Empirical Master Equations. Part II: Application to Stratospheric QBO, Solar Cycle, and Northern Annular Mode

Time series of stratospheric climate variables are used to derive master equations in the discretized phase space spanned by three variables. The empirical master equation (EME) predicts the probability density function (PDF) in this phase space. The numerical properties of EMEs have been investigated in the first part of this paper using synthetic time series. In this part of the paper, the time series consist of normalized and deseasonalized daily and zonally averaged meteorologically relevant quantities obtained from the 40-yr ECMWF Re-Analysis (ERA-40) and observations. One EME reproduces the climatological features of the quasi-biennial oscillation (QBO) of stratospheric equatorial zonal wind including the probabilistic character of transitions between phases. Also, the Arctic stratosphere at 10 hPa is about 2 K warmer during the easterly phase of the QBO than during the westerly phase. Another EME including a time series of the solar radio flux at 10.7 cm hints that the relationship between the QBO and the temperature in the Arctic stratosphere is shifted toward warmer (colder) states by about 1 K during periods of high (low) solar activity. Finally, an EME is derived from time series of variables highly correlated with the northern annular mode (NAM). The EME shows that NAM anomalies in the middle stratosphere propagate into the lower stratosphere and then into the lower troposphere with a time scale of about two and four weeks, respectively. The influence of strong tropospheric NAM anomalies is confined to the lower stratosphere.