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Spatial Sampling

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Handbook of Regional Science
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Abstract

In spatial sampling, we collect observations in a two-dimensional framework. Careful attention is paid to the quantity of the samples, dictated by the budget at hand, and the location of the samples. A sampling scheme is generally designed to maximize the probability of capturing the spatial variation of the variable under study. Once initial samples of the primary variable have been collected and its variation documented, additional measurements can be taken at other locations. This approach is known as second-phase sampling and various optimization criteria have recently been proposed to determine the optimal location of these new observations. In this chapter, we review fundamentals of spatial sampling and second-phase designs. Their characteristics and merits under different situations are discussed, while a numerical example illustrates a modeling strategy to use covariate information in guiding the location of new samples. The chapter ends with a discussion on heuristic methods to accelerate the search procedure.

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References

  • Brunsdon C, Fotheringham AS, Charlton ME (1996) Geographically weighted regression: a method for exploring spatial nonstationarity. Geogr Anal 28(4):281–298

    Article  Google Scholar 

  • Burgess TM, Webster R, McBratney AB (1981) Optimal interpolation and isarithmic mapping of soil properties: IV. Sampling strategy. J Soil Sci 32(4):643–659

    Article  Google Scholar 

  • Christakos G, Olea RA (1992) Sampling design for spatially distributed hydrogeologic and environmental processes. Adv Water Resour 15(4):219–237

    Article  Google Scholar 

  • Cochran WG (1946) Relative accuracy of systematic and stratified random samples for a certain class of populations. Ann Math Stat 17(2):164–177

    Article  Google Scholar 

  • Corsten LCA, Stein A (1994) Nested sampling for estimating spatial semivariograms compared to other designs. Appl Stochastic Models Data Anal 10(2):103–122

    Article  Google Scholar 

  • Cressie N (1991) Statistics for spatial data. Wiley, New York

    Google Scholar 

  • Dalton R, Garlick J, Minshull R, Robinson A (1975) Sampling techniques in geography. Goerges Philip and Son Limited, London

    Google Scholar 

  • Das AC (1950) Two-dimensional systematic sampling and the associated stratified and random sampling. Sankhyā 10(1):95–108

    Google Scholar 

  • Delmelle E (2009) Spatial sampling. In: Rogerson P, Fotheringham S (eds) The SAGE handbook of spatial analysis. Sage, London, pp 54–71

    Google Scholar 

  • Delmelle E, Goovaerts P (2009) Second-phase spatial sampling designs for non-stationary spatial variables. Geoderma 153(1–2):205–216

    Article  Google Scholar 

  • Gatrell AC (1979) Autocorrelation in spaces. Environ Plan A 11(5):507–516

    Article  Google Scholar 

  • Griffith DA (2005) Effective geographic sample size in the presence of spatial autocorrelation. Ann Assoc Am Geogr 95(4):740–760

    Article  Google Scholar 

  • Haining RP (1990) Sampling spatial populations. In: Haining RP (ed) Spatial data analysis in the social and environmental sciences. Cambridge University Press, Cambridge, pp 171–196

    Chapter  Google Scholar 

  • Hengl T, Rossiter DG, Stein A (2003) Soil sampling strategies for spatial prediction by correlation with auxiliary maps. Aust J Soil Res 41(8):1403–1422

    Article  Google Scholar 

  • Madow LH (1946) Systematic sampling and its relation to other sampling designs. J Am Stat Assoc 41(234):204–217

    Article  Google Scholar 

  • Madow WG (1953) On the theory of systematic sampling. III. Comparison of centered and random start systematic sampling. Ann Math Stat 24(1):101–106

    Article  Google Scholar 

  • Madow WG, Madow LH (1949) On the theory of systematic sampling. I. Ann Math Stat 15(1):1–24

    Article  Google Scholar 

  • Matérn B (1960) Spatial variation. Springer, Berlin/Heidelberg/New York

    Google Scholar 

  • Matheron G (1963) Principles of geostatistics. Econ Geol 58(8):1246–1266

    Article  Google Scholar 

  • McBratney AB, Webster R (1981) The design of optimal sampling schemes for local estimation and mapping of regionalized variables: II. Program and examples. Comput Geosci 7(4):331–334

    Article  Google Scholar 

  • McBratney AB, Webster R (1983) Optimal interpolation and isarithmic mapping of soil properties: V. Co-regionalization and multiple sampling strategy. J Soil Sci 34(1):137–162

    Article  Google Scholar 

  • McBratney AB, Webster R, Burgess TM (1981) The design of optimal sampling schemes for local estimation and mapping of regionalized variables: I. theory and method. Comput Geosci 7(4):335–365

    Article  Google Scholar 

  • Müller W (1998) Collecting spatial data: optimal Design of Experiments for random fields. Physica-Verlag, Heidelberg

    Google Scholar 

  • Olea RA (1984) Sampling design optimization for spatial functions. Math Geol 16(4):369–392

    Article  Google Scholar 

  • Overton WS, Stehman SV (1993) Properties of designs for sampling continuous spatial resources from a triangular grid. Commun Stat 22(9):2641–2660

    Google Scholar 

  • Rogerson PA, Delmelle EM, Batta R, Akella MR, Blatt A, Wilson G (2004) Optimal sampling design for variables with varying spatial importance. Geogr Anal 36(2):177–194

    Article  Google Scholar 

  • Russo D (1984) Design of an optimal sampling network for estimating the variogram. Soil Sci Soc Am J 48(4):708–716

    Article  Google Scholar 

  • Stevens D, Olsen A (2004) Spatially balanced sampling of natural resources. J Am Stat Assoc 99(465):262–278

    Article  Google Scholar 

  • Thompson SK (2002) Sampling, 2nd edn. Wiley, New York

    Google Scholar 

  • Van Groenigen JW, Stein A (1998) Constrained optimization of spatial sampling using continuous simulated annealing. J Environ Qual 27(5):1078–1086

    Google Scholar 

  • Van Groenigen JW, Siderius W, Stein A (1999) Constrained optimisation of soil sampling for minimisation of the kriging variance. Geoderma 87(3–4):239–259

    Article  Google Scholar 

  • Warrick AW, Myers DE (1987) Optimization of sampling locations for variogram calculations. Water Resour Res 23(3):496–500

    Article  Google Scholar 

  • Yfantis EA, Flatman GT, Behar JV (1987) Efficiency of kriging estimation for square, triangular and hexagonal grids. Math Geol 19(3):183–205

    Article  Google Scholar 

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Correspondence to Eric M. Delmelle .

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Delmelle, E.M. (2019). Spatial Sampling. In: Fischer, M., Nijkamp, P. (eds) Handbook of Regional Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36203-3_73-1

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  • DOI: https://doi.org/10.1007/978-3-642-36203-3_73-1

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  • Print ISBN: 978-3-642-36203-3

  • Online ISBN: 978-3-642-36203-3

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