Architecture of Artificial Neural Network in Identification of Internal Dynamics and Prediction of Dynamic System Rainfall Data Time Series

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1 Archtecture of Artfcal Neural Networ Idetfcato of Iteral Dyamcs ad Predcto of Dyamc System Rafall Data Tme Seres Beyutty Varghese, Gyaesh Shrvastava 2, Saeev Karmaar 3, Mao Kumar Kowar 4 & Pula Guhathaurta 5,2,3&4 Bhla Isttute of Techology, Durg, Bhla House, 4900, Durg, Chhattsgarh, Ida 5 Ida Meteorologcal Departmet, Pue, Sva Nagar, Pue, Mharastra, Ida E-mal : armaar_saeev@gmal.com 3, mowar@gmal.com 4, pguhathaurta@redffmal.com 5 Abstract - The obectve of ths study s to expad ad evaluate the bac-propagato artfcal eural etwor (BPANN) ad to apply the detfcato of teral dyamcs of very hgh dyamc system such log-rage total rafall data tme seres. Ths obectve s cosdered va comprehesve revew of lterature (978-20). It s foud that, detal of dscusso cocerg the archtecture of ANN for the same s rarely vsble the lterature; however varous applcatos of ANN are avalable. The detal archtecture of BPANN wth ts parameters,.e., learg rate, umber of hdde layers, umber of euros hdde layers, umber of put vectors put layer, tal ad optmzed weghts etc., desged learg algorthm, observatos of local ad global mma, ad results have bee dscussed. It s observed that obtag global mma s almost complcated ad always a temporal ervousess. However, achevemet of global mma for the perod of the trag has bee dscussed. It s foud that, the applcato of the BPANN o detfcato for teral dyamcs ad predcto for the log-rage total aual rafall has produced good results. The results are explaed through the strog assocato betwee rafall predctors.e., clmate parameter (depedet parameter) ad total aual rafall (depedet parameter) are preseted ths paper as well. Keywords - Meteorology, Rafall, Spatal, Iterpolato, Neural Networ, Bac-Propagato. I. INTRODUCTION I much scece ad egeerg practce today, there s a creasg demad for techques whch are capable of terpolatg rregularly scattered data dstrbuted space. These techques have may applcatos cludg rafall estmato. Mathematcally, the geeral model for spatal terpolato of values µ a surface R ca be expressed as: φ = f (x, x 2,,, v, v 2,.., v ) Where, (x, x 2,,) s a putted depedet parameters ad v, v 2,..., v are addtoal varables such as weghts to be optmzed. I ths secto, cotrbutos from the year 978 to 20 have bee revewed. It s foud that, there are several terpolato methods for solvg the above problem have bee used. Techques such as geostatstcal co-rgg (Jourel ad Hubregts, 978) ad ANN (Hor et al., 987) are commo [, 2]. Goovaerts, 997, Demyaov, 998, S. va der Hede has suggested four methods for terpolato cludg ANN ther wor [4]. Huag et al. (998), demostrated the use of dyamc fuzzy-reasog-based fucto estmator (DFFE) to terpolate rafall data a case study Swtzerlad [5]. The fuctoal parameters are also optmzed by geetc algorthms (GA). Rcardo ad Palutof, 999, have successfully appled ANN techque for smulato of daly temperature for clmate chage scearos over Portugal [6]. Guhathaurta, 998, has appled hybrd ANN predcto of Ida mosoo rafall ad has foud very sgfcat results almost more tha 85% correctess [7]. Guhathaurta, 999, appled ths ANN method effectvely predcto of surface Ozoe whch s very dyamc ad upredctable ature for very smaller geographcal earth rego. He has also cotrbuted extremely sgfcat fdg the year of 2000 ad 2006 wth the smlar ANN methods especally for clmate varable predcto [7-3]. Raeeva et al. (2000) have gve a power regresso based log-rag mosoo rafall forecastg system for pesular Ida rego [4]. However, Guhathaurta (2006) ad Karmaar et al. (2008) have foud that, the ANN method s better evaluated over the statstcal techque for the same [5-2]. Sell, 2000 has foud a ew method for the spatal terpolato of daly maxmum surface ar temperatures. Ths ew method uses ANN to geerate temperature estmates at eleve locatos gve formato from a lattce of surroudg locatos. The out-of-sample performace Iteratoal Joural of Computer Scece ad Iformatcs ISSN (PRINT): , Vol-, Iss-4, 202

