Atmospheric Research 161–162 (2015) 65–81

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Atmospheric Research

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Application of the Artificial Neural Network model for prediction ofmonthly Standardized Precipitation and Evapotranspiration Index usinghydrometeorological parameters and climate indices in eastern Australia

Ravinesh C. Deo a,⁎, Mehmet Şahin b

a School of Agricultural Computational and Environmental Sciences, International Centre of Applied Climate Science (ICACS), University of Southern Queensland, Springfield 4300, Australiab Department of Electrical and Electronics Engineering, Siirt University, 56100 Siirt, Turkey

Abbreviations:ANN, Artificial NeuralNetwork; BOM, Bglobal circulationmodel;Hardlim, hard limit; I, peak intensmoid;MAE,mean absolute error; POAMA, PredictiveOceanRootMean Square Error; S, severity of drought; SAM, Southdiction error; PET, potential evapotranspirationDO; PDO, PSPOTA,SeasonalPacificOceanTemperatureAnalysis;SST,Shyperbolic-tangent sigmoid; Trainbfg, training BFGS quasTrainscg, training scaled conjugate gradient; Tribas, trainin⁎ Corresponding author. Tel.: +61 7 3470 4430.

E-mail address: ravinesh.deo@usq.edu.au (R.C. Deo).

http://dx.doi.org/10.1016/j.atmosres.2015.03.0180169-8095/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 7 November 2014Received in revised form 8 March 2015Accepted 27 March 2015Available online 8 April 2015

Keywords:Artificial Neural NetworkDrought prediction in AustraliaData-driven modelStandardized Precipitation andEvapotranspiration Index (SPEI)

The forecasting of drought based on cumulative influence of rainfall, temperature and evaporation is greatlybeneficial for mitigating adverse consequences on water-sensitive sectors such as agriculture, ecosystems, wild-life, tourism, recreation, crop health and hydrologic engineering. Predictive models of drought indices help inassessing water scarcity situations, drought identification and severity characterization. In this paper, we testedthe feasibility of the Artificial Neural Network (ANN) as a data-driven model for predicting the monthlyStandardized Precipitation and Evapotranspiration Index (SPEI) for eight candidate stations in eastern Australiausing predictive variable data from 1915 to 2005 (training) and simulated data for the period 2006–2012. Thepredictive variableswere:monthly rainfall totals,mean temperature,minimum temperature,maximum temper-ature and evapotranspiration, which were supplemented by large-scale climate indices (Southern OscillationIndex, Pacific Decadal Oscillation, Southern Annular Mode and Indian Ocean Dipole) and the Sea SurfaceTemperatures (Nino 3.0, 3.4 and 4.0). A total of 30 ANN models were developed with 3-layer ANN networks.To determine the best combination of learning algorithms, hidden transfer and output functions of theoptimum model, the Levenberg–Marquardt and Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newtonbackpropagation algorithms were utilized to train the network, tangent and logarithmic sigmoid equationsused as the activation functions and the linear, logarithmic and tangent sigmoid equations used as the outputfunction. The best ANN architecture had 18 input neurons, 43 hidden neurons and 1 output neuron, trainedusing the Levenberg–Marquardt learning algorithm using tangent sigmoid equation as the activation and outputfunctions. An evaluation of themodel performance based on statistical rules yielded time-averaged Coefficient ofDetermination, Root Mean Squared Error and the Mean Absolute Error ranging from 0.9945–0.9990,0.0466–0.1117, and 0.0013–0.0130, respectively for individual stations. Also, theWillmott's Index of Agreementand the Nash–Sutcliffe Coefficient of Efficiency were between 0.932–0.959 and 0.977–0.998, respectively. Whenchecked for the severity (S), duration (D) and peak intensity (I) of drought events determined from the simulatedand observed SPEI, differences in drought parameters ranged from −1.41–0.64%, −2.17–1.92% and −3.21–1.21%, respectively. Based on performance evaluation measures, we aver that the Artificial Neural Networkmodel is a useful data-driven tool for forecasting monthly SPEI and its drought-related properties in the regionof study.

© 2015 Elsevier B.V. All rights reserved.

ureau ofMeteorology; d,Willmott's Index of Agreement;D, duration of drought; E, Nash–Sutcliffe Coefficient of Efficiency; GCM,ity of drought; IOD, IndianOceanDipole; JISAO, Joint Institute of the Study of theAtmosphere andOcean; Logsig, logarithmic sig-AtmosphereModel of Australia;R2, Coefficient ofDetermination; Radbas, radial bias;RDDI, Rainfall DecileDrought Index;RMSE,ernAnnularMode; SLFM, Single Layer FeedforwardNeuralNetwork; SOI, SouthernOscillation Index; PCN, precipitation; PE, pre-acific Decadal Oscillation; SPI, Standardized Precipitation Index; SPEI, Standardized Precipitation and Evapotranspiration Index;eaSurfaceTemperature;ST,standarddeviation;SVD,singularvaluedecomposition;SVM,supportvectormachine;Tansig, trainingi-Newton; Trainbr, training Bayesian regulation; Trainlm, training Levenberg–Marquardt; Trainoss, training one-step secant;g triangular basis.

66 R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

1. Introduction

A drought is a chronic, albeit a natural climatic feature in mostclimates, although it may occur with varying frequencies, intensitiesor durations (Wilhite, 1996). Droughts pose detrimental impacts onagriculture, economy, recreation, hydropower generation and environ-ments (Mpelasoka et al., 2008; Riebsame et al., 1991). By definition,drought results from temporary imbalance of water resources due topersistently lower than average rainfall (Pereira et al., 2009). Waterresources are also affected by aridity, which is a permanent climaticfeature with an imbalance in water availability or low average annualrainfall and soil moisture expressed through precipitation and evapo-transpiration ratios (Arora, 2002). Nonetheless, both drought andaridity are intrinsically driven by a shortage of usable water, and maybe exacerbated due to higher surface temperatures and evaporationrates. Hence, a combination of both abnormal patterns of precipitationand evapotranspiration changes is a potential indicator of aridity ordry conditions. One particular drought index (DI) for such assessmentsis the Standardized Precipitation Evapotranspiration Index (SPEI),which incorporates precipitation and potential evapotranspiration(PET) in its formulation to express the water supply–demandrelationships in order to accommodate for climate change influences(Vicente-Serrano et al., 2010a,b, 2012a,b). In circumstantial challengesposed by a drying climate, scientists and engineers responsible forplanning, management and adjudicating the distribution of waterresources must have an understanding of rainfall and evapotranspira-tion changes and knowledge about their spatial and temporal distribu-tions and the predicted trends. Thus, predictive models of the SPEImay greatly help stakeholders in assessing drought and aridityimpacts due to unexpected changes in rainfall, temperature andevapotranspiration. Models based on water scarcity conditions canassist in risk management, developing mitigation, forewarning andresponse systems (Wilhite, 1996; Wilhite and Hayes, 1998; Wilhiteet al., 2000).

In forecasting key parameters of drought such as rainfall or evapora-tion, basically two kinds of models are considered in literature: physicalmodel (or global circulation model, GCM), which is based on theinteractive behavior of the ocean, atmosphere, sea ice and land surface,and data-driven (or statistical) model which assimilates the trends inobserved climatic parameters (e.g. rainfall), climate indices and SeaSurface Temperatures to make future predictions. However, physicalmodel provides reliable forecast for ancillary atmospheric variableslike temperature but less reliable information can be obtained forvariables that are crucial determinants of drought (e.g. rainfall)(Hudson et al., 2011; Kuligowski and Barros, 1998). Therefore, thedevelopment of robust predictive models as alternatives to physicalmodels is desirable for improving confidence in rainfall projectionsand assessment of future drought.

For Australia specifically, the Predictive Ocean Atmosphere Modelfor Australia (POAMA) (Hudson et al., 2011; Zhao and Hendon, 2009)and Seasonal Pacific Ocean Temperature Analysis (SPOTA-1) (Dayet al., 2010) are used as predictors of seasonal climates. However, stud-ies that compared forecast of precipitation using data-driven modelswith physical models such as the POAMA have found significantimprovement in the predictions from the former type of model (e.g.Abbot and Marohasy, 2014; Hudson et al., 2011; Inquiry, 2011;Seqwater, 2011). In order to improve and enhance thefidelity ofmodel-ing framework for forecasting hydro-meteorological variables, manyresearchers are testing the viability of data-drivenmodels as alternativepremises for predicting future changes in hydrological, atmospheric andclimatic parameters.

Data-driven models utilize the computational capacity of machinelearning algorithms and mathematical equations that are not based onthe physical interactions of the ocean, atmosphere or sea ice as withthe case of physical models but instead employ historical datasets todeduce the relationships between predictor (inputs) and objective

variables (outputs) (Acharya et al., 2013; Deo and Sahin, 2015; Şahin,2012; Şahin et al., 2014). Consequently, the advantages of such modelsare: the explanation of future trends in climate parameters with lesscomplexities in executing the model or comprehension of the modeloutput compared with physical models, easy experimentation or evalu-ation, low computational cost and less data requirements than thephys-ical model, efficiency in training and the testing phase (e.g. shorterexecution time), applicability to specific areas and the competitive per-formance relative to physicalmodels (Abbot andMarohasy, 2012, 2014;Ortiz-García et al., 2014). More importantly, for the purpose ofpredicting temperature or precipitation, significant improvements inperformance of data-driven models have been noted in recent studies(e.g. Abbot and Marohasy, 2012, 2014).

A longstanding well-established data-driven model is the ArtificialNeural Network (ANN), which was developed in the early 1950s. TheANN is a computational paradigm that mimics the biological structureof the brain (McCulloch and Pitts, 1943). It operates like a black box,and does not require detailed information about the inputs as with thecase of physical models. Instead, the ANN learns from the relationshipsbetween input parameters and controlled or uncontrolled variables bychecking previous trends in data as non-linear regression. ANN alsohas the capability for managing very large and complex datasets withseveral interrelated parameters (Şahin et al., 2013). Therefore, the useof ANN for prediction of complex climatic phenomenon (e.g. drought)is not a new but an enlightening research endeavor.

ANNhas been applied extensively inmanyparts of theworld includ-ing Greece (Nastos et al., 2014), China (Wu et al., 2011), India(Chattopadhyay, 2007; Chattopadhyay and Chattopadhyay, 2008),Iran (Morid et al., 2007), Ethiopia (Belayneh and Adamowski, 2012),Kenya (Masinde, 2013), Turkey (Şenkal et al., 2012; Şenkal, 2010;Şenkal andKuleli, 2009) andAustraliawhere recent research is showingthe relatively good performance of ANNmodels for drought forecasting.Mekanik et al. (2013) used ANN and Multiple Regression models withlagged relationships of the El Nino Southern Oscillation (ENSO) andIndian Ocean Dipole (IOD) as predictors for forecasting rainfall inVictoria. The study found smaller predictive errors using the ANNapproach. In two separate studies in Queensland, Abbot and Marohasy(2012, 2014) used the ANNmodel to demonstrate the relatively smallermean square errors of precipitation predictions compared to the officialpredictive model used by the Bureau of Meteorology (POAMA-1.5). Fora study focusing on Yarra River catchment in Victoria (Australia),Barua et al. (2010, 2012) applied the recursive multistep neural net-work (RMSNN) and the direct multistep neural network (DMSNN)approaches to predict nonlinear aggregated drought index (NADI)for assessing drought conditions considering all significant hydro-meteorological variables. Overall, the ANN model was highly capableof forecasting drought conditions up to 6 months in advance. Quiterecently, the work of Mekanik and Imteaz (2014) attempted to findthe effects of past values of El Nino southern Oscillation (ENSO) andIndian Ocean Dipole (IOD) on rainfall in Horsham, Melbourne andOrbost in Victoria, Australia. Using ANN models, they investigatedlagged-time relationships of single and combined climate mode indiceswith Victorian rainfall. Interestingly, the use of ENSO and IOD indicesappeared to increase the ANN model correlation up to 0.99, 0.98 and0.30 in the three tested regions.

