedtotheAtlasarea.

Thedatausedtopresenttheresultsinthisarticlearethemonthly rainfall in the Bab Marzouka station locatedupstream of the basin and Idrissfirst station located atthe downstream (Figure 2). These valueswere used tocalculatetheSPI.AlsothevaluesoftheNAOindexwereused to estimate the influence of global climate indexNorthAtlantic.

ThefollowingTable2showssomecharacteristicsofthetwostationsused:

Table2:Descriptionofthestations

stations BabMarzouka Idriss1st

Latitude/longitude34°12'2''N/4°8'27''W

34°9'47''N/ 4° 45' 2''W

Altitude(m) 368 200

Periodofdataused 1971‐2011 1975‐2012

Nb. Of observations(months)

480 444

Statisticaldescriptionof MonthlyPrecipitation

Average(mm) 46.86 32.69

Max(mm) 311.1 192.3

Standarddeviation

54.21 37.54

W1j

W2j

W3j

W4j

Wnj

fYj

X1

X2

X3

X4

Xn

Input ValuesWeights

comminationfunction

Weightedsum Aj

Activationfunction

Activation

Bias

j

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Figure2:LocationofrainfallstationsusedwithinthebasinInaouen

3.2 Elaboration and processing of thedatabase

3.2.1 DataCollection

The purpose of this step is to collect data, both todevelopdifferentpredictionmodelsandtotestthem.

In the case of applications on real data, the goal is togather a sufficient number of data to provide arepresentativebasisofdatathatmayoccurduringuseofdifferentpredictionmodels.

The data used in this study are related to themeasurementcollectedduringtheperiod1971‐2011fortheBabMarzoukastationandtheperiod1975‐2012forthefirstIdrissstation.

The independent variables are standardizedprecipitation index, rainfall and the North AtlanticOscillationindex.(Figure3)

Figure3:Inputs/Outputsofpredictionmodel

3.2.2 Dataanalysis

Afterdatacollection,ananalysisisrequiredtodeterminethe discriminating features to differentiate or detectthese data. These characteristics are the input of theneuralnetwork.

The determination of the characteristics hasconsequencesonboththesizeofthenetwork(andthusthesimulationtime),onsystemperformance(separation

power,predictionrate),anddevelopmenttime(learningtime).

Datafilteringcanhelpremovethosethatareabsurdandredundant.

3.2.3.Datanormalization

Ingeneral,databasesrequireapretreatmentinordertobe adapted to the inputs and outputs of the stochasticmathematical models. A common preprocessing is toconduct a propernormalization that takes into accountthemagnitudeofthevaluesacceptedbythemodels.

Normalizationofeachinputxiisgivenbytheformula:

x 2 ∗x min x

max x min x1

However, the output variable is normalized between 0and1bytheformula:

x x min x

max x min x

Thisprovidesastandardizeddatabasebetween‐1and1forthedifferentvariationsof the independentvariables(model inputs) and between 0 and 1 for the differentvariationsofthedependentvariables(modeloutput).

3.3 Designing the architecture of artificialneuralnetworks

WhendevelopinganANNmodel,themainobjectiveistoachieve theoptimalANNarchitecture that captures therelationship between the input and output variables.First, a three‐layerperceptronMLPwaschosensince itwas found that a three‐layer model is sufficient forforecasting and simulation in the field ofwater science[17].Thenthetaskistoidentifythenumberofneuronsineachlayer.Fortheseinputandoutput,itissimpleanditisnormallydictatedbytheinputvariablesandoutputconsidered,tomodelaphysicalprocess.Forthenumberof neurons in the hidden layer, it should be optimizedusingtheavailabledata.Todoso,weproceededbytrialand error based on the measurement of the meanabsolute error (MAE) for thedata used to test for eachmodel. Figure 4 illustrates an exemplary model forestablished SPI 24 (SPI calculated for a window of 24months)andshowsthat,26neuronsinthehiddenlayeristheoptimalnumber.

Figure4:Determinationoftheoptimumnumberofneuronsinthehiddenlayer,dependingonthemeanabsoluteerrorfortheSPI24BabMarzoukastation

SPI (t+1) Mathematical model

SPI (t)

SPI (t‐1)

SPI (t‐2)

P (t)

P (t‐1)

NAO (t)

NAO (t‐1)

NAO (t‐2)

P (t‐2)

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LeardetetraindesiWhefunc

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Table3:Differenttestedmodels

InputVariables PredictedVariable

ModelName

P(t),P(t−1),P(t−2) SPI(t+1) MLP1

SPI (t ), SPI (t− 1), SPI (t− 2), P(t ),P(t−1),P(t−2)

SPI(t+1) MLP2

SPI (t ), SPI (t− 1), SPI (t− 2), P(t ),P(t − 1),P(t− 2), NAO(t),NAO(t − 1),NAO(t−2)

SPI(t+1) MLP3

For these threemodels, the SPI valueswere calculatedforarangeoftimewindowsvaryingfrom3monthsto24months. Assessing the accuracy of predictions for eachmodel was performed using R2, r, MAE and MSEcoefficients.

