Statistical analysis and stochastic modelling of atmospheric boundary layer wind / vorgelegt von Thomas Laubrich. 2009
Content
- Motivation
- I Theoretical Background
- Statistics
- Probability and random variable
- Distribution
- Expected value and other characterisations
- Transformation
- Joint distribution and correlation
- Multivariate transformation
- Sum of continuous random variables and stable distributions
- Random sample estimation
- Kolmogorov-Smirnov test
- Stochastic Processes
- Stationary processes
- Autocorrelation function
- delta-correlated processes
- Gaussian processes
- Transformed Gaussian processes
- Discretisation of continuous processes
- ARMA processes
- Turbulence Theory
- The Navier-Stokes equation
- Periodic boundary condition and non-locality
- Conservation laws
- Reynolds number and turbulence
- Kolmogorov 1941 theory for infinite Reynolds number
- Kolmogorov 1962 theory for infinite Reynolds number
- Increment distribution
- Superstatistics
- II Application and Discussion
- Wind Speed Statistics
- Taylor hypothesis
- Non-stationarity and fluctuation statistics
- Increment statistics
- Superstatistics
- Summary
- Discussion of the Superstatistical Algorithm
- The algorithm in a nutshell
- Application to an ideal series
- Application to a series which is not ideal
- Wind speed increments and conclusion
- Fluctuation Statistics of Stochastic Processes and Wind Speed Modelling
- Conditioned fluctuation distribution
- Stationary Gaussian processes
- chi-squared-distributed white noise
- Geometric AR(1) process
- Increment distribution of the geometric AR(1) process
- Fitting the parameters of the geometric AR(1) process to wind speed data
- Summary and Outlook
- III Appendix
- Frequently used Distributions and their Properties
- Binomial distribution
- Gaussian distribution
- chi-squared-distribution
- Log-normal distribution
- Cauchy distribution
- Lévy distribution
- Uniform distribution
- Exponential distribution
- Interpretation of skewness and kurtosis
- Influence of the Ts-estimation
- Derivation of Fluctuation Statistics
- Stationary Gaussian processes
- chi-squared-distributed white noise
- Geometric AR(1) process
- Symmetry of the stationary AR(1) process
- Bibliography
- Acknowledgements
- Versicherung
- Index