Comparison of tropical cyclogenesis indices on seasonal to interannual timescales

Abstract

This paper evaluates the performances of four cyclogenesis indices against observed tropical cyclone genesis on a global scale over the period 1979–2001. These indices are: the Genesis Potential Index; the Yearly Genesis Parameter; the Modified Yearly Convective Genesis Potential Index; and the Tippett et al. Index (J Clim, 2011), hereafter referred to as TCS. Choosing ERA40, NCEP2, NCEP or JRA25 reanalysis to calculate these indices can yield regional differences but overall does not change the main conclusions arising from this study. By contrast, differences between indices are large and vary depending on the regions and on the timescales considered. All indices except the TCS show an equatorward bias in mean cyclogenesis, especially in the northern hemisphere where this bias can reach 5°. Mean simulated genesis numbers for all indices exhibit large regional discrepancies, which can commonly reach up to ±50%. For the seasonal timescales on which the indices are historically fitted, performances also vary widely in terms of amplitude although in general they all reproduce the cyclogenesis seasonality adequately. At the seasonal scale, the TCS seems to be the best fitted index overall. The most striking feature at interannual scales is the inability of all indices to reproduce the observed cyclogenesis amplitude. The indices also lack the ability to reproduce the general interannual phase variability, but they do, however, acceptably reproduce the phase variability linked to El Niño/Southern Oscillation (ENSO)—a major driver of tropical cyclones interannual variations. In terms of cyclogenesis mechanisms that can be inferred from the analysis of the index terms, there are wide variations from one index to another at seasonal and interannual timescales and caution is advised when using these terms from one index only. They do, however, show a very good coherence at ENSO scale thus inspiring confidence in the mechanism interpretations that can be obtained by the use of any index. Finally, part of the gap between the observed and simulated cyclogenesis amplitudes may be attributable to stochastic processes, which cannot be inferred from environmental indices that only represent a potential for cyclogenesis.

Appendix: cyclogenesis index definition

In the text, we use the label “reanalysis-index” (e.g., NCEP-YGP, ERA40-GPI etc…) for an index calculated with a given reanalysis. The definitions that follow are exact replications of those found in the original papers. They are:-

• 1. GPI

The GPI monthly index is constructed as in Camargo et al. (Camargo et al. 2007a, b) and Emanuel and Nolan (2004) as ${\text{GPI}} = \underbrace {{\left| {10^{5} \eta }\right|^{{3}/{2}}\left( {1 + 0.1V_{\text{shear}} } \right)^{ - 2}}}_{\text{dynamic}}\underbrace {{\left( \frac{H}{50} \right)^{3}\left( {\frac{{V_{\text{pot}} }}{70}} \right)^{3}}}_{\text{thermal}}$ with η is the absolute vorticity at 850 hPa in s⁻¹, H is the relative humidity at 600 hPa, V _pot is the potential intensity calculated using a routine provided by Dr. Emanuel (http://wind.mit.edu/~emanuel/home.html). V _shear is the magnitude of the vertical wind shear between 850 and 200 hPa in ms⁻¹. For consistency with the other indices below, we sometimes refer to thermal and dynamical potentials (see equation).

• 2. TCS (Tippett et al. 2011)

This index uses the same variables as the previous one except for the V _pot which is replaced by an SST index:

$$ \begin{aligned} {\text{TCS}} & = { \exp }(b + b_{\eta } \eta + b_{{V_{\text{shear}} }} V_{\text{shear}} + b_{H} H + b_{T} T + { \log }(\cos \phi )) \\ & = { \cos }\phi *{ \exp }b*\underbrace {{{ \exp }(b_{\eta } \eta + b_{{V_{\text{shear}} }} V_{\text{shear}} )}}_{\text{dynamic}}*\underbrace {{{ \exp }(b_{H} H + b_{T} T)}}_{\text{thermal}}, \\ \end{aligned} $$

with $T = {\text{SST}} - \overline{\text{SST}}^{{[20^\circ {\text{S}} - 20^\circ {\text{N}}]}}$ and $\eta = { \min }(\eta ,3.7)$ is referred to as the “clipped vorticity”, φ is the latitude. The constant used in the calculation is that given by Tippett et al. (2011)’s Table 1 line 6, namely: b = 5.8; b _η  = 1.03; b _H  = 0.05; b _T  = 0.56; b _V  = −0.15.

