Optimal initial perturbations for 2 cases of extratropical cyclogenesis

The skill of optimal initial perturbations in representing the initial phase of observed extratropicalcyclogenesis is tested for two synoptic cases using three-dimensional and four-dimensionalbasic states similar to the actual environment in which the observed cyclones are embedded. Itis assumed that the initial phase of extratropical cyclogenesis is governed by the dry lineardynamics. A linearized version of a dry regional forecast model is used to simulate the linearevolution. 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 afinite time interval. These perturbations are computed numerically subject to a prescribed initialconstraint. The scalar measure and the initial constraint are defined using physical quantitieswhose amplitude represent the strength of the perturbation either in the entire integrationdomain or within a local volume enclosing the observed cyclone. The solutions of severaloptimal initial perturbation problems are compared to the true perturbation that is defined asthe difference between the three-dimensional and four-dimensional basic state and the synopticstate associated with the observed cyclones as represented by the ECMWF analysis and by thedry forecast, respectively. For all basic states the optimal perturbations computed to maximizethe scalar function in the local domain located in the area of the actual cyclone are more similarto the true perturbation than the perturbations that maximize the energy in the whole integrationdomain. Overall, however, our results show that none of the optimal perturbations computedin this study exactly capture the evolution of the true perturbation associated with the observedcyclogenesi for the synoptic cases that are used. This does not imply inexistence of other optimalperturbations that may fit the actual development better, but indicates that the optimal initialperturbation approach does not offer unique way to describe the initial development of theextratropical cyclones.