3.6.1 Isatis
Isatis11is probably the most expensive geostatistical package (>10Ke) available in the market today, but is definitively also one of the most professional packages for environ- mental sciences. Isatis was originally built for Unix, but there are MS Windows and Linux versions also. From the launch of the package in 1993, >1000 licences have been purchased worldwide. Standard Isatis clients are Oil and Gas companies, consultancy teams, mining corporations and environmental agencies.
Isatis offers a wide range of geostatistical functions ranging from 2D/3D isotropic and directional variogram modelling, univariate and multivariate kriging, punctual and block estimation, drift estimation, universal kriging, collocated co-kriging, kriging with external drift, kriging with inequalities (introduce localized constraints to bound the model), factorial kriging, disjunctive kriging etc. From all these, especially, interactivity of exploratory analysis, variogram modelling, detection of local outliers and anisotropy is brought in Isatis to perfection (Fig.3.15).
Fig. 3.15: Exploratory data analysis possibilities in Isatis.
Regression-kriging in Isatis can be run by selecting Interpolation 7→ Estimation 7→ External Drift (Co)-kriging (Fig.3.16). Here you will need to select the target variable (point map), predictors and the variogram model for residuals. You can import the point and raster maps as shape files and raster maps as ArcView ASCII grids (import- ing/exporting options are limited to standard GIS formats). Note that, before you can do any analysis, you first need to define the project name and working directory using
11
The name is not an abbreviation. Apparently, the creators of Isatis were passionate climbers so they name their package after one climbing site in France.
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the data file manager. After you imported the two maps, you can visualize them using the display launcher.
Note that KED in Isatis is limited to only one (three when scripts are used) auxiliary raster map (called background variable in Isatis). Isatis justifies limitation of number of auxiliary predictors by computational efficiency. In any case, a user can first run factor analysis on multiple predictors and then select the most significant component, or simply use the regression estimates as the auxiliary map.
Fig. 3.16: Setting the options for Kriging with External Drift in Isatis.
Isatis offers a variety of options for the automated fitting of variograms. You can also edit the Model Parameter File where the characteristics of the model you wish to apply for kriging are stored. The user manual does not give insight into the algorithm used (except for the mathematical proofs), so I could not tell how exactly are the KED weights estimated and is there any regression modelling involved prior to the interpolation of data.
3.6.2 GRASS GIS
GRASS (Geographic Resources Analysis Support System) is a general-purpose Geo- graphic Information System (GIS) for the management, processing, analysis, modelling and visualisation of many types of georeferenced data. It is Open Source software re- leased under GNU General Public License. The main component of the development and software maintenance is built on top of highly automated web-based infrastructure sponsored byITC-irst(Centre for Scientific and Technological Research) in Trento, Italy with numerous worldwide mirror sites. GRASS includes functions to processraster maps, including derivation of descriptive statistics for maps, histograms, but also to generate statistics for time series. There are also several unique interpolation techniques. One should definitively consider using the Regularized spline with tension (RST) interpo- lation, which has been quoted as one of the most sophisticated methods to generate
smooth surfaces from point data (Mitasova et al., 2005).
The geostatistical functionality in GRASS is achieved mainly via a link to R, actually through an R package calledspgrass6(Bivand, 2005). In the version v5.0 of GRASS, sev- eral basic geostatistical functionalities existed including ordinary kriging and variogram plotting, however, the developer of GRASS finally concluded that there is no need to build geostatistical functionality from scratch when a complete open source package al- ready exist. The current philosophy focuses on making GRASS functions also available in R, so that both GIS and statistical operations can be integrated in a single command line. A complete overview of theGeostatistics and spatial data analysisfunctionality can be found via the GRASS website. Certainly, if you are an Linux user and already familiar with GRASS, you will probably not have many problems to implement the procedures described in chapter§4 and currently adjusted to ILWIS/SAGA GIS.
3.6.3 Idrisi
Idrisiis one of the medium-cost GIS packages but possibly with largest numbers of raster and vector operations. The price per a single licence is aboute500, but you can always order a 7-day evaluation version to test it. Idrisi provides statistical tools for spatial analysis of raster images, including simple regression, autocorrelation analysis, pattern analysis, trend analysis, logistical regression, and many more. In Idrisi, gstat code has been also adjusted and integrated within the GUI, which practically means that you can use Idrisi as a graphical user interface to gstat. Additional integration of statistical and GIS functionality can be achieved through a link to S-Plus.
Fig. 3.17: The spatial dependence modeller in Idrisi.
To run regression-kriging in Idrisi, first import all point and raster maps using Import 7→ Software-specific-formats 7→ ESRI formats 7→ ARCRASTER (Arcinfo ASCII format to raster); or SHAPEIDR (Shape file to Idrisi. First run multiple regression analysis using the points and rasters and then derive the residuals (at sampling locations). You can now model a variogram of residuals by using the Spatial dependence modeller, which also allows modelling of the anisotropy (Fig.3.17).
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Derive the semivariances using a point map, save them and load them in the vari- ogram model fitting environment, where you can (interactively) estimate the variogram model parameters. After you finished fitting the variogram, you can save the vari- ogram parameters and load them later to do kriging or simulations. Once you fitted the variogram model, you can run regression-kriging by selecting GIS analysis 7→ Surface analysis 7→ Interpolation 7→ Kriging and simulations. You will then get an user-friendly kriging dialog window (Fig. 3.18) where you can input: variogram model, variable to predict, auxiliary maps and several other optional arguments.
Fig. 3.18: Universal kriging input window in Idrisi.
In Idrisi, only raster input files are allowed for input maps. The first input file contains the sample data, the second, third etc input file is a fully sampled surface that has attribute values for all prediction locations. This means that, before running regression- kriging in Idrisi, you need to convert the point map (*.vct) to a raster image using the RASTERVECTOR operation. Note that a local neighborhood must be specified for each input file. Unfortunately, Idrisi help warns that the Spatial Dependence Modeler can not calculate generalized least squares residuals, although this was originally implemented in gstat. Also note that Idrisi uses term residuals with somewhat different meaning — unlike in R, Idrisi will not derive residuals for you but you will have to do it yourself.