Geo-Statstcs ad ts Applcato for Creatg Iso Maps Hydrogeologcal Studes, Techcal Study: Electrc Coductvty cotours of Atrak Pla, Golesta Provce, Ira Mohammad Ahmad*, Peyma Shr Zade, Behrouz Yaghoub, Mostafa Safar Komel 3 *Correspodg author: MSc. Studet of cvl Egeerg, Bu Al Sa Uversty, Hameda, Ira. E-mal address: mohammad_ahmad8m@yahoo. Tel: +98-9-97459 Abstract Wth takg dscrete samplg from the water resource parameters quatty ad qualty ad the use of procedures of turg dscrete spots to coected area oe ca study the process of the surface chages of selected area. There are dfferet procedures for turg broke dscrete spots to cotuty of areas such as procedure of Geostatstcs whch coclude Krgg procedure, Iverse Dstace Weghtg (IDW), Radal Bass Fuctos (RBF), Local Polyomal Iterpolato, Global Polyomal Iterpolato ad Co-krgg. Ths research s gog to expla ay applcatos of Geostatstcs for creatg so-maps such as udergroud water table cotours, so-qualty (for example Ec ad ph) cotours, ad place chages of too may other hydro-geologcal parameters. I ths way, statstc sgs such as Mea Absolute Error (MAE), Mea Absolute Relatve Error (MARE), Root Mea Square Error (RMSE), MBE ad Coeffcet of Correlato, could be employed to select the best Geo-Statstc model a GIS framework. Evetually, the power IDW method has bee optmzed ad also best Geo-Statstc method has bee troduced for predctg the Electrc Coductvty (EC) of udergroud water Atrak pla. Fally ay coclusos have bee extracted. Keywords: Geo-statstcs; udergroud water qualty; statstc sgs; GIS. -Itroducto Chage procedure assessmet of objectve value study area could be obtaed by dscrete samplg of varable. I ths regard, crease or decrease evaluato of objectve value ad extractg the crtcal pots study area could be classfed as oe the most mportat techcal problems for geo-scece researchers. The accuracy of future studes whch have bee based o these samplg ad also chage procedure studes of target value study area, have drectly depeded o the accuracy ad effcecy of data gatherg ad the procedure of turg dscrete spots to cotuous surface. It meas that, the exacttude of future studes has wdely depeded o the certtude of spot pot to cotour map coverso method. There are too may ways to create so-maps from spot samplg, Geo-Statstcs (G.S) could be explaed as oe of these methods. The Geo-Statstcs method dvded to some sub-methods such as Iverse Dstace Weghtg (IDW), Radal Bass Fuctos (RBF), Global Polyomal Iterpolato (GPI), Local Polyomal Iterpolato (LPI), Krgg ad Co- Krgg methods. Ths predcto approach, could estmate target value o o-measured pots the study area more accurate tha the classc procedures such as Tragular Irregular Network (TIN). It should be metoed that Geo-Statstcs, there are some costat Rver Egeerg Departmet of Yekom Cosultg Egeers, Tehra, Ira. Drector of Itegratg ad Balace of Water Resources, Hameda Regoal Water Co., Ira. 3 M.S.c Studet of Hydrogeology, Shahd Behesht Uversty, Tehra, Ira. 447
coeffcet that they are effectve o the accuracy of estmato. I ths respect, a statstcal dex, whch has called Root Mea Squared Predcto Error (RMSE), could be defed for selectg the best Geo-Statstc estmator ad fdg the optmzed costat coeffcet. Metoed dex, whch has show dffereces betwee observed target value ad the predcted oe o-measured pots, could help the researcher to fd the best estmator ad optmzed costat coeffcets. Best estmator should have mmum value of RMSE. I preseted study, by employg the results of qualtatve aalyss of udergroud water samples of Atrak pla Golesta provce, the best G.S estmator has bee selected for predctg the Electrcal Coductvty of udergroud water metoed study area. -Methodology Selectg the best Geo-Statstcs estmator to predct Electrc Coductvty, ad also power optmzato of IDW method could be cosdered as the ma purpose of preseted study. Fgure No. descrbes ma steps of ths research. -The Locato of study area Atrak pla s located Golesta provce wth the area of 357 square klometers. Ths study area has a pla ts cetral zoe. Fgure No. shows the locato of the study lmt alog wth the lmt of Atrak pla. Fgure. Research Methodology -Geo-Statstcs -Iverse Dstace Weghtg 3-Local Polyomal Iterpolato 4-Global Polyomal Iterpolato 5-Krgg model (Based o D. G. Krge theorem) Fgure. Locato of Study Area 4-Itroducto related to the procedures of Geostatstcs I geeral Geostatstcs procedures are based o Regoalzed Varable theory. Regoalzed Varable refers to every evrometal feature dstrbuted two or three dmesoal space. The chages of ths set of varables from oe pot to aother are clear ad ther cotuty s obvous. The features such as the Electrcal Coductvty, texture of sol ad/or the amout of dfferet elemets sol are examples of the regoalzed varables. The major dfferece betwee classc statstcs ad Geostatstcs s that t s assumed that the samples collected. EC 448
