Statistics for Spatial Data.

Monographs on statistics and applied probability

Impatti, adattamento e vulnerabilita Le cause e le responsabilita dei cambiamenti climatici sono state trattate sul numero di ottobre della rivista Cda. Approfondiamo l’argomento presentando il documento: “Cambiamenti climatici 2007: impatti, adattamento e vulnerabilita” votato ad aprile 2007 dal secondo gruppo di lavoro del Comitato Intergovernativo sui Cambiamenti Climatici (Intergovernmental Panel on Climate Change). Si tratta del secondo di tre documenti che compongono il quarto rapporto sui cambiamenti climatici.

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Climate Change 2007: Impacts, Adaptation and Vulnerability.

https://www.clw.csiro.au/aclep/documents/McBratney%20et%20al.%202003.pdf

On digital soil mapping

An overview of model-based geostatistics.- Gaussian models for geostatistical data.- Generalized linear models for geostatistical data.- Classical parameter estimation.- Spatial prediction.- Bayesian inference.- Geostatistical design.

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Model-based Geostatistics

Preface 1 Introduction 2 Basic Statistics 3 Prediction and Interpolation 4 Characterizing Spatial Processes: The Covariance and Variogram 5 Modelling the Variogram 6 Reliability of the Experimental Variogram and Nested Sampling 7 Spectral Analysis 8 Local Estimation or Prediction: Kriging 9 Kriging in the Presence of Trend and Factorial Kriging 10 Cross-Correlation, Coregionalization and Cokriging 11 Disjunctive Kriging 12 Stochastic Simulation (new file) Appendix A Appendix B References Index

Geostatistics for Environmental Scientists

Geographical information systems could be improved by adding procedures for geostatistical spatial analysis to existing facilities Most traditional methods of interpolation are based on mathematical as distinct from stochastic models of spatial variation Spatially distributed data behave more like random variables, however, and regionalized variable theory provides a set of stochastic methods for analysing them Kriging is the method of interpolation deriving from regionalized variable theory It depends on expressing spatial variation of the property in terms of the variogram, and it minimizes the prediction errors which are themselves estimated We describe the procedures and the way we link them using standard operating systems We illustrate them using examples from case studies, one involving the mapping and control of soil salinity in the Jordan Valley of Israel, the other in semi-arid Botswana where the herbaceous cover was estimated and mapped from aerial photographic survey

Kriging: a method of interpolation for geographical information systems

Summary
Soil properties mapped in two intensive surveys had large nugget variances, leading to large estimation variances and erratic isarithms when mapped by punctual kriging. It is likely that both surveyors and survey clients are interested in average values of soil properties over areas rather than point values, and such values can be obtained by block kriging. Estimation variances are very much smaller, and maps of sodium and stone content at Plas Gogerddan, Central Wales, kriged over blocks 920m2, and thickness of cover loam at Hole Farm, Norfolk, kriged over blocks of 400m2, are much smoother than the punctually kriged maps. The map of Hole Farm has a distinct and meaningful regional pattern.

Optimal interpolation and isarithmic mapping of soil properties. II. Block kriging.

Quantitative description of variable material sampling and estimation generalization, prediction, and classification relations between variables - covariance and correlation regression relations between individuals - similarity ordination analysis of dispersion and discrimination numerical classification - hierarchical systems numerical classification - non hierarchical methods spatial dependence nested sampling and analysis local estimation - kriging.

Statistical Methods in Soil and Land Resource Survey

Kriging is a means of spatial prediction that can be used for soil properties. It is a form of weighted local averaging. It is optimal in the sense that it provides estimates of values at unrecorded places without bias and with minimum and known variance. Isarithmic maps made by kriging are alternatives to conventional soil maps where properties can be measured at close spacings.
Kriging depends on first computing an accurate semi‐variogram, which measures the nature of spatial dependence for the property. Estimates of semi‐variance are then used to determine the weights applied to the data when computing the averages, and are presented in the kriging equations.
The method is applied to three sets of data from detailed soil surveys in Central Wales and Norfolk. Sodium content at Plas Gogerddan was shown to vary isotropically with a linear semi‐variogram. Ordinary punctual kriging produced a map with intricate isarithms and fairly large estimation variance, attributed to a large nugget effect. Stoniness on the same land varied anisotropically with a linear semi‐variogram, and again the estimation error of punctual kriging was fairly large. At Hole Farm, Norfolk, the thickness of cover loam varied isotropically, but with a spherical semi‐variogram. Its parameters were estimated and used to krige point values and produce a map showing substantial short‐range variation.

Richard Webster

Papers

Geostatistics for Environmental Scientists

Kriging: a method of interpolation for geographical information systems

Optimal interpolation and isarithmic mapping of soil properties. II. Block kriging.

Statistical Methods in Soil and Land Resource Survey

Optimal interpolation and isarithmic mapping of soil properties. I. The semi-variogram and punctual kriging