research article long-term precipitation analysis and...

Research ArticleLong-Term Precipitation Analysis andEstimation of Precipitation Concentration IndexUsing Three Support Vector Machine Methods

Milan Gocic1 Shahaboddin Shamshirband2 Zaidi Razak2 Dalibor PetkoviT3

Sudheer Ch4 and Slavisa Trajkovic1

1Faculty of Civil Engineering and Architecture University of Nis Aleksandra Medvedeva 14 18000 Nis Serbia2Faculty of Computer Science and Information Technology Department of Computer System and Technology University of Malaya50603 Kuala Lumpur Malaysia3Faculty of Mechanical Engineering Department for Mechatronics and Control University of NisAleksandra Medvedeva 14 18000 Nis Serbia4Department of Civil Engineering Indian Institute of Technology Hauz Khas New Delhi 110016 India

Correspondence should be addressed to Milan Gocic milangocicgafniacrs

Received 27 October 2015 Revised 20 December 2015 Accepted 4 January 2016

Academic Editor Stefano Dietrich

Copyright copy 2016 Milan Gocic et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The monthly precipitation data from 29 stations in Serbia during the period of 1946ndash2012 were considered Precipitation trendswere calculated using linear regression method Three CLINO periods (1961ndash1990 1971ndash2000 and 1981ndash2010) in three subregionswere analysed The CLINO 1981ndash2010 period had a significant increasing trend Spatial pattern of the precipitation concentrationindex (PCI) was presented For the purpose of PCI prediction three Support VectorMachine (SVM)models namely SVM coupledwith the discrete wavelet transform (SVM-Wavelet) the firefly algorithm (SVM-FFA) and using the radial basis function (SVM-RBF) were developed and used The estimation and prediction results of these models were compared with each other using threestatistical indicators that is root mean square error coefficient of determination and coefficient of efficiency The experimentalresults showed that an improvement in predictive accuracy and capability of generalization can be achieved by the SVM-Waveletapproach Moreover the results indicated the proposed SVM-Wavelet model can adequately predict the PCI

1 Introduction

Precipitation is one of the important climatic variables due toits changes in the intensity and the amount affecting appear-ing of the hydrological hazards such as flood and drought [1]Therefore numerous studies on precipitation variability anddevelopment of statistical indices to evaluate the changes ofprecipitation have been undertaken [2ndash7] In this study theprecipitation concentration index (PCI) is analysed The PCIallows quantifying the relative distribution of precipitationpatterns It also provides a good presentation to the spatialvariability of monthly precipitation [5 8] and information onlong-term total variability in the precipitation amount record[9 10] The PCI can be used as an indicator of hydrologicalhazard risks such as floods and droughts

In this study the prediction model of PCI is introducedusing the soft computing method namely the SupportVector Machine (SVM) The SVM one of the novel softcomputing learning algorithms has found wide applicationin the field of computing hydrology and environmentalscience [11ndash16] Furthermore it has been majorly applied inpattern recognition forecasting classification and regressionanalysis [17ndash20] The most commonly used kernels includelinear polynomial and radial basis function (RBF) whoseselection depends on the nature of the observed data [21]Shamshirband et al [22] used adaptive neurofuzzy inferencesystem (ANFIS) and support vector regression (SVR) forprecipitation estimation while S Chattopadhyay and GChattopadhyay [23] Nastos et al [24] andWu andChau [25]applied artificial neural networks (ANNs) Chen et al [26]

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2016 Article ID 7912357 11 pageshttpdxdoiorg10115520167912357

2 Advances in Meteorology

42∘00998400

19∘ 00998400

19∘ 30998400

20∘ 00998400

20∘ 30998400

21∘ 00998400

21∘ 30998400

22∘ 00998400

22∘ 30998400

23∘ 00998400

42∘30998400

43∘00998400

43∘30998400

44∘00998400

44∘30998400

45∘00998400

45∘30998400

46∘00998400

(a)

1050

950

850

750

650

550

(b)

Figure 1 (a) Spatial distribution of the 29 meteorological stations in Serbia map (b) spatial distribution of the mean annual precipitation inSerbia for the period of 1946ndash2012

implemented SVM and multivariate analysis to project dailyprecipitationMeyer et al [27] compared fourmachine learn-ing algorithms for their applicability in rainfall retrievals

Metaheuristic optimization algorithms such as ant colonyoptimization (ACO) genetic algorithm (GA) particle swarmoptimization (PSO) and cuckoo search (CS) have beenapplied in different fields of science [28ndash37]These algorithmsare based on the mechanism of selection of the fittest inbiological systems A more recent approach in biologicalinspiredmetaheuristic optimization algorithms is firefly algo-rithm (FFA) developed by Yang [38] The FFA has beenadjudged to be more efficient and robust in finding bothlocal and global optima compared to other biological inspiredoptimization algorithms [39ndash43] The prediction accuracyof the SVM model highly relies on proper determinationof model parameters [44ndash47] Although organized strategiesfor selecting parameters are important model parameteralignment also needs to be made In this study the FFA isused for determination of SVM parameters while the SVMwas coupled with discrete wavelet transform

Wavelet transform (WT) has a number of basis functionsfor selection that depends on the analysed signal Waveletanalysis was used to decompose the time series of data intoits various components after which the decomposed compo-nents can be used as inputs for the SVMmodel Over the pastfew years this technique has become of enormous interestin engineering applications [48ndash51] Nalley et al [52] useddiscrete wavelet transform (DWT) to analyse trends in pre-cipitation in Canada while Hsu and Li [53] clustered spatial-temporal precipitation data using WT Partal and Kucuk[54] analysed long-term precipitation trend using DWT inTurkey Kisi and Cimen [55] applied wavelet-Support Vector

Machine conjunction model for daily precipitation forecastand concluded the proposed model increases the forecastaccuracy

The objectives of the current study are as follows (1)to provide presentation of the spatial variability of monthlyprecipitation and information on long-term total variabilityin the precipitation data using precipitation concentrationindex and (2) to construct develop and evaluate the results ofSVM-Wavelet SVM-FFA and SVM-RBF for PCI prediction

2 Materials and Methods

21 Study Area and Used Data Monthly precipitation datawere chosen from 29 meteorological stations in Serbia (Fig-ure 1(a)) over the period of 1946ndash2012 Data were obtainedfrom the Republic Hydro Meteorological Service of Serbia(httpwwwhidmetgovrs) There are no missing values inthe data set