2 of the ANNs s evaluated relatve to a varety of bechmar methods (spatal average, earest eghbor, ad verse dstace methods). He has foud that, the ANN approach s superor both terms of predctve accuracy ad model ecompassg [22]. Atoć et al. (200) have descrbed Spato-temporal terpolato of clmatc varables over large rego of complex terra usg eural etwors [23]. Preseted terpolato models provde relable, both spatal ad temporal estmatos of clmatc varables, especally useful for dedroecologcal aalyss. Rgol et al. (200) have descrbed spatal terpolato of daly mmum ar temperature usg a feed-forward bac-propagato eural etwor. Smple etwor cofguratos were traed to predct mmum temperature usg as puts: () date ad terra varables; (2) temperature observatos at a umber of eghbourg locatos; (3) date, terra varables ad eghbourg temperature observatos. Ths s the frst tme that tred ad spatal assocato are explctly cosdered together whe terpolatg usg a ANN [24]. Koe et al. (200) suggested a terpolato method based o a multlayer eural etwor (MNN), has bee examed ad tested for the data of rregular sample locatos, He foud that, the ma advatage of MNN s that t ca deal wth geographcal data wth olear behavor [25]. Brya ad Adams (2002) have successfully appled terpolato of Mea Precptato ad Temperature Surfaces for Cha [26, 27]. L (2002) have suggested ANN models could be used to accurately estmate these weather varables. I ths study, ANNbased methods were developed to estmate daly maxmum ad mmum ar temperature ad total solar radato for locatos Georga. Observed weather data from 996 to 998 were used for model developmet, ad data from 999 to 2000 were used for fal ANN model evaluato [28]. Iser et al. (2002) have foud that, the ANN Medum Term Forecastg of Rafall over Ida rego s suffcetly sutable [29]. Slva 2003 has successfully appled ANN techque for specal terpolato of temperature varable carred out the Austra Cetral Isttute of Meteorology ad Geodyamcs ZAMG, o the scope of the COST Acto 79. Ths wor focuses o the capabltes of Neural Networs used the spatal terpolato of some clmate varables showg the advatages ad dsadvatages [30]. The applcato of a ANN o the Austra mea ar temperature dstrbuto for August has produced good results, explaed by the strog alttude depedecy of ths parameter. Tmo ad Saveleva, 2005, have descrbed aother applcato for spatal predcto of radoactvty usg GRNN [3]. Guhathaurta 2006, Karmaar et al. (2008, 2009) have foud that, the Rumelhart,986 learg algorthm based Neural Networ model ca be also approprate for log-rage mosoo rafall predcto over very smaller geographcal rego. Attorre et al. (2007) have compared three methods that have bee proved to be useful at regoal scale: - a local terpolato method based o de-treded verse dstace weghtg (D-IDW), 2 - uversal rgg (.e. smple rgg wth tred fucto defed o the bass of a set of covarates) whch s optmal (.e. BLUP, best lear ubased predctor) f spatal assocato s preset, 3 - multlayer eural etwors traed wth bac-propagato (represetg a complex olear fttg) ad foud ANN terpolator has prove to be more effcet [32]. Chattopadhyay, ad Chattopadhyay, 2008, have foud that, the ANN for Ida Rafall predcto usg ANN s sutable ad especally he suggested archtecture of hdde layer of the etwor. Ultmately t has bee establshed that the elevehdde-odes three-layered eural etwor has more effcacy tha asymptotc regresso the preset forecastg tas [33]. Hug, 