Short-time linear response with reduced-rank tangent map∗∗

The recently developed short-time linear response algorithm, which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation, yields high precision of the response prediction. However, the computation of the shorttime linear response formula with the full rank tangent map can be expensive. Here we propose a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation. We establish the conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid, and examine two practical situations, where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.