Eurasian Journal of Soil Science

Volume 5, Issue 1, Jan 2016, Pages 62 - 73
DOI: 10.18393/ejss.2016.1.062-073
Stable URL: http://ejss.fess.org/10.18393/ejss.2016.1.062-073
Copyright © 2016 The authors and Federation of Eurasian Soil Science Societies



Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture

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Houlong,J., Daibin,W., Chen,X., Shuduan,L., Hongfeng,W., Chao,Y., Najia,L., Yiyin,C., Lina,G., 2016. Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture. Eurasian J Soil Sci 5(1):62 - 73. DOI : 10.18393/ejss.2016.1.062-073
Houlong,J.Daibin,W.Chen,X.,Shuduan,L.Hongfeng,W.Chao,Y.Najia,L.Yiyin,C.,& Lina,G. Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture Eurasian Journal of Soil Science, DOI : 10.18393/ejss.2016.1.062-073
Houlong,J.Daibin,W.Chen,X.,Shuduan,L.Hongfeng,W.Chao,Y.Najia,L.Yiyin,C., and ,Lina,G."Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture" Eurasian Journal of Soil Science, DOI : 10.18393/ejss.2016.1.062-073
Houlong,J.Daibin,W.Chen,X.,Shuduan,L.Hongfeng,W.Chao,Y.Najia,L.Yiyin,C., and ,Lina,G. "Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture" Eurasian Journal of Soil Science, DOI : 10.18393/ejss.2016.1.062-073
J,Houlong.W,Daibin.X,Chen.L,Shuduan.W,Hongfeng.Y,Chao.L,Najia.C,Yiyin.G,Lina "Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture" Eurasian J. Soil Sci, vol., no., pp., DOI : 10.18393/ejss.2016.1.062-073
Houlong,Jiang ;Daibin,Wang ;Chen,Xu ;Shuduan,Liu ;Hongfeng,Wang ;Chao,Yang ;Najia,Li ;Yiyin,Chen ;Lina,Geng Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture. Eurasian Journal of Soil Science,. DOI : 10.18393/ejss.2016.1.062-073

How to cite

Houlong, J., Daibin, W., Chen, X., Shuduan, L., Hongfeng, W., Chao, Y., Najia, L., Yiyin, C., Lina, G., 2016. Comparison of kriging interpolation precision between grid sampling scheme and simple random sampling scheme for precision agriculture. Eurasian J. Soil Sci. 5(1): 62 - 73. DOI : 10.18393/ejss.2016.1.062-073

Author information

Jiang Houlong , Chongqing Tobacco Science Research Institute, Chongqing, China
Wang Daibin , Chongqing Tobacco Science Research Institute, Chongqing, China
Xu Chen , Chongqing Tobacco Science Research Institute, Chongqing, China
Liu Shuduan , Beibei Tobacco Company of Chonqing, Chongqing, China
Wang Hongfeng , Chongqing Tobacco Science Research Institute, Chongqing, China
Yang Chao , Chongqing Tobacco Science Research Institute, Chongqing, China
Li Najia , Chongqing Tobacco Science Research Institute, Chongqing, China
Chen Yiyin , Chongqing Tobacco Science Research Institute, Chongqing, China
Geng Lina , Chongqing Tobacco Science Research Institute, Chongqing, China

Publication information

Issue published online: 01 Jan 2016
Article first published online : 20 Sep 2015
Manuscript Accepted : 18 Sep 2015
Manuscript Received: 13 Aug 2015
DOI: 10.18393/ejss.2016.1.062-073
Stable URL: http://ejss.fesss.org/10.18393/ejss.2016.1.062-073

