Impact of Transient Error Growth on Global Average Predictability Measures

Abstract

The divergence of initially close trajectories sets the limit of dynamical predictability for infinitesimally small errors; its global average measure is given by the first Liapunov exponent. It is shown, within the framework of low-order dynamical systems, that global average error evolution is subject to transient growth. Random errors and analogs are studied and both are found to exhibit transient behavior. The definition of average error that gives the correct asymptotic exponential growth rate is shown to be the one introduced by Lorenz. Transient superexponential growth reduces the predictability time when errors have a finite initial size and explains the apparent dependence of average error growth on the initial error size. The consequences upon short-range forecasting are discussed.