Direct Statistical Simulation: Ensemble Averaging

Low­-order statistics of geophysical fluid models may be directly accessed by solving the equations of motion for the equal-­time cumulants. We investigate a variant of the second ­order cumulant expansion (CE2) in which zonal averaging is replaced by ensemble averaging. The approach is tested on two different highly idealized models of planetary atmospheres on a spherical geodesic grid: A stochastically-forced barotropic jet, and a deterministic jet relaxed toward an unstable profile. The results are compared to the traditional approach of accumulating statistics via numerical simulation, and to zonally-averaged CE2.