form socety are ot deped o each other classc statstcs,therefore the exstece of oe sample does ot gve ay formato about the other samples located certa dstace. For example, Krgg procedure based o models ad statstcal procedures s auto-correlato. It s a estmator based o the logc of weghted movg average ad t s a ubased estmator ad t s determed by the use of Krge's formula. The equato o. shows how t s estmated Krgg procedure. I Iverse Dstace Weghtg or IDW method, the amout of oe quatty spots wth kow coordate ca be attaed by the use of quatty of the same amout other spots wth kow coordate. I other words ths procedure the value of oe varable s couted based o the mea of eghbors specfc zoes. Equato No. () descrbes the IDW predcto procedure. Radal Bass fuctos are a procedure cotas 5 kds of radal fuctos as explaed through followg words. There s ot a bg dfferece amog the results of dfferet fuctos RBF procedure ad the selecto of the radal bass fucto happes by valdatg the estmate results. The equatos o.3 ad 4 troduces some of these fuctos such as CRS ad SWT respectvely. The CRS fucto s used ths research. The procedures ad the fuctos of RBF are the especal form of Artfcal Neural Networks (ANN). z ( x). z( ) () x ( ). r. r z ( r) l( ) E( ) CE (3)! x. r z ( x ) z( ) () z ( r) l( ) K r C 0 (. ) E (4) I whch z(x) s the estmated parameter ad..s the weght or the sgfcace of the quatty that depeded o th sample ad z(x ) s kow parameter ad z ( x) s the estmated parameter ad z( x ) s kow parameter [,,4,5,6, ad 7].I these equatos No. 3 ad 4, s Teso Parameter, E s Expoetal Itegral Fucto, C E s Euler Costat, ad K 0 s Modfed Bessel Fucto [8]. 5-Establshg ad Valdatg Geostatstcs Model I ths stage wth the use of GIS ad radom procedure, establshg samples, ad valdatg samples of models are 80 ad 0 percet of the whole selected data bak, ad are recalled cyber space the form of two separate layers. After ths stage, Krgg models, IDW, ad RBF are establshed ad valdated. The results of models are show the fgure o.4. Oe of the crtera examg of the valdty of the attaed results from models s the crtera of Coeffcet of correlato (r); whatever ts absolute value gets closer to the better adaptato betwee the observed amouts s show. But wth the use of just Coeffcet of correlato oe ca ot declare aythg about the effcecy ad the accuracy of the model; therefore other parameters ad statstcs wll be used for examg the desged models. I ths regard the crtera of Root Mea Square Error (RMSE), Mea Absolute Error (MAE), ad Mea Bas Error (MBE) have bee employed. The equatos umber (5) to (8) shows these parameters order. The amout of stated parameters both stages of establshg (educato) ad valdatg (test) of Geostatstcs models are show table o. [7 ad 8]. r ( p ( p p)( O p) ( O O) O) (5) RMSE (O ) P (6) MAE O P (7). r MBE ( O P ) (8) 449
I these equatos, O s the observed amout, P s the predcted amout ad s the umber of observatos. The above troduced features are the whole statstcal dces whch do ot provde ay formato about the procedure of error dstrbuto; therefore for evaluatg the capacty of the models, statstcal features are eeded whch specfes how the error dstrbuto the establshed models. For ths reaso the Mea Absolute Relatve Error dstrbuto dagram for fal evaluato of used models (besdes statstcal parameter) s used. 5--Optmzato of Power IDW Model ad selecto of best G.S Model I ths secto, by takg the results of Krgg, RBF, GPI, LPI ad optmzed IDW method, the best estmator whch belogs to the mmum of RMSE has bee extracted. For ths purpose, frst of all optmzato of power IDW method has bee carred out. 5--- Power