The predictability of extratropical cyclones: Nonlinear sensitivity to localized potential-vorticity perturbations

There is a range of phenomena which, if misrepresented in a numerical weather prediction model, could cause localized finite-amplitude errors in the potential vorticity (PV). Examples are: convective systems, the tropopause PV trough, and orographic PV perturbations. Motivated by this, the sensitivity of short-range cyclone forecasts (up to two days) to localized finite-amplitude initial PV anomalies is investigated using a method termed 'PV-sensitivity mapping'. An initial PV-anomaly perturbation is applied at each grid point in turn and the corresponding impact in a nonlinear cyclone development is computed. In contrast to the adjoint method, there is no linear approximation. The PV-sensitivity map depicts the forecast time impacts (in energy and pressure) for each initial spatial location of PV perturbation. A nonlinear three-dimensional quasi-geostrophic model is used because it has PV as a prognostic variable, is numerically efficient, and simulates the essence of cyclogenesis. The sensitivity maps are calculated for a dry and a moist cyclone scenario, and for a synoptic-scale and mesoscale initial PV perturbation. The degree of nonlinearity in error growth is significant for the moist case. The most sensitive regions for both cases are in the region of the steering level and the incipient cold and warm fronts. A physical interpretation using PV thinking is given.