Abstract
This paper presents a method of spatial sampling based on stratification by Local Moran’s I i calculated using auxiliary information. The sampling technique is compared to other design-based approaches including simple random sampling, systematic sampling on a regular grid, conditional Latin Hypercube sampling and stratified sampling based on auxiliary information, and is illustrated using two different spatial data sets. Each of the samples for the two data sets is interpolated using regression kriging to form a geostatistical map for their respective areas. The proposed technique is shown to be competitive in reproducing specific areas of interest with high accuracy.
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References
Anselin L (1995) Local indicators of spatial association—LISA. Geograph Anal 27(2): 93–115
Brus DJ, De Gruijter JJ (1997) Random sampling or geostatistical modelling? Choosing between design-based and model-based sampling strategies for soil (with discussion). Geoderma 80(1–2): 1–44
Cochran WG (1963) Sampling techniques. Wiley, New York
Cressie N (1993) Statistics for spatial data revised edn. John Wiley & Sons Inc, New York
De Gruijter JJ, Ter Braak CJF (1992) Design-based versus model-based sampling strategies: comment on R. J. Barnes’ Bounding the required sample size for geologic site characterization. Math Geol 24(7): 859–864
Falk MG, Denham RJ, Mengersen KL (2009) Estimating uncertainty in the revised universal soil loss equation via Bayesian melding. J Agric Biol Environ Stat (In press)
Hengl T, Heuvelink GBM, Stein A (2004) A generic framework for spatial prediction of soil variables based on regression-kriging. Geoderma 120(1–2): 75–93
Hengl T, Heuvelink GBM, Rossiter DG (2007) About regression-kriging: from equations to case studies. Comput Geosci 33(10): 1301–1315
Knotters M, Brus DJ, Voshaar JHO (1995) A comparison of kriging, co-kriging and kriging combined with regression for spatial interpolation of horizon depth with censored observations. Geoderma 67(3–4): 227–246
Marchant BP, Lark RM (2006) Adaptive sampling and reconnaissance surveys for geostatistical mapping of the soil. Eur J Soil Sci 57(6): 831–845
Marin JM, Robert CP (2007) Bayesian core: a practical approach to computational Bayesian statistics. Springer, New York
Minasny B, McBratney AB (2006) A conditioned Latin hypercube method for sampling in the presence of ancillary information. Comput Geosci 32(9): 1378–1388
Moran PAP (1950) Notes on continuous stochastic phenomena. Biometrika 37: 17–23
Müller WG (2007) Collecting spatial data, 3rd edn. Springer, Heidelberg
Poole D, Raftery AE (2000) Inference for deterministic simulation models: The Bayesian melding approach. J Am Stat Assoc 95(452): 1244–1255
R Development Core Team (2008) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org, ISBN 3-900051-07-0
Renard KG, Foster GR, Weesies GA, McCool DK, Yoder DC (1997) Predicting soil erosion by water: a guide to conservation planning with the revised universal soil loss equation (RUSLE). Agriculture Handbook. No. 703. U.S. Department of Agriculture
Sarsby RW (2000) Environmental geotechniques. Thomas Telford Ltd, London
Webster R, Oliver MA (2007) Geostatistics for environmental scientists, 2nd edn. John Wiley & Sons, Ltd, Chichester UK
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Falk, M.G., Denham, R.J. & Mengersen, K.L. Spatially stratified sampling using auxiliary information for geostatistical mapping. Environ Ecol Stat 18, 93–108 (2011). https://doi.org/10.1007/s10651-009-0122-3
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DOI: https://doi.org/10.1007/s10651-009-0122-3