Constructing fast-growing perturbations for the nonlinear regime

Abstract

An iterative method is presented to determine perturbations that maintain their growth rate in the medium-range period. In order to study the efficiency of this approach, experiments are performed with a three-level quasigeostrophic model triangularly truncated at wavenumber 21, together with its tangent linear and adjoint version. The contribution of model errors to the perturbation growth is omitted. When the method is applied to singular vectors, modified perturbations are obtained that show substantially larger perturbation growth in the medium range than the original singular vectors. Large nonlinear interactions between the evolving perturbation and the reference forecast orbit obstruct the fast-growing property of the singular vectors. In the modification procedure, part of this nonlinear error dynamics is taken into account. The spatial patterns of modified and original perturbations still show a great resemblance. Individual cells in the patterns generally differ only in amplitude, not in their location.