Sensitivity of the attractor of the barotropic ocean model to external influences: approach by unstable periodic orbits

A description of a deterministic chaotic system in terms of unstable periodic orbits (UPO) is used to develop a method of an a priori estimate of the sensitivity of statistical averages of the solution to small external influences. This method allows us to determine the forcing perturbation which maximizes the norm of the perturbation of a statistical moment of the solution on the attractor. The method was applied to the barotropic ocean model in order to determine the perturbation of the wind field which provides the greatest perturbation of the model’s climate. The estimates of perturbations of the model’s time mean solution and its mean variance were compared with directly calculated values. The comparison shows that some 20 UPOs is sufficient to realize this approach and to obtain a good accuracy.