Optimal initial perturbations for 2 cases of extratropical cyclogenesis

The skill of optimal initial perturbations in representing the initial phase of observed extratropical cyclogenesis is tested for two synoptic cases using three-dimensional and four-dimensional basic states similar to the actual environment in which the observed cyclones are embedded. It is assumed that the initial phase of extratropical cyclogenesis is governed by the dry linear dynamics. A linearized version of a dry regional forecast model is used to simulate the linear evolution. The optimal initial perturbations are defined similar to the optimal modes by Farrell: as perturbations that maximize a given scalar measure of the perturbation amplitude within a finite time interval. These perturbations are computed numerically subject to a prescribed initial constraint. The scalar measure and the initial constraint are defined using physical quantities whose amplitude represent the strength of the perturbation either in the entire integration domain or within a local volume enclosing the observed cyclone. The solutions of several optimal initial perturbation problems are compared to the true perturbation that is defined as the difference between the three-dimensional and four-dimensional basic state and the synoptic state associated with the observed cyclones as represented by the ECMWF analysis and by the dry forecast, respectively. For all basic states the optimal perturbations computed to maximize the scalar function in the local domain located in the area of the actual cyclone are more similar to the true perturbation than the perturbations that maximize the energy in the whole integration domain. Overall, however, our results show that none of the optimal perturbations computed in this study exactly capture the evolution of the true perturbation associated with the observed cyclogenesi for the synoptic cases that are used. This does not imply inexistence of other optimal perturbations that may fit the actual development better, but indicates that the optimal initial perturbation approach does not offer unique way to describe the initial development of the extratropical cyclones.