Singular Vectors and Perturbation Growth Mechanisms for Barotropic Vortices in Horizontal Shear

When a tropical cyclone approaches the midlatitudes and encounters an environment characterized by strong vertical and horizontal shear, the predictability of the cyclones' motion and intensity evolution is often reduced. Singular vectors (SVs) can be used to investigate the influence of uncertainties in the initial state on the forecast error. They reveal the structure and location of the perturbations that experience optimal growth during the forecast time interval. However, the complex structure of SVs in three-dimensional full-physics models impedes their interpretation and the identification of the perturbation growth mechanisms they are based on. Idealised studies with reduced complexity allow for a clearer view on selected growth processes.

In this work we investigate SVs for vortices in horizontal shear using a nondivergent barotropic model. Our results demonstrate that horizontal shear has a significant influence on the structure and growth rates of the SVs. For typical values of midlatitude shear we find strongly increased singular values. The sensitive regions indicated by initial SVs extend considerably further away from the vortex than without shear and are aligned with streamlines in the frame comoving with the vortex. The evolved SVs are characterized by a dipole mode in the vorticity that can be interpreted as a displacement of the vortex.

A detailed analysis of the vortex displacement caused by the leading SVs reveals that the increased growth rates are related to two factors. Firstly, a vortex displaced from its original position in a horizontal shear background experiences a modified steering flow and is thus displaced further. And secondly, anticyclonic shear slows down the advection of perturbations around the vortex core and thus facilitates the displacement of the vortex by the circulation associated with the perturbations.

We discuss the influence of shear strength, grid resolution, viscosity and different vortex profiles on the SVs. In particular, we show that the growth rates for barotropic unstable vortices do not profit from a background shear flow. Finally, we use the results for single vortices to interpret SVs for the interaction of a tropical cyclone and a tropopause front.