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1 I teratoal Joural of Egeerg Research Ad Maagemet (IJERM) ISSN : , Volume-3, Issue- 5, Ma 16 A rtfcal Neural Network Modelg of the Groudwater Q ualt (Case Stud: Zahrez Bas Algera) F atah Bouteldjaou, Mohamed Besseasse, Ahmed Kettab A bstract A rtfcal eural etworks (ANNs) model are wdel used water resources applcatos to predct ad forecast water resources varables. The objectve of ths stud s to vestgate the abltes of a artfcal eural etworks model t o predct the total dssolved sold (TDS) ad electrcal coductvt (EC). Water qualt varables such as ph, calcum (Ca ), magesum (Mg ),sodum (Na ), potassum (K + ), bcarboate (HCO3-), chlorde (Cl ), trate (NO3 - ) ad sulfate ( SO4 ) were used as the put data to obta the output of the eural etwork(tds ad EC). Performace of the ANN models was evaluated usg correlato coeffcet (R), Nash- Sutclffe coeffcet of effcec (NASH), root mea square error ( RMS), Normalsed Root Mea Square Error (NRMSE) ad Mea absolute error (MAE). computed from the measured ad model computed values of the depedet varables.the results of ths stud reveal that the ANN- MLP (9, 9, 1) model gves the b est estmates for the TDS predcto. The results of eural etwork modelg to predct electrcal coductvt (EC) dcate that the ANN- MLP (9, 1, 1) model showed better predctve ablt the determato of EC. The detfed ANN models ca be used as tools for the computato of g r oudwater qualt parameters Zahrez bas. K e w ords Artf cal eural etwork (ANN), Groudwater M ultlaer perceptro, Zahrez bas I. IN TRODUCTION Zahrez bas s located the Hgh Plateaus of the orth Algera, characterzed b a sem-a rd clmate where aual rafall s hghl rregular. Because of the scarct of surface w ater, groudwater s a major source of water s uppl d fferet ctes aroud the stud area. Groudwater resources the stud area occur four ma hdrogeologcal uts: (1) Moploquaterar cossts of coglomerate ad cla, () Turoa made up of fractured l mestoe, (3) A lba, ad (4) Barrema aqufer made up of s adstoe [1]. The moploquaterar aqufer s a source of fresh water for the ct of Djelfa wth a populato of 1,491,37 habtats. Groudwater qualt s affected b a wde rage of atural ad athropogec factors. Natural p rocesses (hdrologcal, phscal, ad chemcal) ma affect the characterstcs ad cocetrato of chemcal elemets groudwater [- 3 ]. I addto, there are also athropogec mpacts due to urbazato, dustral ad agrcultural a ctvtes the bas. Assessmet of the groudwater qualt as well as developmet of maagemet strateges for the protecto of water resources s oe of the essetal objectves for the future developmet of a coutr, especall whe the Mauscrpt receved Ma, 16. F atah Bouteldjaou, E cole Natoale Poltechque, Alger, Algére M ohamed Besseasse, U versté Saad Dahlab, Blda, Algére. A hmed Kettab, E cole Natoale Poltechque, Alger, Algére rsg demad for clea drkg water s cosdered [4-5]. A rtfcal eural etworks (ANNs) models have bee successfull used hdrologcal processes, water resources, water qualt predcto [6-9 ]. Nroobakhsh et al. [8] used two ANN etworks, multlaer perceptro (MLP) ad radal b ass fucto (RBF) to compute the total dssolved sold (TDS) cocetratos for the Jajrood Rver of Ira. I ther stud, the foud that MLP ad RBF are able to smulate water qualt varables of Jajrood Rver wth more tha 9% accurac. Sgh et al. [8] computed dssolved oge (DO) a d bochemcal oge demad (BOD) levels the Gomt Rver Ida usg three- laer feed