In forecasting problems based on data-driven paradigms, synoptic-scale indices are often used as predictants formedium-range forecastingto explain the behavior of future climate (Dijk et al., 2013; McAlpineet al., 2009; Timbal and Fawcett, 2013; Ummenhofer et al., 2009;Franks and Kuczera, 2002; Kiem and Franks, 2004; Kiem et al., 2003;Verdon-Kidd and Kiem, 2009, 2010). For the case of Australia,researchers have found that the Millennium drought was related to acombination of intensified sea level pressure across southern Australia(Hope et al., 2010), the subtropical ridge (belt of high-pressure systemsrepresenting the descending Hadley cell) (Timbal et al., 2010) and theENSO cycle (Verdon-Kidd and Kiem, 2009; Verdon-Kidd and Kiem,

67R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

2009). Many studies reported that drought is favored by negative phaseof ENSO (Murphy and Timbal, 2008; Trenberth et al., 2014). Likewise,the positive index of Indian Ocean Dipole (IOD) is known to suppressrain-bearing systems (Cai et al., 2011), the Southern Annular Mode(SAM)which describes north–south shift of westerly winds, can impactrainfall in autumn and winter (Meneghini et al., 2007; Hendon et al.,2007) and the Pacific Decadal Oscillation (PDO) acts to moderate rain-fall amounts in monsoonal season (Mantua et al., 1997; Latif et al.,1997; Power et al., 1999). Since large-scale indices are inextricablylinked to drought (Ashok et al., 2003; Holper, 2011), the data-drivenmodels often use climate mode indices as regression covariates formodeling future changes in rainfall amounts.

In this paper, we applied the ANN model for predicting a relativelyrecent drought index known as the Standardized Precipitation andEvapotranspiration Index (SPEI) using large-scale climate indices asthe predictor variables. Prediction of the SPEI is an appealing problemof interest towater resource scientists, as it presents as a useful diagnos-tic tool for identification, monitoring and assessment of dry or aridityconditions (Vicente-Serrano et al., 2010a). The SPEI can assess droughtimpacts on multiple timescales (e.g. 1, 3, 12 or 24 months) and maybe applied to climatically diverse regions (Vicente-Serrano et al.,2010a,b, 2012a). Unlike the Standardized Precipitation Index (SPI) andthe Rainfall–Decile Drought Index (RDDI) that are solely based onrainfall data (Deo et al., 2009; McKee et al., 1993; Mpelasoka et al.,2008), the SPEI considers net effects of rainfall, temperature or evapo-transpiration on evolutionary phases of drought events (Begueríaet al., 2013; Vicente-Serrano et al., 2012a). That is, a drought predictivemodel based on evaporation and transpiration can play an importantrole in assessment of drought severity, or act as a sensitive indicator ofaridity (Yao et al., 2011). Consequently the SPEI has been appliedfor drought studies in Europe, China and the Czech Republic(Beguería et al., 2013; Li et al., 2012; Potop et al., 2012;Vicente-Serrano et al., 2010a,b, 2012a; Yu et al., 2014) but its appli-cation in Australia particularly for forecasting purposes is a newresearch step.

The work described here used the ANN model framework forpredicting the monthly SPEI and assessed the model performanceusing statistical measures such as the Mean Absolute Error, Root-Mean Square Error, Coefficients of Determination, Nash–SutcliffeCoefficient (Nash and Sutcliffe, 1970) and theWilmot's Index of Agree-ment (Willmott, 1982). A suite of 18 predictor (input) variables werechosen including rainfall, mean temperature, maximum temperature,minimum temperature and evapotranspiration computed by theThornthwaite (1948) method. In addition, as supplementary inputdata to enhance the prediction of the index, the ANN models weretrained using synoptic-scale climate drivers (SOI, IOD, SAM & PDO)including the Sea Surface Temperatures (SSTs) (Nino 3.0, 3.4 & 4.0)which are known to impact rainfall and temperature variability in thevicinity of the candidate stations. The use of synoptic-scale drivers wasconsistent with previous approaches in rainfall prediction problemsfor Queensland and Victoria (e.g. Abbot and Marohasy, 2012, 2014;Mekanik et al., 2013) that showed significant improvements in predic-tion capability of machine learning models.

The purpose of this investigation is threefold: A first objectiveconsists of developing and applying ANN models for predictingStandardized Precipitation and Evapotranspiration Index using hydro-meteorological dataset, climate indices and SSTs with various combina-tions of the training algorithms, hidden transfer function and outputfunction using input data from 1915 to 2005 tested over 2006–2012. Asecond objective is a deeper statistical analysis of model performanceusing key statistical parameters. A third objective is to examine theprediction error yield of drought properties over the tested period.The rest of the paper is structured as follows: The next section willdescribe the theoretical basis and computation of the SPEI and develop-ment of the ANNmodels. Section 3 provides the detail of the hydrome-teorological and climate mode index datasets, methodology for

calculating the SPEI and statistical tools for model performance assess-ments. Section 4 contains the model simulation results anddiscussions and finally, Section 5 provides the concluding remarks forclosing the paper.

2. Theoretical framework

2.1. Theory of the Standardized Precipitation and Evapotranspiration Index

In order to apply the ANN model for drought prediction purposes,the SPEIwas first calculated using the freely available R program devel-oped by Vicente-Serrano et al. (2010a) (http://cran.r-project.org/web/packages/SPEI/index.html). In this section, we describe of the computa-tional approach but for a complete theory behind the index and itscomparison with other DIs, the readers are referred to works ofVicente-Serrano et al. (2010a,b, 2012a,b, 2011a,b). For stations in con-sideration, the potential evapotranspiration (PET) was determinedusing the rainfall and temperature data. Note that the PET estimatesthe amount of evaporation and transpiration that could occur if suffi-cient water was available, and therefore, it represents the significanceof evapotranspiration in the hydrologic budget for drought situation(e.g. Hanson, 1988). Depending on which data are available,either the Thornthwaite (1948), Hargreaves (1994) or Penmanmethod as described in Allen et al. (1994) can be used for calculatingthe PET.

The aforementioned approach for estimating PET has merits andconstraints. The Hargreaves method requires mean solar radiation butif such data are not available, they can be estimated from the stationlatitude and month of the year. The Penman method is the most data-expensive approach as it requires incoming solar radiation or alterna-tively percent cloud cover, saturation water pressure, dew pointtemperature or humidity and atmospheric surface pressure in order todetermine the psychometric constant for the PET (Vicente-Serranoet al., 2010a,b, 2012a). When only monthly data is available, as in ourstudy, the Thornthwaite (1948) method is used viz;

PET ¼ 16K10TI

� �m

ð1Þ

where T is the monthly-mean temperature (°C); I is a heat indexcalculated as the sum of 12 monthly index values i, the latter beingderived from mean monthly temperature viz

i ¼ 16KT5

� �1:514ð2Þ

and m is deduced empirically (m = 6.75 × 10−5, I3 + 7.75 × 10−7,I2 + 1.79 × 10−2, I + 0.492), K is a correction coefficient computed asa function of the latitude and month

K ¼ N12

� �NDM30

� �: ð3Þ

NDM is the sumof days of themonth andN is themaximumnumberof sun hours calculated using

N ¼ 24π

� �ωs ð4Þ

and ωs = hourly angle of sun rising (ωs = arccos(−tan ϕ tan δ)), φ =

latitude in radians, δ ¼ 0:4093sen 2π J365−1:405

� �is the solar declination

in radians and J is the average Julian day of the month.The next step is to determine the surplus/deficit of water (Di = Pi −

PETi) as the difference between precipitation (PCN) and PET. The Di

values are aggregated at different time scales, which is similar to theprocedure of the SPI. The difference Dk i, j in a given month j and year I

-4.5

-3.0

-1.5

0

1.5

3.0

0

20

40

60

80

100

120SPEIPCNdrought sample defined by SPEI

end monthonset month

mean PCN

JAN 2004JAN 2003JAN 2002JAN 2001

drought severity

peak intensity

drought duration

mon

thly

SP

EI

mon

thly

PC

N (

mm

)

Fig. 1. Definition of drought properties defined by the Standardized Precipitation andEvaporation Index (SPEI) compared with the precipitation (PCN) for Deniliquin (stationID 74128) during the mega-drought period (2001–2004).

68 R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

depends on the chosen time scale k. For example, the accumulated dif-ference for one month in a particular year i with a 12-month timescale is

Xki; j ¼

X12l¼13−kþ j

Di−1;l þXj

l¼1

Di;l if jbk ð5Þ

Xki; j ¼

Xj

i¼ j−kþ1

Di;l if j≥k ð6Þ

where Di,l is the PCN − PET difference in the first month of year i, inmillimeters.

Unlike the case of the SPI where probability distribution of gammafamily (two-parameter gamma or three-parameter Pearson III) isused, that for SPEI utilizes a three-parameter distribution. Out ofcommon distributions (Pearson III, lognormal and general extremevalue), the log–logistic distribution f(x) is themost appropriate for stan-dardizing the D series (Vicente-Serrano et al., 2010a)

f xð Þ ¼ βα

x−γα

� �β−11þ x−γ

α

� �β� �−2

ð7Þ

whereα, β, and γ are the scale, shape, and origin parameters respective-ly for D values in the range (γ N D b ∞), calculated using the L-momentapproach (Ahmad et al., 1988; Singh et al., 1993) where

β ¼ 2w1−w0

6w1−w0−6w2; α ¼ w0−2w1ð Þβ

Γ 1þ 1=βð ÞΓ 1−1=βð Þ ;

γ ¼ w0−αΓ1þ 1β

� �Γ

1−1β

� �ð8Þ

and T(β) is the gamma function ofβ andprobability-weightedmoments(PWMs) are given by

ws ¼1N

XNi¼1

1−Fið ÞsDi ð9Þ

where Fi is a frequency estimator calculated following the approach ofHosking (1990)

Fi ¼i−0:35

Nð10Þ

where i is the range of observations arranged in increasing order and Nis the number of data points.

After the parameters of log–logistic distribution are determined, theprobability distribution function of D series is calculated as

F xð Þ ¼ 1þ αx−γ

� �β� �−1

: ð11Þ

Finally thedistribution F(x) is used to calculate the SPEI following theclassical approximation of Abramowitz and Stegun (1972) viz;

SPEI ¼ W− C0 þ C1W þ C2W2

1þ d1W þ d2W2 þ d3W

3 ð12Þ

whereW ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi−2 ln Pð Þ

pfor P≤ 0.5 and P is the probability of exceeding

a determined D value, P=1− F(x) and C0 = 2.515517, C1 = 0.802853,C2= 0.010328, d1= 1.432788, d2= 0.189269 and d3= 0.001308. Notethat if P N 0.5, then it is replaced by 1 − P and the sign of the SPEI isreversed. For drought analysis, the grading is similar to the SPI withdrought categories as: extreme (SPEI ≤ −2.0), −1.5 ≤ SPEI b 2.0(severe) and −1.0 ≤ SPEI b −1.5 (moderate).

In Fig. 1 the practical utility of the SPEI for detecting drought onsetand termination months and quantification of drought properties areillustrated. SPEI and the corresponding precipitation data for Deniliquin(located in New South Wales) over the mega-drought period(2001–2004) have also been included. Following earlier approaches(e.g. Kim et al., 2009; Yevjevich et al., 1967), a droughtmonthwas iden-tified when the monthly SPEI became negative (i.e. rainfall conditionswere lower rainfall than the normal period). The severity was thenthe accumulated value of all negative SPEI, peak intensity of droughtwas the minimum of the SPEI and the duration was the sum ofconsecutive months when the SPEI was negative. For example in thecase of Deniliquin, one segment of drought began in March 2002 andterminated in June 2003.Within this dry period, the recorded precipita-tion was less than 30 mm in any given month. Accordingly, the peak ofdrought was recorded in May–June 2003 (SPEI≈−2.25), duration was15months and the severity of droughtwas estimatedwith accumulatedSPEI≈ −16.71.

