• 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

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

• Mesh surface plots surface, z, x, y, shades=bytscl(z,top=255)
• Shaded surface plots shade_surf, z, x, y

• tv, d, x, y
• tvscl, d, x, y

Data files are stored at: http://lightning.sbs.ohio-state.edu/geo820/data/
1.
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.
2.
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.