Data Analysis in the Atmospheric Sciences (METEO 497B/ENNEC 472, 3
credits)
Course Syllabus for Spring 2006
Instructor: Michael
E. Mann, Department of
Meteorology, 523
Meeting Time/Place: T R
Office Hours: You are encouraged to use email for questions when possible. 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/ENNEC472SPR06/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)
within 2-3 days following 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
(40%): There will be several (4-5)
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
(25%): There will be occasional
short in-class quizzes to insure that you keep up with the course material.
Research project
(35%): Your research project will
involve the analysis of an atmospheric, oceanographic, or climatological data
set using tools developed and discussed in class. You are expected to pose a
question or series of questions and to address them using the proper methods.
You are encouraged to analyze a data set that is of interest to you (e.g. a data set you will be using in
conjunction with an undergraduate research project or thesis). You must pose an
appropriate research question and your selection of analysis methods must be
based on answering that question. Some possible research topics that represent
significant extensions of topics addressed in class and in the problem sets may
be mentioned by the instructor over the course of the term. Your research topic will be mutually agreed
upon between you and the instructor (a title and short summary of your chosen
topic will be due in class at the beginning of March).
a. Research paper (25%): due on last day of class. You will be expected to
prepare a research paper in a format that would be suitable for publication in a
major research journal in the fields of atmospheric science, climatology, or
oceanography. The paper should have an
abstract, and the following sections: (i)
introduction, (ii) data, (iii) methods, (iv) results
and discussion, and (v) conclusions. You should list all references used in a
“Reference” section at the end, and use an appropriate convention for citing
referenced materials within the body of the paper. Figures (with captions) and relevant
equations should be included within the context of your paper, rather than at
the end. All figures should have clearly marked titles, axes, and short
descriptive captions. All equations should use standard variable names (i.e.,
symbols should be as defined in class notes or textbook) and any non-standard
symbols should be defined. MATLAB
scripts written by you to perform major statistical calculations should be
provided as an appendix. While there is no precise recommended length, 15-20
pages (not including appendix) of 1.5 spaced text
would typically be appropriate.
b. In-class
presentation (10%): 15 minute presentation on the results of your research to
the class. You should plan on about 12 minutes of presentation and 3 minutes
for Q&A. The final 3 or 4 classes will be reserved for student
presentations. Order of presentations will be determined in class using a
random number generator in MATLAB.
LECTURE
SCHEDULE (tentative and subject to change)
# DATE
TOPIC Reading
(Wilks)/ Notes
|
1 |
T Jan 10 |
Introduction |
|
|
2 |
R Jan 12 |
Distributions |
4.1-4.2 |
|
3 |
T Jan 17 |
Poisson distribution; Gaussian distribution |
4.2-4.4 |
|
4 |
R Jan 19 |
Other Continuous Distributions |
4.4 |
|
5 |
T Jan 24 |
Hypothesis Testing: Gaussian distribution |
5.1-5.1.6 |
|
6 |
R Jan 26 |
Central Limit Theorem; Maximum Likelihood |
4.4; 4.6.1 |
|
7 |
T Jan 31 |
Hypothesis Testing: t-test; F-test |
5.2.1-5.2.4 Prob Set #1 Due |
|
8 |
R Feb 2 |
Chi-squared; Goodness of fit |
5.2.5 |
|
9 |
T Feb 7 |
Linear Regression |
6.2-6.2.2 |
|
10 |
R Feb 9 |
Linear Regression; Analysis of Variance (ANOVA) |
6.2.3-6.2.4 |
|
11 |
T Feb 14 |
Confidence Intervals; Prediction Intervals; Correlation |
6.2.5-6.2.7; 3.5-3.5.5 |
|
12 |
R Feb 16 |
Correlation; Analysis of Residuals and Autocorrelation |
6.2.5, 6.2.7 |
|
13 |
T Feb 21 |
Matrix Algebra Review |
9.3-9.3.2 Prob Set #2 Due |
|
14 |
R Feb 23 |
Multivariate Regression |
6.2.8; |
|
15 |
T Feb 28 |
Multivariate Regression |
6.2.8; 9.3.2 |
|
16 |
R Mar 2 |
Multivariate Regression |
6.2.9; Project Summaries Due |
|
|
T Mar 7 |
No Class [spring break] |
|
|
|
R Mar 9 |
No Class [spring break] |
|
|
17 |
T Mar 14 |
Predictor Selection; Stepwise Multiple Regression |
6.3.3-6.3.4 |
|
18 |
R Mar 16 |
Stopping Rules; Cross-Validation |
6.3.5-6.3.6 |
|
19 |
T Mar 21 |
Principal Components Analysis (PCA) |
9.3.3-9.3.5; 11.1; Prob Set #3 Due |
|
20 |
R Mar 23 |
PCA (continued) |
11.2 |
|
21 |
T Mar 28 |
PCA Selection Rules; Preisendorfer Rule N |
11.3 |
|
22 |
R Mar 30 |
Time Series Modeling; Discrete Series; Markov Chains |
8.1-8.2.4 |
|
23 |
T Apr 4 |
Continuous Series; Simple Autoregressive Models |
8.3-8.3.1 |
|
24 |
R Apr 6 |
Higher Order Autoregressive models; Order Selection |
8.3.2-8.3.4 |
|
25 |
T Apr 11 |
[TBA] |
Prob Set #4 Due |
|
26 |
R Apr 13 |
[TBA] |
|
|
|
T Apr 18 |
Class Presentations |
|
|
|
R Apr 20 |
Class Presentations |
|
|
|
T Apr 25 |
Class Presentations |
|
|
|
R Apr 27 |
Class Presentations |
Papers Due! |