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Pedometrics pp 291–340Cite as

Classical Soil Geostatistics

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Part of the book series: Progress in Soil Science ((PROSOIL))

Abstract

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“All the business of war, and indeed all the business of life, is to endeavour to find out what you don’t know by what you do”.

Arthur Wellesley

Duke of Wellington

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References

  • Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petov BN, Csaki F (eds) 2nd international symposium on information theory. Akademia Kiado, Budapest, pp 267–281

    Google Scholar 

  • Barry RP, Kelley Pace R (1997) Kriging with large data sets using sparse matrix techniques. Commun Stat-Simul Comput 26(2):619–629

    Article  Google Scholar 

  • Beckett PHT, Bie SW (1976) Reconnaissance for soil survey. II. Pre-survey estimates of the intricacy of the soil pattern. J Soil Sci 26:101–110

    Article  Google Scholar 

  • Beckett PHT, Webster R (1971) Soil variability: a review. Soils Fertil 34:1–15

    Google Scholar 

  • Bourennane H, King D, Chéry P, Bruand A (1996) Improving the kriging of a soil variable using slope gradient as external drift. Eur J Soil Sci 47

    Google Scholar 

  • Brus DJ, Heuvelink GBM (2007) Optimization of sample patterns for universal kriging of environmental variables. Geoderma 138:86–95

    Article  Google Scholar 

  • Burgess TM, Webster R (1980a) Optimal interpolation and isarithmic mapping of soil properties I the semi-variogram and punctual kriging. J Soil Sci 31:315–331

    Article  Google Scholar 

  • Burgess TM, Webster R (1980b) Optimal interpolation and isarithmic mapping of soil properties II block kriging. J Soil Sci 31:333–341

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Burrough PA (1983) Multiscale sources of spatial variation in soil. II. A non-Brownian fractal model and its application in soil survey. J Soil Sci 34:599–620

    Article  Google Scholar 

  • Buttafuoco G, Castrignano A (2005) Study of the spatio-temporal variation of soil moisture under forest using intrinsic random functions of order k. Geoderma 128:208–220

    Article  Google Scholar 

  • Chilès J, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley, New York

    Book  Google Scholar 

  • Clark I, Basinger KL, Harper WV (1989) MUCK – a novel approach to cokriging. In: Buxton BE (ed) Proceedings of the conference on geostatistical, sensitivity and uncertainty methods for ground-water flow and radionuclide transport modeling. Battelle Press, Columbus, pp 473–493

    Google Scholar 

  • Corstanje R, Grunwald S, Lark RM (2008) Inferences from fluctuations in the local variogram about the assumption of stationarity in the variance. Geoderma 143:123–132

    Article  Google Scholar 

  • Cressie N (1985) Fitting variogram models by weighted least squares. Math Geol 17:563

    Article  Google Scholar 

  • Cressie N (1993) Statistics for spatial data. Wiley, New York

    Google Scholar 

  • Cressie N, Johannesson G (2008) Fixed rank kriging for very large spatial data sets. J R Stat Soc: Ser B (Stat Methodol) 70(1):209–226

    Article  Google Scholar 

  • Cressie, N., Kang, E.L., 2010. High-resolution digital soil mapping: Kriging for very large datasets. In: Proximal soil sensing. Springer, Dordrecht, pp 49–63

    Chapter  Google Scholar 

  • Davis MW (1987) Production of conditional simulations via the LU triangular decomposition of the covariance matrix. Math Geol 19:91–98

    Article  Google Scholar 

  • Deutsch CV, Journel AG (1998) GSLIB geostatistical software and user’s guide, 2nd edn. Oxford University Press, New York

    Google Scholar 

  • Dowd PA (1984) The variogram and kriging: robust and resistant estimators. In: Verly G, David M, Journel AG, Marechal AŽ (eds) Geostatistics for natural resources characterization. Part 1. Reidel, Dordrecht, pp 91–106

    Chapter  Google Scholar 

  • Goovaerts P (1994) Comparative performance of indicator algorithms for modeling conditional probability distribution functions. Math Geol 26:389–411

    Article  Google Scholar 

  • Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York

    Google Scholar 

  • Goulard M, Voltz M (1992) Linear coregionalization model: tools for estimation and choice of cross-variogram matrix. Math Geol 24:269–286

    Article  Google Scholar 

  • Haas TM (1990) Lognormal and moving window methods of estimating acid deposition. J Am Stat Assoc 85:950–963

    Article  Google Scholar 

  • Halvorson JJ, Smith JL, Bolton H, Rossi RE (1995) Evaluating shrub-associated patterns of soil properties in a shrub steppe ecosystem using multiple-variable geostatistics. Soil Sci Soc Am J 59:11476–11487

    Article  Google Scholar 

  • Isaaks E, Srivastava RM (1989) An introduction to applied Geostatistics. Oxford University Press, New York

    Google Scholar 

  • Journel AG (1983) Non-parametric estimation of spatial distributions. Math Geol 15:445–468

    Article  Google Scholar 

  • Journel AG (1994a) Resampling from stochastic simulations. Environ Ecol Stat 1:63–91

