Long-term Streamflow Forecasting by Adaptive Neuro-Fuzzy Inference System Using K-fold Cross-validation: (Case Study: Taleghan Basin, Iran)

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1 Journal of Water Scences Research, ISSN: eissn: Vol.6, No.1, Wnter 014, 71-83, JWSR Long-term Streamflow Forecastng by Adaptve Neuro-Fuzzy Inference System Usng K-fold Cross-valdaton: (Case Study: Taleghan Basn, Iran) ABSTRACT Reza Esmaeelzadeh 1*, Alreza Borhan Darane 1. Department of Cvl Engneerng, Shahd Chamran Unversty, Ahwaz, Iran. Department of Cvl Engneerng, K. N. Toos Unversty of Tech., Tehran, Iran Receved: 05 February 013 Accepted: 13 August 013 Streamflow forecastng has an mportant role n water resource management (e.g. flood control, drought management, reservor desgn, etc.). In ths paper, the applcaton of Adaptve Neuro Fuzzy Inference System (ANFIS) s used for long-term streamflow forecastng (monthly, seasonal) and moreover, cross-valdaton method (K-fold) s nvestgated to evaluate test-tranng data n the model.then, the results are compared wth those of the typcal valdaton method (.e., usng 75% of data for tranng and the remanng 5% for testng the valdty of the traned model). Study area s Taleghan basn located n northwestern Tehran basn, Iran. The data used n ths research conssts of 19 years of monthly streamflow, precptaton and temperature records. To apply temperature and precptaton data n the model, the whole basn was dvded nto sub-basns and average values of each parameter for each sub-basn were allocated as model nput. Fnally, results were compared wth those of the ANN model. It was found that the K-fold valdaton method leads to better performance than the typcal method n terms of statstcal ndces. In addton, the results ndcated the superorty of ANFIS model over ANN model n long-term forecastng. Keywords Streamflow forecastng, ANFIS, K-fold, Sub-basn, ANN 1. Introducton Streamflow forecastng s an effectve and mportant ssue n water resource management (e.g. flood control, drought management, reservor desgn, etc.). Streamflow forecastng can be approached n many ways by consderng dfferent tme steps and methods (conceptual, physcal, and black box). Regresson based methods are among the earlest and most wdely used procedures n rver flow forecastng. Madment et al. (1985) used short-term tme seres for forecastng daly water demands n the Unted States. Phen et al. (1990) used a regresson model for predctng daly streamflow n the Mekong basn wth satsfyng results. In another study, Darane et al. (004) predcted long-term streamflow n Dez Rver located n southwestern Iran usng satellte mages along wth regresson methods. Artfcal neural networks have succeeded n replacng regresson methods n most applcatons where the relatonshps * Correspondng Author Emal: (Sre_esmaeelzadeh@yahoo.com)

2 Long-term streamflow forecastng... R. Esmaeelzadeh and A. B. Darane among the varables are non-lnear and complex. Therefore, n recent decades, artfcal neural networks have been successfully used n water resource management. Many of those studes report that the ANNs may offer a promsng alternatve especally where the relatonshps among the varables are nonlnear and complex (e.g., Mnns and Hall, 1996; Sajkumar and Thandaveswara, 1999; Prada and Nera, 009; Adamowsk and Karapatak, 010). Ks (004) used neural networks and autoregressve methods (AR) for monthly streamflow predcton at Goksudere Rver n Turkey and concluded that the ANN approach has a better performance than the AR method. Nowadays, neuro-fuzzy system whch has advantages of ANN method and fuzzy logc smultaneously has been appled n streamflow forecastng. Nayak et al. (004) evaluated the potental use of Adaptve Neuro Fuzzy Inference System (ANFIS) n forecastng rver flow at Bataran Rver, Inda. They observed that the ANFIS model presented the ablty of ANN fully and had good performance n terms of varous statstcal ndces. Other studes show the superorty of ANFIS over ANN n modelng usng soft computng methods (e.g., Kurtulus and Razack, 010; Ks, 005; Chang and Chang, 006). Besde the above mentoned black box modellng approaches (.e., regresson method, ANN, and ANFIS), a great range of Physcal and conceptual methods have been also used n developng rver flow forecastng. In general, the results ndcate the superorty of black box methods partcularly at peak flows. Demrel et al. (009) assessed the results of the ANN and Sol and Water Assessment Tool (SWAT) models n Pracana basn located n Portugal and showed that the ANN model estmates peak flows more accurately than the SWAT model. Also, Tale et al. (010) n a smlar study used neuro-fuzzy and Storm Water Management Model (SWMM) to forecast streamflow n Kranj basn n Sngapore. They concluded that ANFIS performs better than SWMM at peak flows. Also, n recent decades, revew of lterature ndcates that combnaton of some of these methods have been used to develop rver flow forecastng models (Puldo and Portela, 007; Kuo et al., 006). Fndng subsets of data whch completely cover data trends s necessary n ncreasng the performance of models that are based on tranng and test perods (e.g., ANFIS, ANN). Burman (1989) compared the repeated learnng-testng method wth K-fold crossvaldaton and notced that the combnaton of K-fold and repeated learnng-testng method enhances the accuracy of results. Kohav (1995) compared dfferent crossvaldaton methods for accurate parameter estmaton and data selecton. Hs results showed that ten-fold cross-valdaton has the best performance. Bagherna and Darane (010) n nvestgaton and comparson of the regresson based runoff forecastng models usng satellte data llustrated the applcaton of a jackknfe cross-valdaton method. They ndcated that use of ths method would result n an ncrease n the relablty of the predcton models. 7