According to Gocic and Trajkovic [56] precipitation in-creases with the altitude that is dry areas in the northeastpart of Serbia have the precipitation below 600mm and thearea along the valley of the South Morava to Vranje has theprecipitation to 650mm while in the mountains precipita-tion may rise up to 1000mm per year The mean annualprecipitation for the observed period for the whole countryis 6624mm The spatial distribution of the mean annualprecipitation in Serbia for the analysed period is illustratedin Figure 1(b)

22 Methodology for Precipitation Analysis The spatial dis-tribution of the number of wet and dry years can be obtained

Advances in Meteorology 3

Table 1 Classification of PCI values

PCI Descriptionlt10 Uniform precipitation distribution11 to 15 Moderate precipitation distribution16 to 20 Irregular distributiongt20 Strong irregularity of precipitation distribution

using a transformed annual precipitation departure 119911 for eachstation as

119911 =119909 minus 120583

120590 (1)

where 119909 is the annual precipitation 120583 is the annual meanprecipitation and 120590 is the standard deviation of the annualprecipitation The dry year existed where 119911 le minus05 and wetone existed if 119911 ge 05 [57]

Precipitation concentration index (PCI) [58] is calculatedas follows

PCIannaul =sum12

119894=1119901119894

2

(sum12

119894=1119901119894)2sdot 100 (2)

where119901119894is the precipitation amount inmonth 119894 Classification

of PCI values is shown in Table 1

23 Soft Computing Methodologies

231 Support Vector Machine Support Vector Machine(SVM) [59 60] is based onmachine learning theory to maxi-mize predictive accuracy that is

Minimize 119877SVM (119908 120585lowast) =

1

21199082+ 119862

119899

sum119894=1

(120585119894+ 120585lowast

119894)

Subject to 119889119894minus 119908120593 (119909

119894) + 119887119894le 120576 + 120585

119894

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120585

119894

120585119894 120585lowast

119894ge 0 119894 = 1 119897

(3)

where 119908 is a normal vector (12)1199082 is the regularizationterm 119862 is the error penalty factor 119887 is a bias 120576 is the lossfunction 119909

119894is the input vector 119889

119894is the target value 119897 is the

number of elements in the training data set 120593(119909119894) is a feature

space and 120585119894and 120585lowast119894are upper and lower excess deviation

The architecture of SVM is shown in Figure 2 The kernelfunction that is radial basis function (RBF) is denoted as

119870(119909119894 119909119895) = exp (minus120574 10038171003817100381710038171003817119909119894 minus 119909119895

10038171003817100381710038171003817

2

) (4)

where variables 119909119894and 119909

119895are vectors in the input space and

120574 is the regularization parameter Lagrange multipliers arepresented as 120572

119894= 120572119894minus 120572lowast119894

The accuracy of prediction is based on the selectionof three parameters that is 120574 120576 and 119862 whose values aredetermined using firefly algorithm

Bias

Input layer Hidden layer Output layer

Hidden nodes(Support vectors)

Weights(Lagrange multipliers)

x1

x2

x3

x4

x5

x6

b

K(x x1)

K(x x2)

K(x x3)

K(x x4)

K(x x5)

K(x x6)

ysum

1205721

1205722

1205723

1205724

1205725

1205726

Figure 2 The network architecture of SVM

232 Firefly Algorithm The firefly algorithm (FFA) [38 6162] is based on the behaviour of insect named firefly Themajor issues in FFA development are the formulation of theobjective function and the variation of the light intensity

A firefly is a kind of insects that uses the principle of biolu-minescence to attractmates or preyThe luminance producedby a firefly enables other fireflies to trail its path in searching oftheir preyThis concept of luminance production helps in thedevelopment of algorithms that solve optimization problems

For example in the optimal design problem involvingmaximization of objective function the fitness function isproportional to the brightness or the amount of light emittedby the firefly Therefore decreasing in the light intensity dueto distance between the fireflies will lead to variations ofintensity and thereby lessen the attractiveness among themThe light intensity with varying distance can be representedas

119868 (119903) = 1198680exp (minus1205741199032) (5)

where 119868 is the light intensity at distance 119903 from a firefly 1198680

represents initial light intensity that is when 119903 = 0 and 120574

is the light absorption coefficient As fireflyrsquos attractivenessis proportional to the light intensity observed by adjacent


fireflies the attractiveness 120573 at a distance 119903 from the fireflycan be represented as

120573 (119903) = 1205730exp (minus1205741199032) (6)

where 1205730represents the attractiveness at distance 119903 = 0

The Cartesian distance between any two fireflies 119894 and 119895 isgiven by

119903119894119895=10038171003817100381710038171003817119909119894+ 119909119895

10038171003817100381710038171003817= radic119889

sum119896=1

(119909119894119896minus 119909119895119896) (7)

The movement of firefly 119894 as attracted to another brighterfirefly 119895 and can be represented as

Δ119909119894= 1205730exp (minus1205741199032) (119909

119895minus 119909119894) + 120572120576

119894 (8)

where the first term in the equation is due to the attractionthe second term represents the randomization with 120572 as ran-domization coefficient and 120576

119894is the random number vector

derived from a Gaussian distribution The next movement offirefly 119894 is updated as

119909119894+1

119894= 119909119894+ Δ119909119894 (9)

Steps in FFA development are presented in Figure 3

233 Discrete Wavelet Transform The wavelet transform(WT) represents amathematical expression for decomposinga time seriesrsquo frequency signal into different components Inthis study wavelet analysis was used to decompose the timeseries of precipitation data into various components afterwhich the decomposed components were used as inputs forthe SVMmodel Flow chart of discretewavelet algorithm thatis used to determine SVM parameters is shown in Figure 4

Continuous wavelet transform (CWT) of a signal119891(119905) is atime-scale technique of signal processing that can be definedas the integral of all signals over the entire period multipliedby the scaled shifted versions of the wavelet function 120595(119905)given mathematically as

119882119909(119886 119887 120595) =

1

radic119886intinfin

minusinfin

119891 (119905) 120595lowast(119905 minus 119886

119887) 119889119905 (10)

where120595(119905) is themother wavelet function 119886 is the scale indexparameter that is inverse of the frequency and 119887 is the timeshifting parameter also known as translation The discretewavelet transform (DWT) can be derived by discretizing (10)where the parameters 119886 and 119887 are given as follows

119886 = 119886119898

0

119887 = 119899119886119898

01198870

(11)

where the variables 119899 and 119898 are integers Replacing 119886 and 119887in (10) gives

