Journal of Water and Soil Vol. 26, No. 1, Mar-Apr 2012, p Kriging. (

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Joural of Water ad Sol Vol. 26, No. 1, Mar-Apr 212, p. 53-64 ( ) 53-64. 1391 1 26 *2 1-89/7/26: 9/8/15:.. (1386-87 1361-62) 26 32.. (GPI) (IDW). (Co-Krgg) (Krgg) (RBF) (LPI) 64/46 6/49 77/2 66/86 IDW RBF. (6/49). GPI LPI. (288/96 ) 5 GPI :....(5).(1) (9). 3 3- Krgg 2 1.. -1-2 ( Emal: mosaed@um.ac.r : -*)

1391-1 26 54 ) (... ). ( ) (. ( ). :(IDW).. ()..(12) :(GPI) ().. :(LPI) GPI. :(RBF).. 1 (14). (IDW) 2 (RBF) (12). 3 RBF IDW 4 (LPI) (GPI). (1).. (3). 5. - (8) IDW 7 6 (KU) (KO).. ( 11) 61 IDW (5) 6 Co-Krgg Krgg RBF LPI GPI 1971-1999 8 (RMSE). Co-Krgg.(7) RBF. 1- Iverse Dstace weghtg 2- Radal Bass Fucto 3- Global Polyomal Iterpolato 4- Local Polyomal Iterpolato 5- Co-Krgg 6- Ordary Krgg (KO) 7- Uversal Krgg (KU) 8- Root Mea Square Error

55......(12) :..(15) 3 6 5 4... 2387.(2) 32 1361-62) 26. (1386-87 ( 24). ( 8) () 3- Ordary Co-Krgg (CKO) 4- Smple Co-Krgg (CKS) 5- Uversal Co-Krgg (CKU) 6- Dsjuctve Co-Krgg (CKD). RBF.. ( ). :.(7) IDW IDW......(11) 2 1. :(KO).. :(KS).. :( ). 1- Smple Krgg (KS) 2- Dsjuctve Krgg (KD)

1391-1 26 56 GSD RMSE Z r 1 1 * Z ( x ) Z ( x ) * ( x ) (5) ( 6) x Z (x ) Z( x ) x Z*(x ) : Z *( x ) x. x GSD MAE RMSE (R). 1 MRE (r).(1) 95-5 ) ( 2. LPI GPI IDW (5 4 3 2 1) RBF ) ( 1.. 1 :IDW (RMSE MRE MAE) (R) 5 (5 4 3 2 1) IDW 1 2 3 4... 95 -.(1) 1.. LPI GPI IDW. 3 5 RBF 5 4 3 2 1 6 5 4 7 ArcGIS. 9.2 2 1 (RMSE) (MRE) (MAE) (GSD) (R). 6 1 (r) 2 [ Z( x ) Z * ( x )] 1 RMSE Z x Z x MAE 1 ( ) *( ) 1 Z( x ) Z *( x ) MRE 1 Z( x ) R 1 [ Z( x ) Z( x )][ Z 2 [ Z( x ) Z( x )] 1 1 * ( x ) Z 1- G-B 2- Ru Test 3- Completely Regularzed Sple 4- Sple wth Teso 5- Multquadc 6- Iverse Multquadrc 7- Th Plate Sple * * 2 [ Z ( x ) Z ( x )] * ( x )] (1) (2) (3) (4)

57... -1. 1 GPI IDW RBF LPI ( ) LPI GPI. -. IDW. (3) (5). IDW (12) (5).. (5 4 3 2 1) :GPI IDW 5 1. 2 3 4. GPI IDW :LPI. IDW 5 4. :RBF 1 5...

