Abstract
Geostatistical simulation provides a means to mimic spatial and or temporal variation of processes that are relevant to precision agriculture. Simulation by computer models aids decision making when it is too difficult, time consuming, costly or dangerous to perform real-world experiments. Spatio-temporal processes are often considered as uncertain because it is impossible to make accurate and comprehensive observations. Geostatistical simulation incorporates uncertainty into modelling to obtain a more realistic impression of the variation. This chapter provides a short introduction to the background of geostatistical simulation and explains sequential Gaussian simulation in more detail because it is the method most commonly applied. Three case studies demonstrate the application of geostatistical simulation in precision agriculture. They deal with the risk of under- and over-liming because of uncertainty about the accuracy of a pH map, the economic costs of GPS errors and the identification of factors that are most relevant to the accuracy of mapping.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Reprinted from Computers and Electronics in Agriculture, 63/2, S. de Bruin, G.B.M. Heuvelink and J.D. Brown, Propagation of positional measurement errors to agricultural field boundaries and associated costs, pp 247–248, Copyright (2008), with permission from Elsevier.
- 2.
Gebbers, R., Herbst, R., & Wenkel, K.-O. (2009). Sensitivity analysis of soil nutrient mapping. In E. J. van Henten, D. Goense, & C. Lokhorst (Eds.), Precision Agriculture ’09. Proceedings of the 7th European Conference on Precision Agriculture (pp. 513–519). Wageningen, The Netherlands: Wageningen Academic Publishers.
References
Adamchuk, V. I., Lund, E. D., Reed, T. M., & Ferguson, R. B. (2007). Evaluation of an on-the-go technology for soil pH mapping. Precision Agriculture, 8, 139–149.
Agnew, D., & Larson, K. (2007). Finding the repeat times of the GPS constellation. GPS Solutions, 11, 71–76.
Amiri-Simkooei, A. R., & Tiberius, C. C. J. M. (2007). Assessing receiver noise using GPS short baseline time series. GPS Solutions, 11, 21–35.
Bivand, R. S., Pebesma, E. J., & Gómez-Rubio, V. (2008). Applied spatial data analysis with R. New York: Springer.
Bogaert, P., Delincé, J., & Kay, S. (2005). Assessing the error of polygonal area measurements: a general formulation with applications to agriculture. Measurement Science & Technology, 16, 1170–1178.
Bona, P. (2000). Precision, cross correlation, and time correlation of GPS phase and code observations. GPS Solutions, 4, 3–13.
Bourgault, G. (1997). Using non-Gaussian distributions in geostatistical simulation. Mathematical Geology, 29, 315–334.
Bramley, R. G. V. (2009). Lessons from nearly 20 years of precision agriculture research, development, and adoption as a guide to its appropriate application. Crop and Pasture Science, 60, 197–217.
Chilès, J-P., & Delfiner, P. (1999). Geostatistics. Modeling spatial uncertainty. New York: Wiley.
de Bruin, S. (2008). Modelling positional uncertainty of line features by accounting for stochastic deviations from straight line segments. Transactions in GIS, 12, 165–177.
de Bruin, S., Heuvelink, G. B. M., & Brown, J. D. (2008). Propagation of positional measurement errors to agricultural field boundaries and associated costs. Computers and Electronics in Agriculture, 63, 245–256.
Demougeot-Renard, H., de Fouquet, C., & Renard, P. (2004). Forecasting the number of soil samples required to reduce remediation costs uncertainty. Journal of Environmental Quality, 33, 1694–1702.
Deutsch, C. V., & Journel, A. G. (1998). GSLIB: geostatistical software library and user’s guide (2nd ed.). New York: Oxford University Press.
Düngeverordnung (2007). Verordnung über die Anwendung von Düngemitteln, Bodenhilfsstoffen, Kultursubstraten und Pflanzenhilfsmitteln nach den Grundsätzen der guten Fachlichen Praxis beim Düngen (Düngeverordnung – DüV). Neufassung der Düngeverordnung (27.02.2007). Bundesgesetzblatt I, 2007, 221 (Federal act on the use of fertilizers in Germany).
European Space Agency (2005). The EGNOS signal explained, EGNOS fact sheet 12. EGNOS fact sheet http://www.egnos-pro.esa.int/Publications/2005\%20Updated\%20Fact\%20Sheets/fact\_sheet\_12.pdf (accessed August 18 2009).
Faechner, T., Pyrcz, M., & Deutsch, C. V. (1999). Soil remediation decision making in presence of uncertainty in crop yield response. Geoderma, 97, 21–38.