    Article  Google Scholar 

  • Journel AG (1994b) Modelling uncertainty: some conceptual thoughts. In: Dimitrakopoulos R (ed) Geostotistics for the next century. Kluwer Academic, Dordrecht, pp 30–43

    Chapter  Google Scholar 

  • Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic Press, London

    Google Scholar 

  • Kaufman CG, Schervish MJ, Nychka DW (2008) Covariance tapering for likelihood-based estimation in large spatial data sets. J Am Stat Assoc 103(484):1545–1555

    Article  Google Scholar 

  • Künsch HR, Papritz A, Bassi F (1997) Generalized cross-covariances and their estimation. Math Geol 29:779–799

    Article  Google Scholar 

  • Lark RM (2000) A comparison of some robust estimators of the variogram for use in soil survey. Eur J Soil Sci 51:137–157

    Article  Google Scholar 

  • Lark RM (2002) Robust estimation of the pseudo cross-variogram for cokriging soil properties. Eur J Soil Sci 53:253–270

    Article  Google Scholar 

  • Lark RM (2003) Two robust estimators of the cross-variogram for multivariate geostatistical analysis of soil properties. Eur J Soil Sci 54:187–201

    Article  Google Scholar 

  • Lark RM, Bishop TFA (2007) Cokriging particle size fractions of the soil. Eur J Soil Sci 58:763–774

    Article  Google Scholar 

  • Lark RM, Ferguson RB (2004) Mapping risk of soil nutrient deficiency or excess by disjunctive and indicator kriging. Geoderma 118:39–53

    Article  Google Scholar 

  • Lark RM, Papritz A (2003) Fitting a linear model of coregionalization for soil properties using simulated annealing. Geoderma 115:245–260

    Article  Google Scholar 

  • Lark RM, Bellamy PH, Rawlins BG (2006) Spatio-temporal variability of some metal concentrations in the soil of eastern England, and implications for soil monitoring. Geoderma 133:363–379

    Article  Google Scholar 

  • Lark RM, Ander EL, Cave MR, Knights KV, Glennon MM, Scanlon RP (2014) Mapping trace element deficiency by cokriging from regional geochemical soil data: a case study on cobalt for grazing sheep in Ireland. Geoderma 226–227:64–78

    Article  Google Scholar 

  • Leenaers H, Okx JP, Burrough PA (1990) Comparison of spatial prediction methods for mapping floodplain soil pollution. Catena 17:535–550

    Article  Google Scholar 

  • Marchant BP, Lark RM (2006) Adaptive sampling for reconnaissance surveys for geostatistical mapping of the soil. Eur J Soil Sci 57:831–845

    Article  Google Scholar 

  • Marchant BP, Lark RM (2007) Optimized sample schemes for geostatistical surveys. Math Geol 39:113–134

    Article  Google Scholar 

  • Matérn B (1986) Spatial variation. Springer, Berlin

    Book  Google Scholar 

  • Matheron G (1962) Traité de géostatistique appliquée, Tome I: Mémoires du Bureau de RecherchesGéologiques et Minières, vol 14. Editions Technip, Paris

    Google Scholar 

  • Matheron G (1976) A simple substitute for conditional expectation: the disjunctive kriging. In: Guarascio M, David M, Huijbregts C (eds) Advanced geostatistics in the mining industry. D. Reidel, Dordrecht, pp 221–236

    Chapter  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 34:137–162

    Article  Google Scholar 

  • McBratney AB, Webster R (1986) Choosing functions for semivariances of soil properties and fitting them to sample estimates. J Soil Sci 37:617–639

    Article  Google Scholar 

  • McBratney AB, Webster R, Burgess TM (1981) The design of optimal sampling schemes for local estimation and mapping of regionalised variables. I. Theory and method. Comput Geosci 7:331–334

    Article  Google Scholar 

  • McBratney AB, Webster R, McLaren RG, Spiers RB (1982) Regional variation of extractable copper and cobalt in the topsoil of south-east Scotland. Agronomie 2:969–982

    Article  Google Scholar 

  • Meerschman E, Van Meirvenne M, Van De Vijver E, De Smedt P, Islam MM, Saey T (2013) Mapping complex soil patterns with multiple-point geostatistics. Eur J Soil Sci 64:183–191

    Article  Google Scholar 

  • Minasny B, McBratney AB (2005) The Matérn function as a general model for soil variograms. Geoderma 128:192–207

    Article  Google Scholar 

  • Minasny B, McBratney AB, Whelan BM (2006) VESPER version 1.62. Australian Centre for Precision Agriculture, McMillan Building A05, The University of Sydney. NSW

    Google Scholar 

  • Myers DE (1991) Pseudo-cross variograms, positive definiteness, cokriging. Math Geol 23: 805–816

    Article  Google Scholar 

  • Odeh IOA, McBratney AB, Chittleborough DJ (1994) Spatial prediction of soil properties from landform attributes derived from a digital elevation model. Geoderma 63:197–214