2009, preseted ANN techque to mprove rafall forecast performace over Bago Thalad [34]. Medes ad Marego, 200 have developed ad tested a ovel type of statstcal dowscalg techque based o the ANN, appled of the clmate chage. The ANN used here are based o a feed forward cofgurato of the multlayer percepto that has bee used by a growg umber of authors [35]. Svapragasam et al. (200) have foud that, the terpolato of Hydrologcal varable such as rafall, groud water level, etc for Taml Nadu state Ida usg ANN s useful. However, 8 statos data samples have bee used to develop ANN. It s observed that, by more statos, ths methodology ca produce better result [36]. Ghazafar et al. (20), have suggested a ew model PERSIANN (Precptato estmato from remotely sesed formato usg artfcal eural etwor) model wors based o the ANN system whch uses multvarate olear put-output relatoshp fuctos to ft local cloud top temperature to pxel ra rates. I ths study, PERSIANN model ad two terpolato methods (Krgg & IDW) are employed to estmate precptato cover for North-Khorasa betwee the years 2006 utl He has foud better correlato betwee PERSIANN output ad stato data tha the other two terpolato methods. Whle correlato coeffcet for Kedal s test s betwee model ad Boord Stato data, ths coeffcet s ad for Krgg method [37]. By revew of very sgfcat cotrbutos of all the authors from 978 to 20, t s cocluded that, ANN method s suffcetly sutable for detfyg teral dyamcs of rafall varables, as well as sgfcat to develop a assocato betwee depedet ad depedet varable predcto as well as terpolato. However, t s also foud that, the selecto of approprate archtecture of ANN s Iteratoal Joural of Computer Scece ad Iformatcs ISSN (PRINT): , Vol-, Iss-4, 202 2

3 exceptoally trcy addto to ts trag. Selecto of ts parameters,.e., umber of put vectors, hdde layers, ad hdde euros s aga very dyamc depedg o data seres. Trag of ANN s also aga eormous challegg tas. It s foud that, the selecto of parameters ad trag process may cause of temporal ervousess as well. To tra the etwor, how may epochs are requred, how to obta global mma durg error mmzato process (.e., trag) s ot ofte clearly avalable the lterature although very wde rage of applcatos of ANN has bee foud. No author has foud who have clearly descrbed these aspects ther cotrbutos. The developmet of BPANN wth these essetal aspects, applcato detfcato of teral dyamcs of hgh dyamc system such as log rage total aual rafall by developg a relatoshp betwee rafall ad ts predctors ad ts performaces are clearly descrbed the subsequet sectos. II. DATA DESCRIPTION AND PREPROCESSING A data tme seres ( ) of total aual rafall (TAR) of locato Baster of Chhattsgarh (Geologcal stuato Lattude 7046' N to 2405'N Logtude 8005' E to 84020' E s cosdered ths study. The eght clmate parameters data tme seres ( ) those are physcally coected wth the TAR of ths locato are detfed ad used to put the ANN as depedetly. These parameters are total evaporato, maxmum temperature, mmum temperature, sushe, vapor pressure, wd, humdty ad total rafall of prevous year as show Table. These parameters are show good Correlato Coeffcet (CC) wth TAR. The all data tme seres depedet as well as depedet was the splt to two sets. About thrtee years ( ) of data are used for trag. Other four years ( ) are used for observato (testg). Accordg to Demyaov, 998, Brya ad Adams, 200, 2002, mportat aspect s to ormalze the data because etwor trag algorthms are lmted to the tervals 0 to ad de-ormalze t after the testg phase [4, 26]. To ormalze the data tme seres the equato R = (x + m (x ))/ (x + max (x )) s used ad other had the equato the equato x = (m (x ) - R max (x )) / (R -) s used to deormalze. Table. Iput Parameters No. Parameters (Prev. Year) CC Evaporato x Maxmum Temperature