ur

, M6500Hydpart

ff reInt

ff mingerfoed Eas

R2 v

2010 Elsevier Ltd. All rights reserved.

1. Introduction

sful mge polentalto obtalp of tf data,ese ap

successful results are obtained. The applications such as rainfallprediction, runoff prediction, underground water modelling andreservoir management with ANN and ANFIS were carried out

The composition of ANN is inspired from biological neural net-works. A neuron is one of the basic components of neural net-works. It can vary in terms of size and shape, according to itsfunction and mission in neural systems. ANNs have a simple con-struction and an oriented network style, as shown in Fig. 1. Thenetwork consists of layers of parallel processing elements, alsocalled neurons. Each layer is fully connected to the backow layerby interconnections which are characterized by interconnectionstrengths, or weights. Fig. 1 illustrates a three-layer neural networkconsisting of layers i, j, and k, with the interconnection weightsWijandWjk between the layers of neurons. During the training process,

* Corresponding author. Tel.: +90 332 223 19 88; fax: +90 332 241 06 35.E-mail addresses: adorum@gazi.edu.tr (A. Dorum), ayarar@selcuk.edu.tr (A.

Yarar), mfsevimli@selcuk.edu.tr (M. Faik Sevimli), m13yildiz@selcuk.edu.tr (M.Onyildiz).

1 Tel.: +90 312 2028867; fax: +90 312 2120059.2 Tel.: +90 332 223 19 78; fax: +90 332 241 06 35.

Expert Systems with Applications 37 (2010) 65876593

Contents lists availab

Expert Systems w

journal homepage: www.e3 Tel.: +90 332 223 21 49; fax: +90 332 241 06 35.box approach. Contrary to analytical models where all parametersaffecting the desired value are needed, less parameter are used inblack box models. These models having advantages in terms ofboth time and economy are frequently used. Since runoff dataare affected from a great many parameters such as hydrological,geological and topographic and also rainfall values are quite easilyobtained, its convenient to make rainfallrunoff modelling in or-der to obtain runoff data.

Fuzzy Logic and Articial Neural Networks in the black box classhave been recently used widespread in hydrologic modellings and

long years were used for modelling. Some of the runoff values wereused for model training and some of them for the testing and theirperformances were evaluated by investigating the error values ofthe obtained data.

2. Model description

2.1. Articial Neural Network (ANNs)Runoff data are required in successources, in development of water usaof many engineering and environmdata are not obtained, its necessarysight values for runoff data by the hethe prediction and foresight of runofent approaches are used. One of th0957-4174/$ - see front matter 2010 Elsevier Ltd. Adoi:10.1016/j.eswa.2010.02.127anagement of water re-itics and in the solutionproblems. When thesein prediction and fore-hese set up models. Formodels based on differ-proaches is the black

(Baratti et al., 2003; Chang, Chang, & Chiang, 2004; Chang & Chen,2001; Dawson & Wilby, 1998; Grimes, Coppola, Verdecchia, & Vis-conti, 2003; Hasebe & Nagayama, 2002; Hsu, Gupta, & Sorooshian,1995; Karunanithi, Grenney, & Whitley, 1994; Lallahem & Mania,2003; Luk, Ball, & Sharma, 2000; Xu & Li, 2002; Yang et al., 1997;Yarar, Onucyldz, & Copty, 2009).

In this study, rainfallrunoff model of Susurluk Basin was triedto be set up with ANN and ANFIS methods. 7 ow observation sta-tions in the basin where measurements could have been taken forand 0.8005, respectively. The high values of predicted errors, belonging to peak values at stations wheremulti variable ow is seen, affected R2 and RMSE values negatively.Modelling the rainfallrunoff data of sus

Atila Doruma,1, Alpaslan Yarar b,*, M. Faik Sevimli c,2

aGazi University, Faculty of Technical Education, Construction Education Department, 0b Selcuk University, Engineering and Architecture Faculty, Civil Engineering Departmentc Selcuk University, Engineering and Architecture Faculty, Environmental Engineering De

a r t i c l e i n f o

Keywords:Modelling of rainfallrunoffArticial Neural NetworksNeuro fuzzySusurluk Basin

a b s t r a c t

In this study, rainfallrunoand Adaptive Neuro Fuzzyseven streams where runooff data was used for trainmance of the models. The p(R2) and Root Mean Squarwith traditional methods wacceptable results such asll rights reserved.luk basin

