EOF Analysis

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

EOF analysis

Assume d is the data time series, its auto-covariance is

C=ddT

Calculate the singular value decomposition of C:

C=UUT

Then the columns of U are the empirical orthogonal functions (EOFs), and gives the weight of each EOF.

EOF1

EOF2

x

Y

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

Image display

• tv, d, x, y

• tvscl, d, x, y

In-class assignment VIIIData 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.