Mapping of Temperature and Rainfall Using DEM and Multivariate Kriging No-Wook Park* Dong-Ho Jang** DEM 2005 1 4 8 10 DEM Abstract We investigate the potential of digital elevation model and multivariate geostatistical kriging in mapping of temperature and rainfall based on sparse weather station observations. By using elevation data which have reasonable correlation with temperature and rainfall, and are exhaustively sampled in the study area, we try to generate spatial distributions of temperature and rainfall which well reflect topographic effects and have less smoothing effects. To illustrate the applicability of this approach, we carried out a case study of Jeju island using observation data acquired in January, April, August, and October, 2005. From the case study results, accounting for elevation via colocated cokriging could reflect detailed topographic characteristics in the study area with less smoothing effects. Colocated cokriging also showed much improved prediction capability, compared to that of traditional univariate ordinary kriging. According to the increase of the magnitude of correlation between temperature or rainfall and elevation, much improved prediction capability could be obtained. The decrease of relative nugget effects also resulted in the improvement of prediction capability. : kriging, digital elevation model, temperature, rainfall (Assistant Professor, Dept. of Geoinformatic Engineering, Inha University), nwpark@inha.ac.kr (Assistant Professor, Dept. of Geography, Kongju National University), gisrs@kongju.ac.kr 1002
2007 AWS(Automatic Weather System) 300m 2007 GIS Goovaerts 1997 Creutin et al. 1988 Hevesi et al. 1992 Radarsat Glenn and Carr 2003 Daly et al. 2003 PRISM(Parameter-elevation Regressions on Independent Slopes Model) GIS Ninyerola et al. 2000 Perry and Konrad 2006 Simbahan et al. 2006 Goovaerts et al. 2005 Patriarche et al. 2005 Park et al. 2008 IKONOS 2007 2008 GIS PRISM 1995 2005 1003
Digital Elevation Model: DEM 1 250 000 DEM ordinary kriging DEM cokriging 1,438 4mm 200 500mm 1 800mm 2006 1 950m 2004 DEM 1 250 000 100m 100m 2005 AWS 1 4 8 10 1999 15 6 1 4 8 10 3 901-110 6 120 7 10 7 3 11 113 8 125 8 17 4 5 80 115 4 127 9 19 7 32 0 133 5 125 0 21 5 mm 47 4 112 0 253 4 53 5 69 5 329 0 577 0 96 0 1004
DEM 19 1 1 2005 vs. vs. 1 0 974 0 492 4 0 920 0 700 8 0 953 0 757 10 0 981 0 534 2007 2 0 9 0 01 10 0 981 2007 2 8 0 757 1 0 492 0 01 4 8 1 10 0 05 Goovaerts 1997 2002 n {z(u å ), å=1,, n} 1 h 1 N(h) çˆz(h)= Ç [z(u å ) z(u å h)] 2 1 2N(h) å=1 N(h) h h anisotropy isotropy 1005
h z* OK (u) 2 Goovaerts 1997 n(u) z* OK (u)= Ç O å K (u)z(u å ), Ç O å K (u)=1 2 å=1 n(u) O å K (u) universal kriging Deutsch and Journel 1998 2 å=1 Goovaerts 1997 colocated Colocated Goovaerts 1997 Deutsch and Journel 1998 Ma and Journel 1999 n(u) z* CK (u)= Ç C å K (u)z(u å ) CK (u)[y(u) m Y m Z ] 3 å=1 y(u) u m Y m Z 4 1 çˆzy(h)= 2N(h) N(h) Ç å=1 [z(u å ) z(u å h)][y(u å ) y(u å h)] 4 4 1006
linear model of coregionalization 2 Markov Goovaerts 1997 Markov sill Sill ZY nugget effect Nugget ZY Sill Z Sill Y Nugget Z Nugget Y Goovaerts 1997 1 n MAE= Ç z(u å ) z * (u å ) n å=1 1 RMSE= n n Ç å=1 [z(u å ) zu * (Uu å U)] 2 U (MAE RI MAE = OK MAE CK ) *100 MAE OK (RMSE RI RMSE = OK RMSE CK ) *100 (6) RMSE OK z * (u å ) MAE OK MAE CK RMSE OK RMSE CK Sill ZY ÁSill Z \ Sil l Y Nugget ZY ÁNug get Z \ Nu ggët Ÿ 5 Isaaks and Srivastava 1989 1 Mean Absolute Error: MAE Root Mean Square Error: RMSE Relative Index: RI 19 DEM VARIOWIN Pannatier 1996 GSLIB Deutsch and Journel 1998 Fortran 2 2005 1 8 1007
1008
2002 (3h) ç(h)=c[1 exp( 2 )] 7 a 2 c a 2 19 3 4 1 7 1 19m 4 1 5 8 49m 4 71m 13 9 19m 15 4 8 10 1 1 1 5 4 10 8 10 21 11 4 4 120mm 8 256mm 1009
