The following (edited) observations on facilities provided in available geostatistical software (stand-alone or within/linked to GIS) are taken from AI-GEOSTATS. The AI-GEOSTATS original website (www.ai-geostats.org) has very recently undergone substantial re-development, so the comments have been updated and to some extent superseded with more up-to-date material.

Display of proportional/classed symbol maps: often the first step in the analysis of geostatistical data. Showing symbols with a size that is proportional or characteristic of their attributed value can help the data analyst to identify outliers and trends.

Moving windows statistics: geostatistics assumes second order stationarity in the data: the mean has to exist and is constant and independent of location within the region of stationarity. The covariance has to exist as well, and is only dependent on the distance between any two values, and not on the locations. One way to evaluate second order stationarity is to divide the studied area into cells and compare the mean and the covariance between all cells. The moving windows technique uses an overlap of the cells as if a window was moving over the whole dataset.

Sampling network analysis: techniques used to quantify the degree of irregularity of the sampling network. These include the analysis of: Thiessen polygons; the fractal dimension of the sampling network; and the use of the Morishita Index. Nearest-neighbours statistics and many other tests can also be used to describe the spatial distribution of the measurements.

Trend analysis: An underlying trend may appear in the data and needs to be taken into account when applying Ordinary Kriging (Universal Kriging is supposed to take the drift into account). The drift is frequently modelled with a simple linear or a quadratic model.

Declustering: When global estimations are desired one needs to obtain statistics that are representative of the whole area of interest. By attributing lower weights to clustered measurements one can reduce their influence and so limit the bias one would have obtained without a prior declustering. Two declustering techniques are frequently used: the cell and the polygonal declustering method.

Variogram analysis: The use of spatial autocorrelation being one of the main keys in a geostatistical case study, one would expect the GIS to provide at least the possibility to calculate the experimental semivariogram.

Interactive variography: The display of the experimental semivariogram is not enough to analyse the spatial autocorrelation. Prior to the modelling of the experimental semivariogram one needs to evaluate its robustness. The software Variowin is a tool for the interactive analysis of the spatial autocorrelation. Its success comes from the high level of interactivity between pairs of samples, h-scatterplots, variogram clouds and the experimental variogram. Such interactivity is necessary in order to identify and remove outliers as well as to evaluate the impact of the choice of the distance of the lags.

Whilst many software packages provide automatic fitting functions of the experimental semivariograms, most practitioners still prefer to adjust their model by hand. As an example, the additional knowledge of a component of the nugget effect (e.g. documented measurement errors) will help to define a more realistic value of the nugget than the one that would have been calculated with an automatic fitting. Therefore, the interactivity during the variogram modelling still remains an essential requirement of a good package.

In many case studies a spatial structuring of the studied phenomenon appears in a particular direction. Not taking this anisotropy into account may strongly affect conclusions derived from the analysis of the spatial correlation or from the estimations.

Models implemented: Very often, spatial interpolation functions are implemented like black boxes in GIS or contouring software. It is even truer with geostatistical techniques that require the users to understand properly the underlying theory. The quality of the documentation of the available geostatistical functions should be a key for the GIS users willing to apply their tools to a geostatistical case study.

Additional interpolation/estimation functions are more than welcome since a geostatistical case study can be very time consuming, especially with very large datasets. On the other hand if one has the time to compare the efficiency of the various functions, one can expect to find that sometimes a non-geostatistical method has performed better, according to the user’s criteria, than geostatistical techniques. Here again, clear documentation of the implemented functions is essential.

Search strategies: The search strategy of the neighbouring measurements to use during the estimation/interpolation step has clearly a strong impact on the estimates. One should ideally have the possibility to select: the number of measurements to use; the maximum distance at which one should search; and the measurements according to their locations. For example, one should have the possibility to select few points in each quarter of the circle used to select the neighbours. As for the analysis of the spatial correlation, one should have the possibility to use an ellipse of search rather than a circle

Masking: When the studied area has an irregular shape, or when estimates are not desired at certain locations, one should have the option to prevent certain regions from being interpolated by defining inclusive or exclusive polygons.