Linking GIS and Geostatistics.

As evidenced by current pop music, just about anybody can create orchestral compositions using modern electronic keyboard equipment without having mastery or even experience with individual instruments. Is it likewise possible to embed modern geostatistical software inside a Geographic Information System (GIS), which can be used without an exhaustive in-depth understanding of geostatistics?

Geostatistics are statistical methods to describe spatial relationships among sample data and to apply this analysis to the prediction of spatial and temporal phenomena. In addition to the description of spatial patterns and interpolation of data, important components of geostatistical analysis include error analysis and the integration of secondary data in prediction algorithms through the use of cokriging. One can assess the performance of the interpolation as well as detect errors in the source data using error analysis, which includes mapping the error of estimation and performing both validation and cross-validation. Cokriging allows one to perform an optimum estimation while considering more than one variable. The spatial relationships among several associated variables (easily captured and manipulated with GIS technology) may be used to improve the estimation of another variable, which is difficult to measure, by using data, which can be collected more easily.

Sampling and mapping in the earth sciences are complicated by complex spatial and temporal variations. The structure and intensity of patterns being sampled often cannot be determined or predicted reliably with deterministic models because of uncertainties in the data and the phenomena under investigation. The best we can do using interpolation and estimation methods is to be as objective as possible and to consider the interrelations of the data under investigation.

Deterministic approaches to interpolation (trend surface, inverse distance weighting, triangulation, and splining) are based upon a priori mathematical models of spatial variation. They assume the sampled data has no errors, which is often an incorrect assumption. In practice, error can not be eliminated but only minimized. Therefore, in most cases one cannot produce the best representative map of estimated values in unsampled locations with these techniques.

Currently, in order to integrate advanced methods of spatial data interpolation including geostatistics into GIS, users are required to use separate statistical packages to process and store the results of interpolation into a GIS supported format. To analyze complicated environmental problems and to present the results of an analysis on a map requires a group of specialists who are familiar with both GIS techniques and complicated statistical software. In general, statistical software, which includes geostatistical tools, can be divided into two groups:
1. Simple programs which include standard ordinary kriging estimation along with a few additional tools.
2. Advanced programs with a complete compliment of geostatistical tools for any type of data.

Using programs from the first group does not promote an understanding of the advantages of geostatistics. The time burden of mastering software from the second group has been an enormous impediment for its routine use by researchers and students, who are utilizing GIS technology. As a result there are many articles devoted to spatial interpolation in agriculture, meteorology, environment and other disciplines where geostatistics are used inaccurately – primarily because researchers used non-optimal data processing techniques.

We shall discuss an approach of combining advanced spatial statistics and GIS. This combination was first presented in the software package, GIS MapStudio [1-3], which integrated both modern GIS visualization techniques and easy to use geostatistical methods of spatial data analysis. These methods are currently being considered for further development and implementation into ESRI’s GIS product line.

The advantages of a geostatistical approach to spatial data analysis are:

•  Problems associated with selecting appropriate parameters for the interpolation are solved using the sound procedures of declustering, normal score transform, detrending and variogram/covariance modeling.
•  It is possible to investigate the anisotropical structure of the data and to use this information for estimation.
•  Cokriging allows one to carry out an optimum estimation by taking advantage of the relationships among additional variables.
•  Geostatistics allows one to create a map of the probability that a predefined threshold has been exceeded or not.
•  Geostatistics allows one to consider measurement errors and to create a map of the error of estimation.
•  Using error analysis tools it is possible to find data outliers and to correct their values.
•  Geostatistics allows decision-makers to make informed decision about the reliability of maps.

An implementation of such tools in a commercial GIS package would provide a user-friendly interface for the rapid analysis and display of data using geostatistical tools within a GIS environment without the requirement of an in-depth understanding of the statistical techniques for:

•  Spatial correlation analysis and modeling of multivariate data sets.
•  Creation of continuous surfaces from sampled locations.
•  Error analysis and quantifying uncertainty for data sampling.
•  High-quality visualization of the interpolation results.

Examples of data analysis and spatial interpolation will be presented and then discussed. The answer to the question about the possibility of implementing sound geostatistical analysis within a GIS will be known by ESRI product users in the near future.
 

References

1. Krivoruchko K., Gribov A., Figurin I., Karebo S., Pavlushko D., Remesov D., Zhigimont A. Mapstudio: The Specialized GIS Integrating Possibilities of Geostatistics. Third Joint European Conference and Exhibition on Geographical Information, Vienna, Austria, April, 1997, pp. 187-196.
2. Krivoruchko K. Geostatistical Picturing of Chernobyl Fallout and Estimation of Cancer Risk Among Belarus Population. Third Joint European Conference and Exhibition on Geographical Information, Vienna, Austria, April 1997, Vol. 2, pp. 676-685.
3. Krivoruchko K., Maignan M. Integration GIS and Geostatistics: A Software and a Case Study. Proceedings 18th ICA/ACI International Cartographic Conference. Stockholm, Sweden, 23-27 June 1997, Vol.2, pp. 925-932.

In May 1998, I began a three year contract with ESRI for the Software Development Team.  Prior to that, I was an Assistant Professor and Director of the GIS Laboratory at the Sakharov Institute of Radioecology in Minsk, Belarus.  My responsibilities include the development and utilization of the GIS Software MapStudio, encompassing databases from the Belarussian National Cancer Registry; data pertaining to radionuclides contamination in soil and food from Belarussian National Academy of Sciences; the development of GIS/spatial statistics curriculum; and supervision of Ph.D. and graduate candidate research projects pertaining to GIS applications and spatial data analysis based on geostatistical approach.  Prior to joining the Sakharov Institute, I was a divisional chief at the Belarussian National Academy of Sciences, Nuclear Power Institute, focusing on issues concerning radioecology and epidemiology.

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