Basic dynamics on temporal variations of the atmospheric predictability is investigated both with conceptual models of one- and two-dimensional dynamical systems and with a simplified atmospheric circulation model introduced by Legras and Ghil (1985). As a measure of the predictability, we use the Lorenz index alpha that gives an ensemble average of the error growth rate for a prescribed time interval (Lorenz, 1965). We try to find the relation between the predictability variation and quasi-stationary (QS) states, which occur when the trajectory of the solution passes near a local minimum point (MP), which is either an unstable stationary point (US) or a non-stationary local minimum point (MIN), in phase space. At a MIN the speed of the trajectory has a local minimum value in phase space (Mukougawa, 1988).
In any one-dimensional dynamical system there is a unique relation that alpha increases monotonically during QS states. In multi-dimensional dynamical systems, on the other hand, there is not such a relation between alpha and the QS states. During QS states related to a US, it is possible that alpha varies in more than one manner; alpha increases monotonically, decreases monotonically, has a maximum, or has a minimum, depending on the trajectory. During QS states related to a MIN, on the assumption that the trajectory exists close enough to the MIN, alpha shows one of the four relations mentioned above depending on the property of each MIN.
If we consider trajectories only on the attractor, every QS state related to MP has its own tendency in the variation of alpha, which is one of the four relations. The same relation as in one-dimensional dynamical systems is found in some chaotic solutions in the Legras and Ghil model, although it seems to be just one of the four possibilities.