x M Temperature x Sushe x Vapor Pressure x Wd x Humdty x Rafall x III. ARCHITECTURE OF ANN Multlayer Bac Propagato Artfcal Neural Networ (BPANN) s show Fgure. The modfed archtecture of ths etwor as show Fgure 2 s used ths study. Where, t has put layer (at the bottom), oe hdde layer (at the mddle) ad output layer (o the top). It has put vectors at the put layer ( x... x... x ), p euros hdde layer z... z... z ) ad oe euro y ) ( p ( output ut to observe desred meteorologcal data as target varable. Bas o hdde ut.e. V o ad bas o output ut.e. w o wth p + p traable weghts are used the etwor. Output target value for the etwor s actual data to be predcted. The euros output ca be obtaed as f (x ). Where f s a trasfer fucto (axo), typcally the sgmod (logstc or taget hyperbolc) fucto. Sgmod fucto = f ( x), where δ δ +η + e x determes the slope ad η s the threshold. I the proposed model δ =, η =0 s cosdered such that + ± I, the output of the euro wll be close terval [0, ] as show Fg. 3. Fg. : Archtecture of geeral multlayer BPANN Fg. 2 : Archtecture of BPANN Iteratoal Joural of Computer Scece ad Iformatcs ISSN (PRINT): , Vol-, Iss-4, 202 3

4 The etwor performace s determed through comparso betwee mea absolute devato (MAD) (% of mea) ad stadard devato (SD) (% of mea) as show Equato ad 2 respectvely. Where x s radom varable wth mea μ, ad p s predcted value. Fg. 3. Output of Sgmod Axo MAD = SD = = ( x p ) ( x μ ) = IV. DESIGN OF TRAINING ALGORITHM Rumelhart et al. (986) frst troduced BPANN based o gradet descet method (Kumar, 2007) [38]. Beg a gradet descet method, t mmzes the mea square error (MSE) of the output computed by the etwor durg the feed-forward ad bac-propagato process. I ths study, BPANN s traed by supervsed learg method. Supervsed trag s the process of provdg the etwor wth a seres of sample puts ad comparg the output wth the expected respose. The followg algorthm a has bee desged specfcally for ths applcato to tra BPANN. The am of ths trag was to tra the BPANN order to acheve a relatoshp betwee the putted depedet parameters x, x 2, x 8 (see Table ) ad the depedet parameter.e., TAR. Algorthm a: Desged ad mplemeted trag Algorthm of BPANN through Java for ths applcato where- Iput trag vector x ( x x ) : x Output target vector t ( t ) :... t m δ : Error at output ut y. α : Learg rate. V o : Bas o hdde ut. Z : Hdde ut. 2 w o : Bas o output ut. y : Output ut. Set tal weghts w such that ( 0 < ) w. < Cosder trag perod: m; Set umber of put vector ρ such that ρ < m. do{ { ( = ; ( m ρ + + ) for ); for( = ; ( ρ + ); + + ) { put vector x ; } /* Feed-Forward ad calculate target/output varable y...*/ Each put ut receves the put sgal x ad trasmts ths sgals to all uts the layer above.e., hdde uts. Each hdde ut ( z, =... p) sums ts weghted put sgals z = vo + = x v () applyg actvato fucto Z = f z ) ( ad seds ths sgal to all uts the layer above.e., output uts. Each output ut ( y, =... m) sum ts weghted put sgals y p = wo + = z w (2) Applyg actvato fucto y = f y ) ( Calculate error factor δ = actual(z) - target (y); Italze predcted value P ρ + = target (y); /* Bac-Propagato ad calculate ew weghts w */ Iteratoal Joural of Computer Scece ad Iformatcs ISSN (PRINT): , Vol-, Iss-4, 202 4

