Abstract :
Stochastic dynamical systems have been used to model a broad range of atmospheric and oceanic
phenomena. Previous work has focused on the stochastic differential equation formulation of these
systems, has largely remained in a single coordinate system, and has highlighted the role of nonnormality
of the deterministic dynamics. Here, the coordinate independent properties of stochastic
dynamical systems are studied. The properties previously attributed to non-normality, which can be
removed by a coordinate transformation, are more fundamentally seen to be coordinate-dependent
manifestations of violations of detailed balance. Systems violating detailed balance can both amplify
and rectify the random forcing.Newcoordinate-invariant measures of noise amplification are introduced
and shown to achieve their lower bound when detailed balance is satisfied. Rectification results in a
coherent phase space velocity which gives rise to a structured nonzero flux of all physically important
quantities such as energy and momentum. The qualitative and quantitative features of these fluxes
provide new predictions which can be used to further validate previously proposed stochastic models
of geophysical systems
