1. Development and applications of an index for tropical cyclone genesis
Michael K. Tippett,
International Research Institute for Climate and Society, Columbia University
Suzana J. Camargo,
Lamont-Doherty Earth Observatory, Columbia University
Adam H. Sobel,
Department of Applied Physics and Applied Mathematics, Department of Earth and Environmental Sciences, Columbia University
Gabriel A. Vecchi and Ming Zhao
Geophysics Fluids Dynamics Laboratory, NOAA

2. Outline Development of an new index
Tippett, M.K., S.J. Camargo, and A.H. Sobel, 2010: A Poisson regression index for tropical cyclone genesis and the role of large-scale vorticity in genesis, submitted to J. Climate, April 2010
Application to the GFDL 50km global climate model
Work in progress
Collaboration with Gabriel Vecchi and and Ming Zhao (GFDL)

3. Motivation
Relationship: tropical cyclone genesis (TCG) and large-scale climate - empirical
Incremental improvement on Emanuel and Nolan’s GPI
Index development: clear, objective and reproducible
Role of potential intensity (PI) as a thermodynamic predictor
Choice of relative humidity on a single level as a thermodynamic predictor
Systematic biases of GPI (Atlantic Main Development Region)
Application of TCGI to GFDL 50km model

4. Poisson Regression Poisson regression appropriate: model TC counts
Poisson distribution:
P (N=n) = e- n / n!
Poisson linear regression model:
= exp (bT x + log cos)
Offset term log cos ( is latitude): units number of TCG events per area.
Coefficients: maximizing the log-likelihood
Variables - similar to Emanuel’s GPI - climatology:
Absolute vorticity 850hPa
Relative humidity at 600hPa / column relative humidity
Vertical shear between 200hPa & 850hPa
Relative SST (difference SST and tropical mean SST)

5. Relative humidity 600hPa

6. Relative Humidity:
Column relative humidity (procedure developed in Bretherton et al. 2004)*
W = SSMI column-integrated liquid water (daily average)
W* = Daily saturation water vapor path (temperature from reanalysis) from saturation specific humidity at each pressure level
H = W/W* ---> monthly means, and monthly climatology
Column vs. 600hPa relative humidity:
Better fit to observations (ERA+NCEP)
Separate fits ERA & NCEP: improvement over NCEP but not ERA.
* Thanks to Larissa Back for scripts for calculating column relative humidity

7. Potential Intensity and relative SST
Strong empirical relationship with PI (Vecchi & Soden 2007)
Easy to calculate
More appropriate than absolute SST: influence of climate variability to genesis
Potential Intensity (PI)
TC theoretical maximum intensity - not necessarily optimal choice for genesis
More complex computation
Includes atmospheric data
Better fit of Poisson model with relative SST than PI.

8. Role of vorticity
Experiment adding powers and products of variables in the Poisson regression
Vorticity: square with negative coefficient:
Large absolute vorticity: reduced number TCGs
High latitudes: high vorticity and lack of TCGCs

9. Interpretation of vorticity dependency
Clipped vorticity: better performance!
Vorticity: necessary for genesis (no genesis very near the equator)
Once vorticity ABOVE a threhsold: not a limiting factor for genesis - other variables more critical role (SST, shear).
Daily time-scales: vorticity in precursor important.
Monthly time-scales: genesis probability does not increase over a vorticity threshold.

10. TCGI = exp(-11.18 + 1.22 min(||,3.7) +
TCG index
Best fit TCG index:
TCGI = exp( min(||,3.7) +
0.10 H RSST VS)
|| = absolute vorticity (850hPa) x 105
H = column relative humidity
RSST = relative SST (SST - mean tropical SST)
VS = vertical shear (200hPa and 850hPa)

14. Application to GFDL 50 km global model

15. Climatology model is good. Index is good
Climatology model is good. Index is good. Sensitivities similar to before.

16. Raw differences in first position. Sampling makes it hard to interpret.

17. Basin and hemisphere averages. Some agreement. Some differences.
Zhao et al., J. Climate, 2009

18. Differences in the index clearer. Reduction in Atlantic

22. Summary New tropical cyclone genesis index developed
Dependence on relative SST, column relative humidity explored
Vorticity dependency suggests that increasing the value of environmental vorticity over a certain value does not increase the probability of genesis.
Application of TCGI to GFDL model shows the validity of using the index in models.
Preliminary diagnostics on GFDL model in warm climates show the importance of the SST patterns on TC response.
Future work:
Quantitative diagnostic using TCGI coefficients
Comparison with Emanuel’s new GPI (different humidity variable)