Abstract

Sampling methods are important factors that can potentially limit the accuracy of predictions of spatial distribution patterns. A 10 ha tobacco-planted field was selected to compared the accuracy in predicting the spatial distribution of soil properties by using ordinary kriging and cross validation methods between grid sampling and simple random sampling scheme (SRS). To achieve this objective, we collected soil samples from the topsoil (0-20 cm) in March 2012. Sample numbers of grid sampling and SRS were both 115 points each. Accuracies of spatial interpolation using the two sampling schemes were then evaluated based on validation samples (36 points) and deviations of the estimates. The results suggested that soil pH and nitrate-N (NO3-N) had low variation, whereas all other soil properties exhibited medium variation. Soil pH, organic matter (OM), total nitrogen (TN), cation exchange capacity (CEC), total phosphorus (TP) and available phosphorus (AP) matched the spherical model, whereas the remaining variables fit an exponential model with both sampling methods. The interpolation error of soil pH, TP, and AP was the lowest in SRS. The errors of interpolation for OM, CEC, TN, available potassium (AK) and total potassium (TK) were the lowest for grid sampling. The interpolation precisions of the soil NO3-N showed no significant differences between the two sampling schemes. Considering our data on interpolation precision and the importance of minerals for cultivation of flue-cured tobacco, the grid-sampling scheme should be used in tobacco-planted fields to determine the spatial distribution of soil properties. The grid-sampling method can be applied in a practical and cost-effective manner to facilitate soil sampling in tobacco-planted field.

Keywords

Grid sampling scheme, Interpolation precision, simple random sampling scheme, precision agriculture

Corresponding author

References

Bremner, J.M., Mulvaney, C.S., 1984. Total nitrogen In: Methods of Soil Analysis, page, A.L. (ED.). 2nd Edn. Agron. No. 9, Part 2: Chemical and microbiological properties. Am. Soc. Argon. Madison, WI. USA. pp. 595-624.

Brus, D.J., de Gruijter, I.J., van Groenigen, J.W., 2006. Designing spatial coverage samples using the k-means clustering algorithm. In: Digital Soil Mapping: An Introductory Perspective. P. Lagachene, A. B. McBratney, M. Voltz (eds.). Elsevier, Amsterdam, Netherlands.

Caeiro, S., Goovaerts, P., Painho, M., Costa, H., Sousa, S., 2002. Optimal spatial sampling design for mapping estuarine sediment management areas. AGILE Conference on Geographic Information Science, Palma, p. 1-6.

Cahn, M.D., Hummel, J.W., Brouer, B.H., 1994. Spatial analysis of soil fertility for site-specific crop management. Soil Science Society America Journal 58: 1240-1248.

Cambardella, C.A., Moorman, T.B., Parkin, T.B., Karlen, D.L., Novak, J.M., Truko, R.F., Konopka, A.E., 1994. Field-scale variability of soil properties in central Iowa soils. Soil Science Society America Journal 58: 1501-1511.

Chapman, H.D., 1965. Cation exchange capacity. In: methods of soil analysis, black, C.A. (ED.). Part 2. Number 9 in the series agronomy: American institute agronomy, Madison, Wisconsin. pp. 891-901.

Christman, M.C., 2000., A review of quadrat-based sampling of rare geographically clustered populations. Journal of Agricultural Biological and Environmental Statistics 5: 168–201.

Ferguson, R.B., Hergert, G.W., Schepers, J.S., Gotway, C.A., Cahoon, J.E., Peterson, T.A., 2002. Site-specific nitrogen management of irrigated maize: Yield and soil residual nitrate effects. Soil Science Society America Journal 66: 544-553.

Frogbrook, Z.L., 1999. The effect of sampling intensity on the reliability of predictions and maps of soil properties. In: Proceedings of the 2nd European Conference on Precision Agriculture. Sheffield Academic Press, Sheffield, UK. pp. 71-80.

Goovaerts, P., 1998. Geostatistical tools for characterizing the spatial variability of microbiological and physico-chemical soil properties. Biology and Fertility of Soils 27: 315-334.

Goovaerts, P., 2000. Estimation or simulation of soil properties? An optimization problem with conflicting criteria. Geoderma 97: 165-186.

Gotway, C.A., Ferguson, R.B., Hergert, G.W., Peterson, T.A., 1996. Comparison of kriging and inverse-distance methods for mapping soil parameters. Soil Science Society America Journal 60: 1237-1247.

Gupta, R.K., Mostaghimi, S., McClellan, P.W., Birch, J.B., Brann, D.E. 1999. Modeling spatial variability of soil chemical parameters for site-specific farming using stochastic. Water Air and Soil Pollution 110: 17–34.

Haining, R. 1990. Spatial data analysis in the social and environmental sciences. Cambridge University Press. 409 pp.

Issaks, E., Srivastava, R.M. 1989. An Introduction to Applied Geostatistics. Oxford University Press, New York.

Jiang H.L., Liu G.S., Wang X.Z., Song, W.F., Zhang, R.N., Zhang, C.H., Hu, H.C., Li, Y.T., 2010. Spatial variability of soil properties in a long-term tobacco plantation in central China. Soil Science 175: 137-144.