• 3. YGP

For consistency with the GPI, we have constructed monthly YGP and CYGP indices rather than seasonal indices as initially proposed by Gray (1979), Watterson et al. (1995), Royer et al. (1998). The monthly YGP is calculated as ${\text{YGP}} = \underbrace {{\left| f \right|I_{\zeta } I_{s} }}_{\text{dynamic}}\underbrace {{EI_{\theta } I_{\text{RH}} }}_{\text{thermal}}$ where f is the Coriolis parameter in 10⁻⁵s⁻¹, $I_{\zeta } = \zeta_{r} \frac{f}{\left| f \right|} + 5$ with $\zeta_{r}$ the relative vorticity at 925 hPa in 10⁻⁶ s⁻¹, $I_{s} = \left( {\left| {\frac{\delta V}{\delta P}} \right| + 3} \right)^{ - 1}$ where $\frac{\delta V}{\delta P}$ is the vertical shear of the horizontal wind between 925 and 200 hPa in m s⁻¹/750 hPa, $I_{\theta } = \left( {\frac{{\delta \theta_{e} }}{\delta P} + 5} \right)$ where $\frac{{\delta \theta_{e} }}{\delta P}$ is the vertical gradient of the equivalent potential temperature between 925 and 500 hPa in K/500 hPa, $I_{\text{RH}} = { \max }\left( {{ \min }\left( {\frac{{{\text{RH}} - 40}}{30},1} \right),0} \right)$ with RH is the average relative humidity in percent between 700 and 500 hPa. More simply put, if RH is greater than 70% then I _RH = 1 and if RH lower than 40%, I _RH = 0. $E = \int_{0}^{60m} {\rho_{w} } c_{w} (T - 26)dz$ is the thermal energy of water above 26°C in the top 60 m of the ocean. ρ _w and c _w are the density and specific ocean heat capacity taken as constant. We have access to two OGCMs (Ocean General Circulation Model) outputs forced by NCEP and ERA40 reanalyses from the OPA model (Rodgers et al. 2008) with which to calculate E but we do not have similar outputs for the NCEP2 reanalyses. However, the averaged E over 25°S–25°N, 0–360° and for the 1970–2001 time period yields 7.6 10³ cal cm⁻² for NCEP-OPA (referring to the OPA output forced by NCEP) and 7.9 for ERA40-OPA outputs. The two time series correlate at 0.98 and their respective standard deviation are 0.92 and 0.99. Thus, despite differences in the two wind fields, the OGCM thermal energy E yields very similar quantities. Hence, it is reasonable to think that NCEP2-OPA, if it existed, would have also given a very similar E. Thus, we have confidently used E from NCEP-OPA in the calculation of the NCEP2 YGP.

• 4. CYGP

The CYGP replaces the thermal potential of the YGP by a convective potential $k(P_{c} - P_{0} )$where k is an arbitrary constant to be adjusted depending on the reanalysis or data set used. P _c is the convective precipitation in mm day⁻¹ and P ₀ is a threshold below which the convective potential is set to zero to avoid spurious cyclogenesis off the tropics. We chose P ₀ = 3 from previous studies (Chauvin and Royer 2011; Royer and Chauvin 2009) but tests on this threshold do not change the analyses performed in that paper. k was adjusted for each reanalysis in order to yield a ~85 cyclone/year global mean, as observed (see also main text).

For consistency with the GPI, we have constructed monthly YGP and CYGP indices rather than seasonal indices as initially proposed by Gray (1979), Watterson et al. (1995), Royer et al. (1998). It was checked that introducing monthly variations rather than 3-month seasons does not induce significant differences in the seasonal index estimates.