Abstract
Nonlinear dynamical systems theory has inspired a new set of useful tools to be applied in climate studies. In this work we presented specific examples where information has been gained by the application of methods from nonlinear dynamical systems theory. The main goal is to understand the relative importance of stochastic forcing versus deterministic coupling within the context of Coupled General Circulation Models. This work address this important subject by approaching this goal through the development of a hierarchy of models with increasing complexity that we assert contain the essential dynamics of ENSO. We examined the effect of noise in a low order model and found that it is not restricted to blurring the attractor trajectories in phase space, but includes important changes in the dynamics of the system. The main results indicate that the presence of noise in a nonlinear system has two different effects. The presence of noise acts to increase the maximum Lyapunov exponent and can result in noise induced chaos if the system was originally stable. However, the same arguments are not valid if the original system is already in the chaotic regime, where the noise inclusion acts to decrease the maximum Lyapunov exponent, therefore increasing the system stability. The system of interest includes coupled ocean-atmosphere interactions and here we mimic this interaction by coupling two low order models with very different dominant time scales. These subsystems interact in a complex, nonlinear way and the behavior of the whole system cannot be explained by a linear summation of dynamics of the system parts. We used information theory concepts to detect the influence of the slow system dynamics in synchronizing the fast system in coupled models. We introduced a fast-slow coupled system, where both the slowness of the ocean model and the intensity of the boundary forcing anomalies contribute to the asymmetry and phase locking of both subsystems. The mechanisms controlling the fast modelspread were uncovered revealing uncertainty dynamics depending on the location of ensemble members in the model’s phase space. As an intermediate step between low order models and CGCMs we study the effect of noise on an intermediate complexity model. The addition of gaussian noise to the Zebiak-Cane model in order to understand the effects of noise on its attractor led to a way of estimating the noise level based on the effects of noise on the correlation dimension curves. We investigate the intrinsic predictability of the coupled models used here, and the different time scales associated with fast and slow modes were detected using the Finite Size Lyapunov Exponents. We found new estimates for the prediction horizon of ENSO for the Zebiak-Cane model as well as for the NCAR CCSM3 model and observations. The whole analysis of observations and CCSM3 was possible after applying noise reduction techniques. We also improved our understanding of three different noise reduction techniques by comparing the Local Projective Noise Reduction, the Interactive Ensemble strategy, and a Random Interactive Ensemble applied to CCSM3. The main difference between these two noise reduction techniques is when the process is applied. The Local Projective Noise Reduction can be applied to both model and observations, and it is done a posteriori in phase space, therefore the trajectories to be adjusted already posses the physical mechanisms embedded in them. The Interactive Ensemble approach can only be applied to model simulations and has shown to be a very useful technique for noise reduction since its done a priori while the system evolves instead of a posteriori, besides the fact that it allows to retrieve the spatial distribution of the noise level in physical space.