台风

Shapiro and Montgomery (1993) developed the asymmetric balance theory for studying hurricane dynamics;
Wang and Zhang (2003) extended DE91’s PV inversion to TC dynamics, with quasi-balanced algorithm;



Useful for understanding dynamics, unbalanced flows (adjustment), weather prediction, 4D-Var, …
Previous work
Rossby (1947) introduced PV as a conservative, dynamic variable; Hoskins, McIntyre, and Robertson (1985) developed the invertibility principle for balanced flows; Haynes and McIntyre (1987) found no net transport of PVS (PV) across any isentropic surface, and no creation or destroying of PVS within a layer bounded by two isentropic surfaces - challenged by Kieu and Zhang (2009)?
Penetration depth - Scale analysis
A family of surface frontal cyclogenesis from a train of upper-level PV anomalies
QuickTime?and a decompressor are needed to see this picture.
2. QG PV inversion
Define the QGPV
f 0 2 q - f = /f0 + p ( ) p
Given P – f, a 3D -field can be inverted to obtain T and V via the hydrostatic and geostrophic equations - invertibility. One may consider as induced by q – f. Since (1) is linear, the total response [(x, y, p)] to n q concentrations [q1, q2, ... qn] is the sum of the n individual responses (1 + 2 + ... + n) – piecewise PV inversion.
Outline
• Introduction • Review: QGPV diagnostics • Theory of mesoscale PV diagnostics (Davis and Emanuel 1991; Davis 1992) • Applications (Huo, Zhang and Gyakum 1999a,b)
Surface cyclogenesis by an upper-level PV anormaly
Qu i c k T i m e ? a n d a T I F F (L Z W ) d e c o m p re s s o r a re n e e d e d to s e e t h i s p i c t u re .
Qu i c k T i m e ? a n d a T I F F (L Z W ) d e c o m p re s s o r a re n e e d e d to s e e th i s p i c t u re .
Given a PV anormaly with a scale of L near the tropopause, to what extent will it be felt by the flow above and below?
QuickTime?and a decompressor are needed to see this picture.
Zhang, D.-L., W. Cheng and J. Gyakum 2002: The impact of various potential vorticity anomalies on multiple frontal cyclogenesis events. Q. J. Roy. Meteor. Soc., 128, 1847-1878. P, M & N denote the centres of the parent, major, and northern frontal cyclones, respectively.
Potential Vorticity Inversion and Balanced Dynamics
Z.-H. Huo, Da-Lin Zhang and J. Gyakum Department of Atmospheric & Oceanic Science University of Maryland
Kieu and Zhang (2009) extended WZ03 to piecewise PV inversion
Shapiro and Moller (2002) studied the impact of asymmetrical flows on the intensification of Hurricane Opal (1995). Shapiro and Franklin (1999) examined the effects of steering flows on TC movements; Zhang and Kieu (2006) studied the quasi-balanced secondary circulations associated with diabatic heating, vertical wind shear, and the PBL friction; Kieu and Zhang (2009) examined the effects of different PVAs on the intensity and structures of TCs, including the double eyewalls.
Penetration depth - Governing equations
Penetration depth - Deriving the PV invertion equation
Penetration depth - Linearization for piecewise PV inversion
Davis and Emanuel (1991) developed a piecewise PV inversion for NLB flows associated with many different PVAs.
Huo, Zhang and Gyakun (1998) improved the model initial conditions with the oceanic surface observations;
a) Static PV inversion b) Vertical and lateral interactions c) Use of PV inversion to study initial value problems
Huo, Z.-H., D.-L. Zhang and J. Gyakum, 1999a: The interaction of potential vorticity anomalies in extratropical cyclogenesis. Part I: Static piecewise inversion. Mon. Wea. Rev., 127, 2546-2561. Huo, Z.-H., D.-L. Zhang and J. Gyakum, 1999b: The interaction of potential vorticity anomalies in extratropical cyclogenesis. Part II: Sensitivity to initial perturbations. Mon. Wea. Rev., 127, 2563-2575. Zhang, D.-L., W. Cheng and J. Gyakum 2002: The impact of various potential vorticity anomalies on multiple frontal cyclogenesis events. Q. J. Roy. Meteor. Soc., 128, 1847-1878.
Huo, Zhang and Gyakum (1999a) studied the vortex-vortex interactions of upper-level troughs in surface cyclogenesis;
Huo, Zhang and Gyakum (1999b) studied initial-value problems associated with the upper-level merging troughs on the rapid deepening of a snow sຫໍສະໝຸດ Baiduorm. Zhang, Cheng and Gyakum (2002) investigated the influences of upper-level PVAs on a family of surface frontal cyclogenesis with piecewise PV inversion.

Weakness: only applicable to Ro 0.1
Qu i c k T i m e ? a n d a T I F F (L Z W ) d e c o m p re s s o r a re n e e d e d to s e e t h i s p i c t u re .
Previous work (continued)
Wu and Emanuel (1995a, b), and Shapiro and Franklin (1995) showed the importance of large-scale environmental PVAs in determining the movements of hurricanes.
Why interested in the PV and balanced dynamics?

Balanced flows are slowly evolving, long lasting mesoscale evolution can be viewed as a series of quasiequilibrium balanced stage; Conserved or pseudo-conserved properties to trace welldefined features; Balanced flows are mathematically elliptic problems – well behaved;