Jiang H.L., Liu G.S., Wang, R., Liu, S.D., Han, F.G., Yang, Y.F., Ye, X.F., Zhang, Q.J., Wang, X.J., Wang, Z.H., Hu, H.C., 2011. Delineating site-specific quality-based management zones for a tobacco field. Soil Science 176: 206-212.

Johnston, K., Hoef, J.M.V., Krivoruchko, K., Lucas. N., 2001. Using ArcGIS Geostatistical Analysis. GIS User Manual by ESRI, New York.

Kumar, N. 2009. An optimal spatial sampling design for intra-urban population exposure assessment. Atmospheric Environment 43: 1153–1155.

Li, Q.Q., Wang, C.Q., Yue, T.X., Li, B., Yang, J., Shi, W.J., 2008. Error analysis of soil property spatial interpolation with RBF artificial neural network with different input methods. Acta Pedologica Sinica 459: 360-365.

Li, Y., Shi, Z., Wu, C.F., Li, F., Li, H.Y., 2007. Optimised spatial sampling scheme for soil electriclal conductivity based on Variance Quad-Tree (VQT) method. Agricultural Sciences in China 6: 1463-1471.

Lindsley, C. M., Bauer, F. C. 1929. Test your soil for acidity. University of Illinosis, College of Agriculture and Agricultural Experiment Station, Circular No. 346. USA.

Liu, G.S., 2003. Tobacco Cultivation. China Agricultural Press, Beijing, China. (In Chinese)

Liu, G.S., Wang, X.Z., Zhang, Z.Y., Zhang, C.H., 2008. Spatial variability of soil properties in a tobacco field of central China. Soil Science 173: 659-667.

Liu, G.S., Jiang, H.L., Liu, S.D., Wang, X.Z., Yang, X.M., Hu, H.C., Liu, Q.H., Xie, D.P., Gu, J.G.., Li, Y.T., 2010. Comparison of kriging interpolation precision with different soil sampling intervals for precision agriculture. Soil Science 175: 405-415.

Lu, R.K., 1999. Chemical analysis of agricultural soil, Beijing, China. Agricultural Science Technology Press, p. 34–56. (In Chinese)

Mallarino, A.P., Wittry, D.J., 2004. Efficacy of grid and zone soil sampling approaches for site-specific assessment of phosphorus, potassium, pH, and organic matter. Precision Agriculture 5: 131–144.

McBratney, A.B., Whelan, B.M., Walvoort, D.J.J., Minasny, B., 1999. A purposive sampling scheme for precision agriculture. In: Proceedings of the 2nd European Conference on Precision Agriculture. Sheffield Academic Press, Sheffield, UK. p. 101-110.

National Soil Survey Office. 1993. Soil series of China. Beijing, China Agriculture. Press.

Nelson, D.W., Sommers, L.E., 1982. Total carbon, organic carbon and organic matter. In: methods of soil analysis. Part 2. Agron. Monogr. 9. ASA and SSSA, Madison, WI. P. 539-577.

Olsen, S.R., Cole, C.V., Watanabe, F.S., Dean, L.A., 1954. Estimation of available phosphorus in soils by extraction with sodium bicarbonate. United States Department of Agriculture, Circular No. 939, Washington, DC. USA.

Paramasivam, S., Alva, A.K., Fares, A., Sajwan, K.S., 2002. Fate of nitrate and bromide in an unsaturated zone of a sandy soil under citrus production. Journal of Environmental Quality 31: 671-681.

Peck, T.R., 1990. Soil testing: Past, present and future. Communication in Soil Science and Plant Analysis 21: 1165-1186.

Pooler, P.S., Smith, D.R., 2005. Optimal sampling design for estimating spatial distribution and abundance of a freshwater mussel population. Journal of the North American Benthological Society 24: 525–537.

Quine, T.A., Zhang, Y., 2002. An investigation of spatial variation in soil erosion, soil properties and crop production within an agricultural field in Devon, UK. Journal of Soil and Water Conservation 57: 55-65.

Richards, L.A., 1954. Diagnosis and improvement of saline and alkaline soil. Unites States Department of Agriculture, Agriculture HandBook. No. 60. Washington, DC. USA.

