A relaxation technique applied to the ECMWF model is used to analyse 11, 21 and 31 year trends in the boreal winter mean 500 hPa North Atlantic Oscillation (NAO), Pacific North America pattern (PNA) and Southern Annular Mode (SAM) indices. For the PNA, the results indicate a strong influence from the tropics on all time scales, whereas for the NAO, the stratosphere is important on time scales of 11 and 21 but with an indication of feedback from extratropical sea surface temperature and sea-ice (SSTSI) anomalies on the 11 year time scale. For the SAM, the tropics emerge as the most important influence. We find an influence from the stratosphere consistent with expectations based on ozone depletion, although no clear role for stratospheric forcing of the SAM is found in these experiments. © 2012. American Geophysical Union. All Rights Reserved.