2.2. Theory of the Artificial Neural Network model

ANNs have been applied for modeling purposes for many years inmathematics, engineering, medicine, economics, hydrology,meteorolo-gy, psychology, neurology and other subjects (e.g. Chow et al., 2002;Kumar et al., 2011; Sözen and Ali Akçayol, 2004). Their popularity hasgrown since their first inception in 1943 (McCulloch and Pitts, 1943)mainly to solve prediction problemswith variables of stochastic nature,nonlinear or unknown variations or those that must be determinedfrom less controlled environments (Moustris et al., 2011). An ANNmodel weaves through mathematical components derived fromstochastic time-series datasets to tackle the prediction of very complexsystems (e.g. rainfall or drought prediction). As they are flexible and lessassumption-dependent, there is no need to define the underlying phys-ical process between the inputs and outputs (Morid, et al., 2007). Thismakes the ANN very suitable for drought forecasting where variablesthat trigger a drought may not be fully understood. Basically, the ANNmodel learns from previous history of how the input signal has variedover the time. It constructs logically an input–output mapping systemto perform the future predictions. In order to train and test an ANNmodel or predicting a variable, the input data and its corresponding out-put values are necessary (Şahin, 2012; Şahin et al., 2013)

ANN is a computational paradigm composed of non-linear elements(neurons) operating in parallel and massively connected by networkscharacterized by different weights. A single neuron computes the sumof its inputs, adds a bias term, and drives the result through a generallynonlinear activation function to produce a single output termed theactivation level of the neuron. ANN models are specified by network

69R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

topology, neuron characteristics, and training or learning rules(Lippman, 1987) with inputs, output(s) and hidden layers with inter-connections. The fundamental processing unit is a neuron, whichcomputes a weighted sum of its input signals, yi, for i=0,1,2,…, n, hid-den layers, wij and then applies a nonlinear activation function toproduce an output signals uj.

A neuronal model as shown in Fig. 2a consists of an externallyapplied bias, bk which has the effect of increasing or decreasing thenet input of the activation functions depending onwhether it is positiveor negative. Mathematically, a neuron k may be described by

uk ¼Xmj¼1

wkxj ð13Þ

yk ¼ Φ uk þ bkð Þ ð14Þ

where x1, x2,…, xm are the input signals;wk1,wk2,…,wkm are the synap-tic weights of neuron k; uk is the linear combiner output due to inputsignals; bk is the bias;Φ(.) is the activation function and yk is the outputsignal of the neuron. Bias bk has the effect of applying an affine transfor-mation to the output uk of the linear combiner in the model (Fig. 2b) asshown by

vk ¼ uk þ bk: ð15Þ

In particular, depending on whether bk is positive or negative, therelationship between the induced local field or activation potential vkof neuron k and linear combiner output uk can be modified (Fig. 2b).

Fig. 2. (a) Nonlinear model of a neuron and (b) affine transformation

Note that as a result of this affine transformation, the graph of vk versusuk no longer passes through the origin. The bias bk is an external param-eter of artificial neuron k. It may be accounted for its presence as inEq. (14). Equivalently, the combination of Eqs. (13) and (14) may beformulated as follows (Haykin, 2010)

vk ¼Xmj¼0

wkjx j ð16Þ

yk ¼ Φ vkð Þ: ð17Þ

The tangent sigmoid, ϕ(x) logarithmic sigmoid, ψ(x) and linear, χ(x)transfer function are described as follows (Vogl et al., 1988)

ϕ xð Þ ¼ 21þ e−2x −1 ð18Þ

ψ xð Þ ¼ 11þ e−x ð19Þ

χ xð Þ ¼ linear xð Þ ¼ x ð20Þ

where Eqs. (18)–(20) may be trialed to determine the best predictivemodel (e.g. Şahin, 2012, 2013; Karlik and Olgac, 2011; Harrington,1993).

Computationally efficient ANN networks employ second-ordertraining methods, primarily the Levenberg–Marquardt (LM) orthe Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton

produced by the presence of a bias; note that vk = bk at uk = 0.

136oE 140oE 144oE 148oE 152oE

36oS

30oS

24oS

18oS

12oS

Moruya

Palmerville

Wilsons

Y amba

Bathurst

G abo Island Deniliquin

Maree

Longitude

Latit

ude

Fig. 3. A spatial map of study locations for stations considered in this study.

70 R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

backpropagation learning algorithms (Dennis and Schnabel, 1983;Marquardt, 1963) that minimize the mean squared error betweenthe predicted and observed variable (Tiwari and Adamowski, 2013).An LM algorithm uses an approximation to the Hessian matrix asfollows

xkþ1 ¼ xk− JT Jþ μIh i−1

JTe ð21Þ

where J is the Jacobian matrix calculated using standard back-propagation techniques (Hagan andMenhaj, 1994) and is less complexthan computing the Hessian matrix (Marquardt, 1963). The J containsfirst derivatives of network errors with respect to the weights andbiases and e is a vector of errors. The BFGS quasi-Newton is an

Table 1The geographic details and climatic characteristics of data stations in this study.

Station ID Latitude longitude E

Bathurst 63005 149.56°E 33.43°S 7Gabo Island 84016 149.91°E 37.57°S 1Moruya Heads 69018 150.15°E 35.91°S 1Palmerville 28004 144.08°E 16.00°S 1Wilsons Promontory 85096 146.42°E 39.13°S 1Yamba Pilot 58012 153.36°E 29.43°S 1Deniliquin 74128 144.95° 35.56°SMarree 17031 29.65°S 138.06°E

alternative to the conjugate gradient methods for fast optimization,which uses the following equation:

xkþ1 ¼ xk−A−1k gk ð22Þ

where A−1k is the Hessian matrix (second derivatives) of the

performance index at the current values of the weights and biases(Dennis and Schnabel, 1983).

3. Materials and methodology

3.1. Study area and model input data

For prediction of the monthly SPEI, we have used a total of 18 input(or predictor) variables that described the geographic and climaticattributes of the eight candidate stations (Fig. 3) considered in easternAustralia. The site-specific inputs were the station ID, year, month, lati-tude, longitude and the station elevation, with meteorological inputs asthe monthly rainfall, maximum temperature, minimum temperature,mean temperature and evapotranspiration estimated using theThornthwaite (1948) method. Additionally, the large-scale climatemode indices (SOI, PDO, IOD, SAM) and the Sea Surface Temperatures(Nino 3.0 5°N–5°S, 150°W–90°W; Nino 3.4 5°N–5°S, 170°W–120°W;Nino 4.0 5°N–5°S, 160°W–150°W) were incorporated as regressioncovariates for training the ANN models.

Table 1 provides the geographic details and climatic properties ofeight stations considered. Fig. 4 shows a histogram of seasonal precipi-tation patterns for the candidate stations averaged over 1915–2012.The annual precipitation statistics (mean, maximum and minimumvalues) were highly discernible for each station, with the maximumrainfall spanning from about 408.7 to 2716.8 mm, minimumrainfall from 39.3 to 679.0 mm and the mean rainfall from 164.7 to1483.2 mm. The seasonal precipitation climatology, shown in Fig. 4revealed distinct climatic patterns for the candidate stations, with wetwinters and comparatively dry summers for Marree, Palmerville,Wilsons and Deniliquin. Out of these four stations, Deniliquin was thedriest over all seasons. For the case of Yamba, Moruya and Gabo Island,the autumn season appeared to be the wettest of all whereas for Bath-urst, the summer season was the wettest while the second highestrainfall was recorded in the spring season.

For the development of ANNmodels, the monthly rainfall andmeantemperature datasets for the period 1915–2012 were acquired. Therainfall data were obtained from the Australian Bureau of Meteorology(BOMHQ) archive and the air temperature from the Australian ClimateObservations Reference Network–Surface Air Temperature (ACORN-SAT) http://www.bom.gov.au/climate/change/acorn-sat/. Both of thesedatasetswere originally collated fromhourly observations at daily time-scales (Della-Marta et al., 2004; Jones et al., 2009; Lavery et al., 1997;Menne and Williams, 2009). The qualities of both data were checkedusing the Standard Normal Homogeneity Tests. Accordingly, the rawvalues had been adjusted for inhomogeneities caused by external

levation (m) Climatological precipitation (PCN) (mm year−1)

Mean Minimum Maximum

13.0 646.5 214.2 1028.549.9 923.5 562.9 1537.050.2 675.1 472.0 1822.244.1 697.6 360.6 1028.346.4 1061.5 659.1 1490.453.4 1483.2 679.0 2716.894.0 402.60 167.7 803.950.0 164.70 39.3 408.7

70

110

150

190Yamba

60

70

80

90

100Moruya

10

30

50

70Maree

10

30

50

70Bathurst

PC

N (

mm

)

65

70

75

80

85S

ON

JJA

MA

M

DJF

Gabo Island

PC

N (

mm

)

20

40

60

80

100

SO

N

JJA

MA

M

DJF

Palmerville

50

70

90

110

130Wilsons

30

32

34

36

38

40Deniliquin

SO

N

JJA

MA

M

DJF

SO

N

JJA

MA

M

DJF

Fig. 4. Histogram of seasonal precipitation patterns averaged over 1915–2012. Acronyms are: DJF (summer); MAM (autumn); JJA (winter); and SON (spring).

71R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

factors such as station relocations, instrumental errors and adverseexposures to the measurement sites (Alexandersson, 1986; Torok andNicholls, 1996). The process also detected and removed gross single-day errors in data records. Rather than making inhomogeneityadjustments in themean values, daily records were adjusted for discon-tinuities at the 5, 10… 90, 95 percentiles. Missing data were deduced bygenerating artificial rainfall based on cumulative rainfall distributions(Haylock and Nicholls, 2000). Consequently both temperature andrainfall datasets have since been used extensively for climate changestudies in Australia (Alexander et al., 2006; Suppiah and Hennessy,1998).

The training dataset used as regression covariates for predicting themonthly SPEIwere: SOI and IOD acquired from the Australian Bureau of

X1

X2

X17

X18

Input Layer Hidden Nod

Fig. 5. The topological structure of the Artificial Neural Network used for prediction of the Standcific characteristics (station ID, year, month, latitude, longitude, elevation) and hydro-meteoroltion), large-scale climate mode indices are Southern Oscillation Index, Pacific Decadal OscTemperatures are Nino SSTs 3.0, 3.4 and 4.0 parameters.

Meteorology (Trenberth, 1984), the PDO index acquired from the JointInstitute of the Study of the Atmosphere and Ocean (JISAO) (Mantuaet al., 1997; Zhang et al., 1997) and the Southern Annular Modeacquired from the British Antarctic Survey database (Marshall, 2003).Recall that the SOI is typically calculated using the Troup's methodusing the values of pressure differences from Tahiti and Darwin. ThePDO is determined using the UKMO Historical SST data set for 1900–81 and the Reynolds Optimally Interpolated SST (V1) (Morid et al.,2007) for January 1982–Dec 2001 and OI.v2 SST fields from January2002 onwards.

Like the positive and negative phases of the SOI which is known toimpact rainfall variability in eastern Australia and consequently,drought events in the region, the IOD (coupled ocean and atmosphere

SPEI

es (n) Output Layern1

n 2

n50

ardized Precipitation and Evaporation Index (SPEI). The 18 inputs, “Xn” represent site-spe-ogical inputs (rainfall, minimum, mean and maximum temperatures and evapotranspira-illation Index, Southern Annular Mode, and Indian Ocean Dipole and the Sea Surface

Table 2The input parameters used in the ANN models.

