Static quasigeostrophic potential vorticity (QGPV) inversion is used to attribute a particular geopotential height field to the QGPV associated with the precursor disturbances. Prognostic QGPV inversion is used to quantify the instantaneous geopotential height tendencies attributable to the flow components obtained from the static inversion. The full flow is partitioned into the following components: the northern upper precursor, the southern upper precursor, and the background flow.
The static-inversion results for the upper precursors exhibit the structure of baroclinic vortices, with maximum amplitude near the tropopause. During the 48 h period spanning the period of study of this event, these vortices rotate cyclonically about a point between them with the rate of rotation increasing as the vortices draw closer together. The background flow appears as a synoptic-scale trough, with the meridional tilt of the trough axis positive (negative) prior to (during) rapid surface cyclogenesis. Prior to surface cyclogenesis, the background flow is also confluent in the vicinity of the vortices, acting to bring them closer together. Rapid surface cyclogenesis occurs as the vortices achieve their closest approach (i.e., ``merge").
Three types of interaction are identified and quantified with the prognostic inversion: vortex--vortex, vortex--retrogression, and background advection. The first interaction is due to vortex-induced flows advecting the QGPV of other vortices; the second interaction is due to vortex-induced flows advecting background QGPV; and the third interaction is due to the background flow advecting vortex QGPV. This interpretation rests upon the assumption that these interactions dominate the ``self-advections'' by individual vortices (i.e., the advection of vortex QGPV by its self-induced flow) and by the background flow. Solutions for the observed case confirm that the vortex--vortex interactions become more robust as the vortices come closer together. However, the background advections are dominant and act to bring the vortices closer together. A local maximum in 500 hPa geopotential height falls in the cyclogenetic region is due to the superposition of advections of the southern vortex by the northern vortex and by the background flow, a combined effect of vortex--vortex and background-advection interactions.
A simple model is proposed that includes the three primary elements of this case: two vortices and background flow. For a barotropic atmosphere on an f-plane, the vortices are represented by rigid vortex patches, and the background flow by a hyperbolic deformation field that is fixed in time. Solutions representative of observed parameters exhibit many of the properties of the observed case, including ``merger.'' Solutions corresponding to merger are found to be extremely sensitive to small changes in the deformation field for a given set of initial conditions describing vortex position, size, and strength, suggesting limitations to the predictability of the merger phenomenon.