**ENVR 468
/ ENST 468
TEMPORAL GIS AND GEOSTATISTICS**

**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.

The 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

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 r**eal-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

**Prerequisite: **

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%