faa

sgh

g, S

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the catchments and so on. Although a physically-based simulation and forecasting purposes. An ANN withmoderate number of hidden layer(s) is capable of approxi-mating any smooth function to any desired degree ofaccuracy. In addition, ANNs are computationally robust,having the ability to learn and generalize from examplesto produce meaningful solutions to problems even when

* Corresponding author. Address: Faculty of Engineering, ShirazUniversity, Iran.

E-mail addresses: mm_nasseri@yahoo.com (M. Nasseri), kasghari@cc.iut.ac.ir (K. Asghari), abedini@shirazu.ac.ir (M.J. Abedini).

Available online at www.sciencedirect.com

Expert Systems with Applications1. Introduction

Rainfall forecasting is one of the most dicult andimportant processes of the hydrologic cycle. This is largelyrelated to the variability it displays over a wide range ofscales both in time and space. Flash ooding, being a prod-uct of intense rainfall, is a life-threatening phenomenon.Developing a rainfall forecasting and ood warning systemfor typical catchments is not considered a simple task. Bothinternal and external characteristics of rainfall eld dependon many factors including: pressure, temperature, windspeed and its direction, meteorological characteristics of

approach for rainfall forecasting has several advantages,given the short time scale, the small catchments area, andthe massive costs associated with collecting the requiredmeteorological data, it is not a feasible alternative in mostcases because it involves many variables which are inter-connected in a very complicated way. An approach basedon statistical mechanics which attempts to model the pat-tern of the underlying physical processes manifested inthe observed rainfall data in a lumped articial neural net-works (ANNs) is an ecient alternative (Govindaraju,2000a). This complexity and nonlinearity inherent in rain-fall pattern makes it attractive to try neural network forAbstract

Rainfall forecasting plays many important role in water resources studies such as river training works and design of ood warningsystems. Recent advancement in articial intelligence and in particular techniques aimed at converting input to output for highly non-linear, non-convex and dimensionalized processes such as rainfall eld, provide an alternative approach for developing rainfall forecast-ing model. Articial neural networks (ANNs), which perform a nonlinear mapping between inputs and outputs, are such a technique.Current literatures on articial neural networks show that the selection of network architecture and its ecient training procedure aremajor obstacles for their daily usage. In this paper, feed-forward type networks will be developed to simulate the rainfall eld and a so-called back propagation (BP) algorithm coupled with genetic algorithm (GA) will be used to train and optimize the networks. The tech-nique will be implemented to forecast rainfall for a number of times using rainfall hyetograph of recording rain gauges in the UpperParramatta catchment in the western suburbs of Sydney, Australia. Results of the study showed the structuring of ANN network withthe input parameter selection, when coupled with GA, performed better compared to similar work of using ANN alone. 2007 Elsevier Ltd. All rights reserved.

Keywords: Rainfall forecasting; Articial neural networks; Genetic algorithms; Input determinationOptimized scenario for rainalgorithm coupled with

M. Nasseri a,b,*, K. Aa Faculty of Engineerin

b Department of Water and Environmental Ec Department of Civil Engineering,

d Department of Civil Engineering, Facu0957-4174/$ - see front matter 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.eswa.2007.08.033ll forecasting using geneticrticial neural network

ari c, M.J. Abedini d

hiraz University, Iran

eering, Sazeh Pardazi Co. Engineering, Iran

han University of Technology, Iran

of Engineering, Shiraz University, Iran

www.elsevier.com/locate/eswa

35 (2008) 14151421

Expert Systemswith Applications

iththe input data contain errors or are incomplete. Theapplication of an ANN, however, involves a complicateddevelopment process. If carelessly used, it can easily learnirrelevant information (noises) in the system (over-tting).Such a model might be doing well in predicting past inci-dents, but unable to predict future events. Govindaraju(2000a, 2000b) reported a number of studies which haveused ANNs to forecast rainfall over a short time interval.In the literature, French, Krajewski, and Cuykendal(1992) developed the rst simulation scheme, whereby syn-thetically generated rainfall storms were used to both cali-brate and validate ANN models. The results of theirinvestigation indicate that an ANN is quite capable of cap-turing the complex relationship associated with spatiotem-poral evolution of rainfall inherent in a complex rainfallsimulation model. Tohma and Igata (1994) used three-layerANNs to predict rainfall elds based on visible and infra-red remote sensing cloud images. An ANN model to fore-cast summer monsoon rainfall over India was developed byNavone and Ceccatto (1994). They used a mixed andhybrid type of ANNs. Hsu, Gupta, Sorooshian, and Gao(1996, 1997) have developed a modied counter propaga-tion ANN for transforming satellite infrared images torainfall rates over a catchment. Their approach was likethe one utilized by Rizzo and Dougherty (1994), in thatboth used a Kohonen hidden layer and a Grossberg outputlayer in the three-layer structure.