forward eural etworks wth back propagato learg. The coeffcet of determato for modeled values ad observed DO values w ere.7,.74, ad.76 for the trag, valdato ad test s ets, respectvel. The ma objectve of ths stud s to costruct a artfcal eural etwork (ANN) model for the predcto of total dssolved solds (TDS) ad electrcal c oductvt (EC) Zahrez bas ad demostrate ts applcato to comple water qualt data as how t ca mprove the terpretato of the results. Here, we have vestgated the possblt of trag ANN models correlatg the prmar water qualt varables (depedet) w th ther secodar attrbute (depedet varable). The TDS ad EC of the groudwater were take as the depedet varables here ad set of other parameters costtuted the depedet varables. A. S tud area I I. MA TERIALS AND METHODS T he Zahrez bas (Fg.1) s oe of the edorhec bass of the vast steppes rego the cetral orther part of Algera. The Zahrez hdrologcal bas covers appromatel 8,989 km. Topograph of the area s relatvel flat wth a elevato ragg from 9 to 133 meters above mea sea l evel [1]. The catchmet les betwee logtudes 15 to 4 8 E ad lattudes t o 35 3 N. The area s characterzed b a sem- ard clmate, tpcall M edterraea, wth a rregular aual rafall. The mea a ual rafall ad potetal evapotrasprato are 5 ad 138 mm, respectvel, eceedg rafall for most of the ear. The mea mothl temperature vares betwee 3 C ad 5 C. The precptato perod a tpcal ear s betwee O ctober ad March ad the dr perod ca eted from Aprl to September [1]. The ephemeral rvers of the rego, locall called wad, have a termttet flow regme, because the d r seaso s tpcall ver log (6 8 moths) ever ear. The ma wads ths bas are the Melah ad Hadja rvers w hch receve ma mportat flow trbutares. The draage d est of the area rages betwee 1.4 ad 1.8 km/km [ 1]. 158

2 A rtf cal eural etwork modelg of the groudwater qualt (case Stud: Zahrez bas Algera) B. W ater qualt data set A tot al of 47 water samples groudwater samples were collected durg samplg campags carred out October 1 at wells varous parts of the stud area (Fg. 1). Electrcal coductvt (EC), temperature ad ph were measured the feld, usg the portable Oro EC ad ph m eters. Water samples were fltered through a.45 µ m cellulose membrae ad collected 1 ml polethlee bottles for major ad mor elemet aalss whch have bee doe at the Natoal Agec for Water Resources + + (ANRH). Catos (Ca, Mg, Na + +, K ) were aalzed b - atomc absorpto spectrometr, aos (Cl, SO4 - ad NO3 - ) b hgh performace oc lqud chromatograph (HPILC). Bcarboates (HCO3 - ) were determed b acd- base ttrato m ethod [11]. C. D ata processg Before the etwork trag, the orgal data were ormalzed accordace wth the requremets of the BP a lgorthm. The values appled the put ad output laers were ormalzed b the followg formula the rage of ( 1 ). orm m ( 1) ma m m ma orm Where,,, ad deote, respectvel, values of put (output) varables, mmum value of put (output) varable, mamum value of put (output) varable ad the ormalzed value of. The de- ormalzed value of the ANN was computed usg: t m orm ma m ( ) Where t, m, m a ad orm are, respectvel, real valued output varable, mmum ad mamum values of real- valued output ad the ormalzed output value from the eural- A NN model. T he proporto of ANN trag set from the avalable data raged geerall from 5% to 8%.The proporto of ANN testg set from the avalable data s about 15 to % ad the proporto of the valdato data set s a bout (5 to 15%) [ 1]. D. A rtf cal eural etworks