Abstract
Abstract Herein we present the first systematic derivation of stochastic mode rate equations for a geophysical hydrodynamic system. Coarse graining concepts from nonequilibrium statistical mechanics are applied to the vorticity equations for barotropic motion on a β-plane. The projection of the initial field equations onto a restricted subspace yields nonlinear stochastic mode rate equations for the physical observables with completely determined statistical properties. It is shown that the usual assumptions of ergodicity and Markovicity are valid only under some very restrictive conditions.
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