Interpreting Petterssen s Extratropical Cyclone* Self-Development Eqn. (based in part on notes by James T. Moore)

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1 Interpreting Petterssen s Extratropical Cyclone* Self-Development Eqn. (base in part on notes by James T. Moore) P.S. Market ATMS-97 Avance Synoptic Meteorology University of Missouri *Works for anticyclones too!

2 Introuction Seeks to escribe/explain influences of various physical processes on the evelopment of cyclones an anticyclones Expans on the work of Bjerknes an Sutcliffe (1947)

3 Introuction Sutcliffe (1947) expression aapte by Petterssen (1956) to become: 1 t V L L R f 1 R A T S H A B C D

4 Introuction Where Term A is the vorticity avection at the level of non-ivergence (LND) Term B is the Laplacian of the thickness avection in the 1-LND layer Term C is the Laplacian of the stability term Term D is the Laplacian of the iabatic heating/cooling term

5 Term A: V L L Vorticity Avection at the level of non-ivergence (LND) Positive Vorticity Avection (PVA): V L L This woul make 1 t Negative Vorticity Avection (NVA): V L L This woul make 1 t

6 Term B: 1 f V The Laplacian of the thickness avection (A T ) in the 1-LND layer. First, we note the sign of V uner col an warm avection patterns

7 Term B Col Air Avection (CAA) = V cos V Where = the angle between an CAA = V V V

8 Term B Warm Air Avection (WAA) = V cos V WAA = V V

9 Asie: Laplacians Now, recall that the Laplacian measures the change in the change in the fiel Or, more simply the change in graient Or, more formally the secon erivative of a scalar fiel It is sensitive to the non-linearity of a fiel an its shape.

10 Asie: Laplacians Non-linearity factor col air avection C B A warm air avection x ( Temp. Avect.) A C B 5 ( 1) () x ( Temp. Avect.) since strong CAA weakens to weak WAA in the easterly irection

11 Asie: Laplacians Non-linearity factor Thus, the entire term 1 A T An cyclogenesis is encourage, i.e., f 1 t Note: 1) If the CAA or WAA were constant everywhere, the first an secon erivatives =. ) If the CAA or WAA changes linearly, then but A T A T

12 Asie: Laplacians Shape factor Generally in a trough of a scalar fiel, an in a rige of a scalar fiel This can be visualize in the examples that follow

13 Asie: Laplacians Consier a Thermal Trough With the exception of point, the temperatures surrouning point are warmer. T T+1 T T1 T T3 T4 4 T T T in a thermal trough

14 Asie: Laplacians Consier a Thermal Rige With the exception of point 4, the temperatures surrouning point are cooler T+1 T T+ T in a thermal rige

in the heart of the WAA) A T», an A T. Thus: 1 A T f an surface cyclogenesis encourage.

15 Laplacians an Term B So, if col an warm air avection patterns get wrappe up in the cyclone, then cyclogenesis / anticyclogenesis is enhance: -5 C/hr C/hr In the WAA rige (esp. in the heart of the WAA) A T», an A T. Thus: 1 A T f an surface cyclogenesis encourage. -1 C/hr Bright blue fill +5 C/hr +1 C/hr Bright re fill In the CAA trough (esp. in the heart of the CAA) A T «, an A T. Thus: 1 A T f an surface cyclogenesis encourage.

16 Term C: R p 1 fg ln p LND Laplacian of the stability term Controlle by the signs of ω an ( γ γ ) If static stability term, S g p p ln 1 LND then S tens to be > (see example with thermal trough)

17 Upwar motion with static stability < an Assume that S< an S R S f 1 t Generate anticyclogenesis evelopment at 1 mb level Act as a governor on cyclone evelopment

18 Upwar motion with statically unstable conitions < an Assume S> an S R 1 S f t Generate cyclogenesis evelopment at 1 mb Unlikely to have upwar motion Or large area of static instability present Less governor than over the cyclone region

19 Downwar motion an statically stable > an Assume S> an S R S f 1 t Like those in case 1 Associate with an anticyclone Act like governor on anticyclonic vorticity at 1 mb

20 Downwar motion an statically unstable conitions > an Assume S< an S R S f 1 t Similar to case Not likely to have large areas of statically unstable air in an near a wave cyclone.

21 Term D: R Q P 1 1 f C p t ln P LND Laplacian of the iabatic heating/cooling term. Controlle by Q t Thus, the right configuration of latent heat release or surface heat flux from warm water Great Lakes Gulf Waters Enhance cyclogenesis Col waters/ anticyclogenesis

22 Summary of Petterssen First two terms are ominant terms Vorticity avection at the LND Laplacian of thickness avection Stability term acts like a governor Important over small regions

Synoptic-Dynamic Meteorology in Midlatitudes

Synoptic-Dynamic Meteorology in Midlatitudes VOLUME II Observations and Theory of Weather Systems HOWARD B. BLUESTEIN New York Oxford OXFORD UNIVERSITY PRESS 1993 Contents 1. THE BEHAVIOR OF SYNOPTIC-SCALE,