Geostatistics and GIS

This Phd course is an introduction to the analysis, description and modelling of geographical referenced data or spatial data in short. The practical applications of software tools, underlying theory, and the correct application of these tools is emphasized through the use of software to analyze and model spatial data. The software used is Geostatistical Analyst and Spatial Analyst in ArcGIS and packages geoR and gstat for R. Prerequisites for the course are an introductory statistics course, an introductory GIS course, and a matrix algebra course. The course covers nine days, see schedule below.

Location and dates

The course start 12 April 2010 and takes places over four weeks in April+May 2010. The location is the DJF building in Aarhus. Willemoesgade 15, 8200 Aarhus N, building 2114, rooms 168 and 166 (see here and here).

Course Description

The following subjects will be covered during the course in greater or lesser details as time permits. See below for a detailed course description.

Overview, Course Topics and Case Study: Overview of applications and techniques to be covered in the course: univariate and multivariate statistics, spatial correlation analysis, modelling, estimation, simulation.

Exploratory Data Analysis: Statistical analysis, vs. summarization, mapping, representing spatial data, continuous vs. categorical data, histograms and probability distibutions, cross-correlation in multivariate data, data transformations (logarithmic, square root, etc), software use and applications

Spatial Correlation: Spatial correlation and associated statistical measures, calculation of experimental variograms, fitting model autocorrelation functions, variogram anisotropy and nested structures, indicator variograms, crosscorrelation (spatial co-variability of multiple variables).

Spatial Estimation (Kriging): Techniques for spatial estimation, 'best' linear unbiased estimation, the kriging system of equations, use and misuse of kriging variance, sensitivity of kriging estimation to variogram structure, kriging strategy, cross-validation of spatial data, co-kriging.

Stochastic Simulation: Simulation vs. kriging, differences, philosophy.

Geographical Information Systems and Geostatistics: The use of GIS and geostatistics via ArcGIS Geostatistical Analyst.

Model based geostatistics: Maximum likelihood, REML, the Gaussian assumption (important or not), kriging with external trend, generalised least square (GLS) estimator. Probability map of Threshold exceedance.


Most of this course is based on the book by Webster and Oliver (2007). Material about exercises in Arc-map and geoR will be handed out.

Main Literature

Supplementary litterature

Computers and Software

The room we are using contains computers with dual screans. Arc-map (and Arc-GIS) will be used for the exercises on the first 5 days. Possibility to install on your own labtop. The statistical programming environment R with add-on package geoR will be used in the later part of the course. Participants will get detailed information on how to use the software.

The Lecture Plan

In general the individual course day starts at 9:00 in the morning and ends at 16.00 with a lunch break between 12.00 and 13.00.


The workload amounts to 5 ECTS.

Evaluation of participants

To pass the course the participants need to take part in the lectures by active discussion. Doing two written exercises to be evaluated by the teachers.


The teachers on the geostatistics module are:
Ole F. Christensen , e-mail:
Mogens H. Greve , e-mail:


Enrollment can be done by sending an e-mail containing your name and affilitation.


A list is given below :
  • Korhan Ozkan (Bio, AU)
  • Lars Dalby (DMU/Bio, AU)
  • Roy Mathew Francis (DJF)
  • Kristian T. Nielsen (Bio, AU)
  • Kabindra Adhikari (JPM, DJF)
  • Gerardo Ojeda (IMAR, Universidade Coimbra, Portugal)
  • Allan Timmermann (DMU/Bio, AU)
  • Fan Deng (JPM, DJF)
  • Philipp Trenel (AgroTech)
  • Anne Mette Kjeldsen (AgroTech)
  • Mette Vestergaard Odgaard (JPM, DJF)

    Last modified: 06-05-2010 by Ole F. Christensen"