SIOC 221A Analysis of Physical Oceanographic Data
Fall 2021
Professor: Sarah Gille
SIO Office: Nierenberg Hall 348
Office (Landline) Telephone: 822-4425
e-mail: sgille at ucsd.edu
Meetings:
Monday and Wednesday: 8:30-9:50, Spiess 330
Discussion: Friday: 9:00-9:40, Spiess 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 problem set will be an independent project, which you will present
during the final exam time slot (Monday 6 December, 8:00-11:00). A draft write up will be due
during the final week of classes, and the final write up of your project will be due no later than
11 am on Monday 6 December.
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 Canvas for slides, since they may contain
copyrighted material.)
- Bia Villas Boas' github with python notebook versions of the notes
- September 24: No discussion
- September 27: Introduction to the course (time series, mean, variance, standard
deviation, probability density functions) Homework #1
- September 29: Probability density functions (common distributions, error analysis, outliers)
- October 1: Discussion
- October 4: Probability density functions (error propagation, the central limit theorem, chi-squared distributions, evaluating whether data are drawn from different PDFs) Homework #2.
- October 6: Least-squares fitting (linear fits,and fitting sines and cosines)
- October 8: Discussion.
- October 11: Introducing the Fourier transform (chi-squared fitting, Nyquist frequency, cosine and sine transformations) Homework #3
- October 13: Fourier transform notation, great traits of the Fourier transform
- October 15: Field trip to the SIO Pier with Melissa Carter: Meet at the entrance to the pier at 9 am.
- October 18: Three important traits of the Fourier transform (derivatives, convolution, Parseval's theorem), Homework #4
- October 20: Spectra, error bars on spectra
- October 22: Discussion
- October 25: More on error bars, normalization, and the sinc function, Homework #5 (due Tuesday, November 2)
- October 27: More on windowing, and degrees of freedom
- October 29: Discussion
- November 1: Alternatives to segmenting to compute spectra: averaging in frequency, spectra from the autocovariance., Homework #6 (due Tuesday, November 9)
- November 3: Aliasing
- November 5: Discussion
- November 8: Spectra from the autocovariance, variance preserving spectra, and frequency-wavenumber spectra
- November 10: Frequency-wavenumber practicalities, correlation and coherence, Homework #7 (due Tuesday, November 16)
- November 12: Discussion
- November 15: Coherence and cross-spectra, Homework #8 (due Tuesday, November 23)
- November 17: Coherence: Uncertainties and some practical examples, Final Homework
- November 19: Discussion
- November 22: Transfer function
- November 24: Transfer function and salinity spiking
- November 26: Thanksgiving break---no class
- November 29: Noise and coherence
- December 1: Course themes and conclusions
- December 3: Discussion:
- December 6: Final exam: Student presentations
Topics:
Core topics
- 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
Time permitting
- Rotary spectra
- Alternative approaches for computing spectra: multitaper and maximum entropy methods
- Filter design
- Introduction to linear systems
- Spectral modeling; spectral physics
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