modelg (ANNs) A NN models have bee used successfull to model comple olear put output relatoshps partcularl stuatos where the eplct form of the relato betwee the varables volved s ukow [13-14]. As a olear statstcal t echque, ANNs ca be used to solve problems that caot be addressed b tradtoal approaches [15]. The ANN archtecture s composed of a put laer, a certa umber of hdde laers ad a output laer forward coectos. T he put laer troduces data to the model ad calculates the weghted sum of the put(s). The hdde laer or laers processes data, ad the output laer produce the results of the ANN model. Each laer s com- posed of oe or more basc e lemet(s) called a artfcal euro or a ode, whch s coected to a etwork b a weght factor. A feed- forward eural etwork s commol used for predctg ad forecastg water qualt varables[16-18]. The major steps f or developmet of ANN models clude defg the s utable model puts, specfg etwork tpe, pre- processg ad parttog of the avalable data; d etermg etwork archtecture; defg model performace crtera; trag (optmzato of coecto weghts); ad valdatg the model [19-1]. E. Mult- l aer perceptro (MLP) A multlaer feed-forward etwork or mult- laer perceptros (MLP), orgall proposed b Rumelhart ad McClellad [], are the most commol used ad well- researched class of ANNs [3]. A MLP cossts of a put laer, whch receves the values of the put varables, a output laer, whch provdes the model output, ad oe or more hdde laers. Nodes each laer are tercoected through weghted acclc arcs from each precedg laer to t he followg, wthout lateral or feedback coectos [4]. F. Actvato f ucto The actvato (trasfer) fucto determes the respose of a ode to the total put sgal t receves. The most commol used actvato fucto, amed logstc sg- mod- tpe fucto was used ths stud for the hdde laer [5-6]. However, a lear- tpe actvato fucto was used for the output laer, as suggested b Maer ad Dad [1] ad Rumelhart et al. [7]. The sgmod fucto s a bouded, mootoc, o- decreasg fucto that provdes a graded, o-l ear respose [8], whereas a lear- trasfer fucto calculates a euro s output b smpl returg the value passed to t. The mathematcal e pressos for these two fuctos are as follows: Lear fucto: L ogstc s gmod fucto: f ( ) ( 3 ) 1 f ( ) ( 4) 1 e( ) Aother sgmod fucto s the ta- sgmod fucto, def ed b T a sgmod fucto: 1 e( ) f ( ) 1 e( ) G. M odelg performace crtera trasfer To determe the performace of each of the selected etwork model, fve dfferet crtera were used: the root mea square error (RMSE, the ormalzed Root Mea Square Error (NRMSE), the Nash- Sutclffe Effcec Ide ( NASH), ad the mea absolute absolute error (MAE), ad t he correlato coeffcet (R). The fve dces are c omputed accordg to the followg equatos: a ) Root Mea Square Error s RMSE: ( 5) 159

3 I teratoal Joural of Egeerg Research Ad Maagemet (IJERM) ISSN : , Volume-3, Issue- 5, Ma 16 b ) Normalzed NRMSE RMSE 1 ( ) 1 Root Mea Square Error (NRMSE): RMSE ma m ( 6) 1 ( ) 1 ( 7) ma m c) Nash- S utclffe coeffcet of effcec: NASH d ) Mea MAE 1 1 ( 1 ( ) ) absolute error (MAE) 1 1 e ) Correlato Coeffcet ( R ) R N 1 N 1 N 1 where, ad are actual ad obtaed values of output, ad N s the umber of values. s the mea estmato from the observed records for ste, s the mea estmato obtaed from the model for ste, ad s the mea of the mea estmato from the o bserved records of the stes. W here, ad are actual ad obtaed values of output, s t he mea of actual output values. I II. RESULTS