3 In ths study, ANFIS usng K-fold crossvaldaton s appled for long-term streamflow forecastng wth monthly and seasonal tme steps n Taleghan Basn, northwest of Tehran. In many studes, the n-stu dscharge measurement s appled n streamflow forecastng (e.g., Shr and Ks, 010) whereas n ths study n order to mprove model performance, the other parameters (ranfall and temperature) are utlzed as well as dscharge parameter n forecastng model. Also, n many studes where the ANNs and other black-box models are used, manly the pont staton data (such as ranfall and temperature) have been used as nputs for the model. In ths study, t s shown that the use of basn data could enhance the results obtaned by the model.. Methods.1. Artfcal Neural Networks (ANNs) Artfcal neural networks (ANNs) are resembled to the bologcal nervous system. ANNs are composed of processng elements n each layer called neurons whch are connected to neurons n the adjacent layer by modfable weghts. A smple ANN could consst of nput and output layers wth known number of neurons, and one or two hdden layers wth varable number of neurons. The model s traned by adjustng the weghts n an attempt to mnmze the sum of squared errors between the model output and observed data. The back-propagaton algorthm s the man method for tranng the model. It conssts of two steps. In the frst step, the nput sgnal (dscharge, ranfall, Journal of Water Scences Research, Vol. 6, No. 1, Wnter 014, temperature, etc.) s propagated forward to compute the output (dscharge). Then, a backward step s used to adjust the weght vectors between layers wth an objectve to mnmze the network error (Hagan et al., 1996). In ths study, a multple-layer feedforward neural network that comprses of an nput layer, an output layer and one ntermedate (hdden) layer s used... Adaptve Neuro-Fuzzy Inference System (ANFIS) Neuro-fuzzy systems are fuzzy systems, whch use ANNs to determne ther characterstcs (fuzzy sets and fuzzy rules) by processng data samples. Neuro-fuzzy systems cover the propertes of both ANNs (tranng data, no pror knowledge) and fuzzy systems (lngustc descrpton, human thnkng) n a complementary way to overcome ther dsadvantages. Novel archtecture of ANFIS frst ntroduced by Jang (1993) and has been used massvely n studes because of ts good performance n nonlnear relatonshps. Generally, the ANFIS model archtecture conssts of fve layers whch are llustrated n Fg.1. Selecton of the FIS based on specfc target system s mportant. Fg. 1. General archtecture of an ANFIS network (Jang, 1993) 73

