Data-based master equations for the stratosphere [Elektronische Ressource] / vorgelegt von Mauro Dall'Amico

Data-based Master Equations for theStratosphereMauro Dall’AmicoMunchen 2005¨Data-based Master Equations for theStratosphereMauro Dall’AmicoDissertationan der Fakulta¨t fu¨r Physikder Ludwig–Maximilians–Universitat¨Munchen¨vorgelegt vonMauro Dall’Amicoaus ThieneMu¨nchen, im Mai 2005Erstgutachter: Prof. Dr. J. EggerZweitgutachter: PD Dr. M. DamerisTag der mundlichen Prufung: 28. Juni 2005¨ ¨ContentsList of Figures viList of Tables viiPreface viiiZusammenfassung ixSommario xAbstract xi1 Introduction 11.1 Master equations in climate research . . . . . . . . . . . . . . . . . . . . . 11.2 Stratospheric modes and the troposphere . . . . . . . . . . . . . . . . . . . 32 Data-based master equations 52.1 Architecture of a master equation . . . . . . . . . . . . . . . . . . . . . . . 52.2 Estimating transition coefficients from time series . . . . . . . . . . . . . . 82.3 Probability density and dynamics in phase space . . . . . . . . . . . . . . . 92.4 The Markovian assumption . . . . . . . . . . . . . . . . . . . . . . . . . . 102.5 Correlation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.5.1 Estimate of correlations from time series . . . . . . . . . . . . . . . 112.5.2 Correlations given by a master equation . . . . . . . . . . . . . . . 113 On the numerical properties of master equations 133.1 The Lorenz model extended with Gaussian white noise . . . . . . . . . . . 133.2 Numerical parameters . . . . . . . . . . .