IMPACT OF TRANSIENT ERROR GROWTH ON GLOBAL AVERAGE PREDICTABILITY MEASURES

The divergence of initially close trajectories sets the limit of dynam ical predictability for infinitesimally small errors; its global avera ge measure is given by the first Liapunov exponent. It is shown, withi n the framework of low-order dynamical systems, that global average er ror evolution is subject to transient growth. Random errors and analog s are studied and both are found to exhibit transient behavior. The de finition of average error that gives the correct asymptotic exponentia l growth rate is shown to be the one introduced by Lorenz. Transient s uperexponential growth reduces the predictability time when errors hav e a finite initial size and explains the apparent dependence of averag e error growth on the initial error size. The consequences upon short- range forecasting are discussed.