Optmzato The best ad accurate estmato of objectve value could be metoed as the ma purpose of G.S. I ths regard, costat coeffcet optmzato to reach the mmum RMSE plays the ma rule. Ths part of research wats to optmze the power IDW method as a example for costat coeffcet optmzato. Comparso betwee results of optmzed models wth o-optmzed models expresses the ecessty of lear of olear optmzato such these studes. Fgure No. 3 shows the relatoshp betwee RMSE ad power varato IDW results. By havg had the results whch has preseted metoed Fgure, The optmzed power IDW method s.38 ad the results that related to ths power have the mmum RMSE. 5--- Best Estmator Selecto As t oted paragraph No. (5--), ths research ams to provde a optmal method for calculatg the objectve value o-measured locatos, chage procedure studes ad create Iso-Maps for presetg the chage surface of varable Raster maps a GIS frame work. For ths purpose, havg had the estmated results wth dfferet G.S methods ad corporate statstcal dex Correlato Coeffcet (r), RMSE, MAE ad MBE, the best estmator could be extracted. I order to table No., Krgg Method has the best correlato betwee estmatos ad measuremet ad the mmum RMSE. Also, by employg the results whch has bee preseted fg o. 4, krgg method has the best Mea Absolute Relatve Error (MARE) (the MARE of more tha %89 of datasets test stage s less tha %38), so the Krgg Geo-Statstc method could be troduced as the best EC estmator Atrak pla. Table No. : Comparso of Statstcal Idces for Best Estmator Selecto G.S Method r RMSE MBE MAE Krgg 0.8 00 485 740 RBF 0.79 63 47 66 GPI 0.63 98 347 03 LPI 0.64 94 349 00 Power Optmzed IDW 0.459 486-83 845 Geo-Statstcs Root Mea Squared Predcto Error 450
00 90 80 70 60 50 40 30 0 0 0 0 0 0 30 40 50 60 70 Mea Absolute Relatve Error (%) GPI LPI RBF Krgg Fgure No. 3: Power optmzato IDW method ad the mmum of RMSE Fgure No.4: Evaluato of Mea Absolute Relatve Error chage Number of Data sets for evaluated Methods 6-Results ad Coclusos Wth the use of Geostatstcs procedures ad statstcal aalyss of results t s tred to fd out the best estmator of Electrc Coductvty the pots apart from the measured pots Atrak pla.the best estmator s krgg model respectg part No.5--. Respectg to ths pot that determg place chages of some quatty ad qualty parameters are couted as the put data of other stages of water resource study, selectg the best estmator model ad ts careful estmato has a drect fluece o the carefuless of further stages. 7-Suggestos Optmzato of costat coeffcets such as teso parameter RBF procedure, Geostatstcs models ad the comparso of dfferet procedures happe the presece of optmzed factor. The comparso of the results of Geostatstcs procedures ad the procedure of Tragular Irregular Network (TIN) provdg the map of the so-level of EC. Refereces [] Ghohroud Tal, Maje, "Geographc Iformato System Three Dmesoal Evromet, Three Dmesoal GIS Arc Gs Evromet", Jahad Daeshgah publcato of Tarbat Moalem Uversty, frst edto, sprg 005. [] Sajer. Sara, "GIS Trag use", Abed publcatos, 3 rd edto, 008. [3] Mohammad Jahagard, "Geostatstcal Evaluato of salt chages of sol Ramhormoz zoe, - Krgg Method", Scetfc ad techcal studes of Agrculture ad Natural Resources Joural, Vol, Number 4, Wter 007. [4] C.P. Lo, Albert K. W. Yeug, Cocepts ad Techques of Geographc Iformato Systems, Pretce Hall of Ida Prvate Lmted, New Dehl, 005. [5] Ahmad M., Parta, S., Zabh M., "GIS Applcato Clmate-Mcrozoato hot ad ard areas, Case study: Raze Dam", Proceedg of the st Iteratoal coferece o Water crss, Zabol Uversty, wter 009. 45
[6] Mohammad Jahagard, "Geostatstcal Evaluato of salt chages of sol Ramhormoz zoe, - Krgg Method", Scetfc ad techcal studes of Agrculture ad Natural Resources Joural, Vol 3, Number, sprg 999. [7] Ghohroud Tal, Maje, "Establshg ad Modfcato methods of creatg elevated models, Case study: Golesta Dam", Geographc Researches Joural, Number 57, fall 006. [8] Asada F., Ahmad M., Arzja Z., Parta S., Prmorad R., " A Comparso of Dfferet Procedures of Geostatc the Study of Place Chages of the Level of Udergroud Water by GIS (A Case Study of Raza-Ghahavad Pla Hameda Provce, Ira)", Proceedg of Iteratoal Coferece o Water Resources (ICWR009), Shahroud Uversty, Summer 009. 45