Dynamics of Singular Vectors in the Eady model with nonzero β

A non-modal approach based on the potential vorticity (PV) perspective is used to compute the singular vector (SV) that optimizes surface kinetic energy growth for the βplane Eady model without upper rigid lid. The basic state buoyancy and zonal velocity profile are chosen such that the background potential vorticity gradient is zero. If the f0-plane approximation is made, the SV growth at the surface is dominated by resonance, resulting from the advection of background potential temperature by the interior PV anomalies. This resonance generates a potential temperature (PT) anomaly at the surface. PV unshielding and PV-PT unshielding contribute less to the surface kinetic energy at optimization time. The general conclusion of the present paper is that surface cyclogenesis (of the 48hr SV) is stronger if β is included. Three cases have been considered. In the first case, the vertical shear of the basic state is modified in order to retain zero background potential vorticity gradient. The increased shear enhances SV growth significantly first because of a lowering of the resonant level (enhanced resonance), and second because of a more rapid PV unshielding process. Resonance is the most important contribution at optimization time. In the second case, the buoyancy of the basic state is modified. The surface cyclogenesis is stronger than in the absence of β but less strong than if the shear is modified. It is shown that the effect of the modified buoyancy profile is that PV unshielding occurs more efficiently. The contribution from resonance to the SV growth remains almost the same. Finally the SV is calculated for a more realistic buoyancy profile based on observations. In this experiment the increased value of the surface buoyancy reduces the SV growth significantly as compared to the case in which the surface buoyancy takes a standard value. All growth mechanisms are affected by this change in surface buoyancy.