Kuligowski and Barros (1998) have presented an ANNapproach for short term rainfall forecasting. Their modelused feed-forward neural network (FFNN) architecturewith upper atmospheric wind direction and antecedentrainfall data from a rain gauge network to generate a06 h precipitation (short term rainfall) forecast for a tar-get location. Luk, Ball, and Sharma (2000, 2001) havedeveloped and presented a scheme for rainfall eld mod-eling. They used the recorded rainfall as time series to feedthe models. By using rainfall series events from the net-work of rain gauges as input(s), they have predicted thedepth of precipitation in the next time step in a target raingauge. Modication of their modeling and the basin usedby them is the core of this paper. Along the same line ofresearch, Ramirez, Velhob, and Ferreira (2005) developedan analysis for two statistical models for rainfall forecastin the Sao Paulo State, Brazil. It was concluded thatbetter performance of ANN model compared to multiplelinear regression (MLR) model can be achieved especiallywith nonlinear phenomenon such as rain forecasting.Importance of input determination for ANN models stud-ied by Bowden, Dandy, and Maier (2005a, 2005b) andtwo methodologies, namely partial mutual information(PMI) and self-organizing map (SOM) integrated with agenetic algorithm and general regression neural network,tested with synthetic data were presented. The results indi-cated improvement in input selection by PMI as it wasable to exclude all insignicant inputs. Compare to

1416 M. Nasseri et al. / Expert Systems wPMI, SOM determines the inputs in two steps, rst toreduce the input dimensionality and then to select thesubset of important model inputs using the GA and theregression network. And the last in the literature, Linand Chen (2005) have developed a two hidden layersneural network to forecast typhoon rainfall in a riverbasin in northern Taiwan. The eect of nearby stationsis considered for advancing the model performance. Inorder to detect the invaluable nearby stations and improvethe network performance a semivariogram is also applied.Results indicate that applying too much spatial rainfallinformation cannot improve the models prediction abil-ity, because the inclusion of irrelevant information canadd noise on the network and reduce the modelperformance.

Current literatures on ANNs show that selection of net-work architecture (both input selection and network archi-tecture) and its ecient training are very time consuming,and considered major obstacles for their day to day appli-cations. In this paper, event-based modeling is selected as ahelpful way to be closer to online prediction. The currentarticle proposes a new way to improve rainfall estimationby optimizing the network scenarios by coupling MLP withGA. Among the most important parameters are input(s)selection and the network weights associated with eachneuron. The eect of each rain gauge on the target stationwill be analyzed by sensitivity analysis technique and thepowerful method of cross-validation will be used to moni-tor the over training phenomena as well.

2. Articial neural networks and genetic algorithm

ANN has been innovated as a exible mathematicalstructure based on the biological functioning of the ner-vous system. Sarle (1994) argued that the same roots ofclassical regression can be found in ANNs originally devel-oped as a model of information storage and computingusing neuronal processes found in nature (Hykin, 1999).The most popular type of ANN, i.e. multilayer feed-for-ward neural network (MFNN), the three-layer feed-for-ward neural network (TFNN), is shown in Fig. 1. ANNtraining is performed to determine the weights associatedwith the network in an optimal way using an appropriatealgorithm. Many researchers have reported diculties intraining the network parameters caused by parameterinterdependence, parameter insensitivity and multi-localoptima (Hykin, 1999). Montana and Davis (1988) andManiezzo (1994) applied GA in training a BPNN. In theirworks, GA determined the best topology of ANNs. ANNhas to go through three phases for its operational applica-tion. In the rst phase, a subset of inputoutput datasetS1 x1; d1; x2; d2; . . . ; xp1 ; dp1 is used to train thenetworks (calibration phase) while in the second phase,another subset of inputoutput dataset S2 x01; d 01;x02; d 02; . . . ; x0p2 ; d

0p2 is used to validate the calibrated net-

works. Imrie, Durucan, and Korre (2000) suggested tohave an intervening phase, so-called the testing phase,

Applications 35 (2008) 14151421whereby a third subset of dataset S3 x001; d 001;x002; d 002; . . . ; x00p3 ; d

00p3 is used to guide the network to test

4. Application

r feed-forward articial neural network.

ith Applications 35 (2008) 14151421 1417over training (over generalization) phenomena duringtraining phase. In this case, ANN training exercise becomesan unconstrained, nonlinear optimization problem in theweight space, and an appropriate algorithm may be usedto solve this problem. In the ANN testing phase, the objec-tive is to determine the suitability of the weighting coe-cients with regard to over-tting process.

