Data-based Master Equations for the Stratosphere - Dall'Amico, Mauro (Ludwig-Maximilians-Universität München, 2005)
Three-dimensional data-based master equations are developed and subsequently used to study climate variability in the stratosphere. Master equations are used to develop understanding of observed systems where no dynamic equations are available. Master equations are used in this thesis as prognostic equations for the probability density in a discretized phase space spanned by climate variables. The evolution of the probability density may then reveal information about the relationship between these variables. The phase space is partitioned into several hundred boxes of equal grid size representing at any one time states that the system can assume. In this discretized version of the phase space, the coefficients of a master equation may be estimated from the relative frequencies of transitions observed in a time series of the variables obtained from observations or numerical model runs. Data-based master equations are numerical structures whose success depends among other things on the resolution and volume of the available time series. These dependencies are studied on the basis of data from the famous three-component Lorenz convection model extended with a stochastic forcing. Time series of the desired length and time resolution can thus be generated easily. Furthermore, the results can be compared directly. Best results are obtained through the combination of a long data record and a coarse time resolution. The choice of the variables and their number also play a crucial role in the success of a master equation. Time series of stratospheric climate indices obtained from the reanalyses ERA-40 lead also to these last results. The stratosphere serves now as an implementation area. The master equation shows that during the eastern phase of the quasi-biennial oscillation (QBO) of equatorial zonal wind the arctic stratosphere is about 2 K warmer than during the western phase. Thus the relationship between QBO and arctic stratosphere can be quantified. The influence of the 11-year solar cycle is described by the master equation. It emerges that the relationship between QBO and temperature anomaly of the arctic stratosphere shows a dependence on solar variability. The implications of stratospheric processes on the climate in the troposphere are analysed with a master equation for a time series of an index of the Arctic Oscillation (AO) at stratospheric and tropospheric pressure levels. The master equation captures the main features of this interaction between stratosphere and troposphere. It is shown that anomalies of the AO in the middle stratospere propagate deeply into the troposphere with a time scale of 4 weeks. Furthermore the master equation shows that the influence of strong tropospheric AO-anomalies remains confined to the lower stratosphere.