Atms 4320 / 7320

1. Atms 4320 / 7320 Lab 8 Cyclone development

2. Cyclone development • Cyclone development or Decay occurs when the local pressure tendency changes. Thus, we would get development (decay) at the center when local pressures are falling (rising). With high pressure we argue the opposite. • These concepts apply whether we are looking at a system at the surface or aloft.

3. Cyclone Development • Diagramatically or mathematically:

4. Cyclone Development • At center: • This applies to closed systems or open waves, with an open wave we must look along the trough or ridge axis.

5. Cyclone Development • Thus, to comment on development, we want to quantify this via changes in the mass field (height or pressure tendencies), or changes in the circulation (vorticity tendencies) • Recall, we said that various dynamic and thermodynamic relationships can be used to represent atmospheric forcing. These forcing mechanisms result in pressure changes at the surface.

6. Cyclone Development • Thus, we can derive equations that measure development in terms of height and pressure changes (LHS), that occur as the result of well-known dynamic and thermodynamic forcing processes (RHS) • Thermodynamic (K/s) Dynamic (1/s) • -Temp Adv. -Vort. Adv. • -Radiative heating -vort. Tilting • -Latent Heating -divergence • -adiabatic heating -friction • -sensible heating

7. Cyclone Development • Equations- Vorticity equation:

8. Cyclone Development • Then there is the “Sutcliffe-type” equations (variations of the vorticity equations, the first of which was the Sutcliffe equation (1947), which examined the “thermal vorticity field” (znon-div. level - zsurf). • The latest and most comprehensive is the Zwack - Okossi equation. Zwack and Okossi (1986, MWR, 655 - 666) – P. Zwack 1943 – 2005 (RIP).

9. Cyclone Development • This is a geostrophic vorticity tendency equation. • Recall geostrophic vorticity is proportional to the height field, thus geostrophic vorticity tendency is proportional to height (pressure tendency), or the mass field.

10. Cyclone Development • Geostrophic Vorticity • Also, geostrophic vorticity, like geostrophic winds are close to the observed tendencies.

11. Cyclone Development • Now, the Z-O equation is derived as such; • We start with hydrostatic balance:

12. Cyclone Development • Then, invoke “the snake”:

13. Cyclone Development • Use equation of state; • Then take

14. Cyclone Development • Include dynamic forcing (vorticity equation)

15. Cyclone Development • And thermodynamic forcing; (1st law of thermodynamics),

16. Cyclone Development • And you get a vorticity tendency equation (the Z-O equation) (after applying the snake again!)

17. Cyclone Development • How do the forcing mechanisms work? • Thermodynamic: • Warming leads to pressure falls below and rises above! • This means increases in vorticity below and decreases above!

18. Cyclone Development

19. Cyclone Development • Dynamic: (vorticity advection, tilting, friction) • Cyclonic vorticity advection (shear and cyclonic):

20. Cyclone Development

21. Cyclone Development • The End!