The leading mode of variability of the lower atmosphere circulation in the Northern Hemisphere is a largely zonally symmetric mode known as the Arctic Oscillation. We calculate Arctic Oscillation (AO) indices on a range of levels from 1000 to 10 hPa by means of a principal component analysis of National Centers for Environmental Prediction daily geopotential height anomalies. We find the apparent downward propagation of anomalies noted by other authors to be statistically significant compared to a red noise model. By examining histograms of these indices for each month, we note that the distribution of the index is generally close to Gaussian in the troposphere. In the stratosphere, however, the index is negatively skewed in the winter and positively skewed in the spring. We conclude that the positive skewness in April results from the coexistence of distinct summer and winter circulation states, and by examining polar stratospheric temperatures, we conclude that the negative skewness in January may be due to the radiatively determined limit on the vortex strength. This radiative limit responds relatively slowly to anthropogenic forcing, whereas changes in planetary wave forcing could have a much faster impact on the number of warm events. This suggests a hypothesis that the vortex strength may respond nonlinearly to anthropogenic forcing, which is supported by an observed change in the shape of the histograms of 20--200 hPa AO indices in January over the past 40 years. ¿ 2001 American Geophysical Union