ustafa Onyildiz b,3

Besevler, Ankara, Turkeyraulics Division, 42031 Konya, Turkeyment, 42031 Konya, Turkey

lationship was tried to be set up by using Articial Neural Networks (ANN)erference Systems (ANFIS) models at Flow Observation Stations (FOS) oneasurement has been made for long years in Susurluk Basin. A part of run-of ANN and ANFIS models and the other part was used to test the perfor-rmance comparison of the models was made with decisiveness coefcientrrors (RMSE) values. In addition to this, a comparison of ANN and ANFISmade by setting up Multi-regressional (MR) model. Except some stations,alue for ANN model and R2 value for ANFIS model were obtained as 0.7587

le at ScienceDirect

ith Applications

lsevier .com/locate /eswa

learning rate is increased by the factor of learning increment. If

th Athe performance increases, the learning rate is adjusted by the fac-tor of learning decrement.

2.2. Adaptive neuro fuzzy Inference Systems (ANFIS)

Adaptive neuro fuzzy inference system (ANFIS), rst introducedby Jang (1993), is a universal approximation methodology and, assuch, is capable of approximating any real continuous functionon a compact set to any degree of accuracy (Jang, Sun, & Mizutani,1997). ANFIS is functionally equivalent to fuzzy inference systems.Specically, the ANFIS system of interest here is functionally equiv-alent to the Sugeno rst-order fuzzy model (Drake, 2000; Janget al., 1997). To explain the computations involved, we considerinitially estimated weight values are progressively corrected bycomparing estimated outputs with known outputs. Any errorsare then back propagated to determine the appropriate weightadjustments necessary to minimize the errors (Kisi, 2006).

The methodology used in this study for adjusting the weights iscalled momentum back propagation, and is based on the gener-alized delta rule, as presented by Rumelhart, Hinton, andWilliams(1986). Throughout all ANN simulations, the adaptive learningrates were used for increasing the convergence velocity. For eachepoch, if the performance decreases toward the goal, then the

Fig. 1. ANNs architecture used for the prediction of the ow.

6588 A. Dorum et al. / Expert Systems wia simple fuzzy inference system with two inputs x and y, andone output z. A typical rule set for rst-order Sugeno-fuzzy modelthat includes two fuzzy If-Then rules can be expressed as;

Rule 1 : If x is A1 and y is B1; then f 1 p1x q1y r1 1Rule 2 : If x is A2 and y is B2; then f 2 p2x q2y r2 2

Fig. 2 shows the Sugeno-fuzzy reasoning system for this Sugeno-fuzzy model, while Fig. 3 shows the corresponding equivalent ANFISarchitecture. Nodes at the same layer have similar function for thisANFIS structure. The output of the ith node in layer l is specied asOl,i. The 5 layers comprising the ANFIS structure are briey de-scribed below:

Layer 1: Every node i in this layer is an adaptive node, whoseoutput is dened as follows;

Ol;i lAix; for i 1;2 or 3Ol;i lBi2x; for i 3;4

Where x (or y) is the input to the ith node and Ai (or Bi_2) is a fuzzylabel. The membership functions for A and B can be any member-ship functions parameterized appropriately; for instance:lAx 1

1 xciai 2 bi 4

where {ai, bi, ci} is the parameter set. As the values of these param-eters change, the bell-shaped function varies accordingly, thusexhibiting various forms of membership functions on linguistic la-bel Ai. In fact, any continuous and piecewise differentiable func-tions, such as commonly used triangular-shaped membershipfunctions, are also qualied candidates for node functions in thislayer (Jang, 1993). Parameters in this layer are referred to as pre-mise parameters. The outputs of this layer are the membership val-ues of the premise part.

Layer 2: Each node in this layer, labeled P, is a stable nodewhich multiplies incoming signals and sends the product out. Forexample,

O2;i wi lAix lBiy; i 1;2: 5The output of each node represents the ring strength of a rule.

Layer 3: Each node in layer 3, denoted N, is a stable node. Theith node in this layer calculates the proportion of the ith rules r-ing strength to the sum of ring strength of all rules.

O3;i wi wiw1 w2 ; i 1;2 6

The outputs of this layer are called normalized ring strengths.Layer 4: Each node in this layer is an adaptive node, whose node

function is dened as follows:

Fig. 2. Two inputs of rst-order Sugeno-fuzzy model with two rules.

pplications 37 (2010) 65876593O4;i wifi wipix qiy ri 7where wi is the output of layer 3, and {pi,qi, ri} is the parameter set.Parameters of this layer are referred to as consequence or outputparameters.