AND DISCUSSION (8) (9) (1) coductvt (EC), the avalable 47 measured data set + cludg Ca, HCO3 - +, Mg, Na + + -, K, Cl, NO3 - ad SO4 - ; a d ph varables were dvded to three phases : 75%, 15% ad 1 % of data set were chose for trag, testg, ad valdato phase, respectvel. Dfferet ANN models were costructed ad tested order to determe the o ptmum umber of odes the hdde laer ad trasfer fuctos. Selecto of a approprate umber of odes the hdde laer s ver mportat aspect as a larger umber of these ma result over- fttg, whle a smaller umber of odes ma ot capture the formato adequatel. The s utable umber of odes (euros) hdde laers rages f rom to ( + 1), where s the umber of put odes ad m s the umber of output odes [ 9]. T o cofrm the optmum structure of the AN N model, several models were costructed. The results are provded T ab le ad 3. C. Total dssolved solds (TDS) models The archtecture of the best ANN models for the total dssolved solds (TDS) ad electrcal coductvt (EC) the Zahrez groudwater s preseted Table. The best A NN model for the TDS s composed of oe put laer wth e put varables, oe hdde laer wth e odes a d oe output laer wth oe output varable. It ca be see f rom Table that the MLP (9,9,1) model provded a best ft m odel for the trag ad test data sets. The respectve values of RMSE, NRMSE, ad MAE for the two data sets are 99.1,.4 ad 81.8 for trag, ad 14.4,.34 ad for testg. The correlato coeffcets betwee the observed ad predcted TDS values were.995,.976 a d.984 for the trag, test ad valdato sets, respectvel. The NASH values correspodg to the trag ad testg sets are.95 ad.94, respectvel, s uggestg good ft of the model to the data set. The c omparso of the measured ad predcted TDS values for the trag, testg, ad valdato data sets are show F g. ad 3. The correlato coeffcets of trag, testg, ad valdato were.995,.976, ad.984, respectvel, s uggestg good f t of the model to the data set. A. Descrptve statstcs The detals of descrptve statstcs for groudwater qualt p arameter s are gve Table 1. Recorded g roudwater p H v ares from 7.6 to 1, dcatg that the groudwater s amples are mal alkale. The TDS values the groudwater raged from 3 to 4,1 mg/l, wth a mea value of 1546 mg/l. TDS the stud area varg over two o rders of magtude from fresh (TDS < 1 mg/l) to bracksh (1, mg/l < TDS < 1, mg/l). The most + + domat major catos are Na ad Ca, whle major aos - are domated b Cl followed b SO4 -. Also, Table 1 reflects a moderate to hgh varablt (stadard devato ad c oeffcet of varato) of samples parameters. The hghest varablt was for CO , followed b K, ad Na wth a coeffcet of varato greater tha 1., reflectg the spatal v arato of groudwater qualt the Zahrez bas. B. Artf cal eural etwork (ANN) I order to costruct a artfcal eural etwork ANN model for the total dssolved solds (TDS) ad electrcal 16

4 A rtf cal eural etwork modelg of the groudwater qualt (case Stud: Zahrez bas Algera) F g. 1. L ocato map ad geologcal formatos of the Zahrez Table 1. D escrptve statstcs of groudwater qualt parameters measured the stud area P arameter M Ma Mea Varace SD CV E C (μs/ cm) C a (mg/l) M g (mg/l) N a (mg/l) K (mg/l) C l (mg/l) H CO3 ( mg/l) NO 3 ( mg/l) p H CO 3 ( mg/l) T DS (mg/l) S O ( mg/l ) 161

