Wednesday, 16 January 2002: 5:00 PM
Predictability of linear stochastic dynamics
During the past decade, the paradigm for error growth and
predictability in Earth Science systems has expanded from the classical notion of exponentially growing, normal mode instabilities to include the behavior of nonnormal evolution operators. Generally speaking, error growth in nonnormal systems is magnified compared to that of equivalent normal systems. Nonnormal systems have faster growing initial perturbations. The error variance of nonnormal systems forced with unitary noise is larger than that of equivalent normal systems. The enhanced error growth of nonnormal systems raises the question of whether predictability is lost at a faster rate in a nonnormal systems than in an equivalent normal system.
Here we show analytically that for linear, time-independent stable dynamics where the source of error is unitary stochastic forcing, nonnormality increases predictability as measured by the size of forecast error relative to climatological variability. The theoretical results are illustrated in some simple physical models.