Recent studies have reaffirmed a global threshold sea surface temperature (SST) of 26°C for tropical cyclone (TC) genesis. However, it is well understood that other thermodynamic variables influence TC genesis and that high SST in isolation is not a sufficient criterion for genesis. Here, a basin-by-basin analysis of the SST distributions in the five most active ocean basins is performed, which shows that there is no global SST threshold for TC genesis. The distributions of genesis SST show substantial variations between basins. Furthermore, analysis of the conditional probability of genesis for a given TC season main development region SST suggests that the SST bounds for TC genesis are largely determined by the climatological bounds of the basin and that the SST values within this environmental range have similar probabilities of genesis. The distribution of relative SST (the difference between local and tropical mean) and tropical cyclone potential intensity at TC genesis are more distinct from those of the TC season environment, consistent with their utility in TC genesis indices.
After World War II, scientists proposed a sea surface temperature (SST) threshold of 26°C as a necessary condition for tropical cyclone (TC) genesis (Palmen 1948; Gray 1968). Subsequent research has revealed that other thermodynamic variables are more directly associated with TC intensity (Emanuel 1995, 2003; Emanuel and Nolan 2004), such as potential intensity (PI) and surface enthalpy fluxes, and these have been incorporated as predictor variables in multivariate “genesis potential indices” (Camargo et al. 2007a,b; Tippett et al. 2011). Furthermore, a threshold SST in the current climate is not likely to be relevant in a perturbed climate [as is understood for the case of moist convection in the tropics (Graham and Barnett 1987; Zhang 1993; Johnson and Xie 2010)], so the utility of such a threshold in the out-of-sample case of interest—climate change—is suspect. Indeed, simulations of TCs in perturbed climate states do not show the geographic or frequency changes in genesis that would be expected from a fixed SST threshold for genesis (Bengtsson et al. 2007; Emanuel et al. 2008; Sugi et al. 2009; Zhao et al. 2009; Knutson et al. 2010; Merlis et al. 2013; Zhao et al. 2013; Merlis et al. 2016) and there is an observed warming trend in SST at the time of TC genesis (Defforge and Merlis 2017).
In spite of the wealth of physical reasoning and numerical simulations that argue against the relevance of a SST threshold for TC genesis, recent work has revisited the existence of a TC genesis SST threshold with contemporary datasets for the era of satellite observations (Dare and McBride 2011; Tory and Dare 2015). These studies have confirmed the existence and value of SST threshold of 26°C that had been suggested decades earlier. In light of this apparent disconnect between these observational studies and the evidence provided by numerical simulations and physical reasoning, we reexamine observations of SST at time of TC genesis (hereinafter referred as SSTG) to assess the observational support for a global SST threshold for TC genesis.
We examine two dimensions of this question. First, to what extent does a “global” threshold arise from regional variations? McTaggart-Cowan et al. (2015) recently examined the different TC development pathways that commonly occur at cold SSTs (<26.5°C) and found a critical role for baroclinic disturbances. The cold events analyzed in their study were most common in the North Atlantic basin and almost never occur in the west Pacific basin. In the present study, we examine if the location of cold TC genesis events can be explained by climatological differences between the basins, rather than by closely analyzing differences in transient meteorological conditions. Second, how does the probability of genesis evolve with SST and to what extent is the probability density function (PDF) of SSTG shaped by the environmental conditions of the main development region (MDR)? For example, TC genesis is not observed at SSTs greater than 32°C simply because SSTs are very rarely this warm, providing an environmental upper bound on SSTG. Therefore, we compare the MDR environment’s SST distribution during the whole TC season (hereinafter referred as SSTS) to that observed during genesis. In addition, we compare the environment’s relative SST, vertical difference in equivalent potential temperature, and maximum potential intensity to that observed during genesis to determine if these variables, which have been used in recent genesis potential indices, have more distinct distributions at TC genesis than absolute SST.
We use the TC track information from release v03r08 of the International Best Track Archive for Climate Stewardship (IBTrACS) database (Knapp et al. 2010), which comprises data from 11 TC observation centers, including the position and a near-surface wind speed estimate every 6 h along the storm track. The IBTrACS database also indicates the nature of the storm (“tropical,” “subtropical,” “extratropical,” etc.), as determined by the individual regional specialized meteorological centers when available.
The TC tracks are combined with the 0.25° daily Optimum Interpolation Sea Surface Temperature (OISST) dataset (Reynolds et al. 2007) from the National Oceanic and Atmospheric Administration (NOAA) to determine the genesis SST. This dataset provides daily mean values of SST with a horizontal resolution of 0.25° from 1982 to the present.