GA is considered to be a heuristic, stochastic, combina-torial, optimization technique based on the biological pro-cess of natural evolution developed by Holland (1975).Goldberg (1989) and Michalewicz (1992) discussed themechanism and robustness of GA in solving nonlinearoptimization problems. Three heuristic processes of repro-

Fig. 1. The structure of a three-laye

M. Nasseri et al. / Expert Systems wduction, crossover, and mutation are applied probabilisti-cally to discrete decision variables that are coded intobinary or real numbers strings. In this article, GA will beutilized eectively to determine the weights correspondingto various connections.

3. Sensitivity analysis

Sensitivity analysis should be considered an essentialpace to all mathematical-based modeling. The main advan-tage of performing sensitivity analysis is to identify sensi-tive parameters or processes associated with modeloutput (Skaggs & Barry, 1996). In ANN modeling, likeany mathematical-based model, sensitivity analysis pro-vides feedback as to which input parameters are the mostsignicant. It has to be emphasized that computation ofsensitivity coecients in a typical inputoutput model isnot a trivial task as we are not faced with a closed formfunction, but a complex procedure to convert input to out-put. For the networks which are developed in this research,sensitivity coecients are computed by using mean value ofeach parameter as a base value, having a bound dened bystandard deviation.Recording precipitation gauges from the Upper Parram-atta River basin were chosen for this study. The catchmentis located in the western suburbs of Sydney, Australia(Fig. 2) with a catchment size of about 112 km2. Withinthe catchment, the land use is typical of urban environmentwith a mix of commercial, agricultural and parkland areas.In the study area, there are fourteen recording rain gauges.The data set had a length of four years consisting of event-wise recording precipitation from 1996 to 2000. The tempo-ral resolution of rainfall measurement for all fourteen rainFig. 2. Location of the study area and positions of 14 recording raingauges, after Luk et al. (2000).

gauges is 5-min interval. After doing some sort of prelimin-ary exploratory data analysis, a total of 26 storm eventswere selected keeping zeros among data sets for synchroni-zation purposes. Eighteen of the events were used for train-ing, four events for validation and the other four fortesting. Due to chaotic behavior of rainfall eld, some sortof transformation has been implemented to reduce the var-iance of variation, in order to achieve better performanceand faster convergence in training procedure. The transfor-mation, y = 0.5Log10(x + 1), was used for the input data(Luk et al., 2000, 2001); where x is the original rainfall dataand y is the data after transformation.

modeling the rainfall, an ANN procedure (MFNN) inte-

grated with an evolutionary optimization method such asGA was applied. The model input(s), the most eectiveneighborhood stations and their rainfall lag times, will be

Table 1Parameter and comparative results of various models

Models Time step (min) Pc% Pm% MSE NMSE R2

1 5 92 1.2 0.007 0.161 0.842 10 96 1.4 0.020 0.351 0.663 10 94 1.2 0.030 0.400 0.744 15 96 1.2 0.009 0.280 0.715 15 94 1.2 0.010 0.310 0.76 15 96 1.2 0.121 0.002 0.997 15 96 1.2 0.018 0.360 0.66

7263 7265 7267 7269 7273 7283 7285 7299

0.01 0.05 0.01 0.05 0.03 0.0 0.05 0.020.05 0.0 0.0 0.06 0.0 0.06 0.09 0.00.09 0.11 0.0 0.18 0.0 0.09 0.16 0.00.0 0.09 0.01 0.04 0.03 0.0 0.1 0.13 0.11 0.0 0.09 0.14

0.02 0.03 0.02 0.03 0.02 0.0 0.00 0.020.02 0.0 0.1 0.0 0.02 0.0 0.0 0.0

Table 4Results of sensitivity analysis for models 6 and 7

Models Previous lags

1 2 3 4

6 1.24 0.23 0.08 07 0.32 0.18 0.1 0

Cumulative Rainfall Prediction

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Com

pute

d

1418 M. Nasseri et al. / Expert Systems with Applications 35 (2008) 14151421Table 2Results of sensitivity analysis for network modeling by discrete data

Models Sensitivity of target station to stations Nos.

