Climate Predictions: The Chaos and Complexity in Climate Models

Abstract

Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Gödel’s theorem and Rosen’s definition of complexity and predictability is discussed. Occurrence of chaos in computing the environmental interface temperature from the energy balance equation given in a difference form is pointed out. A coupled system of equations, often used in climate models, was analyzed. It is shown that the Lyapunov exponent mostly has positive values allowing presence of chaos in this system. The horizontal energy exchange between environmental interfaces, which is described by the dynamics of driven coupled oscillators, was analyzed. Their behavior and synchronization, when a perturbation is introduced in the system, as a function of the coupling parameter, the logistic parameter, and the parameter of exchange, were studied calculating the Lyapunov exponent under simulations with the closed contour ofN=100environmental interfaces. Finally, we have explored possible differences in complexities of two global and two regional climate models using their air temperature and precipitation output time series. The complexities were obtained with the algorithm for calculating the Kolmogorov complexity.