University of California

Geostatistical theory and application to variability of some agronomical properties


S. R. Vieira
J. L. Hatfield
D. R. Nielsen
J. W. Biggar

Authors Affiliations

S. R. Vieira was a former graduate research assistant; presently Soil Scientist, Institute Agronomico de Campinas, Campinas, Brazil; J. L. Hatfield was Associate Professor of Meteorology and Land, Air and Water Resources and Associate Biometeorologist in the Experiment Station, University of California, Davis; D. R. Nielsen was Professor, Soil and Water Science and Land, Air and Water Resources and Water Scientist in the Experiment Station, University of California, Davis; J. W. Biggar was Professor, Land, Air, and Water Resources, University of California, Davis.

Publication Information

Hilgardia 51(3):1-75. DOI:10.3733/hilg.v51n03p075. June 1983.

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In agronomic problems the sampling procedure may create some confusion and bias in the analysis. Geostatistics provides a method for the analysis of the spatial and temporal properties in a data set and a method of interpolation between selected points. This paper describes the theory of geostatistics and its application to selected agronomic problems. Geostatistics considers a set of data collected in either space or time at discrete intervals. These samples may be correlated with each other to provide some unique information about the parameters which would not be detected in the classical statistical methods. Through the application of geostatistics to this type of problem, we can estimate the spatial or temporal dependence of samples and from this knowledge arrive at an estimation of the sampling procedures or structure at a field. The application of these techniques is shown for air temperature, surface temperature, yield, clay content, and fertilizer content in various fields and reveals the versatility of the techniques.

Geostatistics also allows for the evaluation of the dependence between two parameters in either time or space. From this information it is possible to develop sampling procedures which would allow the more costly or time consuming variable to be sampled less frequently and estimated from the other variable by the method of kriging. This report summarizes all of these techniques and provides several different examples of their utilization. Examples of the computer code are provided for the reader wishing to apply these techniques.

Literature Cited

Ball D. F., Williams W. M. Variability of soil chemical properties in two uncultivated brown earths. J. Soil Sci. 1968. 19:379-391. DOI: 10.1111/j.1365-2389.1968.tb01548.x [CrossRef]

Bartlett M. S. Stochastic Processes. 1966. 2nd Ed.Cambridge Univ. Press. DOI: 10.2307/1402301 [CrossRef]

Beckett P. H. T., Webster R. Soil variability: a review. Soils Fert. 1971. 34:1-15.

Blais R. A., Carlier P. A. Applications of geostatistics in ore evaluation. 1968. 9:Canadian Institute of Mining and Metalurgy, Ore Research Estimation and Grade Control. p. 41-48. Special Volume, Montreal, Quebec

Burgess T. M., Webster R. Optimal interpolation and isarithmic mapping of soil properties. I. The semivariogram and punctual kriging. J. Soil Sci. 1980a. 31:315-331.

Burgess T. M., Webster R. Optimal interpolation and isoarithmic mapping of soil properties. II. Block kriging. J. Soil Sci. 1980b. 31:333-341. DOI: 10.1111/j.1365-2389.1980.tb02085.x [CrossRef]

Campbell J. B. Spatial variation of sand content and pH within single contiguous delineation of two soil mapping units. Soil Sci. Soc. Am. J. 1978. 42:460-464.

David M. The geostatistical estimation of porphyry-type deposits and scale factor problems. Proc. Pribram Science and Technique. 1970. M5:91-109.

David M. Geostatistical ore reserve estimation. 1977. Elsevier Scientific Publ. Co. 364p.

Delhomme J. P. Kriging in hydrosciences. 1976. Fontainebleau, France: Centre D’Informatique Geologique. DOI: 10.1016/0309-1708(78)90039-8 [CrossRef]

Grossman R. B. Partial Soil Inventory of Agronomy Research Center. 1978. Boone County: Missouri. 30p.

Hajrasuliha S., Baniabbassi N., Metthey J., Nielsen D. R. Spatial variability of soil sampling for salinity studies in southwest Iran. Irrigation Sci. 1980. 1:197-208. DOI: 10.1007/BF00277625 [CrossRef]

Harradine F. F. The variability of soil properties in relation to stage of profile development. Soil Sci. Soc. Am. Proc. 1949. 14:302-311.

