Superposition Effects in Rapid Cyclogenesis—Linear Model Studies

Quasi-geostrophic baroclinic instability theories generally do not satisfactorily explain the large deepening rates often observed in extratropical cyclones. An initial value method by B. Farrell includes the continuous spectrum of neutral waves in addition to the normal modes. Farrell shows that perturbations can grow much faster than normal mode analysis indicates, provided they have a favorable structure. This favorable structure, or superposition, is an important factor in baroclinic instability, because the proper vertical tilt of the growing wave is required to convert zonal available potential energy to eddy potential energy, and then to eddy kinetic energy. This research uses a two-level analytical model and the Navy Operational Regional Atmospheric Prediction System (NORAPS) to investigate the effects of superposition between finite-amplitude perturbations in the lower and upper troposphere. Superposition of a jet streak aloft and a finite amplitude low-level perturbation is also investigated using NORAPS. For given mean flow and static stability conditions, the most rapid growth occurs when relatively strong perturbations at both levels are favorably superposed. The initial zonal (along-stream) superposition is crucial to the subsequent intensification of the low-level perturbation. A westward tilt with height of slightly less than a quarter wavelength is most favorable. If both the upper-level and low-level perturbations are relatively robust, the deepening rate decreases abruptly as the superposition varies from the optimal. The initial meridional superposition only modifies the growth rate that is established by the optimum zonal phase difference. The strength and location of low-level baroclinity or of the upper-level shear vorticity, which depend on the structure of the mean flow, govern whether the most favorable low-level perturbation position is displaced to the south or to the north. In the jet streak case with strong upper-level forcing, the lower perturbation quickly moves to the most favored meridional position under the left front quadrant. These finite amplitude perturbation studies support the critical nature of superposition effects in baroclinic instability.