Layer 5: As the last layer, layer 5 includes a stable and singlenode, labeled R, which sums up all signals to calculate the totaloutput:

O5;i Riwifi

Riwifi

Riwi

8

The above equations describe an adaptive network which is func-tionally equivalent to a Sugeno rst-order fuzzy inference system.The learning rule species how the premise parameters (layer 1)and consequent parameters (layer 4) should be updated to mini-mize a prescribed error measure, E. The error measure is a mathe-matical expression that measures the difference between thenetworks actual output and the desired output, such as the squarederror. The steepest descent method is used as the basic learning ruleof the adaptive network. In this method, the gradient is derived by

repeated application of the chain rule. Calculation of the gradient ina network structure requires use of the ordered derivative, denotedas @, as opposed to the ordinary partial derivative @. This techniqueis called the back propagation rule (Drake, 2000; Jang, 1993). Thecore of this learning rule involves how to recursively obtain a gradi-ent vector in which each element is dened as the derivative of anerror measure with respect to a parameter (Haykin, 1998). The up-date formula for the generic parameter a using the steepest descent

f w1w1 w2 f1

w2w1 w2 f2

w1p1x q1y r1 w2p2x q2y r2 w1xp1 w1yq1 w1r1 w2xp2 w2yq2w2r2 10

which is linear in the consequent parameters p1, q1, r1, p2, q2, and r2.

S = set of total parameters,

Fig. 3. Equivalent ANFIS architecture.

A. Dorum et al. / Expert Systems with Applications 37 (2010) 65876593 6589method is:

Da g @E@a

9

where, g is the learning rate.While the back propagation learning rule can be used to identify

the parameters in an adaptive network, this method is often slowto converge. The hybrid learning algorithm (Jang, 1993), whichcombines back propagation and the least-squares method, can beused to rapidly train and adapt the equivalent fuzzy inference sys-tem. It can be seen from Fig. 3 that if the premise parameters arexed, the overall output can be given as a linear combination ofthe consequent parameters. The output f can be written as:Fig. 4. SusurlS1 = set of premise (nonlinear) parameters,S2 = set of consequent (linear) parameters.

Given some values of S1, P training data are substituted into Eq.(10) leading to the matrix equation:

Ah y 11where, h is an unknown vector whose elements are parameters inS2, the set of consequent (linear) parameters.

The set S2 of consequent parameters can be identied with thestandard least-squares estimator (LSE):

h ATA1ATy 12Consequently, we dene the following parameter sets:uk Basin.

of A if A A is nonsingular. The recursive least-square estimator (RLS)could also be used to calculate h* (Jang, 1993).

Table 1Data and numbers used in modelling

Station Modelled data (Q) Used data Data numbers

Training Test

302 Q(t) = Q(t)302 (Q(t)311 + Q(t)328) Q(t 1), Q(t 2), R(t 1)Emet, R(t 2)Emet, R(t 1)Dursunbey, R(t 2)Dursunbey, R(t 1)Mustafa Kemalpasa,R(t 2)Mustafa Kemalpasa

105 100

311 Q(t) = Q(t)311 Q(t 1), Q(t 2), R(t 1)Emet, R(t 2)Emet, R(t 1)Tavsanl, R(t 2)Tavsanl 116 100314 Q(t) = Q(t)314 Q(t 1), Q(t 2), R(t 1)Balkesir, R(t 2)Balkesir, R(t 1)Bandrma, R(t 2)Bandrma 168 100316 Q(t) = Q(t)316 (Q(t)324 + Q(t)Reservoir) Q(t 1), R(t 1)Kepsut, R(t 2)Kepsut, R(t 1)Mustafa Kemalpasa, R(t 2)Mustafa Kemalpasa R(t 1)Bigadic,

R(t 2)Bigadic, R(t 1)Balikesir, R(t 2)Balikesir,50 35

317 Q(t) = Q(t)317 Q(t)316 Q(t 1), Q(t 2), R(t 1)Mustafa Kemalpasa, R(t 2)Mustafa Kemalpasa, R(t 1)Mudanya, R(t 2)Mudanya,R(t 1)Bandrma, R(t 2)Bandrma

