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The EOF analysis has to start from calculating the
covariance matrix.
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For our case, the state of the Pacific SST is described by values at
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model grid points Xi.
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Let’s assume the observational network in the Pacific
has 10 grids in
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latitudinal direction and 20 grids in longitudinal
direction, then there
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are 10x20=200 grid points to describe the state of
pacific SST. So we
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have 200 state variables:
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Xm(t),
m =1, 2, 3, 4, …, 200
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In our case, there are monthly observations of SSTs over
these 200
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grid points from 1900 to 1998. So we have N (12*99=1188)
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observations at each Xm:
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Xmn
= Xm(tn),
m=1, 2, 3, 4, …., 200
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n=1, 2, 3, 4,
….., 1188
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