Fagroud, M., & Van Meirvenne, M. (2002). Accounting for soil spatial autocorrelation in the design of experimental trials. Soil Science Society of America Journal, 66, 1134–1142.
Farahani, H. J., & Flynn, R. L. (2007). Map quality and zone delineation as affected by width of parallel swaths of mobile agricultural sensors. Biosystems Engineering, 96, 151–159.
Favis-Mortlock, D. T., Boardman, J., Parsons, A. J., & Lascelles, B. (2000). Emergence and erosion: a model for rill initiation and development. Hydrological Processes, 14, 2173–2205.
Gebbers, R., Herbst, R., & Wenkel, K.-O. (2009). Sensitivity analysis of soil nutrient mapping. In E. J. van Henten, D. Goense, & C. Lokhorst (Eds.), Precision Agriculture ’09. Proceedings of the 7th European Conference on Precision Agriculture (pp. 513–519). Wageningen, The Netherlands: Wageningen Academic Publishers.
Gentle, J. E. (1989). Random number generation and Monte Carlo methods. New York: Springer.
Goovaerts, P. (1997). Geostatistics for natural resources evaluation. New York: Oxford University Press.
Goovaerts, P. (1999). Geostatistical tools for deriving block-averaged values of environmental attributes. Journal of Geographical Information Sciences, 5, 88–96.
Gotway, C.A., & Rutherford, B. M. (1996). The components of geostatistical simulation. In Mower, H.T. (Ed.), Proceedings of the Second International Symposium on Spatial Accuracy in Natural Resources and Environmental Sciences. Fort Collins: USDA Forest Service. (http://www.osti.gov/bridge/servlets/purl/228463-cOfkGn/webviewable/228463.pdf, accessed September 29 2009).
Gotway, C. A., Ferguson, R. B., Hergert, G. W., & Peterson, T. A. (1996). Comparisons of kriging and inverse-distance methods for mapping soil parameters. Soil Science Society of America Journal, 60, 1237–1247.
Härdle, W., Müller, M., Sperlich, S., & Werwatz, A. (2004). Nonparametric and semiparametric models. Berlin: Springer.
Herbst, R., Lamp, J., & Reimer, G. (2001). Inventory and spatial modelling of soils on PA pilot fields. In: G. Grenier, & S. Blackmore (Eds.), Third European Conference on Precision Agriculture (pp. 395–400). Montpellier, France: Agro Montpellier.
Heuvelink, G. B. M. (1998). Error propagation in environmental modelling with GIS. London, UK: Taylor & Francis.
Heuvelink, G. B. M. (1999). Propagation of error in spatial modelling with GIS. In Longley, P. A., Goodchild, M. F., Maguire, D. J., & Rhind, D. W. (Eds.), Geographical information systems (2nd ed., pp. 207–217). New York: Wiley.
Heuvelink, G. B. M., Brown, J. D., & van Loon, E. E. (2007). A probabilistic framework for representing and simulating uncertain environmental variables. International Journal of Geographical Information Science, 21, 497–513.
Hoskinson, R. L., Rope, R. C., Blackwood, L. G., Lee, R. D., & Fink, R. K. (2004). The impact of soil sampling errors on variable rate fertilization. In D. J. Mulla (Ed.), Proceedings of 7th International Conference of Precision Agriculture (pp. 1645–1654). Minneapolis, USA: Precision Agriculture Center, University of Minnesota, Department of Soil, Water and Climate.
Kerry, R., & Oliver, M. A. (2003). Variograms of ancillary data to aid sampling for soil surveys. Precision Agriculture, 4, 261–278.
Kiiveri, H. T. (1997). Assessing, representing and transmitting positional uncertainty in maps. International Journal of Geographical Information Science, 11, 33–52.
Lantuéjoul, C. (2002). Geostatistical simulation. Models and algorithms. Berlin: Springer.
Lapen, D. R., Topp, G. C., Hayhoe, H. N., Gregorich, E. G., & Curnoe, W. E. (2001). Stochastic simulation of soil strength/compaction and assessment of corn yield risk using threshold probability patterns. Geoderma, 104, 325–343.
Leuangthong, O., Khan, K. D., & Deutsch, C. V. (2008). Solved problems in geostatistics. Hoboken: Wiley.
MAFF (2000). Fertilizer recommendations for agricultural and horticultural crops. London: The Stationery Office.
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.
MATLAB: The MathWorks, Natick, MA. (http://www.mathworks.com).
Mueller, T. G., Pusuluri, N. B., Mathias, K. K., Cornelius, P. L., & Barnhisel, R. I. (2004). Site-specific soil fertility management: a model for map quality. Soil Science Society of America Journal, 68, 2031–2041.