We also use data from the Modern-Era Retrospective Analysis for Research and Applications (MERRA; Rienecker et al. 2011) to assess the atmosphere’s vertical stability and potential intensity. MERRA is a NASA atmospheric reanalysis for the satellite era that has a horizontal resolution of ⅔° longitude by 0.5° latitude and 2-h temporal resolution. The prescribed SST boundary condition uses the 1° resolution NOAA OISST product. Though we use the higher-resolution OISST for the genesis SST, the conclusions are not sensitive to the spatial resolution of the SST dataset.
The present analysis is performed over the 33-yr period from 1982 to 2014 (the period covered by both the OISST and IBTrACS datasets). All the storms that developed during this period are filtered in order to examine only those that reach TC intensity within the tropics. The genesis of the TC is defined as the moment when the estimated winds of the storm exceed 18 m s−1 (i.e., 1-min-average sustained winds of 40 kt). To account for different wind averaging periods used in IBTrACS dataset, different values in knots of wind threshold are used to consistently define TC genesis, following the conversion formulas given in Knapp and Kruk (2010).
Consistent with previous studies, we excluded the storms that are not labeled as tropical in the IBTrACS database and those that developed at latitudes poleward than 35° (Dare and McBride 2011; Tory and Dare 2015). Some other methods based on dynamical criteria, such as the subtropical jet position, may be used to distinguish tropical from nontropical storms (Tory and Dare 2015). We investigated alternative methods that only consider the latitude at the time of TC genesis and that define the boundaries of the tropics according to dynamical criteria. However, the SSTG distributions are not sensitive to the method used to exclude nontropical storms, so only the one using IBTrACS labels is presented here, following Dare and McBride (2011).
For the selected TCs, we linearly interpolate the SST between daily means to the time of genesis and average meridionally the SST over a 1.5° latitude radius, following McTaggart-Cowan et al. (2015). Averaging over a 1.5° latitude radius gives similar SST distributions to those obtained considering pregenesis SST (e.g., maximum SST 24 or 48 h prior to genesis). The results are not sensitive to including a pregenesis period or to the wind threshold used to define genesis. The TCs are sorted according to the basin in which they developed and the five most active basins are examined here: west Pacific (WP; 753 TCs examined), east Pacific (EP; 524 TCs), south Indian Ocean (SI; 467 TCs), North Atlantic (NA; 334 TCs), and South Pacific (SP; 307 TCs). The other basins are excluded from the analysis because of the small number of TCs and, in the north Indian Ocean Basin, the TC nature is frequently not reported in IBTrACS. The probability distributions are obtained using averaged shifted histograms with bins of 1°C width, shifted by 0.25°C (Scott 2010). In figures of probability distributions, the horizontal axis corresponds to the center of the bin and the vertical-axis value is the percentage occurrence of the genesis events’ SSTs contained in the bin.
For each basin, the SST throughout the 33 TC seasons is also examined (SSTS) Figure 1 shows the spatial extent of each basin and the months that define the TC season are given in the caption. The months that define TC season are selected such that approximately 80% of the tropical cyclone genesis events occur during these months and are similar to those used by Wing et al. (2015). For each basin, the MDR region is defined as the smallest contiguous area that contains 75% of all the TC genesis events observed between 1982 and 2014. The TC genesis events that are excluded are those that did not occur during TC season and those that are the farthest from any other TC genesis location. In other words, the latitude and longitude limits of the MDR are extended to the nearest TCs until 75% are encompassed. The sensitivity to the fraction of TCs analyzed is assessed in appendix A. We have also performed the analysis using simple latitude–longitude regions defined in Defforge and Merlis (2017) and obtained similar results. As in our analysis of SSTG, the values of SSTS are sorted in bins of 1°C using averaged shifted histograms.
