modelling the rainfall–runoff data of susurluk basin

Expert Systems with Applications 37 (2010) 6587–6593

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Expert Systems with Applications

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Modelling the rainfall–runoff data of susurluk basin

Atila Dorum a,1, Alpaslan Yarar b,*, M. Faik Sevimli c,2, Mustafa Onüçyildiz b,3

a Gazi University, Faculty of Technical Education, Construction Education Department, 06500 Besevler, Ankara, Turkeyb Selcuk University, Engineering and Architecture Faculty, Civil Engineering Department Hydraulics Division, 42031 Konya, Turkeyc Selcuk University, Engineering and Architecture Faculty, Environmental Engineering Department, 42031 Konya, Turkey

a r t i c l e i n f o

Keywords:Modelling of rainfall–runoffArtificial Neural NetworksNeuro fuzzySusurluk Basin

0957-4174/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.eswa.2010.02.127

* Corresponding author. Tel.: +90 332 223 19 88; fE-mail addresses: [email protected] (A. Dorum

Yarar), [email protected] (M. Faik Sevimli),Onüçyildiz).

1 Tel.: +90 312 2028867; fax: +90 312 2120059.2 Tel.: +90 332 223 19 78; fax: +90 332 241 06 35.3 Tel.: +90 332 223 21 49; fax: +90 332 241 06 35.

a b s t r a c t

In this study, rainfall–runoff relationship was tried to be set up by using Artificial Neural Networks (ANN)and Adaptive Neuro Fuzzy Interference Systems (ANFIS) models at Flow Observation Stations (FOS) onseven streams where runoff measurement has been made for long years in Susurluk Basin. A part of run-off data was used for training of ANN and ANFIS models and the other part was used to test the perfor-mance of the models. The performance comparison of the models was made with decisiveness coefficient(R2) and Root Mean Squared Errors (RMSE) values. In addition to this, a comparison of ANN and ANFISwith traditional methods was made by setting up Multi-regressional (MR) model. Except some stations,acceptable results such as R2 value for ANN model and R2 value for ANFIS model were obtained as 0.7587and 0.8005, respectively. The high values of predicted errors, belonging to peak values at stations wheremulti variable flow is seen, affected R2 and RMSE values negatively.

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1. Introduction

Runoff data are required in successful management of water re-sources, in development of water usage politics and in the solutionof many engineering and environmental problems. When thesedata are not obtained, it’s necessary to obtain prediction and fore-sight values for runoff data by the help of these set up models. Forthe prediction and foresight of runoff data, models based on differ-ent approaches are used. One of these approaches is the ‘‘blackbox” 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, it’s convenient to make rainfall–runoff modelling in or-der to obtain runoff data.

Fuzzy Logic and Artificial Neural Networks in the black box classhave been recently used widespread in hydrologic modellings andsuccessful results are obtained. The applications such as rainfallprediction, runoff prediction, underground water modelling andreservoir management with ANN and ANFIS were carried out

ll rights reserved.

ax: +90 332 241 06 35.), [email protected] (A.

[email protected] (M.

(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, Onucyıldız, & Copty, 2009).

In this study, rainfall–runoff model of Susurluk Basin was triedto be set up with ANN and ANFIS methods. 7 flow observation sta-tions in the basin where measurements could have been taken forlong 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. Artificial Neural Network (ANNs)

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 backflow 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 weights Wij

and Wjk between the layers of neurons. During the training process,

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

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

6588 A. Dorum et al. / Expert Systems with Applications 37 (2010) 6587–6593

initially 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, and Williams(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 thelearning rate is increased by the factor of learning increment. Ifthe 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), first 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.Specifically, the ANFIS system of interest here is functionally equiv-alent to the Sugeno first-order fuzzy model (Drake, 2000; Janget al., 1997). To explain the computations involved, we considera simple fuzzy inference system with two inputs x and y, andone output z. A typical rule set for first-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 ¼ p1xþ q1yþ r1 ð1ÞRule 2 : If x is A2 and y is B2; then f 2 ¼ p2xþ q2yþ r2 ð2Þ

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 specified asOl,i. The 5 layers comprising the ANFIS structure are briefly de-scribed below:

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

Ol;i ¼ lAiðxÞ; for i ¼ 1;2 or ð3ÞOl;i ¼ lBi�2ðxÞ; for i ¼ 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:

lAðxÞ ¼1

1þ x�ciai

� �2� �bi

ð4Þ

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 qualified 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 ¼ wi ¼ lAiðxÞ � lBiðyÞ; i ¼ 1;2: ð5Þ

The output of each node represents the firing strength of a rule.Layer 3: Each node in layer 3, denoted N, is a stable node. The

ith node in this layer calculates the proportion of the ith rule’s fir-ing strength to the sum of firing strength of all rules.

