Course Announcement for SMS 595

Data Analysis Methods in Marine Sciences

 

Dr. Huijie Xue

School of Marine Sciences

University of Maine

Phone: 581-4318

hxue@maine.edu

 

Provides theoretical and computational guidance on techniques commonly used in the data analysis. The first half of the course will cover regression methods, and the second half will cover time series analysis and digital filters. Real data will be used to illustrate the practical aspects of the subject with emphasis on developing a hands-on understanding of the methods and correct interpretation of results. Prerequisites: MAT 127 or equivalent. Cr. 3.

 

Syllabus

Week #1

Review of Calculus and Statistics

-    Functions and Derivatives,

-    Maxima, and Mimima

-    Expectation, (Co)Variance, Statistical tests

Week #2

Linear Regressions

-    Type I linear regression

-    Error Analysis

-    Correlation

Week #3

 

-    Rank Correlation

-    Type II Linear Regressions

Week #4

Other Regression Methods

-    Linear Multiple Regression

-    Polynomial Regression

-    Variance Analysis

-    Nonlinear Regression

Week #5

Time Series Analysis

-    Sampling and Aliasing

-    Time Domain Techniques

Week #6

 

-    Harmonic Analysis

Week #7

Review and Mid-Term Exam

 

Week #8

Non-Parametric Spectral Analysis

-    Fourier Transform

-    Autocovariance Method

-    Periodogram

Week #9

 

-    Spectral Leakage

-    Data Tapers

Week #10

 

-    Band- and Block Averaging

-    Bandwidth

-    Confidence interval

Week #11

 Parametric Spectral Analysis

- Auto Regressive Processes

-    Parametric Spectral Analysis

-    Maximum Entropy Method

Week #12

Cross-Spectral Analysis

-    Cross Spectra

-    Rotary Spectra

-    Rotary Cross-Spectra

Week #13

Digital Filters

-    Ideal Filters

-    Design Digital Filters

-    Commonly Used Filters

-    Recursive Filters

Week #14

EOF Analysis

- Mathematical Procedure

-    Examples

-    Interpretations

 

Final Exam (Project and Presentation)

 

Text(s):

-         Edward Laws (1997): Mathematical Methods for Oceanographers. John Wiley & Sons, Inc.

-         W.J. Emery and R.E. Thomson (2001): Data Analysis Methods in Physical Oceanography, ELSEVIER

 

Lecture Notes