119882119909(119898 119899 120595) = 119886

minus1198982

0intinfin

minusinfin

119891 (119905) 120595lowast(119886minus119898

0119905 minus 119899119887

0) 119889119905 (12)

Make a copy of population for movement function

Rank the fireflies and find the current best

Postprocess results

No

No

Yes

Yes

Generate initial population of fireflies xi

Define light absorption coefficient 120574

t lt Max Generation

j = 1 i

i = 1 n

Ij gt Ii

Move fireflies i and j in d-dimension

Attractiveness varies with distance r via exp(minus120574r)Evaluate new solution and update light intensity

Determine light intensity li at xi from f(xi)

Define the objective function f(x)

Figure 3 Flow chart of firefly algorithm

24 Evaluating Accuracy of Proposed Models In this studythe following statistical indicators were applied to comparethe developed SVMmodels

(1) root mean square error (RMSE)

RMSE = radicsum119899

119894=1(119875119894minus 119874119894)2

119899 (13)

(2) coefficient of determination (1198772)

1198772=

[sum119899

119894=1(119874119894minus 119874119894) sdot (119875119894minus 119875119894)]2

sum119899

119894=1(119874119894minus 119874119894) sdot sum119899

119894=1(119875119894minus 119875119894) (14)


Input time series

Decompose input time series using DWT

Wave component

Add the output from each wave series to get final output

Figure 4 Flow chart of proposed discrete wavelet algorithm

(3) coefficient of efficiency (EI)

EI = 1 minussum119899

119894=1(119875119894minus 119874119894)2

sum119899

119894=1(119875119894minus 119875119894)2 (15)

where 119875119894and119874

119894are the experimental and predicted values of

PCI index respectively and 119899 is the size of test data

3 Results and Discussion

31 Analysis of Precipitation Distribution The number of dryand wet years is tabulated in Table 2 The most frequentednumber of dry years is in the north of Serbia while thenumber of wet years is greater than the number of dry yearsin the west of country The number of dry years is 20 whilethe number of wet years is 19 for whole Serbia

According to Gocic and Trajkovic [56] three precipita-tion subregions were detected (1) subregion R1 (12 stations)is located in the north part of the country with the precip-itation ranging from 223 to 1051mm and the average valueof precipitation of 6082mm (2) subregion R2 (7 stations) isthe wettest one and includes stations in the west of countrywith the precipitation between 385 and 1282mm andwith themean value of precipitation of 7845mm and (3) subregionR3 (10 stations) in the east and south part of Serbia withprecipitation between 302 and 1113mm and the mean ofprecipitation of 6233mm

The annual precipitation shows an increasing trend inSerbia during the period of 1946ndash2012 (stronger in R2 andR1) Three CLINO periods (1961ndash1990 1971ndash2000 and 1981ndash2010) were illustrated in Figure 5 The CLINO period 1981ndash2010 shows a significant increasing trend at all subregionsThe most precipitation falls in June and has the value of808mm in Serbia (4115 of total precipitation in summer)which is directly connected with the intensive convection ofcolder and humid usually maritime air masses

Precipitation distribution is determined using the PCIFigure 6 illustrates the spatial distribution of PCI in SerbiaThe minimum PCI values were detected in Zlatibor (1043)and Pozega (1083) while the maximum was in Negotin(1249) The majority of the stations had the values between1112 in Sjenica and 1194 in Banatski Karlovac

32 Performance Evaluation of Proposed SVM Models Pre-cipitation data was used to obtain six parameters such asannual total precipitationmeanwinter precipitation amountmean spring precipitation amount mean summer precipita-tion amount mean autumn precipitation amount and meanof precipitation for vegetable period (AprilndashSeptember) For

Table 2 Number of dry and wet years for the synoptic stations usedin the study

Station name Number ofdry years

Number ofwet years

(1) Banatski Karlovac 22 20(2) Becej 22 19(3) Belgrade 23 20(4) Crni Vrh 20 22(5) Cuprija 23 20(6) Dimitrovgrad 19 19(7) Kikinda 19 18(8) Kopaonik 20 18(9) Kragujevac 21 19(10) Kraljevo 17 19(11) Krusevac 20 17(12) Kursumlija 19 19(13) Leskovac 20 20(14) Loznica 17 20(15) Negotin 18 21(16) Nis 19 20(17) Novi Sad 25 21(18) Palic 21 18(19) Pozega 21 23(20) Sjenica 22 18(21) Sombor 19 17(22) Smederevska Palanka 24 20(23) Sremska Mitrovica 20 18(24) Valjevo 22 22(25) Veliko Gradiste 23 24(26) Vranje 20 22(27) Zajecar 21 20(28) Zlatibor 22 24(29) Zrenjanin 25 21

the experiments 38 years (57 of data) was used to trainsamples and the subsequent 29 years (43 of data) servedto test samples Table 3 illustrates six variables using the fol-lowing statistical indicators that is theminimummaximummedian mean standard deviation and skewness

In this study three SVM models that is SVM-WaveletSVM-RBF and SVM-FFA were analysed to predict the PCIindex The RBF was implemented as the kernel functionto obtain three parameters 119862 120574 and 120576 whose selection


Table 3 Summary statistics for used data sets

(a)

VariablesTraining data set

Min (mm) Max (mm) Median(mm) Mean (mm)

Standarddeviation(mm)

Skewness

Annual total precipitation 5032 9146 6488 6597 902 056Mean winter precipitation amount 364 2481 1305 1410 435 007Mean spring precipitation amount 999 2471 1690 1669 388 001Mean summer precipitation amount 806 3353 2039 1980 591 minus010

Mean autumn precipitation amount 639 2661 1483 1538 501 058Mean of precipitation for vegetableperiod (AprilndashSeptember) 2039 5161 3697 3692 773 minus026

(b)

VariablesTesting data set



Skewness

Annual total precipitation 4148 8720 6783 6639 1169 minus026

Mean winter precipitation amount 467 2164 1313 1412 435 011Mean spring precipitation amount 1014 2733 1660 1660 395 060Mean summer precipitation amount 820 3048 2108 1941 638 minus012

Mean autumn precipitation amount 532 3016 1563 1641 568 027Mean of precipitation for vegetableperiod (AprilndashSeptember) 2336 5721 3667 3716 875 038

directly influences prediction accuracy Table 4 provides theoptimal values of parameters for the proposed SVM modelsFirefly algorithm founds optimal SVM parameters accordingto searching algorithm For the SVM-Wavelet and SVM-RBFapproaches the parameters are selectedmanually after severaltrial and error iterations

