ENVR 468 / ENST 468


Fall semesters, 3 semester hours, Tuesday Thursday 09:30AM-10:45AM


Instructor: Marc Serre


Course description:


There has recently been an increased interest in the creation of environmental maps used for environmental assessment, regulatory compliance analysis, exposure science and risk analysis. This class will introduce students to advanced geostatistical functions of Temporal Geographic Information Systems (GIS) used to create maps describing the geographical distribution of environmental processes, and some diseases. Specific examples will be given on how to access large publicly available datasets of water and air quality monitoring data and how to use these data to map water and air quality across regional and national geographical domains and for recent time periods.


The course focuses on the development of environmental Geostatistics and its application in temporal Geographical Information Systems (TGIS).  TGIS describe environmental, epidemiological, economic, and social phenomena distributed across space and time.  The course introduces the arcGIS software to query and manipulate geographic data, it provides the concepts and mathematical framework of space/time Geostatistics necessary to map environmental contaminants across space and time, and it leads to a real-world TGIS project where students analyze their own data extracted from publicly available datasets of air quality and water quality monitoring data, or of surveillance epidemiology data.


image003The course starts with a 4 to 5 weeks review of basic GIS consisting in intensive computer labs on the ESRI ArcGIS software. Prior knowledge of GIS is highly recommended, but not required. Lessons from these ArcGIS computer labs is tested in a homework where students research and display maps of their own space/time environmental data using basic ArcGIS functions (see Graph 1). In the remainder of the course we then switch to using the BMEGUI software developed especially for this course for the advanced visualization and spatiotemporal geostatistical analysis of space/time data. The use of BMEGUI is tested in the remaining homework of the course, and culminates in an individual final project.


The concepts and mathematical formulation of spatiotemporal Geostatistics are progressively introduced throughout the course. We start with the concept of space/time distance. We then rapidly review multivariate calculus (derivatives and integrals) and basic statistics (probability density function, or pdf, and expected value) of random variables. Multivariate calculus is a pre-requirement for this course, and prior introductory statistics or probability courses are recommended, but not required. Using this foundation in multivariate calculus and basic statistics, we then cover the theory of spatiotemporal Geostatistics, which include 1) bivariate pdf and conditional probabilities, 2) variability in space and time and covariance function, 3) spatial and spatiotemporal random fields and 4) spatiotemporal estimation and uncertainty assessment.  The concepts of the Bayesian Maximum Entropy (BME) method is presented, which provides a powerful framework for space/time mapping, and leads to the classical kriging methods as special cases


The application consists of a real-world mapping TGIS project.  Using skills acquired in basic GIS (i.e. arcGIS), and in advanced TGIS (i.e. BMEGUI) each students research a space/time dataset of concern for society, s/he formulates the space/time mapping problem, and s/he uses concepts and mathematical tools together with the BME method of space/time Geostatistics to provide a realistic representation of the field over space and time.


Textbook recommended:

George Christakos, Patrick Bogaert, and Marc Serre (2002) Temporal GIS: Advanced Functions for Field-Based Applications, Springer-Verlag, New York, N.Y., 250 p., CD ROM included



The prerequisite for this class is calculus of functions of one variable (MATH 231 & 232 or similar).  Introductory courses in GIS, statistics and probability are useful, but not required, as these will be reviewed at the beginning of the course.


Philosophy and grading:

The students should learn the concepts, and not use the tools as a black box.  They will be graded on solving conceptual problems rather than just applying the programs. The students will do homework’s, and a project, which will count for the final grade as follow:

Homework 50%

Student-defined project 50%