Olynik, M., Petovello, M., Cannon, M., & Lachapelle, G. (2002). Temporal impact of selected GPS errors on point positioning. GPS Solutions, 6, 47–57.
Pebesma, E. J. (2001). Gstat users’ manual. Utrecht, The Netherlands: Department of Physical Geography, Utrecht University. http://www.gstat.org/gstat.pdf. Accessed 28. Jan. 2009.
Pebesma, E. J. (2004). Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30, 683–691.
Pokrajac, D., Fiez, T., & Obradovic, Z. (2002). A data generator for evaluating spatial issues in precision agriculture. Precision Agriculture, 3, 259–281.
Praktijkonderzoek Plant en Omgeving (2006). Kwantitatieve informatie akkerbouw en vollegrondsgroenteteelt 2006 (KWIN 2006). Lelystad: Praktijkonderzoek Plant en Omgeving.
R Development Core Team (2008). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. (http://www.r-project.org).
Reichardt, M., Jürgens, C., Klöble, U., Hüter, J., & Moser, K. (2009). Dissemination of precision farming in Germany: acceptance, adoption, obstacles, knowledge transfer and training activities. Precision Agriculture (DOI 10.1007/s11119-009-9112-6, accessed October 1 2009).
Remy, N., Boucher, A., & Wu, J. (2009). Applied geostatistics with SGeMS. New York: Cambridge University Press.
Shi, W., & Liu, W. (2000). A stochastic process-based model for the positional error of line segments in GIS. International Journal of Geographical Information Science, 14, 51–66.
Shiflet, A. B., & Shiflet, G. W. (2006). Introduction to computational science. Princeton: Princeton University Press.
SYSTAT: Systat Software Inc., Chicago, IL. (http://www.systat.com).
Van Buren, J., Westerik, A., & Olink, E. J. H. (2003). Kwaliteit TOP10vector – De geometrische kwaliteit van het bestand TOP10vector van de Topografische Dienst. Kadaster – Concernstaf Vastgoedinformatie en Geodesie: 12.
Vann, J., Bertoli, O., & Jackson, S. (2002). An overview of geostatistical simulation for quantifying risk. In S. M. Searston, & R. J. Warner (Eds.), Quantifiying risk and error. Geostatistical Association of Australasia Symposium. (http://www.qgeoscience.com/images/downloads/vann_bertoli_jackson_simulation_for_risk_distribution.pdf, accessed September 29 2009).
VDLUFA (1996). Kalium-Düngung nach Bodenuntersuchung und Pflanzenbedarf. Richtwerte für die Gehaltsklasse C. Darmstadt, Germany: VDLUFA-Verlag (Potassium fertilization based on soil analysis and crop requirements. Guidelines to maintain optimum soil index).
VDLUFA (2000a). Bestimmung des Kalkbedarfs von Acker- und Grünlandböden. Darmstadt: Verband Deutscher Landwirtschaftlicher Untersuchungs- und Forschungsanstalten (VDLUFA). (Determination of lime needs for arable and grassland soils) (http://www.vdlufa.de/joomla/Dokumente/Standpunkte/0-9-kalk.pdf, accessed August 18 2009).
VDLUFA (2000b). Bestimmung des Kalkbedarfs von Acker- und Grünlandböden. Appendix. Richtwerte für das Rahmenschema zur Kalkbedarfsermittlung in Deutschland. Darmstadt: Verband Deutscher Landwirtschaftlicher Untersuchungs- und Forschungsanstalten (VDLUFA) (Recommendation tables for lime) (http://www.vdlufa.de/joomla/Dokumente/Standpunkte/0-9-kalkanl.pdf, accessed 18.08.2009).
Wang, J., Satirapod, C., & Rizos, C. (2002). Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. Journal of Geodesy, 76, 95–104.
Webster, R., & Oliver, M. A. (2007). Geostatistics for environmental scientists (2nd ed.). Chichester: Wiley.
Zanolin, A., de Fouquet, C., Granier, J., Ruelle, P., & Nicoullaude, B. (2007). Geostatistical simulation of the spatial variability of an irrigated maize farm plot. Comptes Rendus Geosciences, 339, 430–440.
Zhang, J., & Kirby, R. P. (2000). A geostatistical approach to modelling positional errors in vector data. Transactions in GIS, 4, 145–159.
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
Gebbers, R., de Bruin, S. (2010). Application of Geostatistical Simulation in Precision Agriculture. In: Oliver, M. (eds) Geostatistical Applications for Precision Agriculture. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9133-8_11
Download citation
DOI: https://doi.org/10.1007/978-90-481-9133-8_11
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)