ATMO 632: Week 2

       Time Series Analysis: Regression & Principal Component Analysis

 

                              URL: http://www.cgd.ucar.edu/~svn/atmo632/week2.htm

 

Reading Material

 

  1. Wilks: Chapter 6.2 (regression), 9.1-9.3 (Principal Component Analysis)
  2. North: Chapter 2 (regression), 3.1-3.2    (Empirical Orthogonal Functions)

 

 

Concepts

 

            Regression

                        Uncertainty in one variable

                        Least square curve fitting

                        Correlation

                        “Explained” variance

                        t-statistic (null hypothesis of zero correlation)

                        z-statistic (null hypothesis of non-zero correlation)

                        Multiple regression

                        Uncertainty in both variables (PCA/EOF)

 

            Matrix algebra

                        Norm

                        Eigenvalues and Eigenvectors

                        Eigenvectors of a real symmetric matrix

                        Singular Value Decomposition

 

            Principal Component Analysis/Empirical Orthogonal Functions

                        Covariance matrix

                        Scaling conventions

                       

 

           

ATMO 632: Homework for week 2 (due Sep. 14)

           

NOTE: You can obtain the datasets used below by visiting the course home page

                        http://www.cgd.ucar.edu/~svn/atmo632 and clicking the appropriate links.

You do not need to type in the URLs given below, which are provided for reference.

 

  1. Obtain the winter (Dec-Mar) time series of the North Atlantic Oscillation (NAO) index for the period 1864-2003 from the URL http://www.cgd.ucar.edu/~svn/atmo632/nao-djfm-1864-2003.txt This is a text file which contains two columns (year of the January, and NAO index value). The NAO index is computed as the difference of normalized sea level pressure between Lisbon, Portugal and Stykkisholmur/Reykjavik, Iceland, and is described in http://www.cgd.ucar.edu/~jhurrell/nao.stat.winter.html
    1. Plot the time series as a function of time
    2. Compute the mean and standard deviation.

 

  1. Obtain the winter (Dec-Feb) time series of the El Nino (NINO3) index for the period 1851-2003 from the URL http://www.cgd.ucar.edu/~svn/atmo632/nino3-djf-1951-2003.txt This is a text file which contains two columns (year of the January, and NINO3 index value in degrees Centigrade). The NINO3 index is computed as the average of sea surface temperature in the region (150W-90W, 5S-5N), and is obtained from http://www.cdc.noaa.gov/ClimateIndices
    1. Plot the time series as a function of time
    2. Compute the mean and standard deviation.

 

  1. Restrict the NAO index to the period 1951-2003, which overlaps with the NINO3 index period. Normalize the NAO and NINO3 indices by subtracting the mean and dividing by the standard deviation.
    1. Plot both time series in the same plot, using two different line styles or colors for the two indices
    2. Display the two time series in a scatter plot, with the NINO3 index on the X axis and the NAO index on the Y axis
    3. Compute the regression of the NAO index on the NINO3 index
    4. Compute the correlation between the two indices
    5. Test the null hypothesis that the two indices are uncorrelated, with 95% confidence limits