Fall 2016

Professor: Sarah Gille

Meetings: Tuesday and Thursday: 11:00-12:20, Spiess Hall 330

Course Requirements: Complete weekly problem sets. For most of the problem sets, you may work collaboratively, though the work that you submit must be your own. (Please follow the standards of scientific publication and identify your collaborators.) A midterm and final problem must be completed independently. (They will have about the same scope as the the other problem sets.)

The final exam is scheduled to be held Wednesday 7 December, 11:30-2:30. We will plan to use this time slot for final presentations related to the final assignment.

To gain from this class, students are expected to come to class, participate in class discussions, ask questions. There will be some assigned reading (available in electronic form), and students are expected to complete the reading.

Syllabus

Resources:

Lecture notes and handouts: (See TritonED for slides, since they may contain copyrighted material.)

- September 22: Introduction to the course (time series, mean, variance, standard deviation, probability density functions), Homework #1
- September 27: Probability density functions (common distributions, error analysis, outliers)
- September 29: Probability density functions (error propagation, the central limit theorem, chi-squared distributions, evaluating whether data are drawn from different PDFs) Homework #2
- October 4: Least-squares fitting (linear fits, fitting sinusoids, Nyquist frequency)
- October 6: Introducing the Fourier transform (chi-squared fitting, cosine and sine transformations, notation for Fourier transforms), Homework #3
- October 11: Great traits of the Fourier transform
- October 13: Parseval's theorem and computing spectra, Homework #4
- October 18: Error bars on spectra
- October 20: Detrending, windowing, and the sinc function, Homework #5
- October 25: Alternatives to segmenting to compute spectra
- October 27: Spectra from the autocovariance, y-axis units, variance preserving spectra, Homework #6 (midterm, independent assignment) Note the data file for this assignment can be found on TritonEd, or if you recover it from the TAO web site, you'll want 10-minute surface met data at 165E, with a file called "met0n165e_10m.cdf".
- November 1: Aliasing
*guest lecture: Matthew Alford* - November 8: Frequency-wavenumber spectra
*guest lecture: Matthew Alford* - November 10: Correlation and coherence
- November 15: Coherence: Some practical examples, Homework #7
- November 17: Coherence uncertainties
- November 22: Coherence and autocovariance, Homework #8
- November 29: Multi taper methods and transfer functions
- December 1: Salinity spiking and synthesizing course themes

- Shore Stations Symposium, Friday, October 7, 2016, 8:00-12:30, "Is 100 Years of Scripps Pier Data Enough?". Scripps Seaside Forum.

- Introduction: statistics, probability density functions, mean, standard deviation, skewness, kurtosis
- Error propagation
- Least-squares fitting
- The Fourier transform
- Spectra, spectral uncertainties, using Monte Carlo methods (and fake data) to evaluate formal uncertainties
- Windowing and filtering
- Cross-spectra, coherence, uncertainties of coherence
- Multi-dimensional spectral analysis

- Rotary spectra
- Alternative approaches for computing spectra: multitaper and maximum entropy methods
- Filter design
- Introduction to linear systems
- Spectral modeling; spectral physics

Sarah Gille's Home Page