5 Each output ut ( y, =... m) receves a target patter correspodg to a put patter error formato term s calculated as δ = t y ) f ( y ) ( ( z = sums ts delta Each hdde ut,... ) puts from uts the layer above δ m = = δ w The error formato term s calculated as δ = δ f z ( /* Updatg of Weghts ad Bases */ Each output ut ( y, =... m) updates ts bas ad weghts ( = 0... p) The weghts correcto term s gve by ) Δ W = αδ z Ad the bas correcto term s gve by Δ W = αδ o Therefore, W W o ( ew) = W ( ew) = W o ( old) + ΔW ( old) + ΔW Each hdde ut (,... p) bas ad weghts ( = 0... ) the weghts correcto term Δ V z = updates ts = αδ x The bas correcto term o therefore, } V V o ( ew) = V Δ V o = αδ = V ( old) + ΔV, ( old) + ΔV Calculate MSE betwee seres m MSE = X P m = set = ; = ; } whle ( MSE < ); o X ad V. SELECTION OF BPANN PARAMETERS A. Ital Weghts o, P ; It wll fluece whether the etwor reaches a global (or oly a local) mma of the MSE ad f so how rapdly t coverges. It s foud that, f tal weght s too large the tal put sgals to each hdde or output ut wll fall the saturato rego where the dervatve of sgmod has very small value (f (etwor) = 0). If tal weghts are too small, the etwor output to a hdde or output ut wll approach zero, whch the causes extremely slow learg. To get the best result the tal weghts (ad bases) are set to radom umber betwee 0 ad. The tal weghts (bas) ca be doe radomly ad moreover there s a specfc approach. The faster learg of a BPANN ca be obtaed by usg Nguye-Wdrow (NW) talzato (Equato 3). Kumar, 2007 have foud ths method s desged to mprove the learg ablty of the hdde uts [39]. p β = 0.7( ) where, = umber of put uts, p = umber of hdde uts, β = scale factor. B. Learg Rate (α) It s foud that, a hgh learg rate α leads to rapd learg but the weghts may oscllate, whle a lower learg rate leads to slower learg. Kumar, 2007, suggested that tally set α betwee lower value 0 ad ad crease order to mprove performace. It s foud that, α = 0.3 s sutable for almost all of the cases ad ths study [39]. C. Number of Hdde Layers Phllp, 2003 foud that, early all problems, oe hdde layer s suffcet. Usg two hdde layers rarely mproves the model, ad t may troduce a greater rs of covergg to a local mma. Ad also there s o theoretcal reaso for usg more tha two hdde layers [39]. D. Number of put Vector () It s observed that, the MAD (% of mea) s versely proportoal to for all type of put data. MAD I ths study, = 8 s used to put eght clmate parameter.e. x, x 2, x 8 (see Table ). However, more parameter may used as put to detfy TMR as depedet parameter (armaar et al., 2008, 2009) [5-2]. Iteratoal Joural of Computer Scece ad Iformatcs ISSN (PRINT): , Vol-, Iss-4, 202 5

6 E. Neuros Hdde Layer (p) It has bee foud that, f umber of euros ( p) creases the hdde layer, the MAD (% of mea) betwee actual ad predcted value creases (Karmaar et al., 2008, 2009). I other words, the relato betwee euros (p) ad MAD (% of mea) s show as MAD p MAD = cp Where, c s error costat. It s verfed that, f p = 2 the t would provde two fudametal beefts () MAD betwee actual ad predcted values durg trag wll be least ad (2) Tme complexty of etwor trag process wll be ot as much of. Note that, more hdde euros creases more uow varables (.e., traable weghts w ) s requred addtoal process tme to optmzed, t ca be temporal tmdty. Thus, two euros p = 2 have bee used the PBANN. Fally, BPANN have bee developed to predct TAR as show followg Fgure 4. Where eght put vectors.e. x, x 2, x 8, put layer are used to put eght depedet varable. Two euros hdde layer z... ) are used. ( z2 VI. TRAINING OF BPANN: LOCAL AND GLOBAL MINIMA The mmzg mea square error (MSE) of the etwor called parallel process or epoch by usg above algorthm durg the trag perod s show followg Table 2 ad Fgure 5. The trag started wth tal set of weghts betwee 0 ad at pot P where MSE = E-04 usg algorthm. Mmum MSE = E- 04 s ecoutered at pot M L after 0,000 epochs. M L s called local mma. After ths pot the MSE s showg a costat tred. Geerally, scetsts are ofte stoppg trag process ths pot for ther specfc applcatos. Ths s the oly grouds of poor result. The ofte th that more trag wll ot mmze the MSE or may be dffcult or ot possble. Table 2 ad Fgure 5 show some observatos here. However It s cleared that day 3, after 50,00000 epochs, the MSE becomes e-04 