Abstract
In the previous chapters we have introduced techniques to find relations between two or more different fields. In this chapter we describe a more general framework that may provide additional insight into previously analyzed methods. In general a relation between fields can be formulated symbolically as
where, for instance, Z represents the geopotential and S the SST. The exact form of the relation is unknown, but it is probably time dependent and thus includes effects of time lags and so on. In practice, it is really difficult to investigate arbitrary functional forms for f in (8.1); assuming f to be linear represents a simplifying but viable alternative. In this case the function f may be represented by matrices. We have seen in the previous chapters that powerful methods have been devised to identify relations of the form (8.1) assuming that f(S) is a linear function. We have seen linear correlation methods, teleconnection analysis and finally methods that analyze systematically the linear relation between two data sets, such as the Singular Value Decomposition (SVD) or Canonical Correlation Analysis (CCA). We will now define a general framework that includes the latter as special case.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The name is taken from the Greek mythology. Procrustes, the owner of a tavern, had only one bed and therefore took to sawing off the legs of his guests if they were too long for his bed. In a similar way, we are trying to “constrain” the matrix Z into S and we are willing to chop off some part of Z in order to so.
References
Navarra A, Tribbia J (2005) The coupled manifold. J Atmos Sci 62:310–330
Golub H Gene, Charles F Van Loan (1996) Matrix computations, 3rd edn. The John Hopkins University Press, Baltimore
Richman MB, Vermette SJ (1993) The use of procrustes target analysis to discriminate dominant source regions of fine sulfur in the western USA. Atm Environ 27A:475–481
Bretherton CS, Smith C, Wallace JM (1992) An intercomparison of methods for finding coupled patterns in climate data. J Climate 5:541–560
Cherry S (1996) Singular value decomposition and canonical correlation. J Climate 9: 2003–2009
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Navarra, A., Simoncini, V. (2010). Multiple Linear Regression Methods. In: A Guide to Empirical Orthogonal Functions for Climate Data Analysis. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3702-2_8
Download citation
DOI: https://doi.org/10.1007/978-90-481-3702-2_8
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3701-5
Online ISBN: 978-90-481-3702-2
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)