Abstract
This chapter considers the importance of spatial scale in sampling and investigates various methods by which the variogram can be used to determine an appropriate sampling scheme or interval for grid sampling. When no prior information is available on the scale of variation, and the variable of interest is unlikely to be strongly correlated to available ancillary data, a nested survey and analysis provides a first approximation to the variogram and the approximate spatial scale. If the variable of interest appears related to ancillary data such as aerial photographs or elevation, variograms of these data can provide an indication of the likely scale of variation in the soil or crop. Existing variograms of soil or crop properties can be used to determine how many cores of soil or samples from plants should be taken to form a composite (bulked) sample to reduce the local noise. Such variograms can also be used with the kriging equations to determine a grid sampling interval with a specific tolerable error, or an interval of less than half the variogram range can be used to ensure a spatially dependent sample. Finally, if the scale of variation is large in relation to the field size, a variogram estimated by residual maximum likelihood (REML) or standardized variograms from ancillary data can be used to krige data from a small, but spatially dependent sample. Each of the methods investigated is illustrated with a case study.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Blackmore, S. (1994). Precision farming: An introduction.Outlook on Agriculture,4, 275–280.
Bourgault, G., & Marcotte, D. (1991). Multivariable variogram and its application to the linear model of coregionalization.Mathematical Geology,23, 899–928.
Burgess, T. M., & Webster, R. (1984). Sampling and bulking strategies for estimating soil properties in small regions.Journal of Soil Science,35, 127–140.
Frogbrook, Z. L. (2000).Geostatistics as an aid to soil management for precision agriculture. Unpublished PhD thesis, University of Reading, Reading, England.
Godwin, R. J., & Miller, P. C. H. (2003). A review of the technologies for mapping within-field variability.Biosystems Engineering,84, 393–407.
Gower, J. C. (1962). Variance component estimation for unbalanced hierarchical classification.Biometrics,18, 168–182.
Journel, A. G., & Huijbregts, C. J. (1978).Mining geostatistics. London: Academic.
Kerry, R., & Oliver, M. A. (2007). Sampling requirements for variograms of soil properties computed by the method of moments and residual maximum likelihood.Geoderma,140, 383–396.
Kerry, R., & Oliver, M. A. (2008). Determining nugget:sill ratios of standardized variograms from aerial photographs to krige sparse soil data.Precision Agriculture,9, 33–56.
Kerry, R., Ingram, B. R., Goovaerts, P., & Oliver, M. A. (2008). How many samples are required to estimate a reliable REML variogram? In J. M. Ortiz, & X. Emery (Eds.),Geostats 2008.Proceedings of the Eighth International Geostatistics Congress (pp. 1155–1160). Santiago, Chile: Gecamin Ltd.
Lark, R. M. (2000). Estimating variograms of soil properties by the method-of- moments and maximum likelihood.European Journal of Soil Science,51, 717–728.
McBratney, A. B., & Webster, R. (1981). The design of optimal sampling schemes for local estimation and mapping of regionalized variables II. Program and examples.Computers & Geosciences,7, 335–365.
McBratney, A. B., Webster, R., & Burgess, T. M. (1981). The design of optimal sampling schemes for local estimation and mapping of regionalized variables. I. Theory and method.Computers & Geosciences,7, 331–334.
MAFF. (1986).The analysis of agricultural materials (3rd ed.). Reference Book 427. London: Her Majesty’s Stationery Office.
McKenzie, N. J., Grundy, M. J., Webster, R., & Ringrose-Voase, A. J. (Eds.) (2008).Guidelines for surveying soil and land resources (2nd ed.). Collingwood, Australia: CSIRO Publishing.
Matheron, G. (1965).Les variables régionalisées et leur estimation. Paris: Masson et Cie.
Miesch, A. T. (1975). Variograms and variance components in geochemistry and ore evaluation.Geological Society of America Memoir,142, 333–340.
Oliver, M. A., & Badr, I. (1995). Determining the spatial scale of variation in soil radon concentration.Mathematical Geology,27, 893–922.
Oliver, M. A., & Frogbrook, Z. L. (1998).Sampling to estimate soil nutrients for precision agriculture. York, UK: The International Fertiliser Society.
Oliver, M. A., Frogbrook, Z. L., Webster, R., & Dawson, C. J. (1997). A rational strategy for determining the number of cores for bulked sampling of soil. In J. V. Stafford (Ed.),Precision agriculture ‘97. Volume I, spatial variability in soil and crop (pp. 155–162). Oxford: BIOS Scientific Publishers.