4 Long-term streamflow forecastng... R. Esmaeelzadeh and A. B. Darane Dfferent types of FIS are presented n the studes (Sugeno and Kang, 1988; Mamdan and Asslan, 1975; Tsukamoto, 1979). The current study uses the Sugeno frst-order fuzzy model (Sugeno and Kang, 1988) because the consequent part of the FIS model (p, q, r ) s a lnear equaton and the parameters can be calculated by smple Least Square Error (LSE) method. For nstance, consder that the FIS has two nputs (x, y); a common rule set wth two fuzzy f-then rules can be expressed as: Rule 1: f x s A 1 and y s B 1 then z 1 = p 1 x+q 1 y+r 1 (1) Rule : f x s A and y s B then z= px+qy+r () The output z s the weghted average of the ndvdual rule outputs. Nodes at the same layer have smlar functons. Layer 1: The output of the th node s defned as O l O A( x) for = 1, (3) Or l O ( ) B y for = 3, 4 (4) Where x (or y) s the nput to the th node and A (or B - ) s the lngustc label assocated wth ths node functon. O s the membershp functon of A (or B - ). The membershp functon for A and B are usually descrbed by bell-shaped wth a maxmum equal to 1 and mnmum equal to 0 such as: x c A ( x ) exp a (5) Where {a, c } s the parameter set. As the values of the parameters change, the bell-shaped functons vary accordngly. Layer : every node n ths layer s a fxed node labeled П and multples the ncomng sgnals. Each output node represents the frng strength of a rule. For nstance, O ( x). ( y), 1, (6) A B Layer 3: each node n ths layer s a fxed node and the th node n ths layer calculates the rato of the th rule s frng strength to the sum of all rules frng strength: O 3, 1, 1 (7) Layer 4: node th n ths layer s an adaptve node wth a node functon O f ( p x q y r ), 1, (8) 4 Where w s the output of layer 3, and {p, q, r} s the parameters set whch are referred to as consequent parameters. Layer 5: the sngle node n ths layer s a fxed node labeled Σ that calculates the fnal output as the summaton of all ncomng sgnals (Jang, 1993). O f f f 1 1 (9) The overall output can be expressed as a lnear combnaton of the consequent parameters: 1 z f1 f ( 1x) p1 (10) 1 1 ( 1yq ) ( 1) r( xp ) ( yq ) ( ) r 1 1 The learnng rule determnes how the premse parameters (Layer 1) and consequent parameters (Layer 4) should be updated n order to mnmze error whch s calculated by the dfferences between the 74

5 network actual output and the desred output. Hybrd learnng algorthm, that combnes the back propagaton gradent descent and least square method, s used as the basc learnng rule and searchng optmal parameters of the ANFIS. Journal of Water Scences Research, Vol. 6, No. 1, Wnter 014, Each model was mplemented by K value ranges between 4 and 7 folds (ranges 10-5% sample for each fold).the best K values are dentfed wth the best performance based on statstcal evaluaton ndces..3. K-fold Where the parameters consst of hgh ranges, usng subsets of data whch completely cover data trends s more felt to ncrease performance of the models. Nowadays, many cross valdaton methods are utlzed n order to overcome ths problem, whch K-fold cross valdaton s one of them. Due to dynamc nature of K- fold method, ths method s able to cover all data trends n both tranng and test samples. K-fold s a computer ntensve technque, usng all avalable data as tranng and test samples. It mmcs the use of tranng and test sets by repeatng the algorthm K tmes wth a fracton 1/K of tranng samples left out for testng purposes. Each tme, all parttons are used for both tranng and test samples. Test and tranng samples are mplemented ndependently (Fg. ). Fg.. Schematc vew of K-fold cross-valdaton method 3. Case study The Taleghan Basn wth a Medterranean clmate s located n northwestern Tehran regon (ncludng Taleghan, Karaj, Latyan, Mamloo, Frouzkooh sub-basns), Iran. Total area of the Taleghan Basn s 960 km. Maxmum, average and mnmum heghts of ths basn are located 4337, 500, and 1675 meters above the sea level, respectvely. The basn has a east-west slope and extends from the spatal doman of 36 05' to 36 17' N lattude and from 50 35' to 51 10' E longtude (Fg. 3). The mnmum and maxmum temperatures n the basn, accordng to 50 years records, are -5 C and 35 C, respectvely, and the range of average annual precptaton n the Taleghan Basn s mm (Department of Energy, 009). 4. Applcaton 4.1. Data Dgtal Elevaton Model (DEM) operated on Shuttle Radar Topography Msson (SRTM) wth spatal resoluton of 90 m was used n ths study (Fg. 3). In order to extend the number of data, the basn was dvded nto three sub-basns (whch are named A, B and C). Rver flow at the outlet of the last sub-basn s the nflow to Taleghan reservor. In addton, n a wde study performed n Tehran regon (subbasns: Taleghan, Karaj, Latyan, Mamloo and Frouzkooh) the monthly precptaton 75

