Nonlinear Dynamics and Predictability in a Global Circulation Model of the Atmosphere

Abstract

This study analyses the predictability of a global atmospheric circulation model in a dynamical systems framework. Error growth is evaluated by calculating global Lyapunov exponents for varying model setups in terms of resolution and driving temperature forcing. A clear relation between the forcing, the resolution and predictability is found. The global assessment is expanded toward a localised evaluation as finite time Lyapunov exponents are calculated. The fluctuations of these exponents are almost Gaussian distributed and there exists a non negligible probability to observe negative error growth. This is further assessed by linking error growth to the entropy production of dynamical systems. Negative entropy production is conceptually possible in the framework of the fluctuation theorem and the subsequent analysis shows that the fluctuations in error growth are compatible to the laws of the fluctuation theorem. Due to the approximated relation between error growth and entropy production a final proof remains open.

The spatial distribution of error growth and predictability is supported by traditional methods. Eady growth rate and potential vorticity deviations are compared to error growth patterns and similarities are found for potential vorticity, while the Eady growth rate analysis offers some different results. Different concepts of instability and predictability may be responsible for the observed results.

Blocking as an example for a possibly predictable atmospheric setup is analysed for correlation with error growth. Local Lyapunov exponents and blocking seem to be not correlated on a global level. Since a local assessment is not possible with the current framework, the connection between blocking and predictability in terms of error growth remains open.