1. EOF Analysis

2. EOF analysis
The empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal base functions which are determined from the data. It is also called principal component analysis.
It is different from the spectral analysis which uses triangle functions as bas functions.
IDL has math subroutines that are convenient for doing EOF analysis

3. EOF analysis Assume d is the data time series, its auto-covariance is
C=ddT
Calculate the singular value decomposition of C:
C=UUT
Then the columns of U are the empirical orthogonal functions (EOFs), and  gives the weight of each EOF. Y
EOF1
EOF2 x

4. Mesh and shaded surface plots
Mesh surface plots
surface, z, x, y, shades=bytscl(z,top=255)
Shaded surface plots
shade_surf, z, x, y

5. Image display
tv, d, x, y
tvscl, d, x, y

6. In-class assignment VIII
Data files are stored at:
Read the netCDF file skt.mon.mean.nc for NCEP sea surface temperature (skt) data. Select 10 years of data for tropical Pacific (120E-280E, 20N-20S) and conduct the EOF analysis of the data.
Plot for the first 4 modes the EOF, principal component, and the Fourier spectrum of the principal component. Try use surface plot for the EOF.