Meteorological parameters

Monthly mean precipitation (mm) PCNMonthly mean air temperature (°C) TmeanMonthly maximum air temperature (°C) TmaxMonthly minimum air temperature (°C) TminEvapotranspiration (computed by Thornthwaite method) (mm) PET

Climate mode indices

Southern Oscillation Index SOIPacific Decadal Oscillation PDOSouthern Annular Mode SAMIndian Ocean Dipole IOD

Sea Surface Temperatures (SSTs)

Nino 3.4 SST (5 N–5S,170 W–120 W) N3.4Nino 4.0 SST (5 N–5S, 160E–150 W) N4.0Nino 3.0 SST (5 N–5S,150 W–90 W) N3.0

72 R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

phenomenon in the equatorial Indian Ocean) affects drought in thesouthern half of the Australian continent (Ashok et al., 2003) (Sajiet al., 1999, 2005). Likewise, the SAM which has an influence on thestrength and position of cold fronts and mid-latitude storm systems isconsidered as a significant driver of rainfall variability in southeasternAustralia (Hendon et al., 2007). Considering the net impact of alllarge-scale climate drivers on drought events in eastern Australia, theclimate indices used in development of ANN models were appropriateand consistent with rainfall prediction problems previously conductedin Australia (Abbot and Marohasy, 2012, 2014; Deo and Sahin, 2015;Mekanik et al., 2013; Morid et al., 2007) and the prediction of the

Table 3ANNmodels and network architecture listed with the training and testing time and time-avera= training Levenberg–Marquardt algorithm; trainbfg = training BFGS quasi-Newton backproSquare Error; MBE = mean bias error; R2 = Coefficient of Determination. Note that the best A

Modelnumber

Trainingalgorithm

Hidden transferfunction

Output transferfunction

Networkarchitectu

M1 trainlm Tansig Linear 18–14–1M2 trainlm Tansig Linear 18–18–1M3 trainlm Tansig Linear 18–24–1M4 trainlm Tansig Linear 18–26–1M5 trainlm Tansig Linear 18–28–1M6 trainlm Tansig Linear 18–32–1M7 trainlm Tansig Linear 18–38–1M8 trainlm Tansig Linear 18–42–1M9 trainlm Tansig Linear 18–44–1M10 trainlm Tansig Linear 18–48–1M11 trainlm Logsig Linear 18–14–1M12 trainlm Logsig Linear 18–16–1M13 trainlm Logsig Linear 18–28–1M14 trainlm Logsig Linear 18–30–1M15 trainlm Logsig Linear 18–32–1M16 trainlm Logsig Linear 18–36–1M17 trainlm Logsig Linear 18–46–1M18 trainlm Logsig Logsig 18–12–1M19 trainlm Logsig Logsig 18–20–1M20 trainlm Logsig Logsig 18–30–1M21 trainlm Logsig Logsig 18–34–1M22 trainlm Tansig Tansig 18–16–1M23 trainlm Tansig Tansig 18–43–1M24 trainlm Tansig Logsig 18–18–1M25 trainlm Tansig Logsig 18–36–1M26 trainlm Tansig Logsig 18–38–1M27 trainlm Logsig Tansig 18–38–1M28 trainlm Logsig Tansig 18–50–1M29 trainbfg Tansig Linear 18–40–1M30 trainbfg Tansig Linear 18–48–1

Effective Drought Index in Iran and South Africa (Masinde, 2013;Morid et al., 2007).

3.2. Network architecture and ANN model development

All simulations were performed under MATLAB environmentrunning under Pentium 4, 2.93 GHz CPU. Fig. 5 displays a topologicalstructure of ANNmodel where three layer neurons were used to designthe network. In this research, rather than testing the sensitivity of eachpredictor input, the training algorithm, hidden transfer function andoutput transfer function were varied systematically to design the bestANN model (e.g. Şahin, 2012, 2013) while all 18 predictors (X) wereconsidered. Thus, the number of input neurons was pre-selected to be18 (denoted as X1, X2, X3 …, X18), where 6 represented the site-specific properties (station ID, year, month, latitude, longitude, eleva-tion), 5 neurons for the hydro-meteorological properties (rainfall, tem-perature, evapotranspiration), 4 neurons for the climate mode indices(SOI, IOD, SAM, PDO) and the remainder 3 neurons were for the SST(Nino) indices (see Table 2).

As there is no mathematical formula to determine the neuronalstructure in the hidden layer of the ANN model, the number of neuronin hidden layer was decided by trial and error (Şahin, 2012). A maxi-mum of 50 neurons were tested for development of the network archi-tecture. In order to determine the optimum architecture, combinationsof the input, hidden layer and output neurons were tried one by one.This resulted in a total of 30 ANNmodels runwith unique combinationsof the respective model architecture using various training equations,transfer and output functions (Eqs. (18)–(20)). Table 3 shows theparameters of the ANN model architecture used for prediction of theSPEI. Except for models M29 and M30 where the BFGS quasi-Newtonbackpropagation was used, all other ANN models were trained using

ged statistics of model performance. The acronyms of mathematical functions are: trainlmpagation; Tansig = tangent sigmoid; Logsig = logarithmic sigmoid; RMSE = Root MeanNN model (M23) is boldfaced.

reTraining (s) Testing (s) RMSE MBE R2

299.4029 0.0571 0.184 −0.0112 0.9706128.4217 0.0486 0.158 −0.0172 0.9785112.4707 0.0436 0.122 −0.0056 0.9870154.4456 0.0453 0.132 −0.0041 0.984737.7698 0.0397 0.129 −0.0033 0.985564.8970 0.0475 0.105 −0.0003 0.990470.3634 0.0527 0.112 −0.0024 0.9890

153.2417 0.0522 0.119 −0.0010 0.987496.8501 0.0379 0.107 0.0016 0.9900

152.1572 0.0443 0.126 0.0003 0.9860100.2495 0.0383 0.171 −0.0112 0.974671.8536 0.0406 0.129 0.0020 0.985353.1839 0.0436 0.134 −0.0078 0.984580.9947 0.0452 0.113 −0.0002 0.9888

166.6819 0.0590 0.105 −0.0010 0.9902260.8610 0.0507 0.100 0.0010 0.9912164.8453 0.0493 0.098 0.0041 0.9916351.3914 0.0408 0.140 −0.0015 0.982951.5970 0.0403 0.107 0.0029 0.9900

142.6681 0.0385 0.086 0.0043 0.993482.9572 0.0471 0.072 0.0022 0.995453.1316 0.0399 0.125 −0.0061 0.9862

220.1898 0.0484 0.071 0.0002 0.995674.7664 0.0435 0.104 0.0005 0.9906

272.0926 0.0442 0.087 0.0011 0.9934194.7767 0.0489 0.079 0.0007 0.9946235.6059 0.0717 0.092 0.0107 0.9928132.4064 0.0592 0.083 0.0004 0.9940304.0196 0.0578 0.199 −0.0145 0.9655562.1770 0.0534 0.163 0.0006 0.9765

-4

-2

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0 12 24 36 48 60 72 840

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ictio

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ror

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)

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SPEIobserved

SPEIpredicted

PE

SP

EI

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ictio

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)pr

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E)

pred

ictio

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ror

(PE

)

SP

EI

SP

EI

SP

EI

0 12 24 36 48 60 72 84

0 12 24 36 48 60 72 84

Fig. 6. The observed and the predicted SPEI plotted with the corresponding prediction error (PE) over the test period (2005–2012) (a) Bathurst, (b) Gabo Island, (c) Moruya,(d) Palmerville, (e) Wilsons, (f) Yamba, (g) Deniliquin, and (h) Marree.

Table 4The assessment of ANN model performance based on linear regression formula (SPEIp = m SPEIo + C) of observed Standardized Precipitation and Evaporation Index (SPEIo) with thepredicted values (SPEIp) from 2006 to 2012. The square of linear regression coefficient (R2), maximum deviation (maxDev) and standard derivation (σ) of predicted and modeled SPEIare also shown.

Station name m R2 maxDev C σSPEI0 σ SPEIP % diff (σ)

Bathurst Agricultural 0.98 0.9920 0.323 −0.0120 0.00724 0.00760 4.97Gabo Island Lighthouse 1.01 0.9980 0.108 −0.0060 0.00442 0.00465 3.56Moruya Heads 1.00 0.9940 0.195 0.0135 0.00670 0.00635 −5.22Palmerville 0.98 0.9940 0.393 0.0016 0.00755 0.00706 −6.49Wilsons Promontory 0.99 0.9960 0.148 −0.002 0.00522 0.00555 6.32Yamba Pilot Station 0.98 0.9920 0.358 −0.010 0.00654 0.00678 3.67Deniliquin 0.97 0.9880 0.735 −0.004 0.01140 0.01250 9.65Marree 0.95 0.8968 0.894 0.0250 0.00732 0.00392 −37.97

73R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

0 12 24 36 48 60 72 84

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EI

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tion

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E)

e)

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ictio

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)

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SP

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EI

Fig. 6 (continued).

74 R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

the Levenberg–Marquardt learning algorithm. The hidden transferfunctions were alternated from being the tangent sigmoid (M1–M10,M22–M26, M29–M30) to the logarithmic sigmoid function (M11–M21, M27–M28) using Eq. (18) and (19).

The output transfer functions for the ANN model were linear (M1–M17, M29–M30), logarithmic sigmoid (M18–M21, M24–M26) andtangent sigmoid (M22–M23, M27–M28). In each trial, the numbers ofnodes in the hidden layer were gradually increased, resulting in differ-ent combinations of the ANN model architecture (Table 3). Out of the98 years of available input data, 93% of data (i.e. 1915–2005) wereused for the training phase and the remainder 7% data were usedfor the testing phase. After training or learning the networks, afinal weight matrix was obtained which was further applied to the

independent inputs in the “test” set. Then the final outcomes werecompared with the observed (or calculated) values of the monthlySPEI.

3.3. Statistical evaluation of model performance

The performance of the ANN models in predicting the monthlySPEI was statistically evaluated using five prediction score metricscalculated from the test dataset: (1) Root-Mean Square Error(RMSE), (2) Mean Absolute Error (MAE), (3) Coefficient ofDetermination (R2) (Paulescu et al., 2011; Ulgen and Hepbasli,2002), (4) Willmott's Index of Agreement (d) (Acharya et al., 2013;Willmott, 1981, 1982) and (5) Nash–Sutcliffe Coefficient of

Table 5Quantitative measures of the ANN model performance based on overall prediction scoremetrics over the test period (2006–2012). Key measures: are Root Mean Square Error(RMSE), Mean Absolute Error (MAE), Coefficient of Determination (R2), the Wilmort'sIndex of Agreement (d) and theNash–Sutcliffe Coefficient of Efficiency (E) of the observedStandardized Precipitation and Evaporation Index (SPEIo) and predicted StandardizedPrecipitation and Evaporation Index (SPEIp).