74 50

324 Q(t) = Q(t)324 Q(t)329 Q(t 1), R(t 1)Balikesir, R(t 2)Balikesir, 106 100t

6590 A. Dorum et al. / Expert Systems with Applications 37 (2010) 658765933. Study area and model applicationwhere, AT is the transpose of A and (ATA)1AT is the pseudo-inverseT

328 Q(t) = Q(t)328 Q(t 1), Q(t 2), R(t 1)Emet, R(

Table 2Predicted data

Station Model output Predicted runoff

302 Q(t)302,(model output) Q(t)302(Prediction) = Q(t)302,(model output)+ (Q(t)311 + Q(t)328)

311 Q(t)311,(model output) Q(t)311(Prediction) = Q(t)311,(model output)314 Q(t)314,(model output) Q(t)314(Prediction) = Q(t)314,(model output)316 Q(t)316,(model output) Q(t)316(Prediction) = Q(t)316,(model output)

+ (Q(t)324 + Q(t)Reservoir)317 Q(t)317,(model output) Q(t)317(Prediction) = Q(t)317,(model output) + Q(t)316324 Q(t)324,(model output) Q(t)324(Prediction) = Q(t)324,(model output) + Q(t)329328 Q(t)328,(model output) Q(t)328(Prediction) = Q(t)328,(model output)3.1. Study area

Susurluk Basin is in the north west of Anatolian peninsula and isbetween 400 20I in the north, 390 10I in the south, 290 38I in theeast and 270 20I in the west. The area covered by the basin is22,399 km2 and its 2.88% of Turkeys acreage. The basin is sur-rounded by Sakarya Basin in the east, by the Sea of Marmara andits basin in the north, by Marmara and Aegean basins in the westand by Gediz Basin in the south (Fig. 4).

Susurluk Basin is an entire stream basin which occurred eitherby direct combination of Nilfer, Adranos (Kocasu), Emet, Simav(Susurluk), Murvetler and Madra (Kocacay) brooks in Karacabeydistrict or by combination of themwith outlets of Manyas and Ulu-bat Lakes. Adranos and Emet brooks are the most important afu-ents of Susurluk Brook.

Table 3Regression equations

Station Regression equation

302 Q(t) = 0.409Q(t 1) 0.059Q(t 2) 0.067R(t 1)Emet + 0.059Kemalpasa + 0.259R(t 2)Mustafa Kemalpasa + 0.971

311 Q(t) = 0.528Q(t 1) + 0.026Q(t 2) + 0.071R(t 1)Emet + 0.03 R314 Q(t) = 0.184Q(t 1) 0.194Q(t 2) 0.008R(t 1)Balkesir + 0.1316 Q(t) = 0.284Q(t 1) + 0.704R(t 1)Kepsut + 0.405R(t 2)Kepsu

Kemalpasa + 0.125R(t 1)Bigadic + 0.186R(t 2)Bigadic 0.309R(t 317 Q(t) = 0.455Q(t 1) + 0.138Q(t 2) + 0.11R(t 1)Mustafa Kemalpa

Kemalpasa + 0.445R(t 1)Mudanya + 0.417R(t 2)Mudanya 0.048R324 Q(t) = 0.194Q(t 1) + 0.074R(t 1)Balikesir + 0.034R(t 2)Balik328 Q(t) = 0.815Q(t 1) 0.289Q(t 2) + 0.007R(t 1)Emet 0.054R3.2.1. TrainingANFIS and ANN models were made by writing code in MATLAB

programme. Sub-grouping method was selected for the training3.2. Model application

For rainfallrunoff modelling, 7 Flow Observation Stations (FOS)numbered with 302, 311, 314, 316, 317, 324, 328 where measure-ments have been taken for long years and Bigadic, Balkesir, Mus-tafa Kemalpasa, Kepsut, Bandrma, Dursunbey, Emet, Tavsanl,Bursa and Mudanya meteorology stations where rainfall measure-ments have been taken were used. The rainfall values which affectFOS and source of stations were determined by the help of Thies-sen Polygon formed with rainfall stations. Moreover, ThiessenPolygon was controlled by making height analysis with 1/500,000 scaled three-dimensional map of the basin which was ob-tained by Generic Mapping Tools (GMT).

The values measured at the FOS of source of some stations andrunoff values left in reservoirs present in the source were taken asbase of runoff. For the prediction modelling, data sets were formedby examining the correlation of runoff values with the previousrunoff (Q) and rainfall (R) values belonging to each station andmodels such as Qt FQt1;Qt2; . . .; FRt1;Rt2; . . . were setup. Some of the data were used for the training of models and someof them were used for the aim of testing. The data sets in this per-iod were selected randomly. The data sets and numbers used ineach station were given in Table 1.The annual average rain of the basin is 650 mm and this is morein the seaboard. The annual average temperature of the basin isabout 1415 C. Average amount of evaporation is 1054.9 mm.