5 I teratoal Joural of Egeerg Research Ad Maagemet (IJERM) ISSN : , Volume-3, Issue- 5, Ma 16 Table. A NN S tructure P erformace param R eters of the artfcal eural etwork for predctg the TDS N ash R MSE MLP MLP MLP MLP MLP MLP MLP MLP MLP MLP MLP T a ble 3. Performace parameters of the artfcal eural etwork for predctg the TDS cocetrato, trag, testg, ad phase (NRMSE, RMSEr ad MAE) A NN S tructure N RMSE R MSEr M AE MLP MLP MLP MLP MLP MLP MLP MLP MLP MLP MLP T able 4. Performace parameters of the artfcal eural etwork for predctg the EC cocetrato, trag, testg, ad valdato phase (R, Nash ad RMSE). A NN S tructure R N ash R MSE MLP MLP MLP MLP MLP MLP MLP MLP MLP MLP MLP

6 ) mc/ Sµ( CE )l/ g m( S DT det c der P A rtf cal eural etwork modelg of the groudwater qualt (case Stud: Zahrez bas Algera) T able 5. P erformace parameters of the artfcal eural etwork for predctg the EC cocetrato, trag, testg, a d valdato phase (NRMSE, R MSEr ad MAE) A NN S tructure N RMSE R MSEr M AE MLP MLP MLP MLP MLP MLP MLP MLP MLP MLP MLP D. Electrcal coductvt (EC) model Twelve archtectures ANN were used to predct the c oductvt the Zahrez groudwater. The performace parameters of the trag, test ad valdato sets are show Table 3. The selected ANN (MLP ) provded a best ft model for the trag ad test data sets. The costructed A NN model (EC) was traed usg the BFGS quas Newto Algorthm (BFGS 55). For the best MLP etwork model A o- lear trasfer fucto (Tah) was used the hdde laer ad a o- lear trasfer fucto (Logstc) the o utput laer. The respectve values of RMSE, NRMSE, ad MAE for the t wo data sets are ,.5 ad for trag, 97.39,.41 ad.3 for testg. The correlato coeffcets (R) for the trag, test ad valdato sets were.995,.966 ad.98, respectvel. The respectve values o f NASH for the trag ad testg sets were,.993 ad.935 respectvel, suggest for a good- ft of the selected EC model to the data set. The scatter plot of observed versus modeled values of EC are show Fgure. 4 ad 5. The c oeffcet of correlato (R) values for the trag, test, ad valdato sets were.995,.966 ad,.98, respectvel, suggestg a good-ft of the EC model (MLP ) to the d ata set bserved O ) µs/cm EC( redcted P ) µs/cm EC( F 5 F 9 F 3 1 F 7 1 F 1 F 5 F 9 F 3 3 F 7 3 F 1 4 F 5 F4 1 Samples F g. Measured ad predcted TDS cocetratos b MLP ( 9, 9, 1) model trag, testg, ad valdato phase F g. 3. Scatter dagram of the predcted values versus measured values for the trag, testg, ad valdato data s ets (mg/l) Observed TDS 163

7 ) mc/ Sµ( CE det c der P )l/ g m( S DT I teratoal Joural of Egeerg Research Ad Maagemet (IJERM) ISSN : , Volume-3, Issue- 5, Ma TDS Observed TDS 4 Predcted F 5 F 9 F 3 1 F 7 1 F 1 F 5 F 9 F 3 3 F 7 3 F 1 4 F 5 F4 1 EC( O ) µs/cm bserved F g 4. Measured ad predcted EC b MLP (9, 1, 1) m odel trag, testg, ad valdato phase. Fg 5. Scatter dagram of the predcted values versus m easured values for the trag, testg, ad valdato d ata sets. Samples I V. C O NCLUSION I ths stud artfcal eural etwork (ANNs) was developed to predct total dssolved sold (TDS) ad electrcal coductvt (EC) groudwater of the Zahrez bas. The results dcate that, the ANN- MLP (9, 9, 1) model provded a best accurac for predcto of the TDS cocetrato. It s foud that the coeffcet of correlato (R) values for the trag, testg, ad valdato sets were.995,.976, ad.984, respectvel, the respectve values of RMSE, NRMSE, a d MAE for the two data sets are 99.1,.4 ad 81.8 for trag, ad 14.4,.34 ad for testg, ad 89.77,.71 ad for valdato. The results of the predctve ANN models of electrcal coductvt (EC) showed that the ANN- MLP (9, 1, 1) model provdes the b est accurac, wth the coeffcet of correlato (R) of.995,.966 ad,.98 for the trag, test