Station name MAE RMSE R2 d E

Bathurst Agricultural 0.0013 0.0504 0.9979 0.947 0.9956Gabo Island Lighthouse 0.0011 0.0466 0.9990 0.947 0.9980Moruya Heads 0.0039 0.1117 0.9982 0.960 0.9961Palmerville 0.0130 0.0572 0.9977 0.959 0.9953Wilsons Promontory 0.0122 0.0700 0.9989 0.947 0.9770Yamba Pilot 0.0126 0.0634 0.9982 0.949 0.9963Deniliquin 0.0015 0.0639 0.9945 0.949 0.9888Marree 0.0272 0.0799 0.8968 0.932 0.9755Overall–All Station Average 0.0066 0.0679 0.9978 0.9487 0.9928

75R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

Efficiency (E) (Krause et al., 2005; Nash and Sutcliffe, 1970). Theprimary mathematical formulas are

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

Xni¼1

SPEIpi−SPEIoi

� �t

2

vuut ð23Þ

MAE ¼ 1N

Xni¼1

SPEIpi−SPEIoi

� �t

ð24Þ

R2 ¼

Xni¼1

SPEIo;i−SPEIo;i� �

SPEIp;i−SPEIp;i� �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

SPEIo;i−SPEIo;i� �2

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

SPEIp;i−SPEIp;i� �2

s0BBBB@

1CCCCA

2

ð25Þ

d ¼ 1−

XNi¼1

SPEIo;i−SPEIp;i� �2

XNi¼1

SPEI0p;i−SPEIo − SPEI0o;i−SPEIo

� �2

266664

377775; 0≤d≤1 ð26Þ

E ¼ 1−

XNi¼1

SPEIo;i−SPEIp;i� �2

XNi¼1

SPEIo;i−SPEIo� �2

266664

377775; 0≤E≤1 ð27Þ

where SPEIpi and SPEIoi are the predicted and observed monthlyStandardized Precipitation and Evapotranspiration Index in test pe-riod t (test slice) respectively, i is the month of the test dataset andN (=84) is the length (number of samples in the test set) in periodt (2006 to 2012).

When comparing themodel performance by the RMSE and theMBE,the values must be as small as possible to reflect small deviations of thepredictions from observations. However, the MAE is less sensitive toextreme values than the RMSE (Fox, 1981). For best model, the R2

which is determined by a scatter plot of observed and predicted SPEI,is expected to be close to unity. Likewise, the d and E should be unityfor the perfect fit (Krause et al., 2005). A disadvantage of the Coefficientof Determination and the Nash–Sutcliffe efficiency arises from the factthat the differences between observed and predicted SPEI are calculatedas square values. Consequently, larger values in the time-series data canbe overestimated whereas smaller values are neglected (Legates andMcCabe, 1999). This insensitivity was overcome using the Willmott'sIndex of Agreement (Willmott, 1981) where the ratio of mean squareerror and potential error was considered for the ANNmodel assessmentinstead of square of the differences between the simulated andobserved SPEI (Willmott, 1984).

Table 3 summarizes the performance capability of ANN modelsdeveloped in this study. The best ANN model (denoted M23) wastrained using the Levenberg–Marquardt (LM) learning algorithmusing the tangent sigmoid equation (Eq. (17)) as both the hiddentransfer and the output equations, respectively. When compared by itsvalue of the MAE, MBE and R2, the architecture of M23 was 18–43–1(input–hidden–output layer). The model training time using data over1915–2005 was approximately 220 s, its testing time using simulateddata over 2006–2012 was 0.0484 s and the prediction error yieldedmagnitudes were RMSE (0.071), MBE (0.0002) and R2 (0.9956). Notethat in our study, the optimumANNmodelwas not based on the testingor training time used inmodel development but rather using key statis-tical similarity between the observed and predicted SPEI in the testeddataset. Consequently, the best ANN model (M23) had the smallestprediction error yield (MBE & RMSE) and the highest Coefficient ofDetermination (see Table 3).

4. Results and discussion

The goodness of fit of the ANNmodels developed for drought assess-ment at the eight candidate stations was checked using a scatterdiagram of observed and predicted SPEI in the test period using linearregression statistics (Table 4). For the optimum ANN models for ateach site, the gradient of the linear fit ranged between 0.956 (Marree)and 1.010 (Gabo Island). The correlation coefficient (r) was between0.947 and 0.999, maximum deviation of the predicted SPEI from theobserved of 0.108–0.894 and the y-intercepts between −0.012 and0.014. Thus, there was very good agreement between the predictedand the observed SPEI. By comparison, the percentage difference inthe standard deviation of the predicted and the observed SPEI yieldedthe lowest magnitude for Gabo Island (≈−3.56%) relative to theother stations. The worst performance was attained for Marree(≈−37.97%), in accordance with the lowest value of the linear correla-tion coefficient (0.947) and the largest magnitude of maximum devia-tion of predictions from the linear model (i.e. maxDev ≈ 0.894).Overall, good prediction skill of the ANN model was exhibited for allsites considered in the present investigation.

Fig. 6 plots the monthly observed and the predicted SPEI in the testperiod (2006–2012) together with the prediction error (PE) yield ofthe ANN model for each tested month. The magnitude of the PE wasused to check whether the ANN model over-(positive value) or under-(negative value) predicted the observations for any given monthwhereby PE = SPEIp − SPEIo. Note that the ideal value of PE is zerowhen predicted SPEI exactly matches the observed value (Moustriset al., 2010, 2011). Overall, there was good visual agreement betweenthe observed and the predicted SPEI within the test period. However,the prediction error yield for each month appeared to be discerniblefor each station considered. Of the 84 months in the test period, thesmallest prediction error (PE ≈ 0.145) was registered for Gabo Island.This was consistent with the results indicated by summarized statisticsof the scatter between the predicted and the observed SPEI (Table 4). Inorder to deduce the overall prediction skill of the ANN model, an inter-comparison of its performance was conducted based on the variousmeasures of the prediction error estimated by Eqs. (23)–(27). Table 5displays the time-averaged performance statistics for all months withinthe tested dataset in the form of the RMSE, MAE, R2, d and the E values.

By a close observation of the prediction error averaged for the period2006–2012, it was evident that the bestmodel predictionswere obtain-ed for Gabo Island. For this station, the smallest value of both the MAE(≈0.0011) and the RMSE (≈0.0466)was acquired, which also accordedto the highest Coefficients of Determination (0.999). The next betterperformance was for Bathurst, although these predictions were onlyslightly worse than those of Gabo Island. It is imperative to state thatthe ANN model prediction for Marree exhibited the largest value ofboth the RMSE and the MAE relative to the other stations. Thiswas also confirmed by the smallest Coefficient of Determination

76 R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

(R2 ≈ 0.8968). The results for Marree concurred with the results ofTable 4 where themagnitude of themaximumdeviation and the differ-ence in standard derivation of predicted and observed SPEI were thelargest (≈0.894 & −37.69%, respectively).

As additional quantifier of the ANNmodel performance, we comput-ed theWillmott's Index of Agreement and theNash–Sutcliffe Coefficientof Efficiency based on simulated SPEI. According to this criterion, thebest prediction was for Gabo Island (d = 0.967; E = 0.9980). Overall,the ANN model performed very well for all stations considered, whichwas also confirmed by the all-station averaged statistics (d = 0.9487and E = 0.9928). It is imperative to realize that the slightly smaller

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freq

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PE < 0 (19.1%)

PE > 0 (80.9%)

a)

c)

e)

g)

Fig. 7.Histogramof the frequencydistribution of theprediction error (PE) calculated for the test(f) Yamba, (g) Deniliquin, and (h)Marree. In each panel, the cumulative frequency deduced forthe ANN models and comparisons with the Gaussian distribution are shown.

value of the Willmott's Index of Agreement compared to the value ofthe Nash–Sutcliffe Coefficient of Efficiency was as expected, since theformer performance indicator does not square the error values sothere is less chance of over- or under-estimation of the simulateddrought index (e.g. see (Willmott et al., 2012)).

Fig. 7 displays the frequency distribution of the PE for eachstation calculated over the test period. It was obvious that the rangeof the PE for Gabo Island and Wilsons was the narrowest (i.e.−0.1≤ PE≤+0.1) of all stations although a small frequency of outlierswere noted for PE≈−0.20 and 0.15.When compared by the frequencyof the over-predicted and the under-predicted value of the SPEI, the

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30

40

50

prediction error (PE)

fre

qu

en

cy

PE < 0 (52.4%)

PE > 0 (47.6%)

-0.2 -0.1 0 0.1 0.20

10

20

30

40

50

prediction error (PE)

fre

qu

en

cy

PE < 0 (57.1%)PE > 0 (42.9%)

-0.2 -0.1 0 0.1 0.20

20

40

60

prediction error (PE)

fre

qu

en

cy

PE < 0 (58.3%)PE > 0 (41.7%)

-0.2 -0.1 0 0.1 0.20

10

20

30

40

prediction error (PE)

fre

qu

en

cy

PE < 0 (38.1%)

PE > 0 (61.9%)

b)

d)

f)

h)

period (2006–2012) (a) Bathurst, (b)Gabo Island, (c)Moruya, (d) Palmerville, (e)Wilsons,the respective bin representing under-predictions (PE b 0) and over-predictions (PE N 0) by

Table 6Theperformancemetrics of ANNmodel in terms of themaximum,minimumand standarddeviations of prediction error (PE) calculated from the observed StandardizedPrecipitation and Evaporation Index (SPEIo) and predicted Standardized Precipitationand Evaporation Index (SPEIp) over the test period.

Station Prediction error (PE)

Max Minimum Standard deviation

Bathurst Agricultural 0.221 0.0006 0.052Gabo Island 0.145 0.0007 0.032Moruya Heads 0.204 0.0009 0.038Palmerville 0.387 0.0005 0.048Wilsons Promontory 0.159 0.0054 0.029Yamba 0.395 0.0007 0.053Deniliquin 0.811 0.0002 0.097Marree 0.412 0.0008 0.058

77R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

largest difference was evident for Bathurst, Moruya, Deniliquin andMarree. Clearly, the ANN model over-predicted the SPEI for at leastthree out of the four stations (Bathurst, Deniliquin, and Maree), withthe largest difference found for Deniliquin where more than 80% of allmonths were over-predicted and nearly identical value of ≈60% wasobtained for the other two stations.

In terms of the under-predicted values of the SPEI, the largestdiscrepancy was obtained for Moruya whereby more than 70% of allpredictions for this case were lower than the observed values. Bycontrast, the ANN model over-predicted the SPEI for more than 60% ofall tested dataset for Bathurst andMarree andmore than 80% of all test-ed dataset for Deniliquin. Interestingly, the frequency of the over- andthe under-predicted SPEI for Wilsons was in parity with each other (ornearly 50%), which could be visually confirmed by nearly Gaussiandistribution of the PE values (Fig. 7e). Also, for the case of Gabo Island,Palmerville and Yamba, the under-predicted SPEI accumulated toapproximately 52.4%, 57.1% and 58.3%, respectively. Based on thediscernible results obtained for the over-predicted and the under-predicted values of the index, it was deduced that for any individualstation considered the precision of the ANN model forecast was dispa-rate, yielding lower or higher SPEI than the observed values. Additional-ly, it was evident that about 48% of all predictions fell in frequency binwith the PE b 0 when all error values in the test dataset were pooledtogether.

Table 6 summarizes the standard derivation (σ) and the maximumand minimum values of PE. When compared with other stations,the highest prediction error was obtained for Deniliquin (maxPE ≈ 0.811) and the lowest for Gabo Island (max PE ≈ 0.155), whichwas in agreement with the standard deviation of the PE. Fig. 8 plotsthe frequency distribution of the PE. It was noteworthy that almost60% of all predictions yielded very small prediction errors (i.e., PEbetween 0 and 0.05) and the rest 20% of simulations yielded predictionerrors between 0.05 and 0.10. When considered by the value of the PE,the highest prediction error was found for Deniliquin (≈0.811) andthe lowest value (≈0.145) for Gabo Island. This was consistent withthe standard deviation for these stations as PE ≈ 0.097 and 0.032,

0 0.05 0.1 0.15 0.2 0.0

20

40

60

80

freq

uenc

y (%

)

Fig. 8. Histogram of the frequency distribution (in %) of the prediction error (

respectively (Table 6). Taken together, these statistics confirmed theslightly different prediction skills of the ANN models for differentstations within the test dataset. Moreover, the large percentage ofsimulated dataset with relatively small magnitude of prediction errorsdemonstrated good prediction skill of the proposed ANN model.