7251 7253 7255 7257 7259 7261

First lag

1 0.01 0.00 0.05 0.01 0.06 0.062 0.0 0.0 0.15 0.0 0.12 0.23 0.0 0.04 0.19 0.0 0.1 0.194 0.00 0.0 0.1 0.07 0.12 0.155 0.0 0.08 0.15 0.1

Second lag

1 0.02 0.02 0.0 0.0 0.00 0.022 0.0 0.0 0.0 0.06 0.0 0.05. Discussion of test results

Rainfall is illustrative of a nonlinear process and itsforecasting with relatively limited data makes it very com-plex phenomenon. To overcome part of this complexity in3 0.03 0.0 0.05 0.0 0.0 0.03 04 0.06 0.01 0.02 0.0 0.06 0.00 05 0.0 0.0 0.0 0.0 0.02 0

Table 3Results of mean sensitive coecients (SC) for model 4 rank the most eective

Stations Nos.

7251 7253 7255 7257 7259

Mean of SC 0.002 0 0.05 0.08 0.14

Distance-ranked with respect totarget station

5 8 6 13 70 0.2 0.4 0.6 0.8Observed

Fig. 3a. Computed versus observed values for model 6..06 0.0 0.04 0.0 0.0 0.05 0.0 0.02

.05 0.0 0.0 0.0 0.0 0.0 0.0 0.0

.0

station

7261 7263 7265 7267 7269 7273 7283 7285 7299

0.13 0 0.1 0.003 0.02 0.02 0 0.09 0.14

* 9 1 12 2 4 3 10 11

crossover probability (Pc) varies between 92% and 96%.Evaluation of network performance was achieved throughcomputation of three good tness criteria, namely, meansquare error (MSE), normal mean square error (NMSE)and coecient of determination (R2). Table 1 summarizesvarious experimental runs based on GA parameters. Forthe rst ve models (data in discrete form), two previouslags of all surrounding recording rain gauges are used toforecast current rainfall depth at the rain gauge of interest(Station No. 7261). In models 6 and 7, only rainfall infor-mation from the target station, with several subsequentlags, were used as input data. According to Bowden et al.(2005a), mathematical sensitivity analysis is implementedto validate selected input parameters with GA.

Table 2 presents the result of sensitivity analysis for therst ve models using rainfall data from all rain gaugesduring the training phase as input parameter. Zeros inTable 2 indicate gauges in which the GA algorithm disqual-

Discrete Rainfall Prediction

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.1 0.2 0.3 0.4 0.5Observed

Com

pute

dM. Nasseri et al. / Expert Systems with Applications 35 (2008) 14151421 1419derived from optimized ANNs by GA to achieve an e-cient input conguration for minimum error. Basically,by detecting eective inputs, the best input combination(s)for intelligence prediction will appear. Delineation of opti-mum lag time(s) at a particular location, investigation ofthe extend to which inclusion of spatial information mightimprove network performance, and assessment of perfor-mance indicator with regard to application of cumulativeversus discrete data were addressed in this paper as well.

Seven cases of simulation models have been selected toillustrate the performance of the proposed technique. Theseruns dier from one another mainly on the genetic algo-rithm parameters (i.e. Pm and Pc), surrounding rain gaugesused, number of time lags associated with each rain gauge,temporal resolution of rainfall events, and data type

Fig. 3b. Computed versus observed values for model 7.(cumulative versus discrete). The probability of mutation(Pm) varied, traditionally, between 1.2% and 1.4%, while

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 51 101 151 201 251

Elev

atio

n (m

)

Time L

Cumulative Ra

Fig. 4a. Estimated and observed events in timied them either by generating an optimized topology orleft them out based on error minimization as sources ofinput data because of their ineectiveness to predict currentrainfall of the target station. The sensitivity coecientsindicated by - in the 5th model are those eliminated man-ually based on the results obtained in previous model(model four) and they include those gauges with coe-cients of small values (indication of ineectiveness) in orderto reduce the execution time of the model.

Table 2 also reveals that while the rainfall data from therst lag appeared to be relatively sensitive to the target raingauge, the data from the second lag is almost very ineec-tive in predicting the target rainfall. Another importantresult drawn from Table 2 is that when the time resolutiongradually increased in the simulation model, the most eec-tive stations in predicting the target rainfall would appear.Besides the target station itself, stations 7259, 7265, 7285and 7299 have the major contribution on forecasting andthey are not necessarily the closest ones to target station,

301 351 401 451 501 551

Computed

Observed

infall Predictionag (Min)e series form for experimental runs #6.