2)Emet, R(t 1)Tavsanl, R(t 2)Tavsanl 130 86period of ANFIS models and the diameter and epoch values thatgive the best results were used by making trials with group diam-eter in the (D) [0, 1] range and different epoch numbers.

R(t 2)Emet + 0.061R(t 1)Dursunbey 0.024R(t 2)Dursunbey + 0.209R(t 1)Mustafa

(t 2)Emet 0.039R(t 1)Tavsanl + 0.007R(t 2)Tavsanl 0.0773 R(t 2)Balkesir + 0.198R(t 1)Bandrma + 0.037R(t 2)Bandrma 3.334t 0.017R(t 1)Mustafa Kemalpasa + 0.147R(t 2)Mustafa1)Balikesir 0.042R(t 2)Balikesir 7.806

sa + 0.035R(t 2)Mustafa(t 1)Bandrma 0.052R(t 2)Bandrmaesir + 0.747(t 2)Emet 0.003R(t 1)Tavsanl 0.017R(t 2)Tavsanl + 1.26

Fig. 5. 302 Numbered station.

Fig. 6. 317 Numbered station.

A. Dorum et al. / Expert Systems with Applications 37 (2010) 65876593 6591

6592 A. Dorum et al. / Expert Systems with AFor ANN modelling, Forward Feed Backpropagation ANN wasselected and Scaled Conjugate Gradient (SCG) algorithm was used.SCG algorithm is an extremely complex algorithm which wasdeveloped by Moller for the purpose of deriving a prot in the per-iod of direct searching (Moller, 1993). Its basic approach dependson combination of safe areas and reaching model-true approachused also in LevenbergMarquart algorithm. Different layer, differ-ent condential knot number and different epoch numbers weretried for every station in ANN modelling.

3.2.2. TestThe models trained with ANFIS and ANN were then subjected to

testing. The ows of that station were predicted by adding baserunoff values to the ones obtained at the end of the test period.The summary of this period is given in Table 2.

Multi Regression Models were formed in order to compare AN-FIS and ANN models with traditional ones. The data used for the

Fig. 7. 324 Numb

Table 4R2 and RMSE values of the models

Station ANFIS ANN MR

R2 RMSE R2 RMSE R2 RMSE

302 0.5752 30.21 0.6026 28.53 0.0689 45.84311 0.1663 6.00 0.2189 5.52 0.1857 5.72314 0.1831 24.72 0.2357 23.43 0.2162 23.11316 0.3030 42.11 0.3501 36.86 0.4077 35.94317 0.8005 40.84 0.7587 47.31 0.7901 44.33324 0.5883 5.36 0.3428 7.06 0.6454 5.04328 0.3826 4.50 0.3794 4.84 0.4128 4.27pplications 37 (2010) 65876593purpose of training in ANFIS and ANN period were used for the cal-ibration of regression models and the data used for testing wereused for the validity control. The equations obtained with regres-sion model are given in Table 3 and the relationships between pre-dicted values of some stations and their measured values are givenin Figs. 57 Moreover, Root Mean Squared Error (RMSE) values andR2 were calculated for the performance control of the models andare given in Table 4.

4. Conclusion

Since rainfallrunoff relationship mostly does not show a linierbehavior, black box approaches can be useful tools for the deter-mination of the relationship. In this study, rainfallrunoff model ofSusurluk Basin was tried to be set up with ANN and ANFIS meth-ods. Some of the rainfallrunoff data in 7 stations belonging tothe basin were trained with ANFIS and ANN and they were alsosubjected to testing according to the best approaches obtained.Multi Regression Model was formed in order to compare obtainedresults with traditional methods. The comparison was made withR2 and RMSE values obtained as a result of each model. Althougeach model gave close results with each other, the best R2

(0.8005) was obtained in ANFIS model in 317 numbered stationand the worst R2 (0.0689) was obtained in MR model in 302 num-bered station. The big errors in the predictions of peak values ofsome stations affected R2 and RMSE values negatively.

This modelling study showed that ANFIS and ANN are usablemethods in determination of rainfallrunoff relationships ofSusurluk Basin except peak situations. For this reason, it was

ered station.

concluded that these methods are benecial tools one by one in or-der to develop water usage politics.

