This was also
noted by Aurell et al (1996, 1997) who defined a Finite Size Lyapunov
Exponent (FSLE):

The FSLE is clearly related to the
Average Bred Growth Rate

ABGR
is easier to compute than FSLE, but they both converge to the

Lyapunov
exponent for infinitesimal amplitudes and intervals

Boffetta
et al (1998) used a coupled fast/slow Lorenz model to show

that
the predictability is a function of the

tolerance
Δ,
and for small amplitude

fast
modes, predictability is larger than

the
Lyapunov estimation