The spread of the predicted and observed SPEI has been illustrated inFig. 9 using a boxplot. Note that the boxplot represents the degree of thespread in the predicted data using respective quartile values. The lowerend of the plot lies between the lower quartile Q1 (25th percentile) andupper quartile Q3 (75th percentile), with the second quartile Q2 (50thpercentile) as the median of the data is represented by a vertical line.Two horizontal lines (known as whisker) are extended from the topand bottom of the box. The bottom whisker extends from Q1 to thesmallest non-outlier in the data set, whereas the other one goes fromQ3 to the largest non-outlier. It is noticeable that the median of thepredicted and the observed SPEI for the ANNmodels was nearly identi-cal for all eight stations although the whiskers extend to slightlydifference values for each case.

Table 7 lists the statistics of the spread and its percentagedifference for each station under consideration. Consistent with thenotion of slightly different prediction skills of the ANN model foreach case, the percentage difference in the quartiles was between−5.2%≤Q1≤ 1.4%,−21.1%≤Q2≤ 13.1%, and−9.7%≤Q3≤ 4.6%. In-terestingly, this difference in statistics of spread did not follow anyspecific trend. For example, largest difference in the predicted andobserved lower quartiles and the median was obtained for Palmervillebut for the upper quartile, the difference was the largest for Deniliquin.It was obvious that for some stations, the ANNmodel over-predicted theSPEI (positive difference), whereas for some stations, the predictionswere smaller than the observed value (negative difference), as alsoverified by the MBE values (Fig. 6). Nevertheless, the interpretation ofresults should bemadewith cautionwith any outliers bymodel simula-tion taken into account.

The accuracy of ANNmodels in prediction of drought properties wastested by quantifying the severity (S), duration (D) and peak intensity(I) using running-sum approaches (e.g. Kim et al., 2009; Yevjevichet al., 1967). Based on the predicted values of SPEI, a drought monthwas identified when the monthly value of the SPEI was negative (i.e.rainfall conditions were lower rainfall than the normal period). Theseverity of the drought was then the accumulated value of the negativeSPEI and the duration as the sum of all monthswhen this drought statuswas sustained (see Fig. 1 for illustration of drought definition). Fig. 10displays the differences between S, D and I deduced from predictedand observed datasets. When compared by S, there was an insignificantdifference in observed and calculated SPEI for Wilsons. However, theprediction of drought severity for four out of eight stations (Moruya,Palmerville, Deniliquin and Yamba) was smaller than the observedvalues with Palmerville exhibiting the largest under-predicted value ofS (≈−1.5%).

Putting the results together we found that an over-prediction in theseverity of drought event was evident for the stations Bathurst, GaboIsland and Yamba with the highest error (≈1%) for the case of Yamba.

25 0.3 0.35 0.4 0.45 0.5

PE) in the test period (2006–2012) with all simulations pooled together.

Table 7(a) Statistics of the spread of the observed SPEIo and predicted Standardized Precipitationand Evaporation Index (SPEIp).

Station Lower quartile Median Upper quartile

SPEIo SPEIp SPEIo SPEIp SPEIo SPEIp

Bathurst −0.785 −0.794 0.035 0.040 0.725 0.678Gabo Island −1.220 −1.237 0.490 0.520 −0.485 −0.480Moruya Heads −1.070 −1.016 −0.250 −0.272 0.420 0.439Palmerville −0.710 −0.673 −0.130 −0.103 0.795 0.811Wilsons Promontory −0.925 −0.886 −0.040 −0.033 0.755 0.759Yamba −0.775 −0.754 0.195 0.184 0.975 0.987Deniliquin −1.125 −1.092 −0.390 −0.385 0.470 0.425Marree −1.400 −1.355 −0.425 −0.446 0.485 0.445

(b) Percentage difference in spread of predicted and observed SPEI.

Station Lower quartile Median Upper quartile

Bathurst 1.1 13.1 −6.5Gabo Island 1.4 6.0 −0.9Moruya Heads −5.1 8.9 4.6Palmerville −5.2 −21.1 2.0Wilsons Promontory −4.3 −18.5 0.5Yamba −2.7 −5.7 1.3Deniliquin −2.9 −1.3 −9.7Marree −3.2 4.8 −8.2

obs pred

-2

0

2

SP

EI

obs pred

-2

0

2

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EI

obs pred

-2

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-2

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obs pred

-2

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SP

EI

a)

c)

e)

g)

b)

d)

f)

h)

Fig. 9.Boxplot of the Standardized Precipitation and Evaporation Index (SPEI) from theob-served and the predicted datasets using the Artificial Neural Network (ANN) models forthe testing period 2006–2012 (a) Bathurst, (b) Gabo Island, (c) Moruya, (d) Palmerville,(e) Wilsons, (f) Yamba, (g) Deniliquin, and (h) Marree.

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Interestingly, the prediction capability of ANNmodel for drought sever-ity, intensity and durationwas quite disparate, station by station aswellas the respective drought property. For example, the prediction forDeniliquin resulted in a relatively large (negative) difference in thepeak intensity (≈−3.2%) whereas for the duration of drought, the(positive) difference recorded was about 1.92%. It was also noteworthythat there was an insignificant difference in the prediction of droughtduration for the case of Yamba, Bathurst and Gabo Island. Thiscontrasted the prediction of drought severity and intensity wheremodest differences in the two properties were evident.

In comparison with studies on rainfall prediction problems inQueensland (e.g. Abbot and Marohasy, 2012, 2014), the predictionscore metrics obtained from current ANN models exhibited relativelybetter performance, as evidenced by higher Coefficient of Determina-tion and smaller Root-Mean-Square-Errors. The present results werealso more accurate than those obtained using Multiple Regression(MR) analysis and ANN models in Victoria where ANN models showedbetter generalization ability for central and west Victoria with correla-tion of 0.68–0.85 and 0.58–0.97, respectively (Mekanik et al., 2013). Inour study, the significantly better performance of the ANN models waspartly attributable to the standardized nature of the drought indexunlike direct simulation of rainfall in previous studies.

Overall the present ANNmodels showed reasonably good predictionskill of the SPEI and therefore, themodeling techniques offers significantpractical benefits for scientists and engineers. Since the drought indexincorporated the impact of rainfall, temperature and evapotranspiration

and can be used a key metric for water stress or water resource assess-ments, predictive models based on the combined influence of theseparameters are of practical relevance to climate risk detection, agricul-tural engineering and ecosystems management. Furthermore, thesepredictive models are attractive to stakeholders who need to considerclosely future soil moisture status and its impact on dryness, moisturetransfer from the surface to the atmosphere, impacts on aridity andthe overall well-being of the natural ecosystems.

5. Summary and conclusion

The prediction of drought is of great importance to many relevant tometeorology, hydrology, water resource management, sustainableagriculture, wildlife conservation and infrastructure. In this study, weapplied machine learning algorithms for predicting the monthlyStandardized Precipitation and Evapotranspiration Index (Begueríaet al., 2013; Vicente-Serrano et al., 2010a, 2011a,b) using climate vari-ables over the period 1915–2012 for eight candidate stations in easternAustralia. The machine learning approach considered was the ArtificialNeural Network (ANN) where the model was trained using the meteo-rological variables (mean rainfall, mean, maximum and minimumtemperatures), the large-scale climate mode indices (Southern Oscilla-tion Index, Pacific Decadal Oscillation, Indian Ocean Dipole, SouthernAnnular Mode) and the Sea Surface Temperatures (Nino 3.0, 3.4, 4.0)as the predictor (input) variables and the output variable was the SPEI.In developing the ANN model, approximately 94% of the input data(1915–2005) were used for training the network and 6% of the data(2006–2012) used for testing the model output.

The basis of this study was to investigate the feasibility of the ANNmodel in encapsulating the nonlinear relationships between input(predictor) variable and output (objective) variable (SPEI) by using atotal of 18 input variables. The performance of models was assessedusing prediction metrics like the spread, distribution of predicted SPEI,Mean Absolute Error, Root-Mean Square Error, Coefficient of Determi-nation, the Willmott's Index of Agreement and Nash–SutcliffeCoefficient of Efficiency. The primary findings of this study are enumer-ated as follows.

1. After trials and errors on the various training algorithms and thehidden transfer and output functions with a total run of 30 differentANN networks tested, the optimum model was chosen usingLevenberg–Marquardt backpropagation training algorithm for train-ing the input data and tangent sigmoid equation for the hidden

79R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

transfer and output function. For the best model, the architecture ofthe network of neurons was a combination of 18–43–1 as theinput–hidden–output neurons. The selection of optimum modelwas based on smallest value of its Root-Mean-Square-Error (0.071),smallest value of Mean-Bias-Error (0.0002) and largest Coefficientof Determination (0.9978) when compared to its counterparts.

2. Based on analysis of scatter plot between predicted and observedSPEI for the test dataset, the gradient reflecting the 1:1 ratio ofagreement was between 0.95 and 1.01, the Coefficient of Determina-tion was between 0.95 and 0.99 and maximum deviation ofsimulations from the observed SPEI was between 0.108 and 0.894.Relative to other stations, the worst predictions acquired were forMarree, which also exhibited the largest difference in the standardderivation of the predicted and observed SPEI.

3. In terms of quantitative statistics averaged over the test set, ANNmodel performed very well in predicting SPEI at all stationsconsidered. This was verified by all-station average value of MeanAbsolute Error (0.0066), Root Mean Square Error (0.0679) and theCoefficient of Determination (0.997). Moreover, this was verifiedemphatically by the Willmott's Index of Agreement and Nash–

Fig. 10. The performance of the ANNmodel for quantifying drought, as measured by the percentperiod (2006–2012) (Severity, S ≡ accumulated negative SPEI after the onset of drought is deteutive months in which drought status is sustained) (Kim et al., 2009; Yevjevich et al., 1967).

Sutcliffe Coefficient of Efficiency, both of which were very close tounity (0.9487 and 0.9928, respectively).

4. Differences in the spread of predicted and observed SPEI werereasonably small for all stations analyzed. This showed that the pre-dictionmodel returned individualmonthly SPEI close to the observedvalue. However, when compared by the actual prediction statistics,the differences in lower quartile were between−5.2% (Palmerville)and +1.4% (Gabo Island). By contrast, the differences in the medianwere between −21.1 (Palmerville) and 4.8% (Marree) and for theupper quartile were −9.7 (Deniliquin) and 4.6% (Moruya). Clearly,the predictions for individual stations exhibited a notable degree ofdiscrepancy, which were attributable to outliers in the model simu-lated dataset.

5. To examine the performance of ANNmodel in predicting the proper-ties of drought events over the test period, the parametersrepresenting the severity, duration and peak intensity of droughtevents were assessed. For all stations considered, error encounteredin quantifying the drought properties was less than 5% althoughthe magnitudes of differences in predicted and observed propertiesfor individual stations were clearly discernible.

age difference between the predicted and the observed properties of drought over the testcted (SPEI b 0); Intensity, I ≡minimum value of the SPEI; Duration, D ≡ sum of the consec-

80 R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

In a nutshell we summarize that the ANN models developed andtested in this study had good prediction skills of themonthly Standard-ized Precipitation and Evapotranspiration Index for stations in the studyregion. More importantly, the success of embedding historical observa-tions of rainfall totals, air temperatures and evapotranspiration rateswith the large-scale climatemode indices and Sea Surface Temperaturesas predictor variables is a promising approach for drought forecastingthat may be used for future prediction of drought using machinelearning algorithm.

