Abstract Using NCEP–NCAR 51-yr reanalysis data, the interannual and decadal variations of planetary wave activity and its relationship to stratospheric cooling, and the Northern Hemisphere Annular mode (NAM), are studied. It is found that winter stratospheric polar temperature is highly correlated on a year-to-year basis with the Eliassen–Palm (E–P) wave flux from the troposphere, implying a dynamical control of the former by the latter, as often suggested. Greater (lower) wave activity from the troposphere implies larger (smaller) poleward heat flux into the polar region, which leads to warmer (colder) polar temperature. A similar highly correlated antiphase relationship holds for E–P flux divergence and the strength of the polar vortex in the stratosphere. It is tempting to extrapolate these relationships found for interannual timescales to explain the recent stratospheric polar cooling trend in the past few decades as caused by decreased wave activity in the polar region. This speculation is not suppor...