We consider a novel, nonparametric, kernel-based approach for identifying and quantifying environmental effects on output covariances and correlations. The approach is illustrated using the natural frequencies of the KW51 railway bridge under varying temperatures. Based on the eigendecomposition of the conditional covariance matrix, a conditional, supervised version of principal component analysis (PCA) is obtained, with the temperature effects removed from the resulting conditional principal component scores. Specifically, on the KW51 data, artifacts produced by very low temperatures are removed while still being sensitive to changes in the bridge’s behavior due to retrofitting.