Harris J. A. Practical universality of field heterogeneity as a factor influencing plot yields. J. Agr. Res. 1920. XIX(7):

Journel A. G. Geostatistics for conditional simulation of ore bodies. Eco. Geology. 1974. 69:673-687. DOI: 10.2113/gsecongeo.69.5.673 [CrossRef]

Journel A. G., Huijbregts Ch. J. Mining Geostatistics. 1978. London: Academic Press.

Krige D. G. A statistical approach to some basic mine evaluation problems on the witwatersrand. J. Chem. Metall. Min. Soc. S. Afi. 1951. 52:119-139.

Matheron G. Principles of geostatistics. Econ. Geology. 1963. 58:1246-1266. DOI: 10.2113/gsecongeo.58.8.1246 [CrossRef]

Matheron G. The Theory of Regionalized Variables and Its Application 1971. Les Cahiers du Centre de Morphologie Mathematique, Fas. 5, C. G. Fontainebleau

Montgomery E. G. Experiments in wheat breeding: Experimental error in the nursery and variation in nitrogen and yield. U.S. Dept. Agri. Bur. Plant Indust. Bul. 1913. 269:61 DOI: 10.5962/bhl.title.43602 [CrossRef]

Olea R. A. Optimum mapping techniques using regionalized variable theory 1975. Kansas Geol. Survey, Series on Spatial Analysis No. 2, Univ. Kansas, Lawrence, Kansas. 137 p

Olea R. A. Measuring spatial dependence with semivariograms. Kansas Geol. Survey, Series on Spatial Analysis No. 2. 1977. Lawrence, Kansas: Univ. Kansas.

Pendleton R. L. Are soils mapped under a given type name by the Bureau of Soils method closely similar to one another? Univ. Calif. Publ. Agric. Sci. 1919. 3:369-498.

Robinson G. W., Lloyd W. E. On the probable error of sampling in soil surveys. J. Agric. Sci. 1915. 7:144-153. DOI: 10.1017/S0021859600002598 [CrossRef]

Smith L. H. Plot arrangement for variety experiment with corn. Proc. Amer. Soc. Agron. V. I. 1910. 1907/09:84-89.

Snedecor G. W., Cochran W. G. Statistical Methods. 1967. 6th Ed. Ames: Iowa State Univ. Press. 593p. DOI: 10.1097/00010694-195702000-00023 [CrossRef]

Ugarte A. Ejemploes de modelor de estimacion a corto e largo plans. Bol. Geostadist. No. 1972. 4:3-22.

Vieira S. R., Hatfield J. L. Temporal variability of air temperature and remotely sensed surface temperature for bare soil 1982. Inter. J. Remote Sensing (Submitted) DOI: 10.1080/01431168408948839 [CrossRef]

Vieira S. R., Nielsen D. R., Biggar J. W. Spatial variability of field-measured infiltration rate. Soil Sci. Soc. Am. J. 1981. 45:1040-1048.

Waynick D. D. Variability in soils and its significance to past and future soil investigations. I. Statistical study of nitrification in soils. Univ. Cal. Publ. Agr. Sci. 1918. 3(9):243-270.

Waynick D. D., Sharp L. T. Variability in soils and its significance to past and future soil investigations. II. Variation in nitrogen and carbon in field soils and their relation to the accuracy of field trials. Univ. Cal. Publ. Agr. Sci. 1919. 4(5):121-139.

Webster R. Automatic soil boundary location for transect data. Mathematical Geology. 1973. 5(1):27-37. DOI: 10.1007/BF02114085 [CrossRef]

Webster R. de la C., Cuanalo H. E. Soil transects correlograms of north Oxfordshire and their interpretation. J. Soil Sci. 1975. 26(2):176-194. DOI: 10.1111/j.1365-2389.1975.tb01942.x [CrossRef]

Webster R., Burgess T. M. Optimal interpolation and isarithmic mapping of soil properties. iii. Changing drift and universal kriging. J. Soil Sci. 1980. 31:505-524. DOI: 10.1111/j.1365-2389.1980.tb02100.x [CrossRef]

Vieira S, Hatfield J, Nielsen D, Biggar J. 1983. Geostatistical theory and application to variability of some agronomical properties. Hilgardia 51(3):1-75. DOI:10.3733/hilg.v51n03p075
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