**ENVR 468 /
ENEC 468
Temporal GIS and Space/Time Geostatistics **

**for the
Environment and Public ****Health**

**(Short
title: Temporal GIS and Geostatistics)**

** **

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

Instructor: Marc Serre

**Course description: **

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

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 **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

** **

**Prerequisite:**

The prerequisite for this class is Calculus of Functions of One Variable I & II (MATH 231 & 232) and preferably a multivariate calculus course like MATH 233. An introductory course in Statistics or Probability is useful, but not required. Additionally, knowledge of GIS (from beginner to expert) is highly recommended, but not required.

** **

**Philosophy of Grading and
Course Evaluation:**

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 are expected to promptly do their homework, a class project, and fill out the course evaluation at the end of the semester. The grading will be as follow

Homework 50%

Student-defined project 50%

Filling out course evaluation: 1 point bonus