Our method for testing combinations of training algorithms, hiddentransfer functions and output equations yielded relative small predic-tion errors and is therefore, suitable for scientists and engineers fortesting its use in various areas of weather prediction, climate changeand drought studies. We do acknowledge that our study developedANN models by optimizing hidden neurons, activation functions anddifferent combinations of training and testing algorithms. However, itwould be beneficial to assess time-lagged contributions of variousinput parameters, and how the different network architectures couldaffect the model performance. Therefore, a rigorous study is warrantedto test the sensitivity of each predictor variable, and the correspondingnetwork architecture, activation and output functions. Nonetheless, incontext of drought prediction, the ANNmodels which have lesser com-plexity involved in the design, development, testing and applicationphases relative to physical models are of great importance to scientistsand engineers, particularly to assist in forecasting of water resources,water use and planning, sustainable agriculture and other areas inhydrologic engineering.

Acknowledgments

The rainfall, temperature and SOI data were supplied by theAustralian Bureau of Meteorology, the PDO data by the Joint Instituteof the Study of the Atmosphere and Ocean (JISAO) and SAM from theBritish Antarctic Survey database, all of which are greatly acknowl-edged. The School of Agricultural, Computational and EnvironmentalSciences (University of Southern Queensland) supported Dr R.C. Deofor research time allocation on collaboration with Prof. Mehmet(Turkey). We thank the two anonymous reviewers whose in-depthfeedback has improved the overall clarity of our paper.

References

Abbot, J., Marohasy, J., 2012. Application of artificial neural networks to rainfall forecast-ing in Queensland, Australia. Adv. Atmos. Sci. 29, 717–730.

Abbot, J., Marohasy, J., 2014. Input selection and optimisation for monthly rainfallforecasting in Queensland, Australia, using artificial neural networks. Atmos. Res.138, 166–178.

Abramowitz, M., Stegun, I.A., 1972. Handbook of Mathematical Functions:With Formulas,Graphs, and Mathematical Tables. Courier Dover Publications.

Acharya, N., Shrivastava, N.A., Panigrahi, B., Mohanty, U., 2013. Development of an artifi-cial neural network based multi-model ensemble to estimate the northeast monsoonrainfall over south peninsular India: an application of extreme learning machine.Clim. Dyn. 1–8.

Ahmad, M., Sinclair, C., Werritty, A., 1988. Log–logistic flood frequency analysis. J. Hydrol.98, 205–224.

Alexander, L., et al., 2006. Global observed changes in daily climate extremes oftemperature and precipitation. J. Geophys. Res. - Atmos. 1984–2012, 111.

Alexandersson, H., 1986. A homogeneity test applied to precipitation data. J. Climatol. 6,661–675.

Allen, R., Smith, M., Pereira, L., Perrier, A., 1994. An update for the calculation of referenceevapotranspiration. ICID Bull. 43, 35–92.

Arora, V.K., 2002. The use of the aridity index to assess climate change effect on annualrunoff. J. Hydrol. 265, 164–177.

Ashok, K., Guan, Z., Yamagata, T., 2003. Influence of the Indian Ocean Dipole on theAustralian winter rainfall. Geophys. Res. Lett. 30 (15). http://dx.doi.org/10.1029/2003GL017926.

Barua, S., Perera, B.J.C., Ng, A.W.M., Tran, D., 2010. Drought forecasting using an aggregat-ed drought index and artificial neural network. J. Water Clim. Chang. 1 (3), 193–206.

Barua, S., Ng, A.W.M., Perera, B.J.C., 2012. Artificial neural network-based droughtforecasting using a non-linear aggregated drought index. J. Hydrol. Eng. 17 (12),1408–1413.

Beguería, S., Vicente-Serrano, S.M., Reig, F., Latorre, B., 2013. Standardized precipitationevapotranspiration index (SPEI) revisited: parameter fitting, evapotranspirationmodels, tools, datasets and drought monitoring. Int. J. Climatol. 34 (10), 3001–3023.

Belayneh, A., Adamowski, J., 2012. Standard precipitation index drought forecasting usingneural networks, wavelet neural networks, and support vector regression. Appl.Comput. Intell. Soft Comput. (Article ID 794061, 13 pp).

Cai, W., Rensch, P.V., Cowan, T., Hendon, H.H., 2011. Teleconnection pathways of ENSOand the IOD and the mechanisms for impacts on Australian rainfall. J. Clim. 24,3910–3923.

Chattopadhyay, S., 2007. Feed forward Artificial Neural Network model to predict the av-erage summer-monsoon rainfall in India. Acta Geophys. 55, 369–382.

Chattopadhyay, S., Chattopadhyay, G., 2008. Comparative study among different neuralnet learning algorithms applied to rainfall time series. Meteorol. Appl. 15, 273–280.

Chow, T., Zhang, G., Lin, Z., Song, C., 2002. Global optimization of absorption chiller systemby genetic algorithm and neural network. Energy Build. 34, 103–109.

Day, K.A., Ahrens, D.G., Peacock, A., 2010. Seasonal Pacific Ocean Temperature Analysis-1(SPOTA-1) as at November 1, 2010. Report Issued by the Queensland Climate ChangeCentre of Excellence. Queensland Government, Brisbane, Australia (2 pp.).

Della-Marta, P., Collins, D., Braganza, K., 2004. Updating Australia's high-quality annualtemperature dataset. Aust. Meteorol. Mag. 53.

Dennis, J.E., Schnabel, R.B., 1983. Numerical Methods for Unconstrained Optimization andNonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ.

Deo, R.C., Sahin, M., 2015. Application of the extreme learning machine algorithm for theprediction of monthly Effective Drought Index in eastern Australia. Atmos. Res. 153,512–525.

Deo, R.C., et al., 2009. Impact of historical land cover change on daily indices of climateextremes including droughts in eastern Australia. Geophys. Res. Lett. 36 (8). http://dx.doi.org/10.1029/2009GL037666.

Dijk, A.I., et al., 2013. The Millennium Drought in southeast Australia (2001–2009): natu-ral and human causes and implications for water resources, ecosystems, economy,and society. Water Resour. Res. 49, 1040–1057.

Fox, D.G., 1981. Judging air quality model performance. Bull. Am. Meteorol. Soc. 62,599–609.

Franks, S.W., Kuczera, G., 2002. Flood frequency analysis: evidence and implications ofsecular climate variability, New South Wales. Water Resour. Res. 38 (20-21-20-27).

Hagan, M.T., Menhaj, M., 1994. Training feed-forward networks with theMarquardt algo-rithm. IEEE Trans. Neural Networks 5 (6), 989–993.

Hanson, R.L., 1988. Evapotranspiration and droughts. In: Paulson, R.W., Chase, E.B.,Roberts, R.S., Moody, D.W. (Eds.), Compilers, National Water Summary, pp. 99–104.

Hargreaves, G.H., 1994. Defining and using reference evapotranspiration. J. Irrig. Drain.Eng. 120, 1132–1139.

Harrington, P.B., 1993. Sigmoid transfer functions in backpropagation neural networks.Anal. Chem. 65, 2167–2168.

Haykin, S., 2010. Neural Networks: A Comprehensive Foundation, 1994. MacMillan, NewJersey.

Haylock, M., Nicholls, N., 2000. Trends in extreme rainfall indices for an updated highquality data set for Australia, 1910–1998. Int. J. Climatol. 20, 1533–1541.

Hendon, H.H., Thompson, D.W., Wheeler, M.C., 2007. Australian rainfall and surface tem-perature variations associated with the Southern Hemisphere annular mode. J. Clim.20, 2452–2467.

Holper, P.N., 2011. Climate Change, Science Information Paper: Australian Rainfall: Past.CSIRO, Present and Future.

Hope, P., Timbal, B., Fawcett, R., 2010. Associations between rainfall variability in thesouthwest and southeast of Australia and their evolution through time. Int.J. Climatol. 30, 1360–1371.

Hosking, J.R., 1990. L-moments: analysis and estimation of distributions using linear com-binations of order statistics. J. R. Stat. Soc. Ser. B Methodol. 105–124.

Hudson, D., Alves, O., Hendon, H.H., Marshall, A.G., 2011. Bridging the gap betweenweather and seasonal forecasting: intraseasonal forecasting for Australia. Q. J. R.Meteorol. Soc. 137, 673–689.

Inquiry, Q.F.C.o., 2011. Queensland Foods Commission of Inquiry: Interim Report, 1180pp. Queensland Government, Brisbane, Queensland, Australia (1180pp.).

Jones, D.A., Wang, W., Fawcett, R., 2009. High-quality spatial climate data-sets forAustralia. Aust. Meteorol. Oceanogr. J. 58, 233.

Karlik, B., Olgac, A.V., 2011. Performance analysis of various activation functions in gener-alized MLP architectures of neural networks. Int. J. Artif. Intell. Expert Syst. 1,111–122.

Kiem, A.S., Franks, S.W., 2004. Multi‐decadal variability of drought risk, eastern Australia.Hydrol. Process. 18, 2039–2050.

Kiem, A.S., Franks, S.W., Kuczera, G., 2003. Multi‐decadal variability of flood risk. Geophys.Res. Lett. 30 (2). http://dx.doi.org/10.1029/2002GL015992.

Kim, D.-W., Byun, H.-R., Choi, K.-S., 2009. Evaluation, modification, and application of theEffective Drought Index to 200-Year drought climatology of Seoul, Korea. J. Hydrol.378, 1–12.

Krause, P., Boyle, D., Bäse, F., 2005. Comparison of different efficiency criteria for hydro-logical model assessment. Adv. Geosci. 5, 89–97.

Kuligowski, R.J., Barros, A.P., 1998. Experiments in short-term precipitation forecastingusing artificial neural networks. Mon. Weather Rev. 126, 470–482.

Kumar, M., Raghuwanshi, N., Singh, R., 2011. Artificial neural networks approach inevapotranspiration modeling: a review. Irrig. Sci. 29, 11–25.

Latif, M., Kleeman, R., Eckert, C., 1997. Greenhouse warming, decadal variability, or ElNino? An attempt to understand the anomalous 1990s. J. Clim. 10, 2221–2239.

Lavery, B., Joung, G., Nicholls, N., 1997. An extended high-quality historical rainfall datasetfor Australia. Aust. Meteorol. Mag. 46, 27–38.

Legates, D.R., McCabe, G.J., 1999. Evaluating the use of “goodness-of-fit” measures inhydrologic and hydroclimatic model validation. Water Resour. Res. 35, 233–241.

81R.C. Deo, M. Şahin / Atmospheric Research 161–162 (2015) 65–81

Li, W.-G., Yi, X., Hou, M.-T., Chen, H.-L., Chen, Z.-L., 2012. Standardized precipitationevapotranspiration index shows drought trends in China. Chin. J. Eco-Agric. 5, 021.

Lippman, R., 1987. An introduction to computing with neural nets. IEEE ASSP Mag. 4,4–22.

Mantua, N.J., Hare, S.R., Zhang, Y., Wallace, J.M., Francis, R.C., 1997. A Pacific interdecadalclimate oscillation with impacts on salmon production. Bull. Am. Meteorol. Soc. 78,1069–1079.

Marquardt, D., 1963. An algorithm for least-squares estimation of nonlinear parameters.SIAM J. Appl. Math. 11 (2), 431–441.

Marshall, G.J., 2003. Trends in the Southern Annular Mode from observations andreanalyses. J. Clim. 16, 4134–4143.

Masinde, M., 2013. Artificial neural networks models for predicting effective droughtindex: factoring effects of rainfall variability. Mitig. Adapt. Strateg. Glob. Chang. 1–24.

McAlpine, C., et al., 2009. A continent under stress: interactions, feedbacks and risks asso-ciated with impact of modified land cover on Australia's climate. Glob. Chang. Biol.15, 2206–2223.

McCulloch, W.S., Pitts, W., 1943. A logical calculus of the ideas immanent in nervous ac-tivity. Bull. Math. Biophys. 5, 115–133.

McKee, T.B., Doesken, N.J., Kleist, J., 1993. The relationship of drought frequency and du-ration to time scales. Proceedings of the 8th Conference on Applied Climatology.American Meteorological Society, Boston, MA, pp. 179–183.

