GEOS 597e
Spatiotemporal Data Analysis Workshop
Prework 9: Joint analysis
of two (or more) spatiotemporal fields
Last updated 11/8/06. To be
completed prior to class session Weds., Nov. 15th.
Introduction:
This week we'll discuss the
formal development of an analysis of the covariance between two
spatiotemporal fields, and the strengths and weaknesses of the approach
with respect to independent EOF analysis of the fields, and canonical
correlation analysis. Some computational notes in matrix
notation, to help make sense of the mechanics are here.
Reading:
- Wallace et al. 1992:
Singular value decomposition of wintertime sea surface temperature and
500mb height anomalies.
J. Clim., 5, 561-576. Let's concentrate on Sections 1-4
for our discussion.
Optional reading:
- Bretherton et al, 1992: An
intercomparison of methods for finding coupled patterns in climate
data, J. Clim., 5, 541-560. This
paper gives background and algorithms for the demonstration analyses in
Wallace et al. (1992).
- Kutzbach, 1967: Empirical
orthogonal function analysis of sea level pressure, surface temperature
and precipitation complexes over North America. J. Appl.
Meteorology, 6, 791-802. An
introduction to generalized EOF analysis, using familiar notation
convention, which includes a form of joint SVD analysis.
- Hsu and Wallace, 1985:
Vertical structure of wintertime teleconnection patterns. J.
Atmos. Sci., 42(16), 1693-1710. Section
5b describes a joint SVD of SLP and 500mb heights, and the Appendix
describes a common rescaling of orthonormal eigenvectors to reflect
variance associated with each pattern.
Reading questions:
- In general, why would you want to perform an analysis of the
covariance between two spatiotemporal fields? In particular, why
would you want to perform an analysis of the covariance of wintertime
SST and 500mb height anomalies?
- How would you describe the leading spatial patterns identified
from independent analysis of the SST and 500mb height fields?
- In general, what are homogeneous and heterogeneous correlation
maps resulting from a joint SVD analysis, and how are they similar and
different from each other? From the independent EOF
analyses? In particular, what do the heterogeneous correlation
maps indicate about the patterns of covariance between the two fields
studied here (see in particular Figs. 6-9)? How about comparison
of the results of independent EOF analyses with the joint SVD results
(e.g. compare Figs. 8,9 with Figs. 2,3)?
Products to hand in (keep a
copy for yourself to use in class discussion):
- Answers to the three reading questions listed above.
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to Schedule/Syllabus.