Geography 257 – Topics in Climatology
ÒA BeginnerÕs Guide to Empirical Orthogonal Function
(EOF) AnalysisÓ
Spring 2006
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Instructor: Professor John Chiang Email: jchiang [AT] atmos.berkeley.edu office phone: 642-3900 office: 547 McCone Hall office hours: TBA |
Class Location: 135 McCone Class Time: Tu 3-6 Course control number: 36658 Units: 4 Grading options for this seminar are P/NP, enrolling students must choose P or NP. |
Acknowledgements. This seminar is based on a course developed by Prof. Michael Evans at the University of Arizona, Tucson (GEOS 597e ÒSpatiotemporal Data Analysis WorkshopÓ). Thanks, Mike!
Class website: http://www.atmos.berkeley.edu/~jchiang/Geog257/geog257.html
General description. As the name implies, we'll start off from the basics, including a review of the relevant linear algebra. The emphasis will be on 'how to' rather than theoretical, including practical considerations like knowing your data, physical interpretation of the results, pitfalls etc. The goal is to get you comfortable with the technique so that you can use it in your research. The context will be climate data analysis, but the technique is readily translatable to other fields.
I'm assuming you've seen some linear algebra, and that you have access to MATLAB (I won't provide this for you). We'll make heavy use of MATLAB, so ideally you are comfortable programming on it, or at least be a quick learner. As part of the course, you will analyze data of research interest to you, and present it to the class.
Outline. In the first 3 weeks weÕll cover preliminaries, including getting you off the ground in MATLAB, a review of linear algebra, and also understanding the origins of a global sea surface temperature (SST) dataset that is the dataset that many of the examples use. The next few weeks will then get into EOF analysis – theory and use – and in the spatial and temporal domains (the latter being called Ôsingular spectrum analysisÕ or SSA). The final third of the time will be devoted to reading papers of specific interest, and working on your projects.
Assignments. You will be expected to carefully read the material and complete the homework assigned for each week. We will discuss both the readings and the homework during the weekly meeting time.
Course Schedule (color scheme: black is ÔfixedÕ, red is preliminary and subject to change)
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Week (m/d) and Topic |
Prior Reading |
Post-class homework |
Notes and posts |
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1: Class starts next week |
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2: (Tue 1/24) Introduction and logistics. |
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Matlab primers: |
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3: (Tue 1/31) Linear algebra review |
Strang pp.1-58 (focus on pp.1-9, 19-27, and 42-48); Optional: Wilks p403-404, p408-415 |
Strang exercises and matrix manipulations in Matlab |
Data for homework: week3_data.mat |
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4: (Tue 2/7) Know your data; covariance estimation |
Also look at figure 5 of Woodruff et al 87. Also, Wilks pp. 50-55 and pp. 405-407, and 415-417 on correlation and covariance |
Covariance
calculations: pencil and matlab |
Data for homework: |
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5: (Tue 2/14) EOF basics |
Wilks Ch 11 p420-423; and p463-481 |
EOF
calculations – pencil and MATLAB |
Use data from homework 4 |
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6: (Tue 2/21) EOF example (space) |
Wilks p425-426 (on SVD); |
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7: (Tue 2/28) EOF: Truncation, sampling properties |
Wilks pp. 481-492; and |
Analysis
of SST EOFs calculated last time JC.mat –
matrix of synthetic eigenvalues |
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8: (Tue 3/7) Linear Regression No class meeting this week – JC away |
Class handout |
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JC away Tue Mar 7 |
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9: (Tue 3/14) Rotated EOFs |
Wilks pp.492-500 (rotation) |
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10: (Tue 3/21) Rotated EOFs - continued |
No reading |
JC away Thur Mar 23 |
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11: Spring break |
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12: (Tue 4/4) Singular spectrum analysis |
Wilks p501-504; and |
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13: (Tue 4/11) SSA case studies |
Independent project |
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14: (Tue 4/18) Case study – Pacific Decadal Variability |
Independent project |
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15: (Tue 4/25) More on interpretation of EOFs; significance of a
correlation when data are serially correlated |
Independent project |
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16: (Tue 5/2) Project presentations |
Andy Bliss – Interpretion of Antarctic station data Hyo-Seok Park – Asian Monsoon Nicole-Jean Schlegel – Causes of the Santa Ana winds |
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17: (Tue 5/9) Project presentations/ Summary and wrap up |
Andrew Friedman – Zonal mean rainfall analysis Dyuti Sengupta – Climate of Mexico |
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Book References
Strang, G: Linear Algebra and its Applications, 3rd Ed.
Wilks, DS: Statistical Methods in the Atmospheric Sciences, 2nd Ed.
Papers (partial list)
Dommenget and Latif (2002), A Cautionary Note on the Interpretation of EOFs, Journal of Climate: Vol. 15, No. 2, pp. 216–225.
Houghton and Tourre (1992), Characteristics of Low-Frequency Sea Surface Temperature Fluctuations in the Tropical Atlantic, Journal of Climate: Vol. 5, No. 7, pp. 765–772.
Ghil et al. (2002), Advanced spectral methods for climatic time series, Reviews of Geophysics, 40, 1 / March 2002
North et al. (1982), Sampling Errors in the Estimation of Empirical Orthogonal Functions, Monthly Weather Review: Vol. 110, No. 7, pp. 699–706.
Overland and Preisendorfer (1992), A Significance Test for Principal Components Applied to a Cyclone Climatology, Monthly Weather Review: Vol. 110, No. 1, pp. 1–4.
Quadrelli et al. 2005, On sampling errors in Empirical Orthogonal Functions, ???
Weare BC et al (1976), Empirical Orthogonal Analysis of Pacific Sea Surface Temperatures, Journal of Physical Oceanography: Vol. 6, No. 5, pp. 671–678.
Woodruff et al. (1987), A Comprehensive Ocean-Atmosphere Data SetBulletin of the American Meteorological Society: Vol. 68, No. 10, pp. 1239–1250.
Zhang et al. (1997), ENSO-like Interdecadal Variability: 1900–93, Journal of Climate: Vol. 10, No. 5, pp. 1004–1020.