Closures for Ensemble-Mean Linear Dynamics with Stochastic Basic Flows

This paper demonstrates the validity of a second-order closure for the ensemble-mean dynamics using the approach of direct numerical ensemble simulations of a linear barotropic model with stochastic basic flows. For various configurations of the stochastic basic flow and external forcing, the deterministic solutions under the second-order closure capture, with remarkable accuracy, the ensemble means and the associated eddy covariance fields of forced responses simulated by a 500-member numerical ensemble. Thus, the second-order closure is found to be adequate for describing the ensemble-mean linear dynamics with stochastic basic flows. Moreover, simple analytical solutions based on the second-order closure also demonstrate that the stochastic component of a superrotational basic flow not only damps the ensemble-mean Rossby waves, but also enhances their eastward propagation. Various examples of ensemble-mean solutions all show the important role played by the stochastic synoptic eddy component of the basic flow in determining the ensemble-mean responses to external forcing. This study supports the notion that linear frameworks of ensemble-mean dynamics under second-order closure are useful tools for describing and understanding the dynamics of the synoptic eddy and the low-frequency flow (SELF) feedback and extratropical atmospheric low-frequency variability.