Winter 2015
http://www.atmos.washington.edu/~breth/classes/AS552/
MWF 2:30-3:20: ATG 310c
A Canvas page will be used for announcements, grading, and discussions.
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Instructor: Prof. Chris Bretherton breth@washington.edu ATG 704, x5-7414 Office hours: M 12:30-1:20, Th 1:30-2:20 or by appointment. |
| Schedule | Homework and Exams | Syllabus and supplementary notes | Discussion papers | Matlab scripts | Python notebooks |
Exploratory and objective data analysis methods for geophysical scientists. Statistics, including normal distributions, confidence intervals, linear regression. Fourier spectral analysis and filtering for time series, principal component and maximum covariance analysis, cluster analysis, Kalman filter for data assimilation. Pitfalls and best practices illustrated by examples from the scientific literature.
Useful references to supplement lecture notes:
Statistics potpourri (6 lectures)
Fourier spectral analysis and filtering
Principal component and cluster analysis for dimensionality reduction
Smoothing, interpolation and data assimilation
No class:
Makeup classes at 9:30 a.m. in ATG 310c:
| Item | Due Date | Download Solutions |
| Homework #1; uses hw1_dat.mat | due Fr 16 Jan | HW #1 solution |
| Homework #2; uses snow.mat | due Fr 30 Jan | HW #2 solution (with extensions) |
| Homework #3; uses hw1_dat.mat | due Fr. 6 Feb | HW #3 solution |
| Homework #4 ; uses rf18L1.txt | due Fr. 20 Feb | HW #4 solution |
1000 samples of unit normal PDF;
uncorrelated RVs that are not independent
Serially correlated data with several lag-1 autocorrelations r
For the scripts below with a .html link, I've used Matlab's publish capability to make self-documenting web page (html) versions of the scripts. To extract the original Matlab script from the web page, copy the URL (web address). 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.
regression_example.html: Simple and multiple linear regression on a Matlab built-in dataset carsmall.mat of car MPG vs. weight and horsepower.
fft_hw1.m: DFT of HW1 dataset. Makes plot of the amplitudes of the complex-valued DFT components.
DFT_gauss.html: Power spectra of a Gaussian and a half-Gaussian.
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.
rednoise.m: Function to generate a sample of standardized Gaussian red noise with a given lag-1 covariance r.
nino3.html: Uses 1950-2012 monthly Nino3.4 sea-surface temperature anomaly dataset SSTA.mat optionally made by nino1.m. Windowed spectral analysis of the Nino3.4 SSTA time series, using both basic DFT and using Matlab SP Toolbox functions (including confidence ranges).
CrossSpectralNino3NPI.html: Cross-spectral analysis of monthly Nino3.4 sea-surface temperature anomaly (SSTA) time series given in SSTA.mat with North Pacific Index of 30-65N 160E-140W mean sea-level pressure.
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_turbulence.html. Application of single and multilevel Haar wavelet transform to a nonstationary turbulence dataset. Uses w_VOCALSRF03.mat
PCA_SSTA.html. Application of PCA to gridded tropical Pacific sea-surface temperature dataset. Uses SSTPac.mat.
PCA_cities.html. Application of PCA and rotated 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.
cluster_cities.html. K-means cluster analysis of cities dataset. Uses cities.mat.
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.
