Elsevier

Geoderma

Volume 89, Issues 1–2, April 1999, Pages 1-45
Geoderma

Geostatistics in soil science: state-of-the-art and perspectives

https://doi.org/10.1016/S0016-7061(98)00078-0Get rights and content

Abstract

This paper presents an overview of the most recent developments in the field of geostatistics and describes their application to soil science. Geostatistics provides descriptive tools such as semivariograms to characterize the spatial pattern of continuous and categorical soil attributes. Various interpolation (kriging) techniques capitalize on the spatial correlation between observations to predict attribute values at unsampled locations using information related to one or several attributes. An important contribution of geostatistics is the assessment of the uncertainty about unsampled values, which usually takes the form of a map of the probability of exceeding critical values, such as regulatory thresholds in soil pollution or criteria for soil quality. This uncertainty assessment can be combined with expert knowledge for decision making such as delineation of contaminated areas where remedial measures should be taken or areas of good soil quality where specific management plans can be developed. Last, stochastic simulation allows one to generate several models (images) of the spatial distribution of soil attribute values, all of which are consistent with the information available. A given scenario (remediation process, land use policy) can be applied to the set of realizations, allowing the uncertainty of the response (remediation efficiency, soil productivity) to be assessed.

Introduction

During the last decade, the development of computational resources has fostered the use of numerical methods to process the large bodies of soil data that are collected across the world. A key feature of soil information is that each observation relates to a particular location in space and time. Knowledge of an attribute value, say a pollutant concentration, is thus of little interest unless location or time of measurement or both are known and accounted for in the analysis. Geostatistics provides a set of statistical tools for incorporating spatial and temporal coordinates of observations in data processing.

Until the late 1980s, geostatistics was essentially viewed as a means to describe spatial patterns by semivariograms and to predict the values of soil attributes at unsampled locations by kriging, e.g., see review papers by Vieira et al. (1983), Trangmar et al. (1985), and Warrick et al. (1986). New tools have recently been developed to tackle advanced problems, such as the assessment of the uncertainty about soil quality or soil pollutant concentrations, the stochastic simulation of the spatial distribution of attribute values, and the modeling of space–time processes. Because of their publication in a wide variety of journals and congress proceedings, these new developments are generally barely known by soil scientists who must also struggle with different sets of notation to establish links between all these techniques. This paper aims to provide a coherent and understandable overview of the state-of-the-art in soil geostatistics, refer to recent applications of geostatistical algorithms to soil data, and point out challenges for the future.

I have extracted most of the material in this paper from my recent book (Goovaerts, 1997a) on the application of geostatistics to natural resources evaluation. The presentation follows the usual steps of a geostatistical analysis, introducing tools for description of spatial patterns, quantitative modeling of spatial continuity, spatial prediction and uncertainty assessment. Particular attention is paid to practical issues such as the modeling of sample semivariograms, the choice of an interpolation algorithm that incorporates all the relevant information available, or the incorporation of uncertainty assessment in decision making. Some common misunderstandings regarding the modeling of cross semivariograms, the use of the kriging variance or Gaussian-based algorithms will also be reviewed. The different concepts will be illustrated using multivariate soil data related to heavy metal contamination of an area of the Swiss Jura (Atteia et al., 1994; Webster et al., 1994), kindly provided by Mr. J.-P. Dubois of the Swiss Federal Institute of Technology.

Section snippets

Description of spatial patterns

Analysis of spatial data typically starts with a `posting' of data values. For example, Fig. 1 shows the spatial distribution of five stratigraphic classes and of the concentrations of two heavy metals recorded, respectively, at 359 and 259 locations in a 14.5 km2 area in the Swiss Jura. For both continuous and categorical attributes, the spatial distribution of values is not random in that observations close to each other on the ground tend to be more alike than those further apart. The

Modeling spatial variation

Description of spatial patterns is rarely a goal per se. Rather, one generally wants to capitalize on the existence of spatial dependence to predict soil properties at unsampled locations. A key step between description and prediction is the modeling of the spatial distribution of attribute values. Most of geostatistics is based on the concept of random function, whereby the set of unknown values is regarded as a set of spatially dependent random variables. Each datum z(uα) is then viewed as a

Spatial prediction

The main application of geostatistics to soil science has been the estimation and mapping of soil attributes in unsampled areas. Kriging is a generic name adopted by the geostatisticians for a family of generalized least-squares regression algorithms. The practitioner often gets confused in the face of the palette of kriging methods available: simple, ordinary, universal or with a trend, cokriging, kriging with an external drift…. This section presents a brief description of the main methods

Modeling of local uncertainty

There is necessarily some uncertainty about the value of the attribute z at an unsampled location u. In geostatistics, the usual approach for modeling local uncertainty consists of computing a kriging estimate z*(u) and the associated error variance, which are then combined to derive a Gaussian-type confidence interval (Isaaks and Srivastava, 1989, pp. 517–519), see Fig. 11 (right top graph). A more rigorous approach is to model the uncertainty about the unknown z(u) before and independently of

Stochastic simulation

As illustrated by the map of Fig. 15 (left column), kriging tends to smooth out local detail of the spatial variation of the soil attribute. The variance of ordinary kriging estimates is much smaller than the sample variance σ̂2=0.83, and the experimental semivariogram has a much smaller relative nugget effect than the semivariogram model, which indicates the underestimation of the short-range variability of Cd values. Unlike kriging, stochastic simulation does not aim at minimizing a local

Conclusions and perspectives

The growing interest of soil scientists in geostatistics arises because they increasingly realise that quantitative spatial prediction must incorporate the spatial correlation among observations. Also, geostatistics offers an increasingly wide palette of techniques well suited to the diversity of problems and information soil scientists have to deal with. The recent developments of data acquisition and computational resources have provided the geostatistician with large amounts of information

Acknowledgements

This work was partly done while the author was with the Unité Biométrie, Université Catholique de Louvain, Belgium. The author thanks Mr. J.-P. Dubois of the Swiss Federal Institute of Technology at Lausanne for the data and the National Fund for Scientific Research (Belgium) for its financial support. Data can be downloaded from http://www-personal.engin.umich.edu/∼goovaert/.

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