To evaluate SVMmodel performance calculated PCI wasplotted against the predicted ones Figure 7(a) presents theaccuracy of developed SVM-Wavelet PCI predictive modelwhile Figures 7(b) and 7(c) present the accuracy of developedSVM-RBF and SVM-FFA PCI predictive models respec-tively The most of the points fall along the diagonal line forthe SVM-Wavelet prediction model It means the predictionresults are in a very good agreement with themeasured valuesfor the SVM-Wavelet model The confirmation of this is thehigh value for 1198772 (1198772 = 086)

Figure 8 illustrates the spatial distribution of PCI in Serbiausing three SVMmethods that is SVM-Wavelet SVM-FFAand SVM-RBF According to the obtained results it canbe concluded that the spatial distribution using values ofSVM-Wavelet method is similar to the spatial distribution inFigure 6

33 Performance Comparison of SVM Models To illustratethe performance characteristics of the developed SVMmod-els for PCI prediction three SVMmodelsrsquo prediction accura-cies were compared with each otherThe statistical indicators

Table 4 User-defined parameters for SVMmodels

SVMmodel Used parameters119862 120574 120576

SVM-Wavelet 145 034 034SVM-RBF 247 067 062SVM-FFA 174 047 027

Table 5 Comparative performance statistics of the SVM-WaveletSVM-RBF and SVM-FFA models for PCI prediction

SVMmodel Statistical indicatorRMSE 1198772 EI


such as RMSE 1198772 and EI were used for comparison Table 5summarizes the prediction results for test data sets sincetraining error is not credible indicator for prediction potentialof particular model Results in Table 5 are obtained forthe same number of runs and according to the multipleruns average results are calculated for each method Thesame number of interactions is used in order to make thecomparison fair and accurate SVM-Wavelet produced betterresults than the other two approaches since wavelet algorithm


(Year)

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R1

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

Region R2

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R3

Annual precipitationCLINO period of 1971ndash2000

CLINO period of 1981ndash2010CLINO period of 1961ndash1990

Long time trend line

Figure 5 The trend of annual precipitation by regions

decomposes nonlinear series in multiple linearized series inorder to make it easier to regress

The SVM-Wavelet model outperforms the SVM-RBF andthe SVM-FFA models according to the obtained results Thepredictions from the SVM models correlate highly with theactual PCI data

4 Conclusion

The study carried out a systematic approach to create theSVM models for the PCI prediction such as SVM-Wavelet

No available data 10

125

12

115

11

105

Figure 6 Spatial pattern of the precipitation concentration index

SVM-RBF and SVM-FFA The proposed SVM-Waveletmodel was obtained by combining two methods that is theSVM and the wavelet transform The RBF was selected asthe kernel function for the SVM while the FFA was used toobtain the SVM parameters

Each of these SVM approaches has some advantages anddisadvantages SVM-FFA has firefly searching algorithm inorder to find optimal SVM parameters Wavelet approachdivides series into subgroups in order to make it morelinear and at the end all groups are merged SVM-RBFapproach is the basic approach with manual estimation ofSVMparametersTherefore SMV-RBF results are not as goodas the other two approaches as was presented

A comparison of the SVM-Wavelet the SVM-RBF andthe SVM-FFAwas performed in order to assess the predictionaccuracy Accuracy results measured in terms of RMSE 1198772and EI indicate that SVM-Wavelet predictions are superiorto the SVM-RBF and the SVM-FFA

The main advantages of the SVM schemes are as followscomputationally efficient and well-adaptable with optimiza-tion and adaptive techniques The developed strategy is notonly simple but also reliable andmay be easy to implement inreal time applications using some interfacing cards for controlof various parameters This can be combined with expertsystems and rough sets for other applications

The further researchwill test the proposed soft computingmethods in a different part of the world and different climatetypes to confirm the results Also some hybrid soft comput-ing models will be applied to compare with the developedmodels presented in this study

Competing Interests

The authors declare that they have no competing interests


10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples

SVM-Wavelet prediction of PCI SVM-Wavelet prediction of PCI

MeasuredSVM-Wavelet

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI

Actual values of PCI

y = 085x + 168

R2 = 086

(a)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples

SVM-RBF prediction of PCI

MeasuredSVM-RBF

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 073x + 312R2 = 074

(b)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples

SVM-FFA prediction of PCI

MeasuredSVM-FFA

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 080x + 227

R2 = 084

(c)

Figure 7 Scatter plots of actual and predicted values of PCI using (a) SVM-Wavelet (b) SVM-RBF and (c) SVM-FFA method



125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)

Figure 8 Spatial patterns of the PCI obtained using (a) SVM-Wavelet (b) SVM-FFA and (c) SVM-RBF method

Acknowledgments

The study is supported by the Ministry of Education Sci-ence and Technological Development Republic of Serbia(Grant no TR37003) and the ICT COST Action IC1408Computationally Intensive Methods for the Robust Analysisof Non-Standard Data (CRoNoS) This research is supportedby University of Malaya under UMRG grant (Project noRP036A-15AET Efficient Detection and Reporting of FloodWastes usingWireless Sensor Network RP036B-15AETMea-surement of the Flood Waste Volume based on the DigitalImage RP036C-15AET Intelligent Estimation and Predictionof Flood Wastes)

References

[1] Y Zhang W Cai Q Chen Y Yao and K Liu ldquoAnalysis ofchanges in precipitation and drought in Aksu River BasinNorthwest Chinardquo Advances in Meteorology vol 2015 ArticleID 215840 15 pages 2015

[2] B Alijani J OrsquoBrien and B Yarnal ldquoSpatial analysis of pre-cipitation intensity and concentration in Iranrdquo Theoretical andApplied Climatology vol 94 no 1-2 pp 107ndash124 2008

[3] H Feidas CNoulopoulou TMakrogiannis andE Bora-SentaldquoTrend analysis of precipitation time series in Greece and theirrelationship with circulation using surface and satellite data


1955ndash2001rdquoTheoretical and Applied Climatology vol 87 no 1ndash4pp 155ndash177 2007

[4] G Buttafuoco T Caloiero and R Coscarelli ldquoSpatial andtemporal patterns of the mean annual precipitation at decadaltime scale in southern Italy (Calabria region)rdquo Theoretical andApplied Climatology vol 105 no 3 pp 431ndash444 2011

