The predictability of large-scale wind-driven flows

Abstract. The singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving examples of wind-driven, double-gyre circulations in different flow regimes are explored. By changing the Reynolds number in simple quasi-geostrophic models of the wind-driven circulation, steady, weakly aperiodic and chaotic states may be examined. The singular vectors of the steady state reveal some of the physical mechanisms responsible for optimally growing perturbations. In time-dependent cases, the dominant singular values show significant variability in time, indicating strong variations in the predictability of the flow. When the underlying flow is weakly aperiodic, the dominant singular values co-vary with integral measures of the large-scale flow, such as the basin-integrated upper ocean kinetic energy and the transport in the western boundary current extension. Furthermore, in a reduced gravity quasi-geostrophic model of a weakly aperiodic, double-gyre flow, the behaviour of the dominant singular values may be used to predict a change in the large-scale flow, a feature not shared by an analogous two-layer model. When the circulation is in a strongly aperiodic state, the dominant singular values no longer vary coherently with integral measures of the flow. Instead, they fluctuate in a very aperiodic fashion on mesoscale time scales. The dominant singular vectors then depend strongly on the arrangement of mesoscale features in the flow and the evolved forms of the associated singular vectors have relatively short spatial scales. These results have several implications. In weakly aperiodic, periodic, and stationary regimes, the mesoscale energy content is usually relatively low and the predictability of the wind-driven circulation is determined by the large-scale structure of the flow. In the more realistic, strongly chaotic regime, in which energetic mesoscale eddies are produced by the meandering of the separated western boundary current extension, the predictability of the flow locally tends to be a stronger function of the local mesoscale eddy structure than of the larger scale structure of the circulation. This has a broader implication for the effectiveness of different approaches to forecasting the ocean with models which sequentially assimilate new observations.