Predictability of atmospheric eddy motions and reversal changes in systems evolutions.

This paper contains our study on the importance and universality of eddy motions in atmospherical motions. By using the theory of blow-ups of physical evolutions and the method of fractal dimensions, we study the predictability of eddy motions. Our results indicate that these methods basically provide predictions with roughly the same amount of time before the arrivals of atmospherical motions. Also, it is found that the time scale of the predicted arrival of an atmospherical motion is dependent on the special scale of the eddy system and external parameters, such as geographical locations, changes of seasons, etc. If seen from the point of view of the whole evolutionary chains of systems, the predicable time period before the arrival of an eddy system essentially reflects the time period before a reversal change occurs in the system so that predictability should not be considered as continuity of the initial values.