[5] R Coscarelli and T Caloiero ldquoAnalysis of daily and monthlyrainfall concentration in Southern Italy (Calabria region)rdquoJournal of Hydrology vol 416-417 pp 145ndash156 2012

[6] W Shi X YuW Liao YWang and B Jia ldquoSpatial and temporalvariability of daily precipitation concentration in the LancangRiver basin Chinardquo Journal of Hydrology vol 495 pp 197ndash2072013

[7] Q Zhang P Sun V P Singh and X Chen ldquoSpatialtemporalprecipitation changes (1956ndash2000) and their implications foragriculture in Chinardquo Global and Planetary Change vol 82-83pp 86ndash95 2012

[8] T Raziei I Bordi and L S Pereira ldquoA precipitation-basedregionalization for Western Iran and regional drought variabil-ityrdquoHydrology andEarth System Sciences vol 12 no 6 pp 1309ndash1321 2008

[9] M De Luis J C Gonzalez-Hidalgo M Brunetti and L ALongares ldquoPrecipitation concentration changes in Spain 1946ndash2005rdquo Natural Hazards and Earth System Science vol 11 no 5pp 1259ndash1265 2011

[10] D S Martins T Raziei A A Paulo and L S PereiraldquoSpatial and temporal variability of precipitation and droughtin Portugalrdquo Natural Hazards and Earth System Science vol 12no 5 pp 1493ndash1501 2012

[11] W-Z Lu andW-J Wang ldquoPotential assessment of the lsquosupportvector machinersquo method in forecasting ambient air pollutanttrendsrdquo Chemosphere vol 59 no 5 pp 693ndash701 2005

[12] T Asefa M Kemblowski M McKee and A Khalil ldquoMulti-time scale stream flow predictions the support vectormachinesapproachrdquo Journal of Hydrology vol 318 no 1ndash4 pp 7ndash16 2006

[13] P Jain J M Garibaldi and J D Hirst ldquoSupervised machinelearning algorithms for protein structure classificationrdquo Com-putational Biology and Chemistry vol 33 no 3 pp 216ndash2232009

[14] Y Ji and S Sun ldquoMultitask multiclass support vector machinesmodel and experimentsrdquo Pattern Recognition vol 46 no 3 pp914ndash924 2013

[15] S Sun ldquoA survey of multi-view machine learningrdquo NeuralComputing and Applications vol 23 no 7-8 pp 2031ndash20382013

[16] B Zheng S W Myint P S Thenkabail and R M AggarwalldquoA support vector machine to identify irrigated crop typesusing time-series Landsat NDVI datardquo International Journal ofApplied Earth Observation and Geoinformation vol 34 no 1pp 103ndash112 2015

[17] J Alonso A Villa and A Bahamonde ldquoImproved estimationof bovine weight trajectories using support vector machineclassificationrdquoComputers and Electronics in Agriculture vol 110pp 36ndash41 2015

[18] M Fu Y Tian and F Wu ldquoStep-wise support vector machinesfor classification of overlapping samplesrdquo Neurocomputing vol155 pp 159ndash166 2015

[19] F Kaytez M C Taplamacioglu E Cam and F HardalacldquoForecasting electricity consumption a comparison of regres-sion analysis neural networks and least squares support vectormachinesrdquo International Journal of Electrical Power and EnergySystems vol 67 pp 431ndash438 2015

[20] S G Kim Y G No and P H Seong ldquoPrediction of severeaccident occurrence time using support vector machinesrdquoNuclear Engineering and Technology vol 47 no 1 pp 74ndash842015

[21] R Zhang andWWang ldquoFacilitating the applications of supportvector machine by using a new kernelrdquo Expert Systems withApplications vol 38 no 11 pp 14225ndash14230 2011

[22] S Shamshirband M Gocic D Petkovic et al ldquoSoft-computingmethodologies for precipitation estimation a case studyrdquo IEEEJournal of Selected Topics in Applied Earth Observations andRemote Sensing vol 8 no 3 pp 1353ndash1358 2015

[23] S Chattopadhyay and G Chattopadhyay ldquoIdentification of thebest hidden layer size for three-layered neural net in predictingmonsoon rainfall in Indiardquo Journal of Hydroinformatics vol 10no 2 pp 181ndash188 2008

[24] P T Nastos K P Moustris I K Larissi and A G PaliatsosldquoRain intensity forecast using artificial neural networks inAthens Greecerdquo Atmospheric Research vol 119 pp 153ndash1602013

[25] C L Wu and K W Chau ldquoPrediction of rainfall time seriesusing modular soft computing methodsrdquo Engineering Applica-tions of Artificial Intelligence vol 26 no 3 pp 997ndash1007 2013

[26] S-T Chen P-S Yu and Y-H Tang ldquoStatistical downscaling ofdaily precipitation using support vector machines and multi-variate analysisrdquo Journal of Hydrology vol 385 no 1ndash4 pp 13ndash22 2010

[27] H Meyer M Kuhnlein T Appelhans and T Nauss ldquoCom-parison of four machine learning algorithms for their applica-bility in satellite-based optical rainfall retrievalsrdquo AtmosphericResearch vol 169 pp 424ndash433 2016

[28] J S Angelo H S Bernardino and H J C Barbosa ldquoAnt colonyapproaches formultiobjective structural optimization problemswith a cardinality constraintrdquoAdvances in Engineering Softwarevol 80 pp 101ndash115 2015

[29] E Assareh M A Behrang M R Assari and A GhanbarzadehldquoApplication of PSO (particle swarm optimization) and GA(genetic algorithm) techniques on demand estimation of oil inIranrdquo Energy vol 35 no 12 pp 5223ndash5229 2010

[30] M Dorigo G Di Caro and LM Gambardella ldquoAnt algorithmsfor discrete optimizationrdquo Artificial Life vol 5 no 2 pp 137ndash172 1999

[31] M Dorigo and T Stutzle ldquoThe ant colony optimization meta-heuristic algorithms applications and advancesrdquo inHandbookof Metaheuristics vol 57 of International Series in OperationsResearch ampManagement Science pp 250ndash285 Springer BerlinGermany 2003

[32] X-S Yang and S Deb ldquoCuckoo search recent advances andapplicationsrdquo Neural Computing and Applications vol 24 no1 pp 169ndash174 2014

[33] Y Bao Z Hu and T Xiong ldquoA PSO and pattern searchbased memetic algorithm for SVMs parameters optimizationrdquoNeurocomputing vol 117 pp 98ndash106 2013

