ESS210B
Prof. Jin-Yi Yu
Covariance Matrix
qThe EOF analysis has to start from calculating the covariance matrix.
qFor our case, the state of the Pacific SST is described by values at model grid points Xi.
qLet’s assume the observational network in the Pacific has 10 grids in latitudinal direction and 20 grids in longitudinal direction, then there are 10x20=200 grid points to describe the state of pacific SST. So we have 200 state variables:
q                         Xm(t), m =1, 2, 3, 4, …, 200
qIn our case, there are monthly observations of SSTs over these 200 grid points from 1900 to 1998. So we have N (12*99=1188) observations at each Xm:
q                           Xmn = Xm(tn), m=1, 2, 3, 4, …., 200
q                                              n=1, 2, 3, 4, ….., 1188
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