Knowledge

This study is based on Alpaslan YARARs PhD Thesis.

References

Baratti, R., Cannas, B., Fanni, A., Pintus, M., Sechi, G. M., & Toreno, N. (2003). Riverow forecast for reservoir management through neural networks.Neurocomputing, 55(34), 421437.

Chang, L. C., Chang, F. J., & Chiang, Y. M. (2004). A two-step-ahead recurrent neuralnetwork for stream-ow forecasting. Hydrological Processes, 18(1), 8192.

Chang, F. J., & Chen, Y. C. (2001). A counterpropagation fuzzy-neural networkmodeling approach to real time stream ow prediction. Journal of Hydrology,245, 153164.

Dawson, C. W., & Wilby, R. L. (1998). An articial neural network approach torainfallrunoff modeling. Hydrological Sciences, 43(1), 4767.

Drake, J.T., 2000. Communications phase synchronization using the adaptivenetwork fuzzy inference system. Ph.D. Thesis. Las Cruces, New Mexico, USA:New Mexico State University.

Grimes, D. I. F., Coppola, E., Verdecchia, M., & Visconti, G. (2003). A neural networkapproach to real-time rainfall estimation for Africa using satellite data. Journalof Hydrometeorology, 4, 11191133.

Hasebe, M., & Nagayama, Y. (2002). Reservoir operation using the neural networkand fuzzy systems for dam control and operation support. Advances inEngineering Software, 33(5), 245260.

Haykin, S. (1998). Neural networks A comprehensive foundation (2nd ed.). UpperSaddle River, NJ: Prentice-Hall. pp. 2632.

Hsu, K. L., Gupta, H. V., & Sorooshian, S. (1995). Articial neural network modelingof the rainfallrunoff process. Water Resources Research, 31(10), 25172530.

Jang, J.-S. R. (1993). ANFIS: adaptive-network-based fuzzy inference system. IEEETrans. System Management in Cybernetics, 23(3), 665685.

Jang, J.-S. R., Sun, C.-T., & Mizutani, E. (1997). Neuro-fuzzy and soft computing: Acomputational approach to learning and machine intelligence. Upper Saddle River,NJ: Prentice-Hall.

Karunanithi, N., Grenney, W. J., & Whitley, D. (1994). Neural network for river owprediction. Journal of Computational Civil Engineering, 8, 201220.

Kisi, O. (2006). Daily pan evaporation modelling using a neuro-fuzzy computingtechnique. Journal of Hydrology, 329, 636646.

Moller, M. F. (1993). A scaled conjugate gradient algorithm for fast supervisedlearning. Neural Networks, 6, 525533.

Lallahem, S., & Mania, J. (2003). Evaluation and forecasting of daily groundwateroutow in a small chalky watershed. Hydrological Processes, 17(8), 15611577.

Luk, K. C., Ball, J. E., & Sharma, A. (2000). A study of optimal model lag and spatialinputs to articial neural network for rainfall forecasting. Journal of Hydrology,227, 5665.

Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning internalrepresentation by error propagation. In D. E. Rumelhart & J. L. McClelland(Eds.). Parallel distributed processing foundations (Vol. 1). Cambridge, MA: MITPress.

Xu, Z. X., & Li, J. Y. (2002). Short-term inow forecasting using an articial neuralnetwork model. Hydrological Processes, 16, 24332439.

Yang, C. C., Prasher, S. O., Lacroix, R., Sreekanth, S., Patni, N. K., & Masse, L. (1997).Articial neural network model for subsurfacedrained farmland. Journal ofIrrigation and Drainage Engineering, 123, 285292.

Yarar, A., Onucyldz, M., & Copty, N. K. (2009). Modelling level changes in lakesusing neuro-fuzzy and articial neural networks. Journal of Hydrology, 365,329334.

Yarar, A. (2010). Modeling of precipitation-stream ow data of susurluk basn,Selcuk University. Institute of Natural and Applied Sciences, PhD Thesis.

A. Dorum et al. / Expert Systems with Applications 37 (2010) 65876593 6593

Modelling the rainfallrunoff data of susurluk basinIntroductionModel descriptionArtificial Neural Network (ANNs)Adaptive neuro fuzzy Inference Systems (ANFIS)

Study area and model applicationStudy areaModel applicationTrainingTest

ConclusionKnowledgeReferences