QUANTITATIVE
ANALYSIS IN EARTH SCIENCES (ENNEC 472,
3 credits)
Course Syllabus for Spring 2007
Instructor: Michael
E. Mann, Department of
Meteorology, 523
Meeting Time/Place: T R
Office Hours: You are welcome to visit my office for questions during scheduled
office hours (Wed,
Motivation:
Many key questions regarding the behavior of the
atmosphere, ocean and climate, are fundamentally statistical in nature. Is the
character of tropical storms and hurricanes changing with time? Is the warming
of the globe consistent with natural variability or not? What is the influence
of El Nino on global weather patterns?
In this course, we will develop and apply various
tools of data analysis and statistics to addressing these, and other
fundamental questions in the atmospheric and related sciences. We will
emphasize the application of the tools to actual data.
Topics to be
covered:
·
Distributions (applications: characterizing the occurrence of tropical storms
and hurricanes; characterizing tropical Atlantic sea surface temperature
variations; characterizing El Nino events)
·
Hypothesis Testing (applications: Are there distinct regimes of
atmospheric circulation behavior during the 20th century? Of
Atlantic Hurricane activity?)
·
Linear Regression and Trend Analysis (applications:
Is the globe warming? Is El Nino becoming more pronounced over time? Is the
intensity of tropical storms and hurricanes increasing over time?)
·
Multivariate Regression (applications:
What atmospheric and oceanic factors control variations and trends in tropical
storms and hurricane activity?)
·
Time series methods (applications: modeling the behavior of El Nino; modeling the global
temperature series)
·
Analyzing spatial data (applications: determining the spatial pattern
of influence of El Nino and the North Atlantic Oscillation on atmospheric
circulation patterns)
Webpage
We will
regularly draw upon the course homepage as a resource for the course:
http://www.meteo.psu.edu/~mann/Mann/courses/ENNEC472SPR07/index.html
Aside from
links to the course syllabus, there will be links to the readings, problem
sets, and required MATLAB routines, slides from the lectures, and other
course-related materials.
Lectures
Attendance
of all lectures is expected. You are strongly encouraged to ask questions and
participate constructively in class. Copies of slides from the lectures will
usually be made available electronically through the course website (see above)
the morning prior to the lecture.
Textbook
The course textbook is:
Daniel S. Wilks (2005), Statistical Methods in the Atmospheric Sciences: An Introduction, 2nd Edition, Academic Press, 520pp.
Where appropriate, supplementary readings taken from various sources
will be posted on the course website.
Grading
Problem Sets
(30%): There will be 4 problem sets
assigned that will involve applications of topics covered in class. Your analyses
must be done using MATLAB on whatever platform you choose.
Quizzes
(15%): There will be occasional
short in-class quizzes to help insure that you keep up with the course
material.
Mid-term Exam
(20%):
Final Exam (35%)
LECTURE
SCHEDULE (tentative and subject to change)
# DATE
TOPIC Reading
(Wilks)/ Notes
|
1 |
T Jan 16 |
Introduction |
|
|
2 |
R Jan 18 |
Distributions |
4.1-4.2 |
|
3 |
T Jan 23 |
Poisson distribution; Gaussian distribution |
4.2-4.4 |
|
4 |
R Jan 25 |
Gaussian distribution(cont); |
4.2-4.4 |
|
5 |
T Jan 30 |
Gaussian dist(cont); Other Continuous Distributions |
4.2-4.4 |
|
6 |
R Feb 1 |
Hypothesis Testing: Gaussian distribution |
5.1-5.1.6 |
|
7 |
T Feb 6 |
Central Limit Theorem; Maximum Likelihood |
4.4; 4.6.1 |
|
8 |
R Feb 8 |
Hypothesis Testing: t-test; |
5.2.1-5.2.4 Prob Set #1 Due |
|
9 |
T Feb 13 |
Hypothesis Testing: t-test(cont); F-test |
5.2.1-5.2.4 |
|
10 |
R Feb 15 |
Chi-squared; Goodness of fit |
5.2.5 |
|
11 |
T Feb 20 |
Chi-squared; Goodness of fit |
5.2.5 |
|
12 |
R Feb 22 |
Linear Regression |
6.2-6.2.2 |
|
13 |
T Feb 27 |
Linear Regression |
6.2-6.2.2 |
|
14 |
R Mar 1 |
Analysis of Variance (ANOVA) |
6.2.3-6.2.4 Prob
Set #2 Due |
|
15 |
T Mar 6 |
Confidence Intervals; Prediction Intervals; Correlation |
6.2.5-6.2.7; 3.5-3.5.5 |
|
16 |
R Mar 8 |
Multivariate Regression |
6.2.8; 6.2.9; 9.3.2 |
|
|
T Mar 13 |
No Class [spring break] |
|
|
|
R Mar 15 |
No Class [spring break] |
|
|
17 |
T Mar 20 |
Multivariate Regression |
6.2.8; 6.2.9; 9.3.2 |
|
18 |
R Mar 22 |
Analysis of Residuals and Autocorrelation |
|
|
|
T Mar 27 |
Review |
Prob Set #3 Due |
|
|
R Mar 29 |
Review |
|
|
19 |
T Apr 3 |
Mid-term |
|
|
20 |
R Apr 5 |
Predictor Selection; Stepwise Multiple Regression |
6.3.3-6.3.4 |
|
21 |
T Apr 10 |
Stopping Rules; Cross-Validation |
6.3.5-6.3.6 |
|
22 |
R Apr 12 |
Principal Components Analysis (PCA) |
9.3-9.3.5 |
|
23 |
T Apr 17 |
PCA (continued) |
11.1-11.2 |
|
24 |
R Apr 19 |
PCA (continued) |
11.1-11.2 |
|
25 |
T Apr 24 |
PCA Selection Rules; Preisendorfer Rule N |
11.3 |
|
26 |
R Apr 26 |
Time Series Modeling |
8.3-8.3.1 |
|
27 |
T May 1 |
Time Series Modeling (continued) |
8.3-8.3.1 |
|
28 |
R May 3 |
Time Series Modeling (continued) |
8.3.2-8.3.4 Prob Set #4 Due |