Rodríguez, A., Durán, J., Fernández-Palacios, J. Gallardo, A., 2009. Spatial variability of soil properties under Pinus canariensis canopy in two contrasting soil textures. Plant and Soil 322: 139–150.

Tang, G.A., Yang, X. 2006. ArcGIS experimental tutorial of spatial analysis GIS [In Chinese]. Science Press, Beijing, China, 384-385.

Thompson, S.K., Seber, G.A.F., 1996. Adaptive sampling. Wiley, New York.

Wang, X.Z., Liu, G.S., Hu, H.C., Wang, Z.H., Liu, Q.H., Liu, X.F., Hao, W.H., Li, Y.T., 2009. Determination of management zones for a tobacco field based on soil fertility. Computers and Electronics in Agriculture 65: 168-175.

Webster, R., Oliver, M.A. 2001. Geostatistics for Environmental Science. John Wiley and Sons, LTD, Toronto, Ontario, Canada. pp. 271.

Wollenhaupt, N.C., Wolkowski, R.P., Clayton, M.K., 1994. Mapping soil test phosphorus and potassium for variable-rate fertilizer application. Journal of Production Agriculture 7: 441-448.

Yang, T.Z., Lu, L. M., Xia, W., Fan, J.H., 2007. Characteristics of potassium-enriched, flue-cured tobacco genotype in potassium absorption, accumulation, and ın-ward potassium currents of root cortex. Agricultural Sciences in China 6: 1479-1486.

Zhu, Z., Stein, M.L., 2006. Spatial sampling design for prediction with estimated parameters. Journal of Agricultural, Biological & Environmental Statistics 11: 24-44.

Zhu, X.H., Yang, X.C., Cai, Y.L., 2005. Fractal and fractal dimension of spatial distribution of China soil system. Acta Pedologica Sinica 42: 881-888.

Abstract

Sampling methods are important factors that can potentially limit the accuracy of predictions of spatial distribution patterns. A 10 ha tobacco-planted field was selected to compared the accuracy in predicting the spatial distribution of soil properties by using ordinary kriging and cross validation methods between grid sampling and simple random sampling scheme (SRS). To achieve this objective, we collected soil samples from the topsoil (0-20 cm) in March 2012. Sample numbers of grid sampling and SRS were both 115 points each. Accuracies of spatial interpolation using the two sampling schemes were then evaluated based on validation samples (36 points) and deviations of the estimates. The results suggested that soil pH and nitrate-N (NO3-N) had low variation, whereas all other soil properties exhibited medium variation. Soil pH, organic matter (OM), total nitrogen (TN), cation exchange capacity (CEC), total phosphorus (TP) and available phosphorus (AP) matched the spherical model, whereas the remaining variables fit an exponential model with both sampling methods. The interpolation error of soil pH, TP, and AP was the lowest in SRS. The errors of interpolation for OM, CEC, TN, available potassium (AK) and total potassium (TK) were the lowest for grid sampling. The interpolation precisions of the soil NO3-N showed no significant differences between the two sampling schemes. Considering our data on interpolation precision and the importance of minerals for cultivation of flue-cured tobacco, the grid-sampling scheme should be used in tobacco-planted fields to determine the spatial distribution of soil properties. The grid-sampling method can be applied in a practical and cost-effective manner to facilitate soil sampling in tobacco-planted field.

Keywords: Grid sampling scheme, Interpolation precision, simple random sampling scheme,
precision agriculture

References

Bremner, J.M., Mulvaney, C.S., 1984. Total nitrogen In: Methods of Soil Analysis, page, A.L. (ED.). 2nd Edn. Agron. No. 9, Part 2: Chemical and microbiological properties. Am. Soc. Argon. Madison, WI. USA. pp. 595-624.

Brus, D.J., de Gruijter, I.J., van Groenigen, J.W., 2006. Designing spatial coverage samples using the k-means clustering algorithm. In: Digital Soil Mapping: An Introductory Perspective. P. Lagachene, A. B. McBratney, M. Voltz (eds.). Elsevier, Amsterdam, Netherlands.

Caeiro, S., Goovaerts, P., Painho, M., Costa, H., Sousa, S., 2002. Optimal spatial sampling design for mapping estuarine sediment management areas. AGILE Conference on Geographic Information Science, Palma, p. 1-6.