In addition to the local SST, we examine the relative SST (RSST) and a vertical difference in equivalent potential temperature. Relative SST, defined as the local SST difference from the tropical-mean SST, has been used in the construction of genesis potential indices (Tippett et al. 2011) because it is correlated with maximum potential intensity (Vecchi and Soden 2007; Ramsay and Sobel 2011) and is a better measure of moist stability than local SST (Vecchi and Soden 2007). Relative SST is calculated as the difference between the local, daily value of SST and the monthly mean SST averaged between 20°S and 20°N. Given that RSST is an indirect measure of the atmosphere’s vertical moist stability (e.g., Ramsay and Sobel 2011), we also directly examine the vertical difference in equivalent potential temperature θe in the MERRA reanalysis using Bolton’s formula (Bolton 1980). We calculated the vertical difference in equivalent potential temperature between the near-surface air (at 1000 hPa) and at 500 hPa. The choice of a difference between the surface air and midtroposphere is motivated by quasi-equilibrium theory, where the vertical θe difference normalized by the air–sea entropy disequilibrium is critical in determining the convective mass flux (Emanuel 2007) and this has been used as an environmental variable in a genesis potential index (Emanuel 2010). It is also a component of the “ventilation index” that is a theoretically based metric to assess possible changes in tropical cyclone activity. For instance, it has been used to explore changes in the environmental conditions for tropical cyclone genesis associated with climate change (Tang and Camargo 2014), and it successfully distinguishes intensifying and weakening TCs over the 24-h time frame relevant to operational forecasting (Tang and Emanuel 2012). To minimize the potential influence of the TC’s temperature and humidity anomalies relative to differences in the environment and focus on the predevelopment environment, the vertical difference in θe is averaged over the three days preceding genesis (see appendix B for more information). We note that the fixed midtroposphere pressure level does not capture variations in the depth of the troposphere that have been identified as important in the TC genesis events with baroclinic precursors (McTaggart-Cowan et al. 2015).
To complete the analysis of thermodynamic variables used in genesis indices, we also analyzed the PI. The PI at TC genesis is computed using the convective available potential energy algorithm of Bister and Emanuel (2002) with daily SST values, and daily values of atmospheric temperature and humidity at 33 pressure levels between 1000 and 1 hPa from MERRA. The climatological PI is obtained from monthly mean values of SST and atmospheric variables. We present the maximum wind speed PI, calculated using the reversible ascent option for convective available potential energy, including dissipative heating, with a surface wind speed reduction factor of 0.8, and a ratio of the enthalpy to momentum drag coefficients of 0.9.
To normalize the probability distributions of SSTG according to the prevalence of the SST values during the TC season, we compute the ratio of the PDF of SSTG and SSTS. The conditional distributions thus obtained correspond to the probability of genesis at a given environmental temperature. To avoid spurious, large values of conditional probability, the probability of genesis is truncated when the SSTS and SSTG probabilities are smaller than 1%. Similar conditional probability distributions are computed for the other thermodynamic variables.
a. Distribution of SST at TC genesis
Figure 2 shows the cumulative distributions of the SST at TC genesis, SSTG, for each ocean basin separately. It also shows the global distribution of SSTG (thick black line), reproducing the results of Dare and McBride (2011) and Tory and Dare (2015). Note that global refers to the average over the five basins studied in the present analysis. For this figure, all of the TCs that occurred in the given basins are considered, even those that are not included in the spatial and temporal definition of the basin’s TC season. The basins have different characteristics regarding the distribution of SSTG, with the North Atlantic having the coldest genesis events and the west Pacific having the warmest ones. The values for the 5th percentile correspond to the SST such that 95% of the TCs observed between 1982 and 2014 developed over SSTs warmer than this value (Fig. 2b). Only 5% of TCs observed between 1982 and 2014 developed at SSTs below 25.7°C in the NA basin, 26.4°C in the global distribution, and 27.0°C in the WP basin. The bootstrap estimate ( appendix C) of the confidence intervals shown in Fig. 2b span about 0.5°C, suggesting that these are statistically significant differences. The substantial variability between the basins—more than 1°C—indicates that the SST “threshold” necessary for TC genesis is basin dependent. For percentiles smaller than 10%, all of the basins, except the North Atlantic, are either similar to, or warmer than, the global SSTG values. Consequently, the NA basin shifts the low percentiles of the global SST distribution at TC genesis toward colder temperatures, and it is clear that a 26°C threshold is not a stringent genesis condition in the west Pacific.
Across the ocean basins, there is no sharp increase with SST of the cumulative distributions of SSTG (Fig. 2). Even from a basin-specific perspective, the occurrences of SSTG increase smoothly with SST in the cold tail of the distribution and decrease smoothly in the warm tail. This characteristic, taken together with the interbasin differences, casts doubt on the concept of a global SST threshold necessary for TC genesis.
b. Comparison with SST over the TC season and conditional probability of genesis
To compare the SST at TC genesis with the climatological or environmental conditions observed at ocean’s surface, we computed the distribution of the MDR SST over the TC season of each basin (SSTS). Only the months corresponding to the TC season in each basin are considered, because the other environmental parameters influencing TC genesis, such as the vertical wind shear or free-tropospheric humidity (Gray 1968; Nolan and McGauley 2012; Emanuel 2003; Tippett et al. 2011), are generally more favorable during the TC season. The TC genesis events considered in this section and the next one are limited to those that occur within the temporal and geographic extent of the basins shown in Fig. 1. These temporal and geographic criteria are satisfied for more than 75% of genesis events for all the basins, so the PDFs of SSTG are not substantially affected by this restriction, and it allows for a fair comparison of the TC season environmental conditions and the corresponding genesis events.