1010
1011
130mm 4 33mm 135mm 1 10 30mm 2 4 8 10 6 3 5 1 4 8 10 OK CK OK CK OK CK OK CK MAE 11 79 10 88 10 65 10 41 11 26 0 72 13 59 11 57 RI MAE 50 60 37 33 42 73 56 38 RMSE 12 28 11 07 11 02 10 54 11 77 10 83 14 86 12 06 RI RMSE 53 30 47 19 53 24 57 61 MAE 19 71 18 17 49 38 39 18 65 96 42 32 17 38 14 31 RI MAE 15 92 20 70 35 84 17 65 RMSE 11 78 19 88 70 96 50 94 88 51 50 50 21 44 17 38 RI RMSE 16 17 28 21 42 95 18 97 1012
1013
5 5 Kyriakidis and Journel 1999 37 57 16 42 08 C03 CATER 2007 4504 2004 2006 27 2 188-197 2008 GIS PRISM 18 1 71-81 2005 3 26 5 429-435 1014
1999 34 2 123-136 2007 1995 2 2 58-63 2002 2007 GIS PRISM 17 3 255-268 Creutin, J. D., Delrieu, G., and Lebel, T., 1988, Rain measurement by raingage-radar combination: a geostatistical approach, Journal of Atmospheric and Oceanic Technologies, 5, 102-115. Daly, C., Helmer, E. H., and Maya, Q., 2003, Mapping the Climate of Puerto Rico, Vieques and Culebra, International Journal of Climatology, 23, 1359-1381. Deutsch, C. V. and Journel, A. G., 1998, GSLIB: Geostatistical Software Library and User s Guide, Oxford University Press, Oxford. Glenn, N. F. and Carr, J. R., 2003, The use of geostatistics in relating soil moisture to RADARSAT-1 SAR data obtained over the Gread Basin, Nevada, USA, Computers & Geosciences, 29, 577-586. Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation, Oxford University Press, Oxford. Goovaerts, P., AvRuskin, G., Meliker, J., Slotnick, M., Jacquez, G., and Nriagu, J., 2005, Geostatistical modeling of the spatial variability of arsenic in groundwater of southeast Michigan, Water Resources Research, 41, W07013, doi:10.1029/ 2004WR003705. Hevesi, J. A., Flint, A. L., and Istok, J. D., 1992, Precipitation estimation in mountainous terrain using multivariate geostatistics. Part I: structural analysis, Journal of Applied Meteorology, 31, 661-676. Isaaks, E. H. and Srivastava, R. M., 1989, An Introduction to Applied Geostatistics, Oxford University Press, Oxford. Kyriakidis, P. C. and Journel, A. G., 1999, Geostatistical space-time models, Mathematical Geology, 31(6), 651-684. Ma, X. and Journel, A. G., 1999, An expanded GSLIB cokriging program allowing for two Markov models, Computers & Geosciences, 25, 627-639. Ninyerola, M., Pons, X., and Roure, J. M., 2000, A methodological approach of climatological modelling of air temperature and precipitation through GIS techniques, International Journal of Climatology, 20, 1823-1841. Pannatier, Y., 1996, VARIOWIN: Software for Spatial Data Analysis in 2D, Springer-Verlag, New York. Park, N.-W., Jang, D.-H., and Chi, K. H., 2008, Integration of IKONOS imagery for geostatistical mapping of sediment grain size at Baramarae beach, Korea, International Journal of Remote Sensing, in press. Patriarche, D., Castro, M. C., and Goovaerts, P., 2005, Estimating regional hydraulic conductivity fields - a comparative study of geostatistical methods, Mathematical Geology, 37(6), 587-613. Perry, L. B. and Konrad, C. E., 2006, Relationships between NW flow snowfall and topography in the southern appalachians, USA, Climatology Research, 32, 35-47. Simbahan, G. C., Dobermann, A., Goovaerts, P., Ping, J., and Haddix, M. L., 2006, Fine-resolution mapping of soil organic carbon based on multivariate secondary data, Geoderma, 132, 471-489. 314-701 182 gisrs@kongju. ac.kr 041-850-8421 Correspondence: Dong-Ho, Jang, Department of Geography, College of Humanities and Social Sciences, Kongju National University, 182, Shinkwandong, Gongju, Chungnam, 314-701, Korea(e-mail: gisrs@kongju.ac.kr, phone: +82-41-850-8421) 1015