Cahn, M.D., Hummel, J.W., Brouer, B.H., 1994. Spatial analysis of soil fertility for site-specific crop management. Soil Science Society America Journal 58: 1240-1248.

Cambardella, C.A., Moorman, T.B., Parkin, T.B., Karlen, D.L., Novak, J.M., Truko, R.F., Konopka, A.E., 1994. Field-scale variability of soil properties in central Iowa soils. Soil Science Society America Journal 58: 1501-1511.

Chapman, H.D., 1965. Cation exchange capacity. In: methods of soil analysis, black, C.A. (ED.). Part 2. Number 9 in the series agronomy: American institute agronomy, Madison, Wisconsin. pp. 891-901.

Christman, M.C., 2000., A review of quadrat-based sampling of rare geographically clustered populations. Journal of Agricultural Biological and Environmental Statistics 5: 168–201.

Ferguson, R.B., Hergert, G.W., Schepers, J.S., Gotway, C.A., Cahoon, J.E., Peterson, T.A., 2002. Site-specific nitrogen management of irrigated maize: Yield and soil residual nitrate effects. Soil Science Society America Journal 66: 544-553.

Frogbrook, Z.L., 1999. The effect of sampling intensity on the reliability of predictions and maps of soil properties. In: Proceedings of the 2nd European Conference on Precision Agriculture. Sheffield Academic Press, Sheffield, UK. pp. 71-80.

Goovaerts, P., 1998. Geostatistical tools for characterizing the spatial variability of microbiological and physico-chemical soil properties. Biology and Fertility of Soils 27: 315-334.

Goovaerts, P., 2000. Estimation or simulation of soil properties? An optimization problem with conflicting criteria. Geoderma 97: 165-186.

Gotway, C.A., Ferguson, R.B., Hergert, G.W., Peterson, T.A., 1996. Comparison of kriging and inverse-distance methods for mapping soil parameters. Soil Science Society America Journal 60: 1237-1247.

Gupta, R.K., Mostaghimi, S., McClellan, P.W., Birch, J.B., Brann, D.E. 1999. Modeling spatial variability of soil chemical parameters for site-specific farming using stochastic. Water Air and Soil Pollution 110: 17–34.

Haining, R. 1990. Spatial data analysis in the social and environmental sciences. Cambridge University Press. 409 pp.

Issaks, E., Srivastava, R.M. 1989. An Introduction to Applied Geostatistics. Oxford University Press, New York.

Jiang H.L., Liu G.S., Wang X.Z., Song, W.F., Zhang, R.N., Zhang, C.H., Hu, H.C., Li, Y.T., 2010. Spatial variability of soil properties in a long-term tobacco plantation in central China. Soil Science 175: 137-144.

Jiang H.L., Liu G.S., Wang, R., Liu, S.D., Han, F.G., Yang, Y.F., Ye, X.F., Zhang, Q.J., Wang, X.J., Wang, Z.H., Hu, H.C., 2011. Delineating site-specific quality-based management zones for a tobacco field. Soil Science 176: 206-212.

Johnston, K., Hoef, J.M.V., Krivoruchko, K., Lucas. N., 2001. Using ArcGIS Geostatistical Analysis. GIS User Manual by ESRI, New York.

Kumar, N. 2009. An optimal spatial sampling design for intra-urban population exposure assessment. Atmospheric Environment 43: 1153–1155.

Li, Q.Q., Wang, C.Q., Yue, T.X., Li, B., Yang, J., Shi, W.J., 2008. Error analysis of soil property spatial interpolation with RBF artificial neural network with different input methods. Acta Pedologica Sinica 459: 360-365.

Li, Y., Shi, Z., Wu, C.F., Li, F., Li, H.Y., 2007. Optimised spatial sampling scheme for soil electriclal conductivity based on Variance Quad-Tree (VQT) method. Agricultural Sciences in China 6: 1463-1471.

Lindsley, C. M., Bauer, F. C. 1929. Test your soil for acidity. University of Illinosis, College of Agriculture and Agricultural Experiment Station, Circular No. 346. USA.

Liu, G.S., 2003. Tobacco Cultivation. China Agricultural Press, Beijing, China. (In Chinese)

Liu, G.S., Wang, X.Z., Zhang, Z.Y., Zhang, C.H., 2008. Spatial variability of soil properties in a tobacco field of central China. Soil Science 173: 659-667.

