COURSE MATERIALS:

General References:

• The Ocean Circulation Inverse Problem (Cambridge Univ. Press) by C. Wunsch (1996). This is a good "cookbook" of inverse methods for use with oceanographic data. The discussion of physical oceanography is quite in depth in some sections, and perhaps tedious. However, the simple numerical examples given in each section are extremely useful. Least squares inversion and Singular Value Decomposition are covered in detail, in addition to more advanced methods of estimation.


• Statistical Analysis in Climate Research (Cambridge Univ. Press) by H. Von Storch and F. Zwiers (1999). Covers basic estimation techniques for climate data, as well as time series analysis and Empirical Orthogonal Functions. Perhaps easier than Wunsch's book, but lacking the breadth of material.


• Monte Carlo Statistical Methods (Springer Verlag), by C. Robert and G. Casella (1999). Good for background on Monte Carlo methods.


• Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer Series in Statistics), by T. Hastie, R. Tibshirani, J. H. Friedman (2001). This covers many of the current "hot" topics in statistics, has a lot of material on regularization methods (non-Bayesian) related to what is in Wunsch's book, and is very readable.


• Image Analysis, Random Fields and Dynamic Monte Carlo Methods -- A Mathematical Introduction. (Springer-Verlag), by G. Winkler (1995).

Here are some papers that give examples of Monte Carlo approaches to inverse problems.

• Andersen, K.E., Brooks, S.P. and Hansen, M.B. (2001a). A Bayesian approach to crack detection in electrically conducting media. Inverse Problems, 17, 121--136.  PDF file available at http://www.math.auc.dk/~emil/publications.html


• Andersen, K.E., Brooks, S.P. and Hansen, M.B. (2001b). Bayesian inversion of geoelectrical resistivity data. Preprint PDF file available at http://www.math.auc.dk/~emil/publications.html


• Mosegaard, K. (1998). Resolution Analysis of General Inverse Problems  through Inverse Monte Carlo Sampling. Inverse Problems, 14, 405--426.


• Mosegaard, K. and Tarantola, A. (1995). Monte Carlo Sampling of Solutions to Inverse Problems. Journal of Geophysical Research, 10, No B7, 12,431--12, 447.

Other good general papers:

• Breiman, L. (2001). Statistical Modeling: The two cultures. Statistical Science, 16, No 3, 199-231.


• Katz, R. W. (2002). Sir Gilbert Walker and a Connection between El Nino and Statistics. Statistical Science, 17, No 1, 97-112.


• Wunsch, C. (1999). The interpretation of short climate records, with comments on the North Atlantic and Southern Oscillations. Bulletin of the American Meteorological Society. 80, No 2, 245-255.

COURSE DESCRIPTION:

This course will survey statistical methods used in oceanographic research. Attention will be given to examples taken from physical oceanography. Statistical estimation is important in nearly all fields of physical oceanography.  This is particularly true for the climate studies, where data records are both short and noisy.  

COURSE OBJECTIVES:

In this course, you will gain experience in the use of statistical methods to analyze oceanographic data. These analysis methods should help you tackle problems you encounter in your own research.

GRADING/EVALUATION:

Grading will be based on the following weighting:

30% homework
40% presentations
30% contribution to in-class discussion

ASSIGNMENTS/RESPONSIBILITIES:

There will be several assignments given during the semester. These will involve numerical analysis of data using methods presented in class. Numerical analysis software, such as MATLAB(R) or Octave (GNU/GPL), will be needed to complete these assignments.

COURSE CONTENT AND OUTLINE:

Week 1 (08/26, 08/28): Introduction to "The Problem" of estimating ocean circulation and fluxes

Weeks 2-3  (09/04, 09/09, 09/11): Least Squares Inversion

Week 4 (09/16, 09/18): Singular Value Decomposition

Week 5 (09/23, 09/25): Research talks on inverse box models

Week 6 (09/30-10/04): No Class

Week 7-8 (10/07, 10/09, 10/14, 10/16): Principle Component Analysis/EOFs

Week 9-10 (10/21, 10/23, 10/28, 10/30): Markov Chain Monte Carlo Methods

Week 11-12 (11/04, 11/06, 11/13): Bayesian approach to inverse problem

Week 13 (11/18, 11/20): Research talks

Week 14-15 (11/25, 11/27, 12/02, 12/04): Student presentations

ACADEMIC HONOR CODE:

Students are expected to uphold the Academic Honor Code published in The Florida State University Bulletin and the Student Handbook. The Academic Honor System of The Florida State University is based on the premise that each student has the responsibility (1) to uphold the highest standards of academic integrity in the student's own work, (2) to refuse to tolerate violations of academic integrity in the university community, and (3) to foster a high sense of integrity and social responsibility on the part of the university community.

Please see the following web site for a complete explanation of the Academic Honor Code. http://www.fsu.edu/Books/Student-Handbook/codes/honor.html

AMERICANS WITH DISABILITIES ACT:

Students with disabilities needing academic accommodation should: (1) register with and provide documentation to the Student Disability Resource Center; (2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class.

For more information about services available to FSU students with disabilities, contact the Student Disability Resource Center:

Dean of Students Department
08 Kellum Hall
Florida State University
Tallahassee, FL 32306-4400
(850) 644-9566 (voice)
(850) 644-8504 (TDD)
SDRC@admin.fsu.edu
http://www.fsu.edu/~staffair/dean/StudentDisability

SYLLABUS CHANGE POLICY:

This syllabus is a guide for the course and is subject to change with advanced notice.

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