Figure 3 shows the probability of genesis given a certain environmental SST, which corresponds to the conditional probability distribution of SSTG given the SST values during the TC season. The PDF of SSTS for each basin is also shown for comparison. The PDF of SSTS contains 106 more samples than SSTG: TC genesis is, of course, a rare event. Within each basin, SSTG and SSTS span nearly the same range of values, suggesting that the warm and cold bounds of the SSTG distribution are largely determined by the climatological bounds of the basin’s SST. It can be seen that the most likely SSTG is equal to or colder than the peak of SSTS occurrence, except in the east Pacific (Fig. 3). This indicates that the SST at which TC genesis is most likely is in the cold half of the range of SST encountered during the TC season. This is not the case in the east Pacific basin where the SSTG distribution is slightly shifted to warmer values. Figure 3 also shows that the TC genesis conditional probability increases with SST, from cold values up to a basin-dependent temperature. This suggests that during the TC season, when the other parameters influencing TC genesis are favorable, increasing the SST from cold values is favorable for TC genesis. However, the TC genesis conditional probability seems to saturate at a certain basin-dependent temperature that is generally colder than the TC season basin-mean SST. For MDR SSTs warmer than this saturation temperature (about 28°C for the global distribution), the probability of genesis is nearly insensitive to SST, except for the EP basin where the conditional genesis probability continues increasing at warm SSTs. The anticorrelation between SST and the Coriolis parameter at low latitudes provides a potential physical explanation for this saturation in probability at high SSTs.
It is interesting to note that the shape of conditional probability of genesis is similar in the North Atlantic to other ocean basins (Fig. 3). It is perhaps surprising that it is not an outlier given that it has more genesis events at cold SSTs (Fig. 2), many cold genesis events have been shown to be baroclinically influenced (McTaggart-Cowan et al. 2015), and baroclinically influenced TC genesis has been widely discussed in the North Atlantic (Bracken and Bosart 2000; McTaggart-Cowan et al. 2008). The conditional probability of genesis across the range of environmental SSTs indicates that genesis is comparably rare across the range of SSTs, so that favorable conditions in terms of transient meteorological conditions such as baroclinic influences or other environmental factors are more central than absolute SST. Yet, the prevalence of baroclinically influenced genesis in the North Atlantic does not lead to distinctive behavior for the conditional probability of genesis for a given environmental SST. In conclusion, the bounds of the environmental SST shape the interbasin differences in genesis SST.
c. Analysis of other thermodynamic variables: Relative SST, moist stability, and potential intensity
As the distribution of absolute SSTG generally resembles the TC season environment, we analyze other environmental parameters that are relevant to tropical cyclogenesis to see if their distributions at TC genesis are more distinct from climatological environmental conditions and would therefore serve as more sensitive measures of environments favorable to TC genesis. We examined the RSST, the vertical difference in equivalent potential temperature δθe, and the PI. We note that it would be desirable to examine the distribution of the environmental variables for TC genesis events relative to nondeveloping tropical disturbances rather than that of the climatology (see also appendix B), though previous genesis potential index research has taken an approach similar to ours (e.g., McGauley and Nolan 2011). These other variables are characterized in individual basins in Table 1 and Fig. 4 shows their global conditional probability distributions.
The statistical distance between probability distributions of SSTS and SSTG or between distributions of RSSTS and RSSTG, δθe,S and δθe,G, or PIS and PIG is measured here by the Bhattacharyya distance (Bhattacharyya 1943; Kailath 1967). The Bhattacharyya coefficient, upon which the distance is based, is a measure of overlap of two probability distributions that is defined as
for distributions p(x) and q(x), where 0 ≤ ρ ≤ 1. The integration is replaced with a summation for discrete distributions, which are analyzed here. Several distance measures may be associated with this coefficient ρ. Here we use the Bhattacharyya distance Bd = −ln(ρ). As the overlap of two probability distributions increases (ρ → 1), this distance decreases (Bd → 0). For example, a distance of zero indicates identical distributions, while two normal distributions with the same standard deviation of 1°C (a typical value of standard deviation for SSTG distributions) and means that differ by 1°C would have a distance of 0.125.