Liu, G.S., Jiang, H.L., Liu, S.D., Wang, X.Z., Yang, X.M., Hu, H.C., Liu, Q.H., Xie, D.P., Gu, J.G.., Li, Y.T., 2010. Comparison of kriging interpolation precision with different soil sampling intervals for precision agriculture. Soil Science 175: 405-415.

Lu, R.K., 1999. Chemical analysis of agricultural soil, Beijing, China. Agricultural Science Technology Press, p. 34–56. (In Chinese)

Mallarino, A.P., Wittry, D.J., 2004. Efficacy of grid and zone soil sampling approaches for site-specific assessment of phosphorus, potassium, pH, and organic matter. Precision Agriculture 5: 131–144.

McBratney, A.B., Whelan, B.M., Walvoort, D.J.J., Minasny, B., 1999. A purposive sampling scheme for precision agriculture. In: Proceedings of the 2nd European Conference on Precision Agriculture. Sheffield Academic Press, Sheffield, UK. p. 101-110.

National Soil Survey Office. 1993. Soil series of China. Beijing, China Agriculture. Press.

Nelson, D.W., Sommers, L.E., 1982. Total carbon, organic carbon and organic matter. In: methods of soil analysis. Part 2. Agron. Monogr. 9. ASA and SSSA, Madison, WI. P. 539-577.

Olsen, S.R., Cole, C.V., Watanabe, F.S., Dean, L.A., 1954. Estimation of available phosphorus in soils by extraction with sodium bicarbonate. United States Department of Agriculture, Circular No. 939, Washington, DC. USA.

Paramasivam, S., Alva, A.K., Fares, A., Sajwan, K.S., 2002. Fate of nitrate and bromide in an unsaturated zone of a sandy soil under citrus production. Journal of Environmental Quality 31: 671-681.

Peck, T.R., 1990. Soil testing: Past, present and future. Communication in Soil Science and Plant Analysis 21: 1165-1186.

Pooler, P.S., Smith, D.R., 2005. Optimal sampling design for estimating spatial distribution and abundance of a freshwater mussel population. Journal of the North American Benthological Society 24: 525–537.

Quine, T.A., Zhang, Y., 2002. An investigation of spatial variation in soil erosion, soil properties and crop production within an agricultural field in Devon, UK. Journal of Soil and Water Conservation 57: 55-65.

Richards, L.A., 1954. Diagnosis and improvement of saline and alkaline soil. Unites States Department of Agriculture, Agriculture HandBook. No. 60. Washington, DC. USA.

Rodríguez, A., Durán, J., Fernández-Palacios, J. Gallardo, A., 2009. Spatial variability of soil properties under Pinus canariensis canopy in two contrasting soil textures. Plant and Soil 322: 139–150.

Tang, G.A., Yang, X. 2006. ArcGIS experimental tutorial of spatial analysis GIS [In Chinese]. Science Press, Beijing, China, 384-385.

Thompson, S.K., Seber, G.A.F., 1996. Adaptive sampling. Wiley, New York.

Wang, X.Z., Liu, G.S., Hu, H.C., Wang, Z.H., Liu, Q.H., Liu, X.F., Hao, W.H., Li, Y.T., 2009. Determination of management zones for a tobacco field based on soil fertility. Computers and Electronics in Agriculture 65: 168-175.

Webster, R., Oliver, M.A. 2001. Geostatistics for Environmental Science. John Wiley and Sons, LTD, Toronto, Ontario, Canada. pp. 271.

Wollenhaupt, N.C., Wolkowski, R.P., Clayton, M.K., 1994. Mapping soil test phosphorus and potassium for variable-rate fertilizer application. Journal of Production Agriculture 7: 441-448.

Yang, T.Z., Lu, L. M., Xia, W., Fan, J.H., 2007. Characteristics of potassium-enriched, flue-cured tobacco genotype in potassium absorption, accumulation, and ın-ward potassium currents of root cortex. Agricultural Sciences in China 6: 1479-1486.

Zhu, Z., Stein, M.L., 2006. Spatial sampling design for prediction with estimated parameters. Journal of Agricultural, Biological & Environmental Statistics 11: 24-44.

Zhu, X.H., Yang, X.C., Cai, Y.L., 2005. Fractal and fractal dimension of spatial distribution of China soil system. Acta Pedologica Sinica 42: 881-888.



Eurasian Journal of Soil Science