O3;i ¼ wi ¼wi

w1 þw2; i ¼ 1;2 ð6Þ

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

function is defined as follows:

O4;i ¼ wifi ¼ wiðpixþ qiyþ riÞ ð7Þ

where 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 ¼ Ri

wifi ¼Ri

wifi

Ri

wið8Þ

The above equations describe an adaptive network which is func-tionally equivalent to a Sugeno first-order fuzzy inference system.The learning rule specifies 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 thenetwork’s 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

Fig. 3. Equivalent ANFIS architecture.

A. Dorum et al. / Expert Systems with Applications 37 (2010) 6587–6593 6589

repeated application of the chain rule. Calculation of the gradient ina network structure requires use of the ordered derivative, denotedas @þ, 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 defined 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 descentmethod is:

Da ¼ �g@E@a

ð9Þ

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 arefixed, the overall output can be given as a linear combination ofthe consequent parameters. The output f can be written as:

Fig. 4. Susurl

f ¼ w1

w1 þw2f1 þ

w2

w1 þw2f2

¼ w1ðp1xþ q1yþ r1Þ þw2ðp2xþ q2yþ r2Þ¼ ðw1xÞp1 þ ðw1yÞq1 þ ðw1Þr1 þ ðw2xÞp2 þ ðw2yÞq2þðw2Þr2 ð10Þ

which is linear in the consequent parameters p1, q1, r1, p2, q2, and r2.Consequently, we define the following parameter sets:

S = set of total parameters,S1 = 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 ¼ y ð11Þ

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

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

h� ¼ ðAT AÞ�1AT y ð12Þ

uk Basin.

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)Tavsanlı, R(t � 2)Tavsanlı 116 100314 Q(t) = Q(t)314 Q(t � 1), Q(t � 2), R(t � 1)Balıkesir, R(t � 2)Balıkesir, R(t � 1)Bandırma, R(t � 2)Bandırma 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)Bandırma, R(t � 2)Bandırma

74 50

324 Q(t) = Q(t)324 � Q(t)329 Q(t � 1), R(t � 1)Balikesir, R(t � 2)Balikesir, 106 100328 Q(t) = Q(t)328 Q(t � 1), Q(t � 2), R(t � 1)Emet, R(t � 2)Emet, R(t � 1)Tavsanlı, R(t � 2)Tavsanlı 130 86

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)



+ (Q(t)324 + Q(t)Reservoir)317 Q(t)317,(model output) Q(t)317(Prediction) = Q(t)317,(model output) + Q(t)316

324 Q(t)324,(model output) Q(t)324(Prediction) = Q(t)324,(model output) + Q(t)329



where, AT is the transpose of A and (ATA)�1AT is the pseudo-inverseof A if ATA is nonsingular. The recursive least-square estimator (RLS)could also be used to calculate h* (Jang, 1993).

3. Study area and model application

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 it’s 2.88% of Turkey’s 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 Nilüfer, Adranos (Kocasu), Emet, Simav(Susurluk), Murvetler and Madra (Kocacay) brooks in Karacabeydistrict or by combination of them with outlets of Manyas and Ulu-bat Lakes. Adranos and Emet brooks are the most important afflu-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)Balıkesir + 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)Balik

328 Q(t) = 0.815Q(t � 1) � 0.289Q(t � 2) + 0.007R(t � 1)Emet 0.054R

The annual average rain of the basin is 650 mm and this is morein the seaboard. The annual average temperature of the basin isabout 14–15 �C. Average amount of evaporation is 1054.9 mm.

3.2. Model application

For rainfall–runoff 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, Balıkesir, Mus-tafa Kemalpasa, Kepsut, Bandırma, Dursunbey, Emet, Tavsanlı,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 Q t ¼ FðQ t�1;Q t�2; . . .Þ; FðRt�1;Rt�2; . . .Þ 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.

