The eye of a tropical cyclone – some experiments with an axisymmetric numerical model

1. New title: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model Wolfgang Ulrich

2. Motivation: Axisymmetric numerical models of evolving tropical cyclones >>seem<< to >>simulate<< smaller radii of maximum winds (=>eyes) if the resolution is increased. Examples: DeMaria & Pickle 1988 Baik et al 1989 NCM, RKS, HYZ and WU 2002 WU, RKS and NCM 2002

3. Idealized anatomy of a tropical cyclone (eye) At the center of the storm is a cloud-free eye of relatively low surface pressure, warm temperature and subsiding air. (Stull)

4. Observed (eye) characteristic Hurricane Bonnie from space Most (but not all) tropical cyclones that reach hurricane intensity have central clear regions, called >>eyes<<; these range in diameter from 20 km to as much as 200 km (Emanuel).

5. Hurricane Fefa (North Pacific) Without an eye, tropical storms are limited to a pressure of about 1000 mb .... no matter how much condensation is occuring (Anthes).

6. Although the basic structure of tropical cyclones is invariant, there is considerable variability in the both the details of the structure and the overall horizontal scale of the storms. In particular, the characteristic horizontal scale of tropical cyclones varies over a wide range, from “midget typhoons", with eyes only a few kilometers in diameter and with no noticeable wind perturbation outside of 100 km from the storm center, to some “supertyphoons" with eyes up to 200 km in diameter. Thus a midget typhoon can fit entirely within the >>eye<< of a giant supertyphoon! There is no known correlation, however, between the geometric size of a tropical cyclone and its intensity, as measured, for example, by its maximum wind speed (Emanuel).

7. Composite hurricane structure (Stull). Eye: 0...0.5 R0 Eyewall: (0.5...1) R0

8. Axisymmetric finite difference Model Physics: • Latent heat release on the grid scale (horizontal 5 km) • Evaporation of falling rain • Sensible heat transfer at the ocean's surface • Bulk friction • Vertical and horizontal exchange based on mixing length • No radiation • No ice • No cummulus parameterization • Hydrostatic Sigma coordinate 15 layers, top at 50 hPa Numerical methods: • Adams Bashforth • Flux form 6-th order in r, 3-rd order in Sigma.

9. Standard run: Jordan tropical sounding, SST=28 C, 15 deg North Initial disturbance 15 m/s (150 km), 12.4 m/s (300 km) 0 (950 km) Initialisation: balance equation for surface pressure Wang (1995) or Kurihara (1974) type initialisation

10. Numerical diffusion in the eye region: “v” analytic, “p” from gradientwind balance “vnum” from analytic “p” with finite differences.

11. Animation of a standard case

12. Relative humidity Potential Temperature deviation

13. Moist static energy

14. Standard case

15. Eye contraction, basic mechanism Assume tangential profile v(r) => radial profile u(r) from balance (f+v/r) u=Friction Absolute Angular Momentum conservation: AAM=v r + 0.5 f r2

16. What can limit the contraction ? Diffusion subsidence in the eye=> u > 0

17. No advection of u and v

18. Colder SST=25 C SST=28 C 2*Eye P

19. 10 deg 30 deg 40 deg

20. SST drop after 96 h to 20 C in a ring GP 0-5 GP 5-10 eye pressure

21. Thanks to Robert

22. END