mared by the pot M G (Fg. 5). Ths pot s called global mma called maxmum traed etwor pot. I the lterature the varous authors are clearly declared that, obtag ths pot s almost dffcult or temporal tmdty. But ths observato t s clear that ths cocept s ot true. No oe should tal about such type of mscocepto. After ths pot MSE s exhbtg a creasg tred ad s cosdered as over trag of the etwor. Ths expermet s doe wth oe GB RAM wth IBM Petum mache. tme requred to process s three days. The expermetal result s show Table 2 ad Fgure 5. The processes are developed usg Java mathematcal pacage. (5) Fg. 4 : Archtecture of Desged BPANN. Table 2. Observato of Reducg MSE durg Trag Perod Observato Tme MSE Day 4: E-04 5: E-04 Day 2 0: E-04 : E-04 2: E-04 : E-04 2: E-04 3: E-04 4: E-04 Day 3 0: E-04 2: E-04 2: E-04 VII. RESULTS AND DISCUSSIONS I order to chec the performaces of BPANN durg trag perod, t s traed wth the 3 years ( ) trag dataset. The performaces s show Table 3,5 ad Fgure 6. The BPANN presets low MAD (.e., 0.006) ad a hgh CC (.e., 0.86) betwee actual ad predcted values as show Fgure 6. Ths shows strog assocato betwee depedet total rafall, ad depedet parameters x, x 2, x 8.I order to chec the BPANN performace durg the Iteratoal Joural of Computer Scece ad Iformatcs ISSN (PRINT): , Vol-, Iss-4, 202 6

7 testg/depedet perod wth ew data, t was tested wth the 04 years ( ) of the test data. The performace s show Table 4,5 ad Fgure 7. The BPANN aga preseted low MAD ad a hgh CC betwee actual ad predcted values ths perod. The result shows strog assocato betwee depedet parameter rafall, ad depedet varables x, x 2, x 8 durg the testg perod as well. Other tha that, MAD at trag as well as testg perod exceptoally less tha the SD as show Table 5. Thus, t s cocluded that the proposed archtecture of BPANN ad ts optmzed weghts for the varable total rafall s very approprate teral dyamcs of total rafall varable. However, some lmtatos of BPANN durg the trag perod have bee depcted s preseted the followg secto. Fg. 5 : Mmzg MSE: Local Mma (M L ) ad Global Mma (M G ) Fg. 7 : Performace of the BPANN Idepedet Perod ( ) Table 3. Performace of the BPANN Trag Perod ( ) Year Actual rafall ( mm.) Normalzed Actual rafall ( mm.) Deormalzed Predcted Rafall ( mm.) Normalzed Predcted Rafall ( mm.) Deormalzed Fg. 6 : Performace of the BPANN Trag Perod ( ) Year Table 4. Performace of the Model Idepedet Perod ( ) Actual rafall ( mm.) Normalzed Actual rafall ( mm.) Deormalzed Predcted Rafall ( mm.) Normalze d Predcted Rafall ( mm.) Deormalzed Iteratoal Joural of Computer Scece ad Iformatcs ISSN (PRINT): , Vol-, Iss-4, 202 7

8 Table 5. Performace Tatg ad Idepedet Perod Trag Perod Idepedet /Testg Perod SD MAD CC SD MAD CC VIII. CONCLUSIONS Ths study focuses o the capabltes of ANN the predcto of hgh teral dyamcs log-rage rafall varables showg the advatages ad dsadvatages compled. The advatage of ths study s that t has bee cleared that ANN s suffcetly sutable for detfcato of teral dyamcs of hghly dyamc o lear system ad predctos. Dsadvatage s that, t requred may trag effort, possbly over fttg, ad a temporal ervousess. It s foud that, the bac-propagato usg gradet descet (algorthm) ofte coverges very slowly or ot at all. O large-scale problems ts success depeds o userspecfed learg rate ad mometum parameters. There s o automatc way to select these parameters, ad f correct values are specfed the covergece may be exceedgly slow, or t may ot coverge at all. Whle bac-propagato wth gradet descet stll s used the model developmet, t s o loger cosdered to be the best or fastest algorthm. Istead of gradet descet, cougate gradet algorthm ca be used as a future wor to adust weght values usg the gradet durg the bac-propagato of errors through the ANN. Compared to