1391-1 26 58...(2 ). -... -. (9) LPI GPI... (5)... 2 2 :Krgg r 1/7 1/14 1/29 /53 1/4 1/5 1/31 - - 1/11 1/11 1/11 1/1 1/18-1 GSD R MRE RMSE MAE /47 /5 61/55 222/9 196/4 /43 /61 52/55 23/73 165/38 /41 /66 45/92 194/26 14/73 /41 /67 43/69 193/32 13/8 /4 /67 42/83 192/45 124/65 /51 /66 46/51 27/34 156/68 /81 /12 88/62 417/49 233/25 /89 /32 73/1 382/13 226/8 /44 /47 56/68 239/37 165/16 2/87 /31 282/47 1346/87 645/8 /76 /24 58/74 356/43 18/16 /76 /13 63/99 359/ 222/11 /89 /12 86/9 416/4 222/31 - - - - - - - - - - /45 /59 42/5 211/1 124/44 /47 /47 44/35 212/23 136/39 /46 /57 43/56 29/26 133/67 /44 /68 41/73 191/9 124/35 /77 /28 55/9 362/76 154/7 r GSD R MRE 1/5 /33 /69 37/49 1/5 /27 /78 28/63 1/5 /25 /81 23/22 1/5 /24 /82 21/42 1/5 /24 /82 2/93 1/ /32 /77 28/15 1/4 /47 /39 43/61 1/9 /49 /44 4/9 /96 /36 /62 37/18 /83 1/5 /34 116/56 1/1 /41 /53 31/85 /98 /42 /49 32/31 1/8 /47 /48 41/14 - - - - - - - - 1/4 /24 /81 18/88 1/3 /25 /78 2/5 1/3 /28 /79 19/83 1/2 /24 /82 18/84 1/5 /4 /6 24/3 RMSE MAE 17/25 148/2 1 141/86 111/66 2 128/16 89/12 3 125/9 8/15 4 125/8 77/2 5 168/32 118/3 1 253/11 154/62 2 247/22 139/69 3 186/89 123/2 4 78/5 288/96 5 218/79 124/88 1 222/94 126/49 2 247/12 126/8 3 - - 4 - - 5 125/9 66/87 13/6 75/67 129/2 73/7 123/46 66/86 28/4 79/38 IDW GPI LPI RBF

59.... 186/21 ) 238/86 -. (.. ( 15 ) -.. 15%. 2. 3. LPI GPI IDW RBF () LPI GPI IDW. IDW. (77/2) 5 LPI GPI. (/82). (8) (5). (16). ( ). (5).. :Co-Krgg. 4.. - (8).. 2

