The Finite Size Lyapunov Exponent (FSLE) is defined as:**
where is the separation in phase
space between two trajectories, one perturbed in a finite way from the
other, and the denominator represents an ensemble average of doubling times.
Here,
(n is an exponent) and r represents
an error level proportionality constant.
The predictability time based on the FSLE is:
We expect (and hope) that this T is greater than the T obtained from the (classical) LCE.
It can be shown that the FSLE and the concommitant T reduce to the LCE and its T in the limit as the perturbation becomes infinitesimal.
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**Most of the remaining material is taken from [6].