**ENVR 468 / ENST 468
Advanced Functions of temporal GIS**

**Fall semesters**, 3 semester hours, Monday
Wednesday 03:30PM-04:45PM

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 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, following a comprehensive
example using EPA and USGS freshwater contaminant data across an entire state
(e.g. physical, microbial and biological environmental water quality
contaminants in New Jersey and North Carolina), as well as an example using an
infectious disease (e.g. STDs and HIV prevalence across North Carolina).

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,

**Prerequisite: **

The prerequisite for this class is
MATH 383, Linear Algebra and Differential Equations (as well as its
prerequisites MATH 231 & 232, Calculus of Functions of One Variable I &
II, and MATH 233, Calculus of Functions of Several Variables). 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 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%