## MAE 127:   Statistical Methods for Environmental Sciences and Engineering

### Spring 2005

Prof. Sarah Gille
sgille at ucsd.edu

class meets Monday, Wednesday, Friday:  10:00-10:50 am, Sequoyah 148

office hours on main campus:  473 EBUII  Monday and Wednesday mornings from 8:30 until 9:45 or by appointment. phone:  858-822-4915
I'm also available before and after class and by e-mail.

office at Scripps:  348 Nierenberg Hall   phone:  858-822-4425.  (Make an appointment to make sure that I'm available.)

No textbook.  Assigned reading will be available as hand outs and/or through electronic reserves.

### Schedule

Week 1: Introduction
March 28: Introduction to the course. Suggested reading: Press et al., Statistical Description of Data. 14.0, 14.1, 14.2.
March 30:   Basic statistics:  means, medians, modes and all that. (Lecture images.)
April 1Computer session EBUII 239.  Getting started with Matlab.  Homework 1 assigned.
Week 2.
April 4:  More on variances.  Probability density functions.  Suggested reading: Bevington and Robinson, Ch. 1-2.
April 6 Computing means, variances from PDFs.
Computer session EBUII 239.  More Matlab tips.  Homework 1 due.  Homework 2 assigned.
Week 3:
April 11:  Central limit theorem.  Errors on the mean.  Estimating errors.  Suggested reading: Taylor, Ch. 3.
April 13:  Error propagation.
April 15:  What happens if errors aren't Gaussian?  Correlation.  Suggested reading: Press et al. 14.5. Homework 2 due.  Homework 3 assigned.
Week 4:
April 18  What makes a correlation significant?  Autocorrelation.
April 20 Decorrelation and degrees of freedom.
April 22 Least-squares fits:  defining the problem. Matlab and linear algebra. Suggested reading: Wilks, Ch. 6, Press et al., Modeling of Data, 15.0, 15.1, 15.2, 15.3, 15.4. Homework 3 due.  Homework 4 assigned.

Week 5:

April 25  Least-squares fits:  finding solutions.
April 27:  Review.
April 29:  Midterm.
Week 6:
May 2: Least-squares fits:  weighted fits.
May 4:  More weighted least-squares fits; estimating uncertainties.
May 6:  Goodness of fit.  Does adding an extra parameter help?  Homework 4 due.  Homework 5 assigned.

Week 7:

May 9: Fitting complex quantities.  Sinusoidal variability.  Suggested reading: Press et al., Modeling of Data, 15.7
May 11:   Spectral analysis.  Fourier Transforms. Suggested reading: Chatfield, Ch. 7; Press et al., Fast Fourier Transform, 12.0 12.1 12.2
May 13:   The Fast Fourier Transform.   Homework 5 due.  Homework 6 assigned.

Week 8:

May 16:  Spectra and Uncertainties.
May 18:   Windowing, filters, and spectra.
May 20:   Coherence.   Homework 6 due.  Homework 7 assigned. Suggested reading: Chatfield, Ch. 8
Week 9:
May 23:  Two-dimensional spectra.
May 25:  Empirical orthogonal functions.  Suggested reading: Wilks, Ch. 9.3
May 27:  How EOFs differ from spectra.  Homework 7 due.  Homework 8 assigned.
Week 10:
May 30:  Memorial Day.  No Class
June 1:   Uncertainty and EOFs. Summary
June 3:  Exam review.  Homework 8 due.
final exam Tuesday, June 7, 8-11 am, Sequoyah 148, cumulative
Exams, course grades, and uncollected problem sets available from Bruno Etchepare, EBU-II Room 573.