Statistical Models in CPT Part II CCA Simon

Statistical Models in CPT Part II: CCA Simon J. Mason simon@iri. columbia. edu International Research Institute for Climate and Society The Earth Institute of Columbia University CIMH Workshop on the Climate Predictability Tool Bridgetown, Barbados, July / August 2013

Selecting models in CPT MLR can be used when there is one or a very small number of predictors. GCM is a special case – a single predictor is used from th nearest, or an interpolated, gridpoint. PCR can be used to address problems with MLR that arise when there are many predictors. But what if there are many predictands?

What is Canonical Correlation Analysis CCA? June SSTs r=0. 97 JAS rainfall

GCM What is CCA? JAS rainfall r=0. 83 GPCC

Canonical Correlation Analysis (CCA) • The weights VX and VY are defined so that ZX and ZY have maximum correlation. • In CPT, the CCA is performed using principal components of X and Y to avoid over-fitting. • Suitable for multiple predictors, and multiple predictands. • Predictions are spatially consistent.

Exercise • Use gridded June SSTs to predict the Caribbean JAS rainfall. What considerations can we apply for selecting an appropriate SST domain and setting the numbers of modes? What do the CCA maps indicate? • Repeat using the ECHAM GCM predictions.