301 401 501

Observed

Computed

e Lag (Min)

ainfall Prediction

n time series form for experimental runs #7.

ith Applications 35 (2008) 14151421as Luk et al. (2000) concluded in their paper. This is alsoobserved in Table 3 particularly for the model 4, whenthe most eective stations are those in which they rank 7,10, 11, and 13 distance-wise with respect to target station.The sensitivity coecients are average value of training,validation and testing phases.

Table 4 provides the sensitivity coecients of models 6and 7 using cumulative and discrete data respectively. Inboth models, networks with ve lags were attempted.Cumulative-type data as input to the ANN model has sig-nicant advantage over the discrete-type data, since boththe NMSE and R2 error measures increase in model 7.The results from both models validate the fact that the rsttwo lags have a major contribution to forecast the currentrainfall depth at the station of interest, implying short

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1 101 201

Elev

atio

n (m

)

Tim

Discrete R

Fig. 4b. Estimated and observed events i

1420 M. Nasseri et al. / Expert Systems wmemory of rainfall in this region. Also, the convergenceof neural network model deteriorated substantially byusing the rainfall information further than the rst twolags.

Fig. 3a and 3b shows scatter plots of the forecast versusobserved rainfall for models 6 and 7. These plots highlightthe superiority of the cumulative over discrete data whenthey are used as input parameters. Accordingly, Fig. 4aand 4b show the time series of rainfall forecast by thetwo models for four dierent rainfall events. Once again,the cumulative data captures and forecasts the timingand magnitude of observed rainfall in a better way com-pared to discrete data.

Although in previous studies such as the one conductedby Luk et al. (2000, 2001), indicated that the rst two lagshave major contribution in forecasting the rainfall inselected station, this research clearly pointed out that moreaccurate and detailed information can be obtained afterdelineating the eective lag times with respect to the targetstation. Correlation of the lag times can be determinedthrough a statistical analysis such as partial auto-correla-tion function (PACF) of the data series in delineating aunique input vector that best represents the underlying pro-cesses. This was proved with an application of PACF anal-ysis, rst applied by Sudheer, Gosain, and Ramasastri(2002), with the data series used in this problem in delineat-ing a unique input vector that best represents the underly-ing processes. Fig. 5a and 5b shows the autocorrelationplot for the recording rain gauge of interest (i.e. 7261 sta-tion) along with 95% and 99% condence limits consider-ing data in cumulative and discrete mode. Carefulanalysis of Tables 2 and 4 clearly conrm the fact thatthe rst lag has a major contribution, particularly in themodel 6, and other lags fall outside the condence interval.This implies that this tool can be used eectively to delin-eate optimum time lag and consequently network structureespecially in model with cumulative data type.0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6Time Lag

Corr

elat

ion

Coef

ficie

nt

PACF Coefficient

Cofidence Limit 99%

Confidence Limit 95%

1 3 5

Fig. 5a. Autocorrelation function for cumulative data (model 6).

ith6. Conclusion

The focus of this paper was to apply optimized ANNusing GA for short term rainfall forecasting by determina-tion of suitable input parameters and designing the bestnetwork architecture. The study reported in this articlehas led to the conclusion that MLP type network coupledwith GA, consistently performed better compared toMLP type network alone. Compare to previous study(Luk et al., 2000), number of eective rain stations as inputparameters have been decreased in order to forecast a rain

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1Time Lag

Corr

elat

ion

Coef

ficie

nt

PACF Coefficient

Confidenc Limit 99%

Confidenc Limit 95%

2 3 4 5

Fig. 5b. Autocorrelation function for discrete data (model 7).

M. Nasseri et al. / Expert Systems wtarget and reduced the model noise. Furthermore, the inte-gration of the GA method with ANN indicates animprovement in reducing the order of errors compare tothe ANN model alone. Considering the use of dierenttime lags of surrounding gauge stations, through the useof sensitivity analysis along with the special correlationfunction, an eective number of time lags were identiedwhich are also useful tools in reducing the input parame-ters. Also, due to chaotic nature of rainfall and short timememory, it was observed that number of eective input sta-tions decreases as time steps increases. Finally, caused bynature of integration, cumulative data could lead to highlybetter statistical performance in rainfall forecasting com-pared to discrete data type.

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Optimized scenario for rainfall forecasting using genetic algorithm coupled with artificial neural networkIntroductionArtificial neural networks and genetic algorithmSensitivity analysisApplicationDiscussion of test resultsConclusionReferences