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 Walker Building,

Meeting Time/Place: T R 01:00 P- 02:15P (371 WILLARD)

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, 1:30-2:45 PM), or by appointment.


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)


We will regularly draw upon the course homepage as a resource for the course:

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.


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.


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.


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                     


T Jan 10




R Jan 12




T Jan 17

Poisson distribution; Gaussian distribution



R Jan 19

Other Continuous Distributions



T Jan 24

Hypothesis Testing: Gaussian distribution



R Jan 26

Central Limit Theorem; Maximum Likelihood

4.4; 4.6.1                   


T Jan 31

Hypothesis Testing: t-test; F-test

5.2.1-5.2.4                   Prob Set #1 Due


R Feb 2

Chi-squared; Goodness of fit



T Feb 7

Linear Regression



R Feb 9

Linear Regression; Analysis of Variance (ANOVA)



T Feb 14

Confidence Intervals; Prediction Intervals; Correlation

6.2.5-6.2.7; 3.5-3.5.5


R Feb 16

Correlation; Analysis of Residuals and Autocorrelation

6.2.5, 6.2.7                  


T Feb 21

Matrix Algebra Review

9.3-9.3.2                      Prob Set #2 Due


R Feb 23

Multivariate Regression



T Feb 28

Multivariate Regression

6.2.8; 9.3.2        


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]



T Mar 14

Predictor Selection; Stepwise Multiple Regression



R Mar 16

Stopping Rules; Cross-Validation



T Mar 21

Principal Components Analysis (PCA)

9.3.3-9.3.5; 11.1;          Prob Set #3 Due


R Mar 23

PCA (continued)



T Mar 28

PCA Selection Rules; Preisendorfer Rule N



R Mar 30

Time Series Modeling; Discrete Series; Markov Chains



T Apr 4

Continuous Series; Simple Autoregressive Models



R Apr 6

Higher Order Autoregressive models; Order Selection



T Apr 11


                                      Prob Set #4 Due


R Apr 13




T Apr 18

Class Presentations



R Apr 20

Class Presentations



T Apr 25

Class Presentations



R Apr 27

Class Presentations

                                       Papers Due!