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John W. Nielsen-Gammon
and
David A. Gold

Abstract

Quantitative diagnosis of low-Rossby-number flows using potential vorticity (PV) includes using elements of PV advection to deduce instantaneous tendencies of the balanced atmospheric state, most commonly the geopotential field. This technique, piecewise tendency diagnosis (PTD), is here applied with the prognostic balance equations (Bal-PTD) to obtain a quantitative dynamical diagnosis that in principle may be much more accurate than similar diagnoses using the quasigeostrophic (QG) equations.

When both are applied systematically to a case of rapid oceanic cyclogenesis, differences are found to arise owing to a variety of factors. The dominant factor is differences in the vertical influence of PV anomalies, which affects the partitioning between local and remote processes. QG overestimates the effect of lower-level PV, including surface potential temperature, in amplifying and controlling the motion of the upper-level system. Other differences are found, but overall the QG diagnosis gives results that are qualitatively similar to the nonlinear balance diagnosis. Quantitative accuracy requires the use of Bal-PTD.

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John W. Nielsen-Gammon
and
Randy J. Lefevre

Abstract

The intensification and evolution of midlatitude upper-tropospheric mobile troughs may be viewed in terms of the isentropic advection and deformation of the tropopause potential vorticity gradient. The potential vorticity viewpoint allows one to qualitatively assess observed events in the context of existing theories of mobile trough genesis, such as baroclinic instability or downstream development. In order to quantitatively determine the role of distinct dynamical process, the method of piecewise tendency diagnosis, or PTD, is developed. PTD is an extension of piecewise potential vorticity inversion applied to height tendencies, with the forcing terms in the quasigeostrophic height tendency equation partitioned into potential vorticity advection associated with distinct dynamical processes.

A particular case of mobile trough genesis, which occurred during 1–4 December 1980 over North America is diagnosed using PTD. Although about 20% of the intensification of the trough was due to superposition and amplification of the low-level cyclone during surface cyclogenesis, the diagnosis focuses on the height perturbation induced by the upper-level PV anomaly. The trough is found to have formed primarily through down-stream propagation of Rossby wave energy from disturbances over the, northwest Pacific. As the trough amplified, it interacted with an existing surface temperature gradient over the central United States and produced a front wave. As the frontal wave intensified, the favorable vertical tilt allowed mutual baroclinic amplification of the upper and lower systems. Eventually, the upper-level trough grew to sufficient amplitude that it began to lose energy downstream through wave propagation and the trough began to weaken even though a favorable tilt remained between the upper and lower systems. Horizontal deformation and small-scale vortex interaction were less important to the overall development of the mobile trough, but contributed significantly to intensification at various times in its lift cycle. The direct effects of the remaining dynamical processes excluding latent heating and friction, which were not diagnosed) were insignificant.

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Matthew S. Wandishin
,
John W. Nielsen-Gammon
, and
Daniel Keyser

Abstract

The process of tropopause folding is studied in the context of the life cycle of baroclinic waves. Previous studies of upper-level frontogenesis have emphasized the role of the vertical circulation in driving stratospheric air down into the midtroposphere. Here, a potential vorticity–based approach is adopted that focuses on the generation of a folded tropopause. To facilitate comparison of the two approaches, the diagnosis is applied to the upper-level front previously simulated and studied by Rotunno et al. The potential vorticity approach clarifies the primary role played by the horizontal nondivergent wind in producing a fold and explains why folding should be a common aspect of baroclinic development.

Between the trough and upstream ridge, prolonged subsidence within a region of weak system-relative flow generates a tropopause depression oriented at an angle to the large-scale flow. The large-scale vertical shear then locally increases the slope of the tropopause, eventually leading to a tropopause fold. In contrast, tropopause folding in the base of the trough is caused by the nondivergent cyclonic circulation associated with the surface thermal wave. The winds associated with the thermal wave amplify the potential vorticity wave aloft, and these winds, which decrease with height, rapidly generate a tropopause fold within the trough.

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