6 1 26-1391 -2 - MAE RMSE MRE R GSD r MAE RMSE MRE R GSD r 62/66 117/12 18/5 /84 /23 1/4 95/59 186/76 35/69 /71 /4 1/12 6/49 115/86 17/84 /84 /22 1/3 94/73 186/21 35/45 /72 /4 1/12 63/65 117/14 18/7 /84 /22 1/3 1/98 192/67 36/15 /71 /41 1/11 KO 75/9 124/52 2/88 /82 /24 1/4 11/82 197/52 38/68 /67 /4 63/53 92/38 19/43,92 /18 1/5 99/51 14/72 38/27 /91 /3 65/74 94/77 2/35 /92 /18 1/6 12/35 134/2 39/97 /91 /31 1/14 92/71 119/68 28/29 /9 /23 1/7 141/98 165/7 51/19 /9 /35 1/16 KS 72/33 1/ 22/76 /9 /19 1/6 13/94 139/28 4/59 /9 /3 1/16 62/66 117/12 18/5 /84 /23 1/4 95/59 186/76 35/69 /71 /4 1/12 6/49 115/86 17/84 /84 /22 1/3 94/73 186/21 35/45 /72 /4 1/12 63/65 117/13 18/7 /84 /22 1/3 1/98 192/67 36/15 /71 /41 1/11 KU 75/9 124/52 2/88 /82 /24 1/4 11/82 197/52 38/68 /67 /4 65/32 94/56 19/23 /92 1/2 1/5 111/41 145/69 4/53 /92 /34 1/14 72/72 99/73 22/3 /91 /19 1/6 117/89 146/57 43/42 /91 /31 1/16 91/89 114/1 27/3 /91 /22 1/7 137/96 16/95 48/7 /9 /34 1/15 Krgg KD 61/63 91/9 19/2,92 /18 1/6 16/88 135/31 39/9 /92 /29 1/14-2 MAE RMSE MRE R GSD r MAE RMSE MRE R GSD r 67/4 144/42 15/56 /77 /28 1/5 18/85 229/43 41/96 /56 /51 1/17 64/46 143/2 19/48 /77 /27 1/4 17/61 238/86 41/73 /57 /49 1/16 67/84 144/65 19/97 /76 /28 1/4 12/89 25/9 45/42 /54 /53 1/17 CKO 8/4 144/79 22/51 /76 /28 1/5 125/98 259/88 46/14 /53 /52 1/18 79/64 152/32 25/94 /73 /29 1/8 134/67 251/17 54/72 /49 /54 1/24 83/16 159/4 27/48 /71 /31 1/8 142/92 262/22 57/69 /45 /56 1/25 97/73 183/37 3/54 /6 /35 1/8 162/47 3/48 63/57 /32 /64 1/28 CKS 79/34 149/22 25/35 /76 /29 1/8 138/86 244/87 54/66 /53 /52 1/24 67/4 144/42 15/56 /77 /28 1/5 18/85 229/43 41/96 /56 /51 1/17 64/46 143/2 19/48 /77 /27 1/4 17/61 238/86 41/73 /57 /49 1/16 67/84 144/65 19/97 /76 /28 1/4 12/89 25/9 45/42 /54 /53 1/17 CKU 8/4 144/79 22/51 /76 /28 1/5 125/98 259/88 46/14 /53 /52 1/18 76/6 127/18 23/56 /82 /25 1/7 113/5 198/35 45/83 /69 /42 1/22 75/9 127/86 23/87 /82 /25 1/6 114/82 198/39 46/65 /69 /42 1/21 77/48 143/67 27/73 /76 /28 1/7 128/29 212/9 51/24 /63 /45 1/23 Co-Krgg CKD 78/93 128/36 24/29 /81 /25 1/8 128/16 198/71 48/84 /69 /42 1/21

61... 1 1 1 (mm ) 8 6 6 8 1 (mm) (mm ) 8 6 6 8 1 (mm) (mm ) 8 6 6 8 1 (mm) 1 1 1 (mm ) 8 6 6 8 1 (mm) (mm ) 8 6 6 8 1 (mm) (mm ) 8 6 6 8 1 (mm) 1 1 1 (mm ) 8 6 (mm ) 8 6 (mm ) 8 6 6 8 1 (mm) 6 8 1 (mm) 6 8 1 (mm) 1 1 1 (mm ) 8 6 (mm ) 8 6 (mm ) 8 6 6 8 1 (mm) 6 8 1 (mm) 6 8 1 (mm) - 2.CKD - CKU - CKS - CKO - KD - KU - KS - KO - RBF - LPI - GPI - IDW -

1391-1 26 62 N Klometers 15 3 6 9 12 < - -6 6-8 >8 (mm) -3.CKD - CKU - CKS - CKO - KD - KU - KS - KO - RBF - LPI - GPI - IDW -