ad valdato sets, respectvel. The respectve values of RMSE, NRMSE, ad MAE for the two data sets are ,.5 ad f or trag, 97.39,.41 ad.3 for testg, ad ,.68, ad for valdato. Fall, from the results obtaed, a ANN model appears to be a useful tool for predcto of the groudwater qualt parameter the Zahrez b as. AC KNOWLEDGEMENTS T he authors wsh to thak the aomous revewers for ther frutful cotrbuto the mprovemet of the mauscrpt, t hrough ther revsos, suggestos ad crtcal commets. RE FERENCES [ 1] S d Moussa, M. F.. Ressources Hdraulques de la zoe du projet GTZ-HCDS. Coopérato Algero- A llmade. 176 P. [ ] K ettab. A, a d Metache. M. 5 Water desalato prce from r ecet performaces: Mod ellg, smulato ad aalss. Iteratoal J oural of Nuclear Desalato [ 3] K ettab. A, Besseasse. M, a d A. S. M oulla. ( 1) Seawater d esalato: Stud of three coastal statos Algers rego. D esalato [ 4] Kettab. A. ( 1). Water resources Algera: strateges, vestmets, a d vso. D esalato 136 ( 1-3): 5-33 [ 5] Kettab. A, Mtche. R, ad Beaçar. N. ( 8). Water for a s ustaable developmet: challeges ad strateges. Revue des sceces de l 'eau 1 (). [ 6] We. C.G, ad Lee. C. S. ( 1998). A eural etwork approach to multobjectve optmzato for water qualt maagemet a rver bas. W ater Resourc Res 34 (3): [ 7] L obbrect. A.H, ad Solomate. D.P. ( 1999). Cotrol of water levels p older areas usg eural etworks ad fuzz adaptve sstems. Water I dustr Sstems Modelg ad Optmzato Applcatos v ol. 1: [ 8] Nroobakhsh. M.S.H, Musav-J ahrom. S.H, Mashour. M, ad Sedgh. S. ( 1). Predcto of water qualt parameter Jajrood Rver bas: Applcato of mult- laer perceptro (MLP) perceptro ad radal bass f ucto etworks of artfcal eural etworks (ANNs). A frca Joural of A grcultural Research 7 (9): [ 9] S gh. K.P, Basat. A, Malk. A, ad Ja. G. ( 9). Artfcal eural etwork modelg of the rver water qualt a case stud. Ecologcal M odellg., [ 1] ANRH. 9. Agec for water Resources [ 11] Belkhr. L, Boudoukha. A, Mou. L, ad Baouz T. ( 11). Statstcal categorzato geochemcal modelg of groudwater A Azel pla ( Algera). Joural of Afrca Earth Sceces 59: [ 1] Hak. S. ( 9). Neural etworks ad learg mache., 3 rd ed, e dted b P earso [ 13] Gallat. S.I. ( 1993). Neural Network Learg ad Epert Sstems., e dted b M IT press, Massachusetts, USA [ 14] Smth. M. ( 1994). Neural Networks for Statstcal Modellg., edted b V a Nostrad Rehold, NY [ 15] D oga. E, Segorur. B, ad Koklu. R. (9). Modelg bochemcal o ge demad of the Mele Rver Turke usg a artfcal eural etwork techque. J oural E vrometal M aagemet 9 (): [ 16] Maer. H.R, Ja. A, Dad. G.C, ad Sudheer. K.P. ( 1). Methods used for the developmet of eural etworks for the predcto of water resource varables rver sstems: cur- ret status ad future drectos. Evrometal Modellg & Software 5 ( 8): [ 17] Pala. S, Log. S.Y, Tkalch. P. ( 8) A ANN applcato for water qualt forecastg. Mare Polluto. Bullet. 56 (9): [ 18] Zhao. Y, N a. J, C u. F.Y, ad Guo. L. ( 7). Water qualt forecast t hrough applcato o f BP eural etwork at Yuqao reservor. Joural Z hejag Uverst S cece 8 (9): [ 19] Dawso. C.W, ad Wlb. R.L. ( 1). Hdrologcal modellg usg a rtf cal eural etworks. Progress Phscal Geograph 5 (1): [ ] Govda raju. R.S. ( ). Artfcal eural etworks hdrolog. I, prelmar cocepts. J oural of Hdrologc Egeerg 5 (): [ 1] Maer. H.R, ad Dad. G.C. ( ). Neural etworks for the predcto ad forecastg of water resources varables: a revew of 164

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