[34] M Basu ldquoModified particle swarm optimization for nonconvexeconomic dispatch problemsrdquo International Journal of ElectricalPower and Energy Systems vol 69 pp 304ndash312 2015

[35] Z Beheshti S M Shamsuddin and S Hasan ldquoMemeticbinary particle swarm optimization for discrete optimizationproblemsrdquo Information Sciences vol 299 pp 58ndash84 2015

[36] M Kumar and T K Rawat ldquoOptimal design of FIR fractionalorder differentiator using cuckoo search algorithmrdquo ExpertSystems with Applications vol 42 no 7 pp 3433ndash3449 2015


[37] A Teske R Falcon and A Nayak ldquoEfficient detection of faultynodes with cuckoo search in t-diagnosable systemsrdquo AppliedSoft Computing Journal vol 29 pp 52ndash64 2015

[38] X-S Yang ldquoFirefly algorithms for multimodal optimizationrdquoin Stochastic Algorithms Foundations and Applications 5thInternational Symposium SAGA 2009 Sapporo Japan October26ndash28 2009 Proceedings vol 5792 of Lecture Notes in ComputerScience pp 169ndash178 Springer Berlin Germany 2009

[39] I Fister I Fister Jr X-S Yang and J Brest ldquoA comprehensivereview of firefly algorithmsrdquo Swarm and Evolutionary Compu-tation vol 13 pp 34ndash46 2013

[40] X-S Yang ldquoMultiobjective firefly algorithm for continuousoptimizationrdquo Engineering with Computers vol 29 no 2 pp175ndash184 2013

[41] C Sudheer S K Sohani D Kumar et al ldquoA support vectormachine-firefly algorithm based forecasting model to deter-mine malaria transmissionrdquoNeurocomputing vol 129 pp 279ndash288 2014

[42] T Kanimozhi and K Latha ldquoAn integrated approach to regionbased image retrieval using firefly algorithm and support vectormachinerdquo Neurocomputing vol 151 no 3 pp 1099ndash1111 2015

[43] S-U-R Massan A I Wagan M M Shaikh and R AbroldquoWind turbine micrositing by using the firefly algorithmrdquoApplied Soft Computing vol 27 pp 450ndash456 2015

[44] S Rajasekaran S Gayathri and T-L Lee ldquoSupport vectorregression methodology for storm surge predictionsrdquo OceanEngineering vol 35 no 16 pp 1578ndash1587 2008

[45] K-P Wu and S-D Wang ldquoChoosing the kernel parameters forsupport vector machines by the inter-cluster distance in thefeature spacerdquo Pattern Recognition vol 42 no 5 pp 710ndash7172009

[46] H Yang K Huang I King and M R Lyu ldquoLocalized supportvector regression for time series predictionrdquo Neurocomputingvol 72 no 10-12 pp 2659ndash2669 2009

[47] Z Ramedani M Omid A Keyhani S Shamshirband andB Khoshnevisan ldquoPotential of radial basis function basedsupport vector regression for global solar radiation predictionrdquoRenewable and Sustainable Energy Reviews vol 39 pp 1005ndash1011 2014

[48] J Adamowski and H F Chan ldquoA wavelet neural networkconjunction model for groundwater level forecastingrdquo Journalof Hydrology vol 407 no 1ndash4 pp 28ndash40 2011

[49] A M Kalteh ldquoMonthly river flow forecasting using artificialneural network and support vector regression models coupledwith wavelet transformrdquo Computers amp Geosciences vol 54 pp1ndash8 2013

[50] A Araghi M Mousavi Baygi J Adamowski J Malard DNalley and S M Hasheminia ldquoUsing wavelet transforms toestimate surface temperature trends and dominant periodicitiesin Iran based on gridded reanalysis datardquoAtmospheric Researchvol 155 pp 52ndash72 2015

[51] S Li P Wang and L Goel ldquoShort-term load forecasting bywavelet transform and evolutionary extreme learningmachinerdquoElectric Power Systems Research vol 122 pp 96ndash103 2015

[52] D Nalley J Adamowski and B Khalil ldquoUsing discrete wavelettransforms to analyze trends in streamflow and precipitation inQuebec and Ontario (1954mdash2008)rdquo Journal of Hydrology vol475 pp 204ndash228 2012

[53] K-C Hsu and S-T Li ldquoClustering spatial-temporal precipi-tation data using wavelet transform and self-organizing mapneural networkrdquo Advances in Water Resources vol 33 no 2 pp190ndash200 2010

[54] T Partal and M Kucuk ldquoLong-term trend analysis usingdiscrete wavelet components of annual precipitations measure-ments in Marmara region (Turkey)rdquo Physics and Chemistry ofthe Earth Parts ABC vol 31 no 18 pp 1189ndash1200 2006

[55] O Kisi and M Cimen ldquoPrecipitation forecasting by usingwavelet-support vector machine conjunction modelrdquo Engineer-ing Applications of Artificial Intelligence vol 25 no 4 pp 783ndash792 2012

[56] M Gocic and S Trajkovic ldquoSpatio-temporal patterns of precip-itation in Serbiardquo Theoretical and Applied Climatology vol 117no 3-4 pp 419ndash431 2014

[57] J D Pnevmatikos and B D Katsoulis ldquoThe changing rainfallregime in Greece and its impact on climatological meansrdquoMeteorological Applications vol 13 no 4 pp 331ndash345 2006

[58] J E Oliver ldquoMonthly precipitation distribution a comparativeindexrdquoProfessional Geographer vol 32 no 3 pp 300ndash309 1980

[59] V N Vapnik Statistical Learning Theory Wiley-InterscienceNew York NY USA 1998

[60] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 2000

[61] X-S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo International Journal of Bio-Inspired Com-putation vol 2 no 2 pp 78ndash84 2010

[62] X S Yang and X He ldquoFirefly algorithm recent advances andapplicationsrdquo International Journal of Swarm Intelligence vol 1no 1 pp 36ndash50 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of


EarthquakesJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining


Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of


Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering


GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of


OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in


MineralogyInternational Journal of


MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geological ResearchJournal of


Geology Advances in


42∘00998400

19∘ 00998400

19∘ 30998400

20∘ 00998400

20∘ 30998400

21∘ 00998400

21∘ 30998400

22∘ 00998400

22∘ 30998400

23∘ 00998400

42∘30998400

43∘00998400

43∘30998400

44∘00998400

44∘30998400

45∘00998400

45∘30998400

46∘00998400

(a)

1050

950

850

750

650

550

(b)

