GEOS 597e
Spatiotemporal Data Analysis Workshop
Prework 5: Error, stability, truncation and filtering
Last updated 10/2/06. To be
completed prior to class session Weds., Oct. 4th.
Introduction:
This week we'll analyze our
results from Homework 4. How can we assess how many of the EOF
structures are robust with respect to data errors? With that
knowledge, how can we use the EOF analysis to improve the reliability
of subsequent analyses of the results? The answers to these
questions form the bases of informed EOF analysis of the
statistically-derived patterns.
Reading:
- Overland and
Preisendorfer, 1982: A signficance test for principal components
applied to a cyclone climatology. Mon. Wea. Rev.,
100(1), 1-4.
- Optional but worth getting the
gist: North et al., 1982:
Sampling errors in
the estimation of empirical orthogonal functions. Mon. Wea. Rev.,
110, 699-706.
Reading questions:
- What is the fundamental problem which is posed by Overland and
Preisendorfer?
- Write down an algorithm (in words) for how you would apply Rule N
in the case of data set with n time points and m gridpoints, to
determine the 95% confidence level for the normalized eigenvalues of
the covariance matrix of the dataset. Given your experience
computing EOFs for the GOSTA SST anomaly dataset in Homework 4, do you
think this test will be practical for the case n ~300, m ~1000?
- How many EOFs of the correlation matrix of the Bering Sea cyclone
dataset were found to be significant? How about for the EOF
analysis of the covariance matrix for the same data
set? Why might these two significance estimate results turn out
differently (e.g. analysis of the Hayden dataset?)
- If you can find or think of an example in the recent climate
dynamics literature of an author correcting him/herself in the
publoshed literature, please bring it to class to share.
Products to hand in (keep a
copy for yourself to use in class discussion):
- Answers to the four reading questions listed above.
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