Mekanik, F., Imteaz, M.A., 2014. Evaluating the effect of single and combined climatemodes on rainfall predictability. IAENG Transactions on Engineering Technologies.Springer, pp. 571–581.

Mekanik, F., Imteaz, M., Gato-Trinidad, S., Elmahdi, A., 2013. Multiple regression and Arti-ficial Neural Network for long-term rainfall forecasting using large scale climatemodes. J. Hydrol. 503, 11–21.

Meneghini, B., Simmonds, I., Smith, I.N., 2007. Association between Australian rainfall andthe southern annular mode. Int. J. Climatol. 27, 109–121.

Menne, M.J., Williams Jr., C.N., 2009. Homogenization of temperature series via pairwisecomparisons. J. Clim. 22, 1700–1717.

Morid, S., Smakhtin, V., Bagherzadeh, K., 2007. Drought forecasting using artificial neuralnetworks and time series of drought indices. Int. J. Climatol. 27, 2103–2111.

Moustris, K.P., Ziomas, I.C., Paliatsos, A.G., 2010. 3-Day-ahead forecasting of regional pol-lution index for the pollutants NO2, CO, SO2, and O3 using artificial neural networks inAthens, Greece. Water Air Soil Pollut. 209, 29–43.

Moustris, K.P., Larissi, I.K., Nastos, P.T., Paliatsos, A.G., 2011. Precipitation forecast usingartificial neural networks in specific regions of Greece. Water Resour. Manag. 25,1979–1993.

Mpelasoka, F., Hennessy, K., Jones, R., Bates, B., 2008. Comparison of suitable drought in-dices for climate change impacts assessment over Australia towards resource man-agement. Int. J. Climatol. 28, 1283–1292.

Murphy, B.F., Timbal, B., 2008. A review of recent climate variability and climate change insoutheastern Australia. Int. J. Climatol. 28, 859–879.

Nash, J., Sutcliffe, J., 1970. River flow forecasting through conceptual models part I—adiscussion of principles. J. Hydrol. 10, 282–290.

Nastos, P., Paliatsos, A., Koukouletsos, K., Larissi, I., Moustris, K., 2014. Artificial neural net-works modeling for forecasting the maximum daily total precipitation at Athens,Greece. Atmos. Res. 144, 141–150.

Ortiz-García, E., Salcedo-Sanz, S., Casanova-Mateo, C., 2014. Accurate precipitation predic-tion with support vector classifiers: a study including novel predictive variables andobservational data. Atmos. Res. 139, 128–136.

Paulescu, M., Tulcan‐Paulescu, E., Stefu, N., 2011. A temperature-based model for globalsolar irradiance and its application to estimate daily irradiation values. Int. J. EnergyRes. 35, 520–529.

Pereira, L.S., Cordery, I., Iacovides, I., 2009. Coping with water scarcity. Addressing theChallenges. 382. Springer, Dordrecht.

Potop, V., Boroneanţ, C., Možný, M., Štěpánek, P., Skalák, P., 2012. Observed Evolution ofDrought Episodes Assessed With the Standardized Precipitation EvapotranspirationIndex (SPEI) Over the Czech Republic. EGU General Assembly.

Power, S., et al., 1999. Decadal climate variability in Australia during the twentieth centu-ry. Int. J. Climatol. 19, 169–184.

Riebsame, W.E., Changnon Jr., S.A., Karl, T.R., 1991. Drought and natural resourcesmanagement in the United States. Impacts and Implications of the 1987–89 Drought.Westview Press Inc.

Şahin, M., 2012. Modelling of air temperature using remote sensing and artificial neuralnetwork in Turkey. Adv. Space Res. 50, 973–985.

Şahin, M., 2013. Comparison of modelling ANN and ELM to estimate solar radiation overTurkey using NOAA satellite data. Int. J. Remote Sens. 34, 7508–7533.

Şahin, M., Kaya, Y., Uyar, M., 2013. Comparison of ANN and MLR models for estimatingsolar radiation in Turkey using NOAA/AVHRR data. Adv. Space Res. 51, 891–904.

Şahin, M., Kaya, Y., Uyar, M., Yıldırım, S., 2014. Application of extreme learning machinefor estimating solar radiation from satellite data. Int. J. Energy Res. 38, 205–212.

Saji, N., Goswami, B.N., Vinayachandran, P., Yamagata, T., 1999. A dipolemode in the trop-ical Indian Ocean. Nature 401, 360–363.

Saji, N., Ambrizzi, T., Ferraz, S., 2005. Indian Ocean Dipolemode events and austral surfaceair temperature anomalies. Dyn. Atmos. Oceans 39, 87–101.

Şenkal, O., 2010. Modeling of solar radiation using remote sensing and artificial neuralnetwork in Turkey. Energy 35, 4795–4801.

Şenkal, O., Kuleli, T., 2009. Estimation of solar radiation over Turkey using artificial neuralnetwork and satellite data. Appl. Energy 86, 1222–1228.

Şenkal, O., Yıldız, B.Y., Şahin, M., Pestemalcı, V., 2012. Precipitable water modellingusing artificial neural network in Cukurova region. Environ. Monit. Assess. 184,141–147.

Seqwater, 2011. January 2011 Flood Event: Report on the Operation of Somerset Dam andWivenhoe Dam REVIEW OF HYDROLOGICAL ISSUES Queensland Government(Melbourne, Australia, (p. 77pp.)).

Singh, V., Guo, H., Yu, F., 1993. Parameter estimation for 3-parameter log–logistic distribu-tion (LLD3) by Pome. Stoch. Hydrol. Hydraul. 7, 163–177.

Sözen, A., Ali Akçayol, M., 2004. Modelling (using artificial neural-networks) the perfor-mance parameters of a solar-driven ejector-absorption cycle. Appl. Energy 79,309–325.

Suppiah, R., Hennessy, K.J., 1998. Trends in total rainfall, heavy rain events and number ofdry days in Australia, 1910–1990. Int. J. Climatol. 18, 1141–1164.

Thornthwaite, C.W., 1948. An approach toward a rational classification of climate. Geogr.Rev. 55–94.

Timbal, B., Fawcett, R., 2013. A historical perspective on southeastern Australian rainfallsince 1865 using the instrumental record. J. Clim. 26, 1112–1129.

Timbal, B., et al., 2010. Understanding the Anthropogenic Nature of the Observed RainfallDecline Across South Eastern Australia. Centre for Australian Weather and ClimateResearch.

Tiwari, M.K., Adamowski, J., 2013. Urban water demand forecasting and uncertaintyassessment using ensemble wavelet‐bootstrap‐neural network models. WaterResour. Res. 49, 6486–6507.

Torok, S., Nicholls, N., 1996. A historical annual temperature dataset. Aust. Meteorol. Mag.45.

Trenberth, K.E., 1984. Signal versus noise in the Southern Oscillation. Mon. Weather Rev.112, 326–332.

Trenberth, K.E., et al., 2014. Global warming and changes in drought. Nat. Clim. Chang. 4,17–22.

Ulgen, K., Hepbasli, A., 2002. Comparison of solar radiation correlations for Izmir, Turkey.Int. J. Energy Res. 26, 413–430.

Ummenhofer, C.C., et al., 2009. What causes southeast Australia's worst droughts?Geophys. Res. Lett. 36 (4). http://dx.doi.org/10.1029/2008GL036801.

Verdon-Kidd, D.C., Kiem, A., 2009. On the relationship between large-scale climate modesand regional synoptic patterns that drive Victorian rainfall. Hydrol. Earth Syst. Sci. 13,467.

Verdon-Kidd, D.C., Kiem, A.S., 2010. Quantifying drought risk in a nonstationary climate.J. Hydrometeorol. 11, 1019–1031.

Verdon‐Kidd, D.C., Kiem, A.S., 2009. Nature and causes of protracted droughts in south-east Australia: comparison between the Federation, WWII, and Big Dry droughts.Geophys. Res. Lett. 36 (22). http://dx.doi.org/10.1029/2009GL041067.

Vicente-Serrano, S.M., Beguería, S., López-Moreno, J.I., 2010a. A multiscalar drought indexsensitive to global warming: the standardized precipitation evapotranspirationindex. J. Clim. 23, 1696–1718.

Vicente-Serrano, S.M., Beguería, S., López-Moreno, J.I., Angulo, M., El Kenawy, A., 2010b. Anew global 0.5 gridded dataset (1901–2006) of a multiscalar drought index: compar-ison with current drought index datasets based on the Palmer Drought SeverityIndex. J. Hydrometeorol. 11, 1033–1043.

Vicente-Serrano, S.M., et al., 2012a. Performance of drought indices for ecological, agricul-tural, and hydrological applications. Earth Interact. 16, 1–27.

Vicente-Serrano, S.M., Zouber, A., Lasanta, T., Pueyo, Y., 2012b. Dryness is acceleratingdegradation of vulnerable shrublands in semiarid Mediterranean environments.Ecol. Monogr. 82, 407–428.

Vicente‐Serrano, S.M., Beguería, S., López‐Moreno, J.I., 2011a. Comment on “Characteris-tics and trends in various forms of the Palmer Drought Severity Index (PDSI) during1900–2008” by Aiguo Dai. J. Geophys. Res. Atmos. (1984–2012), 116.

Vicente‐Serrano, S.M., et al., 2011b. A multiscalar global evaluation of the impact of ENSOon droughts. J. Geophys. Res. Atmos. (1984–2012), 116.

Vogl, T., Mangis, J., Rigler, A., Zink,W., Alkon, D., 1988. Accelerating the convergence of thebackpropagation method. Biol. Cybern. 59, 257–263.

Wilhite, D.A., 1996. A methodology for drought preparedness. Nat. Hazards 13, 229–252.Wilhite, D.A., Hayes, M.J., 1998. Drought planning in the United States: status and future

directions. The Arid Frontier. Springer, pp. 33–54.Wilhite, D.A., Hayes, M.J., Knutson, C., Smith, K.H., 2000. Planning for Drought: Moving

From Crisis to Risk Management. Wiley Online Library.Willmott, C.J., 1981. On the validation of models. Phys. Geogr. 2, 184–194.Willmott, C.J., 1982. Some comments on the evaluation of model performance. Bull. Am.

Meteorol. Soc. 63, 1309–1313.Willmott, C.J., 1984. On the evaluation of model performance in physical geography. Spa-

tial Statistics and Models. Springer, pp. 443–460.Willmott, C.J., Robeson, S.M., Matsuura, K., 2012. A refined index of model performance.

Int. J. Climatol. 32, 2088–2094.Wu, X., Hongxing, C., Flitman, A., Fengying,W., Guolin, F., 2011. Forecasting monsoon pre-

cipitation using artificial neural networks. Adv. Atmos. Sci. 18, 950–958.Yao, Y., Liang, S., Qin, Q., Wang, K., Zhao, S., 2011. Monitoring global land surface drought

based on a hybrid evapotranspirationmodel. Int. J. Appl. Earth Obs. Geoinf. 13, 447–457.Yevjevich, V., et al., 1967. An Objective Approach to Definitions and Investigations of Con-

tinental Hydrologic Droughts. Colorado State University Fort Collins.Yu, M., Li, Q., Hayes, M.J., Svoboda, M.D., Heim, R.R., 2014. Are droughts becoming more

frequent or severe in China based on the standardized precipitation evapotranspira-tion index: 1951–2010? Int. J. Climatol. 34, 545–558.

Zhang, Y., Wallace, J.M., Battisti, D.S., 1997. ENSO-like interdecadal variability: 1900–93.J. Clim. 10, 1004–1020.

Zhao, M., Hendon, H.H., 2009. Representation and prediction of the Indian Ocean dipole inthe POAMA seasonal forecast model. Q. J. R. Meteorol. Soc. 135, 337–352.