    Article  Google Scholar 

  • Papritz A, Dubois J-P (1999) Mapping heavy metals in soil by (non-)linear kriging: an empirical validation. In: Gomez-Hernandez J, Soares A, Froidevaux R (eds) geoENV II: Geostatistics for environmental applications, Quantitative geology and geostatistics, vol 10. Kluwer Academic Publishing, Dordrecht, pp 429–440

    Chapter  Google Scholar 

  • Papritz A, Flühler H (1994) Temporal change of spatially autocorrelated soil properties: optimal estimation by cokriging. Geoderma 62:29–43

    Article  Google Scholar 

  • Papritz A, Webster R (1995) Estimating temporal change in soil monitoring. 1. Statistical theory. Eur J Soil Sci 46:1–12

    Article  Google Scholar 

  • Papritz A, Kunsch HR, Webster R (1993) On the pseudo cross-variogram. Math Geol 25: 1015–1026

    Article  Google Scholar 

  • Pawlowsky-Glahn V, Olea RA (2004) Geostatistical analysis of compositional data. Oxford University Press, New York

    Google Scholar 

  • Ploner A (1999) The use of the variogram cloud in geostatistical modelling. Environmetrics 10:413–437

    Article  Google Scholar 

  • Rivoirard J (1994) Introduction to disjunctive kriging and non-linear geostatistics. Oxford University Press, Oxford

    Google Scholar 

  • Stein ML (1999) Interpolation of spatial data: some theory for kriging. Springer, New York

    Book  Google Scholar 

  • Sun W, Minasny B, McBratney A (2012) Analysis and prediction of soil properties using local regression-kriging. Geoderma 171:16–23

    Article  Google Scholar 

  • Van Meirvenne M, Goovaerts P (2001) Evaluating the probability of exceeding a site-specific soil cadmium contamination threshold. Geoderma 102:75–100

    Article  Google Scholar 

  • Viscarra Rossel RA, Goovaerts P, McBratney AB (2001) Assessment of the production and economic risks of site-specific liming using geostatistical uncertainty modelling. Environmetrics 12:699–711

    Article  Google Scholar 

  • von Steiger B, Webster R, Schulin R, Lehmann R (1996) Mapping heavy metals in polluted soil by disjunctive kriging. Environ Pollut 94:205–215

    Article  Google Scholar 

  • Webster R (2015) Daniel Krige’s influence on soil science. J South Afr Inst Min Metall 11:165–117

    Article  Google Scholar 

  • Webster R, Burgess TM (1980) Optimal interpolation and isarithmic mapping of soil properties III changing drift and universal kriging. J Soil Sci 31:505–524

    Article  Google Scholar 

  • Webster R, Burgess TM (1984) Sampling and bulking strategies for estimating soil properties in small regions. J Soil Sci 35:127–140

    Article  Google Scholar 

  • Webster R, Butler BE (1976) Soil survey and classification studies at Ginninderra. Aust J Soil Res 14:1–24

    Article  Google Scholar 

  • Webster R, Lark RM (2013) Field sampling for environmental science and management. Routledge, London. pp viii+192

    Google Scholar 

  • Webster R, Oliver MA (1992) Sample adequately to estimate variograms of soil properties. J Soil Sci 43:177–192

    Article  Google Scholar 

  • Webster R, Oliver MA (2007) Geostatistics for environmental scientists, 2nd edn. Wiley, Chichester. pp. x+328

    Book  Google Scholar 

  • Wood G, Oliver MA, Webster R (1990) Estimating soil salinity by disjunctive kriging. Soil Use Manag 6:97–104

    Article  Google Scholar 

  • Yates F (1948) Systematic sampling. Phil Trans R Soc A 241:345–377

    Article  Google Scholar 

  • Youden WJ, Mehlich A (1937) Selection of efficient methods for soil sampling. Contrib Boyce Thompson Inst Plant Res 9:59–70

    Google Scholar 

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Author information

Authors and Affiliations

  1. British Geological Survey, Keyworth, Nottingham NG12 5GG, UK

    R. Murray Lark

  2. Sydney Institute of Agriculture & School of Life and Environmental Sciences, The University of Sydney, Sydney, NSW, 2006, Australia

    Budiman Minasny

Authors
  1. R. Murray Lark
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  2. Budiman Minasny
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Corresponding author

Correspondence to R. Murray Lark .

Editor information

Editors and Affiliations

  1. Sydney Institute of Agriculture & School of Life and Environmental Sciences, The University of Sydney, Sydney, New South Wales, Australia

    Alex. B. McBratney

  2. Sydney Institute of Agriculture & School of Life and Environmental Sciences, The University of Sydney, Sydney, New South Wales, Australia

    Budiman Minasny

  3. Sydney Institute of Agriculture & School of Life and Environmental Sciences, The University of Sydney, Sydney, New South Wales, Australia

    Uta Stockmann

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Lark, R.M., Minasny, B. (2018). Classical Soil Geostatistics. In: McBratney, A., Minasny, B., Stockmann, U. (eds) Pedometrics. Progress in Soil Science. Springer, Cham. https://doi.org/10.1007/978-3-319-63439-5_10

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