PREDICTABILITY EXPERIMENTS ON A SIMPLIFIED THERMAL-CONVECTION MODEL -THE ROLE OF SPATIAL SCALES

The amplification of small initial errors in connection with mesoscale atmospheric variability is studied on a simplified thermal convection model. It is found that when the system is perturbed uniformly over t he physical space, the initial regime of error dynamics follows a path way far from the traditional exponential function whose rate is the la rgest positive Lyapunov exponent. It comprises two stages: (1) a trans ient decrease of the initial error as a result of the displacement of the system out of its attractor and (2) a superexponential increase wh ose origin is in the multifractal character of the attractor. Numerica l experiments in which the initial error is introduced selectively in a particular scale reveal that perturbations at larger scales grow fas ter than those at the intermediate and small scales. A qualitative exp lanation of this unexpected behavior based on intrinsic properties of the dynamics such as the local Lyapunov vectors is advanced.