Statistical Inference in Canonical Correlation Analyses Exemplified by the Influence of North Atlantic SST on European Climate

Abstract

To encourage the use of the standard parametric test procedures in canonical correlation analysis, the tests are applied to investigate the influence of northern Atlantic SST on the Euro?Atlantic atmospheric circulation. A comparison with a Monte Carlo testing procedure shows that the parametric tests perform properly given that at least one of the two multivariate variates is normally distributed. In this case the parametric tests are even superior to a Monte Carlo test procedure, when the estimation of the error level relies on relatively small Monte Carlo samples, which is often the case in climate studies. Even if the parametric test procedures fail due to departures from the independency assumption, they provide qualified variables to perform the more costly Monte Carlo testing procedure. A significant influence of the northern Atlantic tripole on the atmospheric circulation was detected in ensemble simulations with the Hamburg ECHAM3 model forced with prescribed SST. Another signal already described by Czaja and Frankignoul exhibits a lagged influence of the SST on the atmosphere.