TheevaluationofthethreemodelsbuiltshowedthatthepredictionresultsrelatedtoMLP3(Figure6)modelhadthelowesterror(MAEandMSEvaluesarelowerandR2andrvaluesarehigher). It is interesting toexpress theaddition of NAO as an input variable for the MLPimproves the efficiency of prediction models. Thus, inthis study, only the resultsofMLP3arepresentedanddiscussed.

Figure6:ModelANN(three‐layerPerceptron)usedtopredicttheriskofdrought

AllnetworksettingsonMLP3modelaresummarizedinTable4.

Table4:InformationabouttheMLP3modelused

InputLayer

Covariables 9SPI (t ), SPI (t − 1),SPI (t − 2), P(t ),P(t − 1), P(t − 2),NAO(t),NAO(t − 1),

NAO(t−2)

Numberofneurons 9

Hiddenlayer(s)

Number of hiddenlayers

1

Number of neurons inthehiddenlayer

Variable dependingonmodel

ActivationFunction Sigmoïde

OutputLayer

Dependentvariables 1 SPI(t+1)

Numberofneurons 1

Activationfunction Sigmoïde

ErrorFunction Sumofsquares

The estimated precisions of the model MLP3 bycomparisonoftheactualvaluesandthepredictedvaluesfor both stations Idriss 1st and Bab Marzouka fordifferenttimewindows(SPI3toSPI24)andtheoptimalarchitecturesofthemodelsarepresentedinTable5.

Table5:PredictionresultsofSPIvalues(atdifferenttimescales)forMLP3modelatthestationsIdriss1st

andBabMarzouka

Idriss1st

Architecture R2 r MAE MSE

SPI3 [9‐13‐1] 0.47 0.686 0.547 0.486

SPI6 [9‐11‐1] 0.671 0.819 0.433 0.315

SPI9 [9‐17‐1] 0.758 0.871 0.357 0.238

SPI12 [9‐9‐1] 0.828 0.91 0.286 0.153

SPI24 [9‐20‐1] 0.914 0.956 0.214 0.08

BabMarzouka

Architecture R2 r MAE MSE

SPI3 [9‐23‐1] 0.51 0.714 0.536 0.498

SPI6 [9‐20‐1] 0.62 0.788 0.489 0.399

SPI9 [9‐6‐1] 0.786 0.887 0.362 0.219

SPI12 [9‐9‐1] 0.871 0.933 0.275 0.132

SPI24 [9‐26‐1] 0.923 0.961 0.214 0.079

To visualize the evolution of performance indicatorsbasedonthetimewindowofSPI,theresultsinthetable5havebeen transformed into the following twographs(Figure7):

I NPUT L AYER HI DD EN LAYER OU TPU T LAYER

Biais

Biais

SPI (t+1)

SPI (t)

SPI (t-1)

SPI (t-2)

P (t)

P (t-1)

NAO (t)

NAO (t-1)

NAO (t-2)

P (t-2)

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Figure7:Evolutionofperformanceindexesr,R2,MAEandMSEaccordingtothetimewindowofSPIforIdriss1ststations(left)andBabMarzouka(right)

We can see that all the predictions SPI produce verygoodprecisionexceptforSPI3withdifferencesbetweenobservedandpredictedvalues,arenotveryacceptable.Wealsoseethatwhenthetimewindowisincreased,thecorrelationbetweenthemodelpredictionandtheactualvalues increases significantly. This observation can beexplained by the way the time series SPI is calculated.Unliketheseriesofprecipitation,SPIfollowsastandardnormal distribution. This conversion eliminates suddenpeaks leaving a slowly varying smooth curve that iseasiertopredictusingmodelsofneuralnetworks.

Tobettervisualizetheperformanceofthetestedmodel,graphs that compare the observed SPI values and SPIvalues predicted one month ahead, and their scatterdiagramsforthefirstIdrissstationareshowninFigure8.

It can be concluded that the neural network model ofMLP,has successfullypredicted thedroughtonemonthaheadforseveraltimescalesofSPI.

SPI3 SPI6 SPI9 SPI12 SPI24

0

0.2

0.4

0.6

0.8

1

rR2MAEMSE

SPI3 SPI6 SPI9 SPI12 SPI24

0

0.2

0.4

0.6

0.8

1

rR2MAEMSE

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Figure8:ComparisonofpredictedandobservedSPIvaluesforthefirstIdrissstation

5. CONCLUSION

In this study, the drought prediction is made for theregion of Inaouenbasin in northern Morocco using asystembasedonartificialneuralnetworkofMLP.Firstly,the time series of the Standardized Precipitation Index(SPI)builtinfordifferentperiodsoftimerangingfrom3months, 6, 9, 12 and 24 months using the values ofaverage monthly rainfall of the two stations selectedwithinthewatershedweather.ThenanANN‐MLPmodelwas developed and selected for his performance inpredictingSPIcategoriesforperiodsof3,6,9,12and24months.

The model shows superior forecasts when going fromSPI3toSPI24.Theneuralnetworkmodeldevelopedcanbe therefore a very useful tool for planners of waterresources to take the necessary measures in advancewhen there is shortage of water which can eventuallydevelopintodroughtconditions.

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