3.2.1. TrainingANFIS and ANN models were made by writing code in MATLAB

programme. Sub-grouping method was selected for the trainingperiod 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)Tavsanlı + 0.007R(t � 2)Tavsanlı � 0.0773 R(t � 2)Balıkesir + 0.198R(t � 1)Bandırma + 0.037R(t � 2)Bandırma � 3.334

t � 0.017R(t � 1)Mustafa Kemalpasa + 0.147R(t � 2)Mustafa

1)Balikesir � 0.042R(t � 2)Balikesir � 7.806sa + 0.035R(t � 2)Mustafa

(t � 1)Bandırma � 0.052R(t � 2)Bandırma

esir + 0.747(t � 2)Emet –0.003R(t � 1)Tavsanlı � 0.017R(t � 2)Tavsanlı + 1.26

Fig. 5. 302 Numbered station.





For 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 profit in the per-iod of direct searching (Moller, 1993). Its basic approach dependson combination of safe areas and reaching model-true approachused also in Levenberg–Marquart algorithm. Different layer, differ-ent confidential 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 flows 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

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 4.27

purpose 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. 5–7 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 rainfall–runoff relationship mostly does not show a linierbehavior, ‘‘black box” approaches can be useful tools for the deter-mination of the relationship. In this study, rainfall–runoff model ofSusurluk Basin was tried to be set up with ANN and ANFIS meth-ods. Some of the rainfall–runoff 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 rainfall–runoff relationships ofSusurluk Basin except peak situations. For this reason, it was


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

Knowledge

This study is based on Alpaslan YARAR’s PhD Thesis.

References

Baratti, R., Cannas, B., Fanni, A., Pintus, M., Sechi, G. M., & Toreno, N. (2003). Riverflow forecast for reservoir management through neural networks.Neurocomputing, 55(3–4), 421–437.

Chang, L. C., Chang, F. J., & Chiang, Y. M. (2004). A two-step-ahead recurrent neuralnetwork for stream-flow forecasting. Hydrological Processes, 18(1), 81–92.

Chang, F. J., & Chen, Y. C. (2001). A counterpropagation fuzzy-neural networkmodeling approach to real time stream flow prediction. Journal of Hydrology,245, 153–164.

Dawson, C. W., & Wilby, R. L. (1998). An artificial neural network approach torainfall–runoff modeling. Hydrological Sciences, 43(1), 47–67.

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, 1119–1133.

Hasebe, M., & Nagayama, Y. (2002). Reservoir operation using the neural networkand fuzzy systems for dam control and operation support. Advances inEngineering Software, 33(5), 245–260.

Haykin, S. (1998). Neural networks – A comprehensive foundation (2nd ed.). UpperSaddle River, NJ: Prentice-Hall. pp. 26–32.

Hsu, K. L., Gupta, H. V., & Sorooshian, S. (1995). Artificial neural network modelingof the rainfall–runoff process. Water Resources Research, 31(10), 2517–2530.

Jang, J.-S. R. (1993). ANFIS: adaptive-network-based fuzzy inference system. IEEETrans. System Management in Cybernetics, 23(3), 665–685.

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 flowprediction. Journal of Computational Civil Engineering, 8, 201–220.

Kisi, O. (2006). Daily pan evaporation modelling using a neuro-fuzzy computingtechnique. Journal of Hydrology, 329, 636–646.

Moller, M. F. (1993). A scaled conjugate gradient algorithm for fast supervisedlearning. Neural Networks, 6, 525–533.

Lallahem, S., & Mania, J. (2003). Evaluation and forecasting of daily groundwateroutflow in a small chalky watershed. Hydrological Processes, 17(8), 1561–1577.

Luk, K. C., Ball, J. E., & Sharma, A. (2000). A study of optimal model lag and spatialinputs to artificial neural network for rainfall forecasting. Journal of Hydrology,227, 56–65.

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 inflow forecasting using an artificial neuralnetwork model. Hydrological Processes, 16, 2433–2439.

Yang, C. C., Prasher, S. O., Lacroix, R., Sreekanth, S., Patni, N. K., & Masse, L. (1997).Artificial neural network model for subsurfacedrained farmland. Journal ofIrrigation and Drainage Engineering, 123, 285–292.

Yarar, A., Onucyıldız, M., & Copty, N. K. (2009). Modelling level changes in lakesusing neuro-fuzzy and artificial neural networks. Journal of Hydrology, 365,329–334.

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

modelling the rainfall–runoff data of susurluk basin

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