Oliver, M. A., & Webster, R. (1986). Combining nested and linear sampling for determining the scale and form of spatial variation of regionalized variables.Geographical Analysis,18, 227–242.
Oliver, M. A., & Webster, R. (1987). The elucidation of soil pattern in the Wyre Forest of the West Midlands, England. II. Spatial distribution.Journal of Soil Science,38, 293–307.
Pardo-Igúzquiza, E. (1998a). Maximum likelihood estimation of spatial covariance parameters.Mathematical Geology,30, 95–107.
Pardo-Igúzquiza, E. (1998b). MLREML4: A program for the inference of the power variogram model by maximum likelihood and restricted maximum likelihood.Computers & Geosciences,24, 537–543.
Patterson, H. D., & Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal.Biometrika,58, 545–209.
Payne, R. W. (2008).The guide to GenStat for GenStat release 10: Part 2, statistics. Hemel Hempstead, UK: VSN International.
Pettitt, A. N., & McBratney, A. B. (1993). Sampling designs for estimating variance components.Applied Statistics,42, 185–209.
Robert, P. C., Rust, R. H., & Larson, W. E. (Eds.) (1995).Site-specific management for agricultural systems. Proceedings of the 2nd International Conference. Madsion, WI: Agronomy Society of America, Crop Science Society of America, Soil Science Society of America.
Robert, P. C., Rust, R. H., & Larson, W. E. (Eds.) (1996).Precision agriculture, Proceedings of the Third International Conference on Precision Agriculture. Madsion, WI: Agronomy Society of America, Crop Science Society of America, Soil Science Society of America.
Schueller, J. K. (1997). Technology for precision agriculture. In J. V. Stafford (Ed.),Precision agriculture’97. Volume I, spatial variability in soil and crop (pp. 19–33). Oxford, UK: BIOS Scientific Publishers.
Stafford, J. V. (Ed.) (1997).Precision agriculture ‘97. Proceedings of the 1st European Conference on Precision Agriculture, Volumes I and II. Oxford: BIOS Scientific Publications.
Stafford, J. V. (Ed.) (1999).Precision agriculture ‘99. Proceedings of the 2nd European Conference on Precision Agriculture, Volumes I and II. Sheffield, UK: Sheffield Academic Press.
Viscarra-Rossel, R. A., & McBratney, A. B. (1998). Soil chemical analytical accuracy and costs: Implications from precision agriculture.Australian Journal of Experimental Agriculture,38, 765–775.
Webster, R., & Boag, B. (1992). A geostatistical analysis of cyst nematodes in soil.Journal of Soil Science,43, 583–595.
Webster, R., & Oliver, M. A. (1990).Statistical methods in soil and land resource survey. Oxford: Oxford University Press.
Webster, R., & Oliver, M. A. (1992). Sample adequately to estimate variograms of soil properties.Journal of Soil Science,43, 177–192.
Webster, R., & Oliver, M. A. (2007).Geostatistics for environmental scientists. Chichester: Wiley.
Webster, R., Welham, S. J., Potts, J. M., & Oliver, M. A. (2006). Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood.Computers & Geosciences,32, 1320–1333.
Whelan, B. M., McBratney, A. B., & Viscarra-Rossel, R. A. (1996). Spatial prediction for precision agriculture. In P. C. Robert, R. H. Rust, & W. E. Larson (Eds.),Precision agriculture (pp. 331–342).Proceedings of the 3rd International Conference. Madison, WI: Agronomy Society of America, Crop Science Society of America, Soil Science Society of America.
Willers, J., Jenkins, J. N., McKinion, J. M., Gerard, P., Hood, K. B., Bassie, J. R., & Cauthen, M. D. (2009). Methods of analysis for georeferenced sample counts of tarnished plant bugs in cotton.Precision Agriculture,10, 189–212.
Youden, W. J., & Mehlich, A. (1937). Selection of efficient methods for soil sampling.Contributions of the Boyce Thompson Institute for Plant Research,9, 59–70.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Netherlands
About this chapter
Cite this chapter
Kerry, R., Oliver, M.A., Frogbrook, Z.L. (2010). Sampling in Precision Agriculture. In: Oliver, M. (eds) Geostatistical Applications for Precision Agriculture. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9133-8_2
Download citation
DOI: https://doi.org/10.1007/978-90-481-9133-8_2
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9132-1
Online ISBN: 978-90-481-9133-8
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)