101 20082 GEO2INFORMATION SC IENCE Vol110, No11 Feb., 2008 1, 1, 2 (1, 475004; 2, 450003) :,,,, A rcgis 910, Krigig :, : ; ; 1 ( IDW ) ( Krigig),, [ 1 ], : 2,, ;,,,, [ 9, 10 ], [ 2 ], :, Krigig, [ 38 ],,, : :,,,, DEM, :, ( Gaussia) ( bi2square) [ 11 ] :, : : 2007-07 - 10; : 2007-08 - 19. : (200422009 ) : (1982 - ),,,, GIS E2mail: dog1xu@ yahoo1com1c cheg2
1 : 15 : Q = m i w i 2 (1) i y i = A + B x i + i (2) (1) : i, ; w i, w i > 0 w i = 1 (2) i, i : N ( 0, 2 w - 1 i ), ( i = 1, 2,, ) : ^y i = a + bx i (3) : a, ba, B, ( 3 ) : Q = m i w i ( y i - a - bx i ) 2, Q a b, 5 Q 5 a = 0 w i ( y i - a - bx i ) = 0 5 Q 5 b = 0 w i ( y i - a - bx i ) x i = 0 (4) : b = w i x i y i (4) a = gy - bgx ( 5) - gy w i x i x i x 2 i - gx w i x i gx =, w i x i w i y i, gy = w i w i : w i = 1 (D i ) p 1 (D i ) p : w i i ; ; (6) D i i p, 12 3 311 98 31106 3828 40 36 30, 696km 838km, 2 666157m, 832145m, 515103mm,,, 1 201, (NC2 DC) 19712000 800m DEM, (OCS), A rcgis 910DEM 1 1 Fig11Terrai ad climate statios of orthwester Texas 312, Moraπs I [ 12 ], Moraπs I: 01280127 011, Z : 351333131215, 95% I, Z 1196,, ;, Moraπs I
16 2008 ( 2),,,,,,,,,, 2Moraπs I : ( I > 0, Z > 1196), ( I > 0, - 1196 > Z > 1196), ( I < 0, - 1196 > Z > 1196), ( I < 0, Z < - 1196) Fig12LocalMora s I idex of climate statiosπp recip itatio i orthwester Texas (3),, : 795km, : 0, : 4617; : 795km, : 0, : 0112; : 539km, : 01095, : 012, C0 / ( C0 + C1 ) 32% 3 Fig13Sem ivariogram cloud of p recip itatio 4 201 A rcgis 910 VBA 20 2, (MAE)( RMSE), IDWKrigig A rcgis 910( Geostatistical Aalyst) IDWKrigig 4
1 : 17,,, ;, ;,,,, 4 Fig14Spatial distributio of p recip itatio iterpolated by weighted liear regressio model i orthwester Texas, (MAE) (RMSE) [ 8 ] (1),, : 1 Tab11Com par iso of cross2va lida tio results MAE ( % ) RMSE ( % ) MAE ( % ) RMSE ( % ) MAE ( % ) RMSE ( % ) 28196 (516) 38150 (715) 1198 (1116) 2174 (1610) 6135 (1014) 8136 (1317) Krigig 31150 (611) 44145 (816) 2101 (1118) 2170 (1518) 7111 (1117) 10102 (1614) IDW 30173 (610) 43171 (815) 1198 (1116) 2162 (1514) 7162 (1215) 10153 (1713) (1), MAERMSE,,,,,,,, (5),,,,, (2)
18 2008 5 Fig15Spatial distributio of high error poits iterpolated by the weighted liear regressio model,,, 5,,,,, :,, [ 1 ] Daly C, Nellso R P. A statistical2topographic model for mapp ig climatological p recip itatio over moutaious ter2 rai. Joural of App lied Meteorology, 1994, ( 33) : 140,, 158. [ 2 ].., 2003, 22 (6) : 565573. ; [ 3 ],. DEM,., 2004, 59 (3) : 366374., [ 4 ],.,., 2006, 31 (1) : 146152. [ 5 ],. ;,., 2005, 24 (6) : 974980., [ 6 ],. IDW., 2002, 57 (1) : 4756., [ 7 ].., 2006, 25 (2) : 3438. [ 8 ],,. : A IC (Akaike Iformatio., 2006, 8 (4) : 7579. Criterio) [ 9 ] Daly C. Guidelies for assessig the suitability of spatial, climate data sets. Iteratioal Joural of Climatology, 2006, 26: 707721. [ 10 ] Daly C, Helmer E H. Mapp ig the climate of Puerto R i2 co, V ieques ad Culebra. Iteratioal Joural of Clima2
1 : 19 tology, 2003, 23: 13591381. [ 11 ] Kleibaum D G, Kupper L L, Muller K E. App lied Re2 gressio Aalysis ad O therm ultivariable M ethods ( third editio). :, 2003, 250251. [ 12 ].. :, 2006, 76 84. A W eighted L iear Regressio Model for Precip itatio Spatial Iterpolatio i A ltip lao ad Moutai A rea XU Chegdog 1, KONG Yufeg 1, TONG W ewei 2 ( 1 Chia2A ustralia Cooperative Research Ceter for Geographic Iform atio A alysis ad A pplicatios, Hea U iversity, Kaifeg475004, Chia; 2 Hea B ureau of M eteorological A dm iistratio, Zhegzhou450003, Chia) Abstract: Precip itatio is evidetly iflueced by the terrai i the altip lao ad moutai areas, i which the commo m ethods, such as Iverse D istace W eighted ( IDW ), Krigig Statistics ad Polyom ial App roxim atio, caπt effectively estim ate the actual spatial distributio of p recip itatio. Elevatio is a sigificat factor i p recip ita2 tio ad, o a give moutai slope, p recip itatio typ ically icreases w ith elevatio. Accordigly, a local weigh2 ted liear regressio model (WLR) is itroduced attemp tig to accurately iterpolate p recip itatio i the altip lao ad moutai areas. The liear regressio of p recip itatio versus elevatio for spatial iterpolatio m ethod is imp le2 meted i A rcgis 910 software usig VBA p rogramm ig. The weight of each p recip itatio observatio is calculated by the distace betwee the estimated poit ad the observatio poit. Case study of p recip itatio iterpolatio i orthwester Texas shows that: (1) WLR model is better tha the commo methods such as Krigig ad IDW i term s ofmae ad RMSE of cross validatio i altip lao ad moutai areas for specific p recip itatio periods. (2) Due to the seasoal characteristics of the p recip itatio distributio, the p recisio ofwlr iterpolatio varies i dif2 feret periods of p recip itatio; compared w ith the commo methods, the WLR model is better tha IDW ad Krig2 ig methods for August p recip itatio data ad has o evidet differece for Jauary data. ( 3) I the comp lex ter2 rai area, the WLR model has evidet advatages over the commo app roaches, ad i the relatively flat area the model matches the IDW method. Cosiderig that p recip itatio is iflueced by more geographic factors such as moutai slope, aspect ad w id directio, it is expected to develop a multip le liear regressio model for p recip i2 tatio iterpolatio i the future studies. Key words: p recip itatio; spatial iterpolatio; weighted liear regressio model