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

Mauro Dall'Amico

Description

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 . . . . . . . . . . .

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2005
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

Data-based Master Equations for the Stratosphere

Mu ¨ nchen2005

Mauro Dall’Amico

Data-based Master Equations for the Stratosphere

Mauro Dall’Amico

Dissertation anderFakult ¨ atf ¨ urPhysik derLudwig–Maximilians–Universit ¨ at Mu ¨ nchen

vorgelegt von Mauro Dall’Amico aus Thiene

M ¨ unchen,imMai2005

Erstgutachter: Prof. Dr. J. Egger Zweitgutachter: PD Dr. M. Dameris Tagderm ¨ undlichenPru ¨ fung:28.Juni

2005

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1 Introduction 1.1 Master equations in climate research. . . . . . . 1.2 Stratospheric modes and the troposphere. . . . .

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Sommario

Zusammenfassung

Abstract

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Data-based master equations 2.1 Architecture of a master equation. . . . . . . . . 2.2 Estimating transition coefficients from time series 2.3 Probability density and dynamics in phase space. 2.4 The Markovian assumption. . . . . . . . . . . . 2.5 Correlation functions. . . . . . . . . . . . . . . . 2.5.1 Estimate of correlations from time series. 2.5.2 Correlations given by a master equation.

On the numerical properties of master equations 3.1 The Lorenz model extended with Gaussian white noise. . . . . . . . . . . 3.2 Numerical parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Grid size. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 3.2.2 Time series length. . . . . . . . . . . . . . .. . . . . . . . . . . . 3.2.3 Time resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Dimension of the master equation. . . . . . . . . . . . . . . . . . .

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Master equations for stratospheric time series 4.1 Time series of stratospheric climate indices. . . . . . . . . . . . . 4.2 The QBO and the arctic stratosphere. . . . . . . .. . . . . . . . 4.3 The role of the 11-year solar cycle. . . . . . . . . .. . . . . . . . 4.4 The Arctic Oscillation in the stratosphere and in the troposphere

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List of Figures

Contents

Preface

List of Tables

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A

B

Conclusions

List of acronyms

List of symbols

Bibliography

Acknowledgements

Curriculum Vitae of the author

Contents

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List

2.1

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20

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Phase-line intervals and transition coefficients. . . . . . . . .

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The Lorenz attractor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time series of the Lorenz model with stochastic forcing (LMSF). . . . . . Trajectory of the LMSF. . . . . . . . . . . . . . . . . . . . . . . . . . . . Choice of an adequate grid size. . . . . . . . . . . . . . . . . . . . . . . . Noise-to-signal ratio for growing time series length. . . . . . . . . . . . . . Case study. Evolution of an ensemble of initial conditions. . . . . . . . . . PDF forecasts delivered by master equations (role of time series length). . Observed state densityρfor short time series of the LMSF. . . . . . . . . Skills of some master-equation forecasts (role of time series length). . . . . Convergence of transition matrixT(role of the time series length). . . . . PDF forecasts delivered by master equations (role of time resolution). . . Understanding the role of time resolution. . . . . . . . . . . . . . . . . . . Correlation functions (role of time resolution). . . . . . . .. . . . . . . . A two-dimensional master equation (role of the number of variables). . . .

Preparation of a time series ofT ′ from the ERA-40 (daily) daily means. . Time series ofQ I andU e20 . . . . . . . . . . . . . . .. . . . . . . . . . . . Time series ofT ′ . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . Variable set (Q I ,T ′ ,U e20  of states, phase-space partition): distribution. . Correlation functions,Q I ,T ′ , andU e20 . . . . . . . . . . .. . . . . . . . . Evolution of a PDF cloud delivered by a master equation. . . . . . . . . . Mean trajectories in the (Q I ,T ′ ,U e20 ) phase space. . . . . . .. . . . . . . Standard deviation of some PDF clouds. . . . . . . . . .. . . . . . . . . A two-dimensional master equation for the stratosphere. . . . . . . . . . . Time series of the solar radio flux at a wave length of 10.7 cmS 10 7 . . . .  Variable set (Q I ,T ′ ,S 107  of states, phase space partition): distribution. . Correlation functions,Q I ,T ′ , andS 107 . . . . . . . . . . .. . . . . . . . . Mean trajectories (Q I ,T ′ ,S 107 ), QBO East and solar maximum. . . . . . Mean trajectories (Q I ,T ′ ,S 107 ), QBO West and solar maximum. . . . . . Mean trajectories (Q I ,T ′ ,S 107 ), QBO East and solar minimum. . . . . . Mean trajectories (Q I ,T ′ ,S 107 ), QBO West and solar minimum. . . . . . Time series ofA 10 ,A 100 , andA 850 , 1957 - 1972. . . . . . . . . . . . . . . . Time series ofA 10 ,A 100 , andA 850 , 1972 - 1987. . . . . . . . . . . . . . . . Time series ofA 10 ,A 100 , andA 850 , 1987 - 2002. . . . . . . .. . . . . . . . Variable set (A 10 ,A 100 ,A 850  of states, phase space partition): distribution.

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Correlation functions, Arctic Oscillation indices. Mean trajectories in the (A 10 ,A 100 ) phase plane. Mean trajectories in the (A 10 ,A 850 ) phase plane. Mean trajectories in the (A 100 ,A 850 ) phase plane.

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List of Figures

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