A new continuum regression model and its application to climate and rainfall isotope relationships
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Date
2013-07-10
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University of Western Australia
Abstract
Climate field reconstruction using networks of rainfall-isotope proxies is an example of a problem that requires the estimation of a model that aims to predict one field (Y) using another field (X). The general problem is to estimate a subspace of X that retains useful information for predicting Y. Methods to estimate such subspaces include principal components regression (PCR), partial least squares (PLS), redundancy analysis (RDA), and canonical correlation analysis (CCA), but these methods typically do not estimate the same subspace. One solution is to treat these different methods as end members of a continuous manifold of regression subspaces. By weighting the end member solutions in some way, we can search for the best regression subspace over the manifold.
In this study, a new continuum regression model is developed by extending an earlier method known as Principal Covariates Regression (PCovR). PCovR has two end members: PCR and RDA. Here, PCovR is extended by shrinking the covariance matrix of X. As a result, our new method regPCovR includes three end members (PCR, RDA and PLS) and is particularly suited to climate data, where the spatial dimension is larger than the temporal dimension, and where there are missing values in the response field (Y). regPCovR includes both a weighting parameter and shrinkage parameter, which are estimated using crossvalidation.
The benefits of regPCovR are illustrated using two examples. In the first example, the problem of predicting the southern Australian winter rainfall (P) field from the regional winter sea level pressure (SLP) field is investigated. The best rank two regression subspace found by regPCovR explains over 50% of the variance in the rainfall field. This subspace thus estimates the relationship between SLP and P better than the end member subspaces. In the second example, PCovR is used to investigate the relationships between the winter SLP and P fields, and rainfall isotope (d18O) data from Australia and New Zealand. Two main patterns are identified, which explain about half the variance in the southern GNIP d18O sites. Subspace projection is used to relate these patterns to various regional and Southern Hemisphere climate indices. regPCovR will be useful for finding subspaces that better capture the relationships between climate and rainfall isotopes, which is a necessary step for quantitative palaeoclimatology. © The Authors
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Keywords
Climates, Rain, Isotopes, Redundancy, Correlations, Dimensions
Citation
Fischer, M. (2013). A new continuum regression model and its application to climate and rainfall isotope relationships. Paper presented at the 12th Australasian Environmental Isotope Conference, 10th-12th July 2013, University of Western Australia, Perth, (pp. 37-38).