The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themes:
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Linear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.
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Standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc.
Theme (1) is covered by:
Wunsch, C. The Ocean Circulation Inverse Problem. Cambridge: Cambridge University Press, 1996. ISBN: 0521480906.
The relevant chapters do not require any oceanographic knowledge. A set of corrections and additions can be found on this site (I will hand these out in hard copy form). Portions of a revised second edition will be distributed as available.
Partial alternatives are:
Menke, W. Geophysical Data Analysis: Discrete Inverse Theory. 2nd ed. New York: Academic, 1989. ISBN: 0124909213.
Daley, R. Atmospheric Data Analysis. Cambridge: Cambridge University Press, 1991. ISBN: 0521382157.
Theme (2) is discussed in:
Priestley, M. B. Spectral Analysis and Time Series. Combined ed. London: Academic Press, 1981. ISBN: 0125649010.
Other highly recommended useful books are:
Bracewell, R. N. The Fourier Transform and its Applications. 3rd ed. New York: McGraw-Hill, 2000. ISBN: 0073039381.
Percival, D. B., and A. T. Walden. Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques. Cambridge: Cambridge University Press, 1993, pp. 83. ISBN: 052135532X.
There will be homework roughly every two weeks, plus a modest term paper (not to exceed 10 pages) on a theme related to the class. These are most likely to be applications of some methodology to real data, or a theoretical extension of a standard result. The homework will require some small computations as can be done in any of MATLAB®, Maple®, Mathematica®, etc.
Although the course is self-contained, students will find some undergraduate exposure to Fourier analysis and applied linear algebra, least-squares, etc. to be helpful. Useful background includes MIT subject 18.085 and/or the material covered in Strang, G., Introduction to Applied Mathematics. Wellesley, MA: Wellesley-Cambridge Press, 1986. ISBN: 0961408804.
Because of the amount of material to be covered, there is little time for specific scientific applications ("case studies"), but examples from various branches of the earth sciences will be discussed.
First reading assignment (4 Feb 2004). In the Ocean Circulation Inverse Problem, read Chapter 1, pages 7-16, and in Chapter 3, pages 92-113.