Used Statistical Methods
Bifurcation diagram for the 2-layer LOM. It is shown the dependence of the model's state on the temperature difference between equator and pole, T, and the maximum orographic height, hmax. V means vacillations and C chaos.
In order to study the spatio-temporal structure of the climate variability extended long-term runs of different LOM over 10,000 years have been carried out.
The LOM reveal qualitative different solutions for varying forcing parameters. In dependence of the meridional temperature gradient between equator and pole and the height of the orography the figure shows the bifurcation diagram.
It was found that the model shows chaotic behaviour for realistic values of the meridional temperature gradient and the orographic height.
The Empirical Orthogonal Function (EOF) analysis proved to be a qualified tool to determine the most significant structures in the fluctuations of meteorological fields. A set of EOFs for time series is generated by the covariance matrix A which is defined by the components of the data field
Here, ej (j=1,...,J) are the EOFs, and the eigenvalues lj describe the fraction of the total variance represented by the given EOF; J is their total number. By projecting the data vector on the set of EOFs at any time level the time series can be depicted by EOFs amplitudes. The time-dependent amplitude of ej is called the jth principal component (PCj) of the time series.
In order to determine the characteristic periods of this time series different methods of time series analyses are used. This includes the determination of the spectral distribution of energy (power spectra) by means of Fourier transform as well as time-scale analyses by means of Wavelet transform.