A Linear Theory of Extratropical Synoptic Eddy Statistics

Abstract

This paper investigates the extent to which the statistics of extratropical synoptic eddies may be deduced from the assumption that the eddies are stochastically forced disturbances evolving on a baroclinically stable background flow. To this end, a two-level hemispheric quasigeostrophic model is linearized about the observed long-term mean flow and forced with Gaussian white noise. The mean flow is baroclinically stable for a reasonable choice of dissipation parameters. Synoptic-scale eddy disturbances can still grow on such a flow, albeit for a finite time, either in response to the stochastic forcing or through baroclinic and barotropic energy interactions with the background flow. In a statistically steady state, a fluctuation?dissipation relation (FDR) links the covariance of the eddies to the spatial structure of the background flow and the covariance of the forcing. Although not necessary, in this study the forcing is assumed to have always the same trivial statistics (white in both space and time). Under this assumption, the FDR states that the geographical distribution of synoptic eddy covariance is controlled solely by the spatial structure of the background flow, which can therefore be used to predict it. All other second-order eddy statistics, such as eddy kinetic energy, momentum and heat fluxes, and power spectra, can then also be predicted. Despite the apparently drastic underlying assumption of synoptic eddy evolution as a stable linear Markov process, the comparisons of the predicted and observed geographical distributions of eddy kinetic energy and momentum and heat fluxes are found to be encouraging. The FDR is also shown to be sensitive enough to basic-state changes that it is able to predict important aspects of observed storm-track variability associated with seasonal and interannual changes of the background flow. The success of these calculations suggests that it is not necessary to invoke either baroclinic instability or the details of the eddy forcing to understand much of the observed spatial and temporal structure of extratropical synoptic eddy statistics. Rather, the dynamics of nonmodal eddy growth in the Pacific and Atlantic jets, and the downstream propagation and dispersion of the eddy activity in the diffluent regions downstream of the jets, appear sufficient for this purpose.