A potential vorticity and wave activity flux diagnosis of optimal perturbation evolution

A diagnosis of singular vector (SV) evolution (computed for the L2 streamfunction norm) in the Eady model using potential vorticity (PV) and Eliassen-Palm (E-P) flux diagnostics is performed. In addition, a partitioning of the vertical component of the E-P flux vector based on the result s of the piecewise PV inversion is introduced to more clearly elucidate the fundamental mechanisms for SV amplification.

The initial PV structures of the Eady model SVs on both the long and short wave sides of the Eady model short wave cutoff are characterized by initially upshear tilted interior PV anomalies. The results of the PV and the E-P flux diagnostics for optimal perturbations reveal a three stage process for the SV evolution: 1) A superposition of interior PV anomalies (diagnosed by a positive vertical component of the E-P flux), 2) a subsequent intensification (characterized by maxima in the E-P flux near the boundaries) of the SV boundary potential temperature anomalies (BTAs) by winds attributed to interior PV, and 3) finally a transient or sustained mutual interaction between the BTAs (associated with a nearly non-divergent interior E-P flux). PV inversion demonstrates that a significant fraction of the observed SV amplification may be attributed to the initially upshear tilted PV anomalies, and that the initial BTAs, while important in describing the initial SV structure, play a minimal role in the subsequent evolution. The results of the experiments in which the Eady model SV structures were altered by removing either the BTAs or the interior PV suggest that, data assimilation schemes which disproportionately weight targeted surface observations to targeted tropospheric wind and temperature observation s may result in a forecast correction that is either overdone (for short optimization times) or insufficient for optimization times comparable or larger than the time required for the PV to be rendered vertical by the shear flow.