6 Long-term streamflow forecastng... R. Esmaeelzadeh and A. B. Darane (47 statons) and monthly average temperature (13 statons) as shown n Fg. 4 were collected for establshng the regonal relatons. Moreover, a common perod of 19 years startng from through was used n ths study. 4.. Statstcal evaluaton Two statstcal evaluaton crtera were used to assess the model performance. The frst crteron s the Nash-Sutclffe model effcency coeffcent (E) that has a range from - to 1. It s defned as: E 1 T t 1 T t 1 t t ( Q Q ) o m t ( Q Q ) o o (11) Where Q o s observed dscharge and Q m s modeled dscharge. The value of E=1 corresponds to a perfect match of modeled output to the observed output. E=0 expresses that the modeled outputs are as good as the long-term means n predctng the flow. And E<0 ndcates napproprate match of modeled output to the observed output (Nash and Sutclffe, 1970). Scatter ndex (SI) s used as the second crtera and s a dmensonless parameter computed as the rato of Root Mnmum Square Error (RMSE) (Eq. 1) to mean observed streamflowq (Shr and Ks, 010). Ths parameter can be expressed as Eq. (1): n 1 RMSE ( Qo Qm) (1) n 1 5. Results and dscusson 5.1. Streamflow forecastng process Intellgent methods such as ANN and ANFIS requre a suffcent amount of 76 representatve data to properly model the system n order to yeld an enhanced performance. In ths area, the number of observed data s lmted. Therefore, to ncrease the amount of avalable data the study area was dvded nto three sub-basns (Fg. 3). In ths model, several nput combnatons such as monthly streamflow of last three perod, whch are calculated n the outlet of each sub-basn (m 3 /sec), monthly precptaton of prevous perod (P t-1, n mcm) and average temperature of prevous month (T t-1, n C) were used to estmate monthly. streamflows (Q t n m 3 /sec) n each subbasn outlet (Eq. 14). 3 Q f ( Q, P, T ) (14) t tk t1 t1 k 1 Data perod conssts of 19 years ( ) and forecastng s carred out for 6 months startng from Aprl through September n each year. After extractng regonal relatons among elevaton, temperature, and precptaton records n each staton (Whole Tehran Basn, Fg.4), parameter values n each pxel were computed. Fnally, the average values of each parameter for each sub-basn were calculated. To assess model performance n dfferent forecast ntervals, study was focused on estmatng streamflow n two tme steps: monthly and seasonal. In fact, seasonal forecastng s the process of forecastng n next three months. Because ntellgent methods (e.g., ANFIS, ANN) are only based on one type of output, therefore compulsvely, the average values of three next streamflows were used as the output for seasonal forecastng model.

7 Journal of Water Scences Research, Vol. 6, No. 1, Wnter 014, Fg. 3. The study area Fg. 4. Locaton of statons n Tehran regon In ths study, the ANFIS model usng K- fold Cross-valdaton method was appled to long-term streamflow forecastng. Also, results were compared wth those of the typcal method (.e., usng 75% of the whole 77 data set for tranng models and the remanng 5% of the whole data set for testng process). In addton, the performance of the ANFIS was compared wth the ANN method. Therefore,

