Unstable periodic orbits and sensitivity of the barotropic model of the atmosphere

Abstract

In this paper we consider the problem of estimation of the sensitivity of the barotropic atmosphere model to small external impacts, which consist in a change of the external forcing of the system. The general concept of the method is based on approximation of the point distribution density on the attractor of the system with the use of its unstable periodic trajectories. Under this approximation, orbits are taken into account according to their weights related to the characteristics of their instability. Approximately 2000 unstable periodic trajectories were found for the considered model, and approximate response operators of the system mean state to small external perturbations were calculated for different forms of setting for weight coefficients. A comparison of the accuracy of the constructed approximations of the response operator was performed. It is shown that under a correct choice of the weight function one can represent the leading left singular vectors of the response operator with a good accuracy (the correlation level is 0.75 – 0.95), whereas the representation accuracy of the leading right singular vectors (optimal actions) is slightly lower (0.4 – 0.8).