EOF input averaging
Computing Empirical Orthogonal Functions (EOFs) can take a lot of
computer time. First the covariance matrix is estimated, this takes
Nx²Nt time, with
Nx the number of spatial points and
Nt the number of time steps. Next the eigenvalues
are computed, taking
Nx³ time.
The computation can therefore be sped up by computing the EOFs on a
coarser grid than the orginal data, reducing Nx. If
one averages over two grid boxes in longitude and two in latitude,
Nx is reduced by a factor 4, and the EOF are
computed between 16 and 64 times faster.
If an EOF computation takes too long, please kill it (using the
link provided on the next page) and retry with larger numbers in these
fields.
There are more efficient algorithms to compute he EOFs, but as far
as I know these do not work when there is missing data. I plan to
implement a faster method for fields without missing data in the
future.
Percentage valid points
The covariance between two grid points is only considered valid when
percentage of the time series both have valid data. Enter a smaller
number to get more valid data in the EOFs, but the quality of these
data will be lower. A higher number gives fewer but higher-quality
data points. At very low values the EOF procedure will fail, as the
estimate of the covariance matrix is no longer positive-definite.