8 Long-term streamflow forecastng... R. Esmaeelzadeh and A. B. Darane streamflow forecastng was performed by two models (ANFIS, ANN) usng two cross-valdaton methods (K-fold, typcal) and two forecast ntervals (monthly, seasonal). The model was completed n three gradual steps to assess the effect of each varable on the accuracy of forecasted values. Intally, only last three streamflow data was used (model I), then the monthly precptaton was added (II) and fnally the monthly temperature was ncluded n the model (III). 3 Qt f ( Qt k ) (I) k 1 3 Q f ( Q, P ) (II) t tk t1 k 1 3 Q f ( Q, P, T ) (III) t tk t1 t1 k 1 The approprate values of K were determned by tral and error based on statstcal evaluaton crtera (E, SI). Table 1 shows the values of K for each model wth dfferent forecastng tme ntervals. For each specfc value of K, the model was run K tmes and the average results of the statstcal ndces (E, SI) were consdered as the model performance. The man pont n usng k-fold cross-valdaton method refers to ts ablty n proper employment of data for tranng-testng processes whch makes the forecastng model more relable. Table 1. K-values based on tral and error Models Monthly K-values (I) 6 7 (II) 6 5 (III) 7 7 Seasonal ANN model In ths step, the ANN model was used to forecast long-term (monthly, seasonal) streamflows. Table 3 shows the ANN performance model usng dfferent crossvaldaton methods. As t can be seen from Table 3, the model performance n the test perod s mproved by addng new varables. For nstance, The Nash-Sutclffe model effcency coeffcent, E, n model (II) shows mprovements of 0.06 to 0.08 n monthly tme steps and 0.09 n seasonal forecastng n both cross-valdaton methods as compared to model (I). In addton, the results of monthly models are better than those of the seasonal one. For example, the maxmum values of E n monthly and seasonal models are 0.83 and 0.74, respectvely. Smlar trend was observed n the SI ndex. Table 3 also demonstrates that n ANN model the applcaton of K-fold method results n better performances than the typcal one. The maxmum values for the Nash-Sutclffe coeffcent ndex n monthly models are 0.66 and 0.83 for typcal and K- fold methods, respectvely. Also, n seasonal models the Nash-Sutclffe coeffcent ndex has the maxmum values of 0.66 and 0.74 for the typcal and K-fold methods, respectvely. Both results ndcate the superorty of the K-fold over typcal method n terms of the Nash-Sutclffe ndex n the ANN model. However, the man advantage n usng k-fold s the proper employment of data for tranng-testng processes and hence, ncreasng the relablty of the forecastng model. In dong ths, results of k-fold may show nferorty to those of the typcal method, but t does not justfy the use of typcal method snce

9 the evaluaton (testng) perod s carred out usng a very lmted perod of data as compared to the k-fold where, through teratons, the whole data could be used for the evaluaton ANFIS model The fnal archtecture of the ANFIS models s gven n Table. It shows the number of membershp functons of each nput varable. Fuzzy membershp functons could have many forms. It depends on the complexty and characterstcs of data. Among dfferent types of data, hydrologc and clmatologc varables are among those of non-lnear ones; therefore membershp functon wth smlar characterstcs seems to be necessary. Thus, the Gaussan functon, n ths study, s employed and defned as: ( x c ) f ( x,, c) e Journal of Water Scences Research, Vol. 6, No. 1, Wnter 014, (15) Where c s center of Gaussan membershp functon and σ s standard devaton of Gaussan membershp functon. For nstance, the ANFIS model (monthly) for nput combnaton (III) has 3, 3, 3, 3, 3 membershp functons for the last three streamflow data ( Qt k), monthly precptaton ( Pt 1 ) and monthly temperature ( Tt 1) nputs, respectvely. Table. The number of membershp functons Models Monthly Seasonal (I),,,, (II) 1,1,1,1 3,3,3,3 (III) 3,3,3,3,3,,,, Evaluaton processes of ANFIS model are dentcal to those of ANN model. The results of ANFIS model n the test perod are demonstrated n Table 3. It shows that the ANFIS model performance s mproved n test perod by addng parameters gradually, n both monthly and seasonal forecasts. For nstance, the scatter ndex SI usng K-fold cross-valdaton for monthly and seasonal forecastng has 0.33 and 0.47 mprovements n model (III) n comparson wth those of model (I). A smlar trend s observed n the typcal method. Based on results, t can be concluded that the results of monthly ANFIS model are superor to those of the seasonal one. As t was mentoned earler, smlar behavor was also observed n the ANN model. Moreover, results also ndcate the superorty of the K-fold over typcal method n terms of the Nash-Sutclffe ndex n ths model as well (agan smlar to ANN). Fnally, based on both statstcal crtera (E, SI), as shown n Table 3, generally the ANFIS model shows a better performance than the ANN one. For nstance, n the monthly forecastng model (II) usng k-fold cross valdaton method, the ANN has statstcal ndces of E=0.67 and SI=0.79, whle these values mprove to E=0.87 and SI=0.78 for the ANFIS model n the same case. Improvements as hgh as 0.0 n the Nash-Sutclffe ndex can be seen, whle there are rare cases where ANN shows slghtly better results. Smlarly, when the ANFIS model s used, sgnfcant mprovements s notced n the SI ndex n some cases. 79

