QUANTITATIVE ANALYSIS IN EARTH SCIENCES (ENNEC 472, 3 credits)

Course Syllabus for Spring 2009

 

Instructor: Michael E. Mann, Department of  Meteorology, 523 Walker Building, mann@psu.edu

Teaching Assistant: Fangxing Fan, Department of Meteorology, 408 Walker Building, fxf908@psu.edu

Meeting Time/Place: T R 01:00-2:15 PM (112 BUCKHOUT)

Office Hours:

You are welcome to visit the instructor or TA’s office for questions during scheduled office hours or by appointment: Wed 1:30-2:45 PM (instructor); Tu/Th 2:30-3:30 PM (TA). You may also email the TA or instructor at the email addresses indicated above. Responses may be delayed.

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/ENNEC472SPR09/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 13

Introduction

 

2

R Jan 15

Distributions

4.1-4.2

3

T Jan 20

Poisson distribution; Gaussian distribution

4.2-4.4

4

R Jan 22

Gaussian distribution(cont);

4.2-4.4

5

T Jan 27

Gaussian dist(cont); Other Continuous Distributions

4.2-4.4

 

R Jan 29

No class

 

6

T Feb 3

Hypothesis Testing: Gaussian distribution

5.1-5.1.6                           Prob Set #1 Due

7

R Feb 5

Central Limit Theorem; Maximum Likelihood

4.4; 4.6.1                           

8

T Feb 10

Hypothesis Testing: t-test;

5.2.1-5.2.4                        

9

R Feb 12

Hypothesis Testing: t-test(cont); F-test

5.2.1-5.2.4                     

10

T Feb 17

Chi-squared; Goodness of fit

5.2.5                     

11

R Feb 19

Chi-squared; Goodness of fit

5.2.5                     

 

T Feb 24

No class

                                         

12

R Feb 26

Linear Regression

6.2-6.2.2                           Prob Set #2 Due

13

T Mar 3

Guest Lecture

 

14

R Mar 5

Guest Lecture

 

 

T Mar 10

No Class [spring break]

 

 

R Mar 12

No Class [spring break]

 

15

T Mar 17

Mid-term

                           

16

R Mar 19

Linear Regression; Analysis of Variance (ANOVA)

6.2.3-6.2.4                  

17

T Mar 24

Confidence Intervals; Prediction Intervals; Correlation

6.2.5-6.2.7; 3.5-3.5.5

18

R Mar 26

Analysis of Residuals and Autocorrelation

 

19

T Mar 31

Multivariate Regression

6.2.8; 6.2.9; 9.3.2

20

R Apr 2

Multivariate Regression (cont)

6.2.8; 6.2.9; 9.3.2  

21

T Apr 7

Predictor Selection; Stepwise Multiple Regression

6.3.3-6.3.4                        Prob Set #3 Due

22

R Apr 9

Stopping Rules; Cross-Validation

6.3.5-6.3.6                        

23

T Apr 14

Principal Components Analysis (PCA)

9.3-9.3.5

24

R Apr 16

PCA (continued)

11.1-11.2

25

T Apr 21

Guest Lecture

 

26

R Apr 23

Guest Lecture

 

27

T Apr 28

PCA (continued)

11.1-11.2

28

R Apr 30

PCA Selection Rules; Preisendorfer Rule N

11.3                                  Prob Set #4 Due