Figure 1 (a) Spatial distribution of the 29 meteorological stations in Serbia map (b) spatial distribution of the mean annual precipitation inSerbia for the period of 1946ndash2012

implemented SVM and multivariate analysis to project dailyprecipitationMeyer et al [27] compared fourmachine learn-ing algorithms for their applicability in rainfall retrievals

Metaheuristic optimization algorithms such as ant colonyoptimization (ACO) genetic algorithm (GA) particle swarmoptimization (PSO) and cuckoo search (CS) have beenapplied in different fields of science [28ndash37]These algorithmsare based on the mechanism of selection of the fittest inbiological systems A more recent approach in biologicalinspiredmetaheuristic optimization algorithms is firefly algo-rithm (FFA) developed by Yang [38] The FFA has beenadjudged to be more efficient and robust in finding bothlocal and global optima compared to other biological inspiredoptimization algorithms [39ndash43] The prediction accuracyof the SVM model highly relies on proper determinationof model parameters [44ndash47] Although organized strategiesfor selecting parameters are important model parameteralignment also needs to be made In this study the FFA isused for determination of SVM parameters while the SVMwas coupled with discrete wavelet transform

Wavelet transform (WT) has a number of basis functionsfor selection that depends on the analysed signal Waveletanalysis was used to decompose the time series of data intoits various components after which the decomposed compo-nents can be used as inputs for the SVMmodel Over the pastfew years this technique has become of enormous interestin engineering applications [48ndash51] Nalley et al [52] useddiscrete wavelet transform (DWT) to analyse trends in pre-cipitation in Canada while Hsu and Li [53] clustered spatial-temporal precipitation data using WT Partal and Kucuk[54] analysed long-term precipitation trend using DWT inTurkey Kisi and Cimen [55] applied wavelet-Support Vector

Machine conjunction model for daily precipitation forecastand concluded the proposed model increases the forecastaccuracy

The objectives of the current study are as follows (1)to provide presentation of the spatial variability of monthlyprecipitation and information on long-term total variabilityin the precipitation data using precipitation concentrationindex and (2) to construct develop and evaluate the results ofSVM-Wavelet SVM-FFA and SVM-RBF for PCI prediction

2 Materials and Methods

21 Study Area and Used Data Monthly precipitation datawere chosen from 29 meteorological stations in Serbia (Fig-ure 1(a)) over the period of 1946ndash2012 Data were obtainedfrom the Republic Hydro Meteorological Service of Serbia(httpwwwhidmetgovrs) There are no missing values inthe data set

According to Gocic and Trajkovic [56] precipitation in-creases with the altitude that is dry areas in the northeastpart of Serbia have the precipitation below 600mm and thearea along the valley of the South Morava to Vranje has theprecipitation to 650mm while in the mountains precipita-tion may rise up to 1000mm per year The mean annualprecipitation for the observed period for the whole countryis 6624mm The spatial distribution of the mean annualprecipitation in Serbia for the analysed period is illustratedin Figure 1(b)

22 Methodology for Precipitation Analysis The spatial dis-tribution of the number of wet and dry years can be obtained





119911 =119909 minus 120583

120590 (1)



PCIannaul =sum12

119894=1119901119894

2

(sum12

119894=1119901119894)2sdot 100 (2)






1

21199082+ 119862

119899

sum119894=1

(120585119894+ 120585lowast

119894)

Subject to 119889119894minus 119908120593 (119909

119894) + 119887119894le 120576 + 120585

119894

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120585

119894

120585119894 120585lowast

119894ge 0 119894 = 1 119897

(3)







119870(119909119894 119909119895) = exp (minus120574 10038171003817100381710038171003817119909119894 minus 119909119895

10038171003817100381710038171003817

2

) (4)




119894= 120572119894minus 120572lowast119894


Bias




x1

x2

x3

x4

x5

x6

b

K(x x1)

K(x x2)

K(x x3)

K(x x4)

K(x x5)

K(x x6)

ysum

1205721

1205722

1205723

1205724

1205725

1205726





119868 (119903) = 1198680exp (minus1205741199032) (5)






120573 (119903) = 1205730exp (minus1205741199032) (6)



119903119894119895=10038171003817100381710038171003817119909119894+ 119909119895

10038171003817100381710038171003817= radic119889

sum119896=1

(119909119894119896minus 119909119895119896) (7)


Δ119909119894= 1205730exp (minus1205741199032) (119909

119895minus 119909119894) + 120572120576

119894 (8)




119909119894+1

119894= 119909119894+ Δ119909119894 (9)




119882119909(119886 119887 120595) =

1

radic119886intinfin

minusinfin

119891 (119905) 120595lowast(119905 minus 119886

119887) 119889119905 (10)


119886 = 119886119898

0

119887 = 119899119886119898

01198870

(11)


119882119909(119898 119899 120595) = 119886

minus1198982

0intinfin

minusinfin

119891 (119905) 120595lowast(119886minus119898

0119905 minus 119899119887

0) 119889119905 (12)



Postprocess results

No

No

Yes

Yes



t lt Max Generation

j = 1 i

i = 1 n

Ij gt Ii









119894=1(119875119894minus 119874119894)2

119899 (13)


1198772=

[sum119899

119894=1(119874119894minus 119874119894) sdot (119875119894minus 119875119894)]2

sum119899

119894=1(119874119894minus 119874119894) sdot sum119899

119894=1(119875119894minus 119875119894) (14)


Input time series


Wave component





119894=1(119875119894minus 119874119894)2

sum119899

119894=1(119875119894minus 119875119894)2 (15)

where 119875119894and119874











Number ofwet years






(a)




Skewness



(b)




Skewness
















(Year)

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R1

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

Region R2

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R3







4 Conclusion



125

12

115

11

105







Competing Interests



10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-Wavelet

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI


y = 085x + 168

R2 = 086

(a)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-RBF

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 073x + 312R2 = 074

(b)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-FFA

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 080x + 227

R2 = 084

(c)




125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)


Acknowledgments


References











































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





119911 =119909 minus 120583

120590 (1)



PCIannaul =sum12

119894=1119901119894

2

(sum12

119894=1119901119894)2sdot 100 (2)






1

21199082+ 119862

119899

sum119894=1

(120585119894+ 120585lowast

119894)

Subject to 119889119894minus 119908120593 (119909

119894) + 119887119894le 120576 + 120585

119894

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120585

119894

120585119894 120585lowast

119894ge 0 119894 = 1 119897

(3)







119870(119909119894 119909119895) = exp (minus120574 10038171003817100381710038171003817119909119894 minus 119909119895

