Why are Upward EP-Flux and Temperature Positively Skewed in the Stratosphere?

The distribution of temperatures in the wintertime polar stratosphere is significantly positively skewed, which has important implications for the characteristics of ozone-chemistry and stratosphere-troposphere coupling. The typical argument for why the temperature distribution is skewed is that radiative balance sets a firm lower limit, while planetary wave driving can force much larger positive anomalies in temperature. However, the distribution of upward EP-flux is also positively skewed, and this suggests that dynamics may play an important role in setting the skewness of the temperature distribution.

This study explains the skewness of the upward EP-flux distribution by appealing to the ideas of linear interference. In this framework, fluxes are decomposed into a linear term (LIN) that measures the coherence of the wave anomaly and the climatological wave and an additional nonlinear term (NONLIN) that depends only on the wave anomaly. It is shown that when filtered by wavenumber, there is a clear nonlinear dependence between LIN and NONLIN: the terms cancel when LIN is negative but reinforce each other when LIN is positive. This leads to the positive skewness of upward wave activity flux. A toy model of wave interference is constructed, and it is shown that the westward vertical tilt of the climatological wave is the key ingredient to a positively skewed upward EP-flux distribution. The causes of the skews of the LIN and NONLIN distributions themselves are shown to be related to relationships between wave phase and amplitude, and wave phase and vertical tilt, respectively.