10 Long-term streamflow forecastng... R. Esmaeelzadeh and A. B. Darane Table 3. Statstcal measures of ANFIS and ANN models n test perod ANN ANFIS Forecast ntervals K-fold Typcal K-fold Typcal E SI E SI E SI E SI (I) Seasonal Monthly (II) (III) (I) (II) (III) Effect of regonalzaton on model performance One of the most mportant ssues n hydrologc studes s defcency and napproprate dstrbuton of hydrometeorologcal statons that deterorates the model accuracy. On the other hand, n most of the prevous studes observed pont data of statons have been used nstead of areal estmates n the forecastng models (e.g., Shr and Ks, 010). Use of pont data may be applcable to small basns but t would ntroduce errors f the basn s large. The common belef s that n black box methods such as ANN and ANFIS, tranng process could handle the shortcomngs of pont data through proper adjustments of parameters and weghts. In ths paper, we show that although ths mght be a true assumpton to some extent, however, there are at least cases that tranng process by tself would not be able to justfy the use of pont staton data. To prove ths hypotheses, models are appled usng multple sub-basn and then pont data. In the multple sub-basn data, the average value of each parameter n whole area (usng the regonal relatons) s specfed as the model nput. In Taleghan basn, the Glrd, Gatedeh and Dzan statons are dentfed as the precptaton statons, the Zdasht and Jostan statons are specfed as the temperature statons and the Taleghan Reservor nflow s dentfed as the basn outlet dscharge staton (Fg. 5), whereas n the multple sub-basn data, the average value of precptaton and temperature for each sub-basn and the outflow for each sub-basn (A, B and C, whch s Taleghan reservor nflow) whch s shown n Fg. 3, are used as the model nput. For ths purpose, only the typcal cross-valdaton method and monthly forecasts coverng 6 months (Aprl- September) are used. Moreover, the results of ANFIS and ANN methods n the models number II and III are evaluated. Number of nput data n ANN and ANFIS models plays a key role n model performance. In ths regard, the basn s dvded nto three sub-basns as shown n Fg. 3. Therefore, the basn s changed to three sub-basns and outflow data for each sub-basn s also used as the response value of the system for gven sub-basn areal data 80

11 (.e., precptaton, etc.). Consequently, the number of data for models s trpled through ths approach. The results for the test perod as shown n Table 4 ndcate that when multple subbasn data are used, model performances are substantally mproved. For nstance, the Nash-Sutclffe coeffcent Index E for ANFIS and ANN methods usng pont staton data n model III are 0.49 and 0.41, whereas these values are respectvely mproved to 0.87 and 0.66 when multple sub-basn data and multple sub-basn method are used. Fg. 5. Locaton of the data statons A smlar trend s observed n the Scatter Index SI. Therefore, t can be concluded that at least n ths case, and possbly n many other cases, the use of multple subbasn data could substantally enhance the results of forecastng models ncludng black-box methods. In addton, t s worthwhle to set tme and effort necessary for dervng regonal relatons and computng multple sub-basn data n the basn. Journal of Water Scences Research, Vol. 6, No. 1, Wnter 014, Table 4. Statstcal measures of ANFIS and ANN models n test perod Metho ds ANFIS ANN Model s 6. Conclusons Multple Staton Data Sub-Basn Data E SI E SI (II) (III) (II) (III) In ths study, ANN and ANFIS methods are used for long-term streamflow forecastng n Taleghan Basn. The ANFIS model showed a better performance than the ANN model n predctng the streamflows. It was also shown that usng K-fold as the cross-valdaton method ncreases model relablty. Moreover, use of multple subbasn data could substantally enhance the results of forecastng models ncludng black-box methods (.e., ANN and ANFIS). In applyng the multple sub-basn data, the number of nput data n ANN and ANFIS models could be reduced causng serous problems n proper model tranng and testng processes. It was shown that dvdng the basn nto several sub-basns could help n overcomng the problem. Due to problems wth ground based statons ncludng; ther poor dstrbuton, the absence of n-stu measurements especally n mountanous areas, the use of satellte mages can be appled n hydrologc studes, especally streamflow forecastng, for future studes n ths feld. 81

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