10038171003817100381710038171003817

2

) (4)




119894= 120572119894minus 120572lowast119894


Bias




x1

x2

x3

x4

x5

x6

b

K(x x1)

K(x x2)

K(x x3)

K(x x4)

K(x x5)

K(x x6)

ysum

1205721

1205722

1205723

1205724

1205725

1205726





119868 (119903) = 1198680exp (minus1205741199032) (5)






120573 (119903) = 1205730exp (minus1205741199032) (6)



119903119894119895=10038171003817100381710038171003817119909119894+ 119909119895

10038171003817100381710038171003817= radic119889

sum119896=1

(119909119894119896minus 119909119895119896) (7)


Δ119909119894= 1205730exp (minus1205741199032) (119909

119895minus 119909119894) + 120572120576

119894 (8)




119909119894+1

119894= 119909119894+ Δ119909119894 (9)




119882119909(119886 119887 120595) =

1

radic119886intinfin

minusinfin

119891 (119905) 120595lowast(119905 minus 119886

119887) 119889119905 (10)


119886 = 119886119898

0

119887 = 119899119886119898

01198870

(11)


119882119909(119898 119899 120595) = 119886

minus1198982

0intinfin

minusinfin

119891 (119905) 120595lowast(119886minus119898

0119905 minus 119899119887

0) 119889119905 (12)



Postprocess results

No

No

Yes

Yes



t lt Max Generation

j = 1 i

i = 1 n

Ij gt Ii









119894=1(119875119894minus 119874119894)2

119899 (13)


1198772=

[sum119899

119894=1(119874119894minus 119874119894) sdot (119875119894minus 119875119894)]2

sum119899

119894=1(119874119894minus 119874119894) sdot sum119899

119894=1(119875119894minus 119875119894) (14)


Input time series


Wave component





119894=1(119875119894minus 119874119894)2

sum119899

119894=1(119875119894minus 119875119894)2 (15)

where 119875119894and119874











Number ofwet years






(a)




Skewness



(b)




Skewness
















(Year)

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R1

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

Region R2

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R3







4 Conclusion



125

12

115

11

105







Competing Interests



10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-Wavelet

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI


y = 085x + 168

R2 = 086

(a)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-RBF

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 073x + 312R2 = 074

(b)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-FFA

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 080x + 227

R2 = 084

(c)




125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)


Acknowledgments


References











































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



120573 (119903) = 1205730exp (minus1205741199032) (6)



119903119894119895=10038171003817100381710038171003817119909119894+ 119909119895

10038171003817100381710038171003817= radic119889

sum119896=1

(119909119894119896minus 119909119895119896) (7)


Δ119909119894= 1205730exp (minus1205741199032) (119909

119895minus 119909119894) + 120572120576

119894 (8)




119909119894+1

119894= 119909119894+ Δ119909119894 (9)




119882119909(119886 119887 120595) =

1

radic119886intinfin

minusinfin

119891 (119905) 120595lowast(119905 minus 119886

119887) 119889119905 (10)


119886 = 119886119898

0

119887 = 119899119886119898

01198870

(11)


119882119909(119898 119899 120595) = 119886

minus1198982

0intinfin

minusinfin

119891 (119905) 120595lowast(119886minus119898

0119905 minus 119899119887

0) 119889119905 (12)



Postprocess results

No

No

Yes

Yes



t lt Max Generation

j = 1 i

i = 1 n

Ij gt Ii









119894=1(119875119894minus 119874119894)2

119899 (13)


1198772=

[sum119899

119894=1(119874119894minus 119874119894) sdot (119875119894minus 119875119894)]2

sum119899

119894=1(119874119894minus 119874119894) sdot sum119899

119894=1(119875119894minus 119875119894) (14)


Input time series


Wave component





119894=1(119875119894minus 119874119894)2

sum119899

119894=1(119875119894minus 119875119894)2 (15)

where 119875119894and119874











Number ofwet years






(a)




Skewness



(b)




Skewness
















(Year)

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R1

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

Region R2

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R3







4 Conclusion



125

12

115

11

105







Competing Interests



10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-Wavelet

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI


y = 085x + 168

R2 = 086

(a)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-RBF

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 073x + 312R2 = 074

(b)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-FFA

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 080x + 227

R2 = 084

(c)




125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)


Acknowledgments


References











































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Input time series


Wave component





119894=1(119875119894minus 119874119894)2

sum119899

119894=1(119875119894minus 119875119894)2 (15)

where 119875119894and119874











Number ofwet years






(a)




Skewness



(b)




Skewness
















(Year)

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R1

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

Region R2

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R3







4 Conclusion



125

12

115

11

105







Competing Interests



10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-Wavelet

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI


y = 085x + 168

R2 = 086

(a)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-RBF

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 073x + 312R2 = 074

(b)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-FFA

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 080x + 227

R2 = 084

(c)




125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)


Acknowledgments


References











































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



(a)




Skewness



(b)




Skewness
















(Year)

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R1

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

Region R2

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R3







4 Conclusion



125

12

115

11

105







Competing Interests



10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-Wavelet

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI


y = 085x + 168

R2 = 086

(a)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-RBF

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 073x + 312R2 = 074

(b)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-FFA

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 080x + 227

R2 = 084

(c)




125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)


Acknowledgments


References











































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


(Year)

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R1

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

Region R2

0100200300400500600700800900

100011001200

1946 1956 1966 1976 1986 1996 2006 2016

Prec

ipita

tion

(mm

)

(Year)

Region R3







4 Conclusion



125

12

115

11

105







Competing Interests



10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-Wavelet

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI


y = 085x + 168

R2 = 086

(a)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-RBF

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 073x + 312R2 = 074

(b)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-FFA

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 080x + 227

R2 = 084

(c)




125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)


Acknowledgments


References











































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-Wavelet

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI


y = 085x + 168

R2 = 086

(a)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-RBF

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 073x + 312R2 = 074

(b)

10

105

11

115

12

125

13

0 5 10 15 20 25 30

PCI

Data samples


MeasuredSVM-FFA

10

105

11

115

12

125

13

10 105 11 115 12 125 13

Pred

icte

d va

lues

of P

CI



y = 080x + 227

R2 = 084

(c)




125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)


Acknowledgments


References











































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



125

12

115

11

105

(a)


125

12

115

11

105

(b)


125

12

115

11

105

(c)


Acknowledgments


References











































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in








































































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

research article long-term precipitation analysis and...

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