Winter 2013
http://www.atmos.washington.edu/~breth/classes/AM582/

MWF 8:30-9:20: Loew 216

This class is being offered on-line through EDGE, which provides live streaming of each class and archived lecture videos. You'll need to sign in with your UW NetID. If you are an EDGE student, you can also get to this site through the UWEO Moodle portal moodle.extn.washington.edu. If you are registered for an on-campus virtual section, it will be functionally identical to being in the on-campus 'A' section, and you are welcome to come to the classroom to listen to the lectures live (we seem to have enough seats). Assignments and grading for 482 sections will be identical to that for 582 sections.

 

Instructor: Prof. Chris Bretherton breth@washington.edu ATG 704, x5-7414 Office hours: MW 1:30-2:20, or by appointment. TAs: Xing Fu xingf@uw.edu Susie Sargysan ssusie@uw.edu Office hours: Tu and Fr 12:30-1:30 (Gugg 406; also via Skype once we have TA skype accounts).

Course Description

Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression.

Prerequisites

Notes

I will loosely follow Prof. Nathan Kutz's course lecture notes. When appropriate, these will be supplemented with my own notes, linked to the syllabus section below. Useful references:

• D. L. Hartmann, Atm S 552 (Objective Analysis) lecture notes. (freely available at http://www.atmos.washington.edu/~dennis/, follow the Atm S 552 link, then Class Notes link)
• von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

Syllabus and supplementary notes

My supplementary lecture notes are linked here where available.

Review of statistics (3 lectures)

• probability distributions (Lecture 1, 7 Jan.); mean and variance; central limit theorem (Lecture 2, 9 Jan)
• Confidence intervals, statistical hypothesis testing, and some common abuses (Lecture 3, 25-28 Jan, refers to graph of the normal distribution)

Spectral and time series analysis and filtering (13 lectures)

• Digital signal processing and the DFT (Lectures 4-5, 28-30 Jan)
• Power spectrum (Lecture 6, 30 Jan makeup)
• lagged autocorrelation (Lecture 7, 1 Feb)
• white/red noise (Lecture 8, 4 Feb)
• windowed spectral analysis (Lecture 9, 6 Feb)
• its application to El Nino SSTA dataset including Matlab SP toolbox spectral analysis functions (Lecture 10, 6 Feb p.m. makeup)
• its application to music (time-frequency analysis using spectrograms) (Lecture 11, 8 Feb)
• spectral filtering (Lectures 12-13, 11-13 Feb)
• Wavelet decomposition for time-frequency analysis (Lectures 14-15, 13 Feb makeup-15 Feb). Figures: Haar 1-level and 3-level wavelet filter response and Wavelets and scaling vector for 3-level Haar transform.
• Wavelet compression and image processing (Lecture 16, 15 Feb makeup)

Dominant pattern analysis for dimensionality reduction (9 lectures)

• Singular value decomposition (Lecture 17-18, Feb. 25-27)
• Principal component analysis (Lecture 19-20, Feb. 27 makeup and 1 Mar.) Figure: Scatterplot of highly correlated bivariate data (from Hartmann Ch. 4).
• Regression (Lecture 21, 4 Mar.) Figure: Different manifestations of correlation coefficient 0.7 (from Hartmann Ch. 3).
• Maximum covariance analysis (Lecture 22, 6 Mar.)
• Pattern recognition (Lecture 23, 6 Mar. makeup)

Data assimilation and model-data fusion (5 lectures)

• Sequential state estimation (Kalman filter) for a simple 1D system (Lecture 24, 8 Mar.)
• Theory of Kalman filtering (Lecture 25, 11 Mar.)
• Kalman filter for a multivariate ball-tracking problem (Lecture 26, 13 Mar.)
• The Friday 15 Mar. class will be reserved for questions. I will be available for live questions by in-class students and will also answer email questions from on-line students during this time (just don't ask me how to solve the final exam!)

Grading

• Homework (50%), posted to class web page and assigned on a quasi-biweekly basis. Homework is heavily oriented toward problem solving and exploratory data analysis in Matlab based on methods discussed in lectures. Consultation with your fellow students is encouraged, but everyone needs to write out homework assignments in their own words, and write their own Matlab scripts. A GoPost discussion board has been set up for you to discuss homework and other class issues on line. For on-line submission of other homework materials, please use the class Catalyst dropbox; please include supporting Matlab scripts. On-campus students may also submit print versions of their homeworks in class or to the mailbox of either TA in the north office suite of the 4th floor of Guggenheim Hall. Late homework (after 11:59pm on due date) will be accepted until 5 pm on the second day after the due date. There will be a late penalty of 25% on all but the first late assigment. Homework solutions will be posted on the class web page.
• Midterm assignment (20%) and final assignment (30%). Like regular homework, but no consultation with anyone and no late final assigments accepted. Final assignment will be posted on Wed 13 Mar (penultimate class), due by 5 pm on Wed 20 Mar (in finals week).

