Can Quasigeostrophic Turbulence Be Modeled Stochastically?

Abstract

Abstract Numerically generated data of quasigeostrophic turbulence in an equilibrated shear flow are analyzed to determine the extent to which they can be modeled by a Markov model. The time lagged covariances are collected into a matrix, Cτ, and are substituted into the fluctuation-dissipation relation for a first-order Markov model with white noise forcing CτC0−1 = exp (Aτ),to determine whether the relation is satisfied for a single dynamic operator A. The dynamic operator obtained by inverting the relation was found to depend on time lag. In particular, for small time lags (τ < 1 day), the eigenvectors and imaginary eigenvalues were independent of time lag, while the damping rates increased linearly with time lag. It is shown analytically that precisely this discrepancy occurs when the relation is applied to data generated by a red noise Markov model using a time lag that is small compared to the decorrelation time of the noise. Although a fourth-order Markov model with white noise can more accurately ...