1. 台风的暖心结构与强度变化(1)
储可宽 组会

2. 为什么关注这个问题？ Zhang and Chen （2012）
…under hydrostatic balance warming at lower temperatures aloft can produce much greater impact on surface pressure falls than lower-level warming because of the more exponential effects of the upper-level warming
Malkus and Riehl, 1960;
Zhang and Fritsch, 1988;
Hirschberg and Fritsch, 1993;
Holland, 1997

3. Holland (1997)
Potential intensity is highly sensitive to the height of the warm core…
The major limiting factor on cyclone intensity is the height and amplitude of the warm core that can develop…
Hirschberg and Fritsch (1993)

4. Hirschberg and Fritsch (1993)
“On understanding height tendency”
The logarithmic depth in the low-level is smaller than in the upper-level case…

7. Malkus and Riehl (1960)
“On the dynamics and energy transformations in steady-state Hurricanes.”
Since the hydrostatic calculations demonstrated that about 75% of the surface pressure lowering is achieved by warming above 500 mb … ?
201 citations

8. Stern and Nolan (2012JAS)
“On the height of the warm core in tropical cyclone”
Comment on the widespread knowledge on warm core, both observations and theory.
Numerical study on warm core structure (sensitivity to microphysics, the relationship with thermal wind balance )

9. Widespread knowledge on warm core
Strength & height
Numerous study have treated the upper-troposphere warm core maximum as a common characteristics of all TCs.
“the height of the warm core is directly related to intensity, and an apparent rising of the warm core is sometimes cited operationally by NHC as evidence for the intensification of a storm or as the basis for upgrading a subtropical storm to a TC”
Holland (1997): “the maximum height of warm core and vigor of the convection is a major factor for determining TC intensity”
Given current obs and numerical evidence, these arguments are in general not justified.

10. Filght-level temperature observations
La Seur and Hawkins (1963)
Hurricane Cleo (1958)
800, 560, 240 mb
240 mb
Hawkins and Rubsam (1968)
Hurricane Hilda (1964)
900, 750, 650, 500, 180 mb mb
Hawkins and Imbembo (1976)
Hurricane Inez (1966): two maxima
and 300 mb
mb; mb
Much of the knowledge about warm core is based on these three studies.

11. Satellite observations
Knaff et al. (2004MWR)
Vertical profiles of temperautre
AMSU, 57 GHz
186 cases
Low, medium, high vertical wind shear
50 km “at best” resolution
Height of warm core decreased with increasing shear
Mean warm core height: 12-km

12. Can satellite remote sensing really see the warm core?
54 km
2km
2 km

13. Existing theory
Hirschberg and Fritsch (1993)
Eq. (4.1) alone says nothing about either where the maximum perturbation temperature should be found, or whether or not there should be some relationship between its height and intensity.

14. Structure of simulated warm core: D2, D3
Az mean tangential wind
& vertical velocity
+30 m/s
Az mean tangential wind
Perturbation temperature
+5℃
RMW

15. Structure of simulated warm core: D4, D5
+3 m/s
+3℃

16. Structure of simulated warm core: D6, D7

17. Sensitivity of intensity to microphysics
Kessler: warm rain
No ice, no melting effect
WSM3: simple ice
Cloud ice/water 不能共存
WSM5: vapor, rain, snow, cloud ice, cloud water
WSM6: +graupel
Lin: +graupel

18. Sensitivity of intensity to microphysics
WSM3 weakest
Kessler strongest

19. Kessler
WSM3
Sensitivity of warm-core structure to microphysics

20. Vertical structure
of warm core

21. Vertical structure of warm core
The strength of the warm core is simply the integrated effect of the radial temperature gradient.
Thermal wind balance in log-pressure height coordinates (Schubert et al. 2007)

22. Vertical structure
of warm core

23. The strongest maximum is almost always the one at low to mid-levels, this is in contrast to conventional wisdom, which states that the typical height of the warm core is around 250 mb, or about 10.5 km
Variations in the structure of the warm core do not in any obvious manner reflect variations in either intensity or in the decay of maximum tangential wind with height
Therefore, the structure of the warm core and its variability does not actually tell us much about the structure of the tangential winds in the eyewall.

24. The relationship between the height of the warm core and thermal wind balance

25. However, it can be tempting to assume that ›T/›r is well represented by ›y/›z itself, and many studies have implicitly made this assumption.

26. Gradient wind

30. Stern and Nolan’s summary
In contrast to conventional wisdom, the strongest maximum was generally at midlevels. It is currently unclear how often the warm core is centered in the middle versus the upper troposphere, how often there are multiple maxima, and whether or not there is any dynamical significance to this variability.
the height of the warm core plays a less important role in overall tropical cyclone structure than is generally imagined.
the height of the warm core is not in general at the height where the maximum radial temperature gradient is found, …
Therefore, we feel that the apparent height of the warm core should not be used in operational intensity estimates. …

31. Further reading Stern and Zhang (2013a) Stern and Zhang (2013b)
How Does the Eye Warm? Part I: A Potential Temperature Budget Analysis of an Idealized Tropical Cyclone
Stern and Zhang (2013b)
How Does the Eye Warm? Part II: Sensitivity to Vertical Wind Shear and a Trajectory Analysis
Durden (2013MWR)
Observed Tropical Cyclone Eye Thermal Anomaly Profiles Extending above 300 hPa

32. Durden (2013MWR)
The author finds that the pressure altitude of the maximum anomaly varies between 760 and 250 hPa.
The author also finds positive correlations between the maximum anomaly level and storm intensity, size, upper-level divergence, and environmental instability.

35. Thank you! To be continued…