Low-frequency regime transitions and predictability of regimes in a barotropic model

Predictability of flow is examined in a barotropic vorticity model that admits low frequency regime transitions between zonal and dipolar states. Such transitions in the model were first studied by Bouchet and Simonnet (2009) and are reminiscent of regime change phenomena in the weather and climate systems wherein extreme and abrupt qualitative changes occur, seemingly randomly, after long periods of apparent stability. Mechanisms underlying regime transitions in the model are not well understood yet. From the point of view of atmospheric and oceanic dynamics, a novel aspect of the model is the lack of any source of background gradient of potential-vorticity such as topography or planetary gradient of rotation rate (e.g., as in Charney & DeVore '79). We consider perturbations that are embedded onto the system's chaotic attractor under the full nonlinear dynamics as bred vectors---nonlinear generalizations of the leading (backward) Lyapunov vector. We find that ensemble predictions that use bred vector perturbations are more robust in terms of error-spread relationship than those that use Lyapunov vector perturbations. In particular, when bred vector perturbations are used in conjunction with a simple data assimilation scheme (nudging to truth), we find that at least some of the evolved perturbations align to identify low-dimensional subspaces associated with regions of large forecast error in the control (unperturbed, data-assimilating) run; this happens less often in ensemble predictions that use Lyapunov vector perturbations. Nevertheless, in the inertial regime we consider, we find that (a) the system is more predictable when it is in the zonal regime, and that (b) the horizon of predictability is far too short compared to characteristic time scales associated with processes that lead to regime transitions, thus precluding the possibility of predicting such transitions.