Schedule

No class:

• Fr 11, Mo 14, We 16, Fr 18, We 23 Jan (Instructor travel)
• Mo 21 Jan: MLK Day (UW holiday)
• Mo 18 Feb: Presidents Day (UW holiday)
• We 20, Fr 22 Feb (Instructor travel)

Makeup classes for instructor travel days (3:30 in Loew 216 if you want to watch live; otherwise please watch the on-line video before the following Friday class)

• We 30 Jan, We 6 Feb, We 13 Feb, Fr 15 Feb, We 27 Feb, We 6 Mar.

Homework and Exams

Matlab Scripts

Function X=randB(m,n,p) to return an m x n matrix of Bernoulli-distributed random numbers with parameter p.

CentralLimitEx.m: Central limit theorem example using average of 20 Bernoulli RVs, makes this plot. Uses randB.m

fft_hw1.m: DFT of HW1 dataset. Makes plot of the amplitudes of the complex-valued DFT components.

For the scripts below, I've used Matlab's publish capability to make self-documenting web page versions of the scripts. To extract the original Matlab script from the web page, copy the URL (web address), and in Matlab, type grabcode('URL') to bring up an untitled file with the code in an editor window, e. g. to get the file foo.m that generated the web page foo.html below, type grabcode('http://www.atmos.washington.edu/~breth/classes/AM582/matlab/html/foo.html') and save this to foo.m in the Matlab editor.

nino1.html: Uses 1950-2012 monthly Nino3.4 sea-surface temperature dataset nino.mat. Plots the SST, its power spectrum, and the same for the SST anomaly after the mean and first three harmonics of the annual cycle of SST are removed.

nino2.html: Uses 1950-2012 monthly Nino3.4 sea-surface temperature anomaly dataset SSTA.mat optionally made by nino1.m. Plots subannual SSTA power spectrum with red noise fit, and plots of its autocovariance and autocorrelation sequences.

nino3.html: Uses monthly Nino3.4 sea-surface temperature anomaly (SSTA) time series derived by nino1.m, given in SSTA.mat. Plots windowed power spectra of SSTA, using 20-year overlapping Hanning (cosine-taper) windows, both directly and using Matlab signal-processing toolbox spectrum functions, and compares to red noise fit.

music.html. Plays and does windowed tapered power spectral analysis of short segment of Handel Messiah. A copy of the score suggests that the initial notes of the segment are D, A and F, as also visible from our analysis (which also suggests they are played slightly flat).

music2.html. Low, band and high pass filtering of short segment of Handel Messiah with Fourier and Butterworth filters.

runningmean.html. Power spectrum of running mean filter using DFT.

butterworth.html. Calculation of an Nth order Butterworth filter and plots showing its properties.

wavelet_leleccum_notoolbox.html. Application of single and multilevel Haar wavelet transform to an electricity consumption dataset. Uses leleccum.mat (included in Matlab wavelet toolbox) and my functions dwtHaar.m and idwtHaar.m in place of the Matlab wavelet toolbox, for portability.

wavelet_image.html. Image compression example using 2D multilevel Haar wavelet transform. Uses Uses ngc6543a.jpg and my functions dwt2Haar.m and idwt2Haar.m in place of the Matlab wavelet toolbox, for portability.

wavelet_leleccum_cwt.html. Continuous Haar wavelet transform on the electricity consumption dataset. Requires Matlab wavelet toolbox function cwt.

PCA_SSTA.html. Application of PCA to gridded tropical Pacific sea-surface temperature dataset. Uses SSTPac.mat.

PCA_cities.html. Application of PCA to multiparameter dataset of indices for 9 categories contributing to quality of life in 329 U.S. cities. Uses cities.mat; which is also already included in the Matlab Statistics toolbox.

USTA_regress.html. Example of regression, applied to influence of tropical Pacific sea-surface temperature on U. S. land surface temperature. Uses USTA.mat, SSTPac.mat, and SSTA.mat.

MCA_PSSTA_USTA.html. Maximum covariance analysis of coupling of tropical Pacific sea-surface temperature and U. S. land surface temperature. Uses SSTPac.mat and USTA.mat.

classify_one_two.html. Classify spoken 'one's and 'two's using DWT power spectral analysis and PCA. Uses dwtcolHaar.m, ones.m4a, twos.m4a, and ones-twos.m4a. If your Matlab doesn't have audioread or equivalent, load the following .mat files instead: ones.mat, twos.mat, ones-twos.mat ; these also include the 20 sounds being spoken in each file.

sequential_estimation_simple1D.html. Sequential state estimation (Kalman filter) on the simple 1D system x_n = ax_{n-1}.

kalman2.html. Kalman filter on a multivariate ball-tracking problem.