63.... -.. /84 6/49.. (/77) (64/46)....138. -1..1386... -2. 171..1385.. -3.1-13 :(4)29. 4- Alja B., Ghohroud M. ad Arab N. 7. Developg a Clmate Model for Ira usg GIS. Theoretcal ad Appled Clmatology, publshed ole, 16 May 7. Do: 1.17/s74-6-292-y. 5- Apayd H., Somez K. ad Yldrm E. 4. Spatal terpolato techques for clmate data the GAP rego Turkey. J. Clmate Research, 28:31-4. 6- Camplg P., Gob A. ad Feye J. 1. Temporal ad spatal rafall aalyss across a humd tropcal catchmet. Hydrol Process, 15:359 375. 7- Caruso C. ad Quarta F. 1998. Iterpolato methods comparso. Comput Math Applc 35(12):19 126. 8- Coulbaly M. ad Becker S. 7. Spatal Iterpolato of Aual Precptato South Afrca-Comparso ad Evaluato of Methods, Iteratoal Water Resources Assocato, 32(3): 494-52. 9- Drks K.N., Hay J.E., Stow C.D. ad Harrs D. 1998. Hgh-resoluto studes of rafall o Norfolk Islad. Part II: Iterpolato of rafall data. J Hydrol, 28(3-4):187 193. 1- Goovaerts P.. Geostatstcal approaches for corporatg elevato to the spatal terpolato of rafall. J Hydrol, 228:113 129. 11- Issaks E.H. ad Srvastava R.M. 1989. Appled geostatstcs, Newyork, Oxford Uversty Press. 12- Johsto K., Ver Hoef J.M., Krvoruchko K. ad Lucas N. 1. Usg arcgis geostatstcal aalyst. ESRI, Redlads, CA. 13- McGuffe K. ad Hederso-Sellers A. 1. Forty years of umercal clmate modelg. Iteratoal Joural of Clmatology 21(9):167 119. do:1.12/joc.632. 14- Mchaud J.D., ad Soroosha S. 1994. Effect of rafall-samplg errors o smulatos of desert flash floods. Water Resour Res, 3(1):2765 2775. 15- Nalder I.A., ad We R.W. 1998. Spatal terpolato of clmatc ormas: Test of a ew method the Caada boreal forest. Agrc. For. Meteor, 92 (4): 211-225. 16- Tabos G.Q., ad Salas J.D. 1985. A comparatve aalyss of techques for spatal terpolato of precptato. Water Resour Bull, 21(3):365 38.

Joural of Water ad Sol Vol. 26, No. 1, Mar-Apr 212, p. 53-64 ( ) 1 26 64 1391-53-64. 1391 1 26 A Ivestgato o Spatal Patter of Aual Precptato Golesta Provce by Usg Determstc ad Geostatstcs Models Abstract M. Evaz 1 - A. Mosaed 2 Receved: 18-1-21 Accepted: 6-11-211 Precptato s oe of the most mportat clmatc factors wth hgh varatos tme ad space. Determato of the amout of precptato dfferet locatos s partcularly very mportat. For ths reaso, to estmate precptato varous regos of Golesta provce, dfferet terpolato methods have bee used. Precptato data of 32 ra gage statos wth 26-years perod were selected. Frst the accuracy ad homogeety of data were evaluated by usg statstcal tests. The, to determe the best model of spatal patter of aual precptato Golesta provce, sx methods of IDW, GPI, LPI, RBF, Krgg ad Co-Krgg have bee used. The crtera of statstcal error were used to evaluate the results ad to select the most sutable method of terpolato. The results showed that Geostatstcs methods were better tha determstc methods, ad amog the geostatstcal models, Krgg gve better results (MAE=6.49) tha Cokrgg (MAE=64.46). Also cases of usg the determstc methods, RBF ad IDW have more accurate results tha LPI ad GPI. The lowest MAE (6.49) was recorded Krgg method wth sphercal model ad the hghest MAE (288.96) was obtaed GPI method wth power 5. Keywords: Precptato, IDW, GPI, LPI, RBF, Krgg, Co-Krgg, Golesta Provce 1- MSc Graduated, Departmet of Water Egeerg, Gorga Uversty of Agrcultural Sceces ad Natural Resources 2- Assocate Professor, Faculty of Natural Resources ad Evromet, Ferdows Uversty of Mashhad (*-Correspodg Author Emal: mosaed@um.ac.r)

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