gradet descet; the cougate gradet algorthm taes a more drect path to the optmal set of weght values. Usually, cougate gradet s sgfcatly faster ad more robust tha gradet descet. Cougate gradet also does ot requre the user to specfy learg rate ad mometum parameters. I addto, performace of the RBFANN, GRANN ca also be compared wth the appled BPANN as a future wor. REFERENCES []. Jourel, A. G., Hubregts, C. J.,978: Mg geostatstcs. Academc Press, New Yor. [2]. Hor, K., Stchcombe, M., Whte, H., 989: Multlayer feedforward etwors are uversal approxmators. Neural Networs, 2, [3]. Goovaerts, P., 997: Geostatstcs for atural resources evaluato, Oxford Uversty Press, New Yor, Oxford. [4]. Demyaov, V., 998: Neural Networ Resdual Krgg Applcato for Clmatc Data, J. Geographc Iformato ad Decso Aalyss, 2 (2), [5]. Huag, Y., Wog, P. M. Gedeo, T. D., 998: Predcto of reservor permeablty usg geetc algorthms, AI Applcatos, 2(-3), pp [6]. Rcardo, M. T., Palutof, J.P., 999: Smulato of Daly Temperatures for Clmate Chage Scearos over Portugal: A Neural Networ Model Approach, Clmate research (Clm., Res.), 3, [7]. Guhathaurta, P., 998: A Hybrd Neural Networ Model for Log Rage Predcto of All Ida Summer Mosoo Rafall, Proc. WMO teratoal worshop o dyamcal exteded rage forecastg, Toulouse, Frace, November 7-2, 997, PWPR No., WMO/TD. 88, [8]. Guhathaurta, P., 999: Log Rage Forecastg Ida Summer Mosoo Rafall By Prcple Compoet Neural Networ Model, J. Meteor. & Atomos. Phys., 7, [9]. Guhathaurta, P., 999: A Short Term Predcto Model for Surface Ozoe At Pue: Neural Networ Approach, Vayu madal, 29(-4), [0]. Guhathaurta, P., 999 : A Neural Networ Model for Short Term Predcto of Surface Ozoe at Pue, Mausam, 50(), []. Guhathaurta, P., Raeeva, M., Thaplyal, V., 999: Log Rage Forecastg Ida Summer Mosoo Rafall by Hybrd Prcpal Compoet Neural Networ Model, Meteorology ad Atmospherc Physcs, Sprger-Verlag, Austra. [2]. Guhathaurta, P., 2000: New Models for Log Rage Forecasts of Summer Mosoo Rafall over North West ad Pesular Ida, Meteorology ad Atmospherc Physcs,73 (3), [3]. Guhathaurta, P., 2006: Log-Rage Mosoo Rafall Predcto of 2005 for the Dstrcts ad Sub-Dvso Kerala Wth Artfcal Neural Networ, Curret Scece, 90(6), [4]. Raeeva, M., Guhathaurta, P., Thaplyal, V., 2000, New Models for Log Rage Forecastg of Mosoo Rafall over Northwest ad Pesular Ida. Meteorology ad Atmospherc Physcs, 73, [5]. Karmaar, S., Kowar, M. K., Guhathaurta, P., 2009: Artfcal Neural Networ Seleto Determstc Forecast to Recogze Patter of TMRF Ambapur Dstrct, CSVTU Research Joural, 2(2), [6]. Karmaar, S., Kowar, M. K., Guhathaurta, P., 2009: Evolvg ad Evaluato of 3LP FFBP Determstc ANN Model for Dstrct Level Log Rage Mosoo Rafall Predcto, J. Evrometal Scece & Egeerg, 5(2), [7]. Karmaar, S., Kowar, M. K., Guhathaurta, P., 2008: Developmet of Artfcal Neural Networ Models for Log- Rage Meteorologcal Parameters Patter Recogto over the Smaller Scale Geographcal Rego-Dstrct, IEEE Xplore, IEEE Computer Socety. Washgto, DC, USA. [8]. Karmaar, S., Kowar, M. K., Guhathaurta, P., 2008: Developmet of a 8-Parameter Probablstc Artfcal Neural Networ Model for Log-Rage Mosoo Rafall Patter Recogto over the Smaller Scale Geographcal Rego Dstrct, IEEE Xplore, IEEE Computer Socety, Washgto, DC, USA. [9]. Karmaar, S., Kowar, M. K., Guhathaurta, P., Developmet of a 6 Parameter Artfcal Neural Networ Model for Log- Rage July Rafall Patter Recogto over the Smaller Scale Geographcal Rego Dstrct, CSVTU Research Joural, pp [20]. Karmaar, S., Kowar, M. K., Guhathaurta, P., 2009: Log- Rage Mosoo Rafall Patter Recogto & Predcto for the Subdvso EPMB Chhattsgarh Usg Determstc Iteratoal Joural of Computer Scece ad Iformatcs ISSN (PRINT): , Vol-, Iss-4, 202 8

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