Table 1 shows the values of the Bhattacharyya distance between the probability distributions at TC genesis and over the MDRs, for local SST, RSST, δθe, and PI. The table also includes the ratio of the distances for RSST, δθe, and PI compared to the distance for local SST (ΔRSST, Δθ, and ΔPI). The distance for RSST is typically 20% larger than that of local SST. The distances for δθe are smaller than those obtained with RSST and are typically also smaller than local SST, except in the NA and WP basins. Whether the genesis distribution of δθe is more or less distinct from that of the environment compared to SST is sensitive to the definition of the TC season MDR. The small distance for δθe may be the result of competing effects: while larger δθe has the previously described connection to increased convective mass flux, a favorable factor for genesis, it is also larger when the midtroposphere is dry, an unfavorable factor for genesis. The distances between probability distributions at TC genesis and over the MDR are the largest for potential intensity. Higher distances between PIG and PIS distributions correspond to distributions that overlap less, showing that the PIG distribution is more distinct from the PIS distribution than the SSTG distribution is from the SSTS distribution. The Bhattacharyya distances for all of these thermodynamic variables are small and they cannot be used in isolation to assess the environment’s favorability for TC genesis: the maximum conditional probability (shown next) is still a few percent. These thermodynamic variables should therefore be combined with other environmental variables in a multivariate approach, as is standard practice in genesis potential indices (e.g., Tippett et al. 2011). It is interesting to note that the distance for global distributions of these variables is smaller than for most individual basin, which confirms that information is lost when averages over different ocean basins are taken.
Figure 4 shows the global conditional probability distributions of SSTG, RSSTG, δθe,G, and PIG (thick blue lines) and the global PDF of SSTS, RSSTS, δθe,S, and PIS (dash–dotted, orange lines). The shape of the conditional probability distribution of RSSTG is similar to that of SSTG, as the RSST value at which TC genesis is the most likely is close to the peak of RSSTS occurrence (Fig. 4b). Genesis probability increases from negative values of RSST up to approximately 2°C, and for larger MDR values of RSST, the probability of genesis remains between 1.5 and 2. The conditional probability distributions of δθe,G and PIG are distinct from the SST variables in that the values for which TC genesis is the most likely are the largest observed MDR environmental values of δθe and PI (Figs. 4c and 4d). This means that the probability of genesis increases with δθe and PI as the largest observed MDR environmental values are approached. However, the conditional distribution of PI also has a local maximum near 55 m s−1, which is a lower than average value for the TC season in the MDR (about 65 m s−1). These low-PI genesis events contribute to the relatively large Bhattacharyya distances. There is a similar, but smaller local maxima in the conditional distribution of δθe,G near 10°C (vs a mean MDR value of about 15°C). The bimodality of the conditional PDFs of δθe,G and PIG comes from the low frequency of those values in the environmental PDFs. The Bhattacharyya distance can increase from genesis events at the low-value side of the PDF in addition to the high-value side of the PDF, so we have also computed the fraction of genesis events that occur for values above the mean MDR value. This is more analogous to the genesis index paradigm, where more positive values of PI, or other favorable variables, are presumed to favor genesis. For absolute SST, about 60% of genesis events occur at values above the mean MDR value, whereas more than 70% of genesis events occur when the PI exceeds the mean MDR value.
In summary, these other thermodynamic variables (RSST and PI) have certain characteristics in their distribution at time of genesis compared to their distribution in the TC season MDRs that are consistent with their utility in recent genesis indices over that of absolute SST. However, it is clear that any single thermodynamic variable in isolation cannot adequately identify environments where genesis is genuinely likely.
This examination of the distribution of SST at TC genesis shows that individual ocean basins have distinct characteristics. The range of observed SSTs at TC genesis, the mean SST value, and the coldest SST for which TC genesis occurrence is significantly different from zero, all vary from one basin to another. The fact that TC genesis occurs over different ranges of SSTs, according to the basin considered, also indicates that the covariance of SST with other environmental parameters that are important for TC genesis (e.g., vertical shear and humidity) differs between the basins. This is consistent with high-resolution simulations that have shown the deleterious influence of vertical wind shear changes with SST (Nolan and Rappin 2008; Zhou 2015).
The analysis of the conditional probability of TC genesis with SST shows that increasing SST favors TC genesis only for SSTs colder than the most frequent main development region environmental SST. Within each basin, SSTs warmer than the TC season mean have similar probabilities of TC genesis, except for the east Pacific basin where genesis is more likely at warmer temperatures. This comparison also suggests that cold and warm bounds of the SST distribution at TC genesis are largely determined by the climatological SST extrema encountered by the basin during its TC season. A straightforward explanation for differences in SST at tropical cyclogenesis between ocean basins is that they reflect differences in the TC season environment. This environmental explanation for the geographic variations in SSTG is complementary to the body of literature examining differences in genesis pathways. The extent to which TCs develop from baroclinic precursors or convectively coupled waves also have documented geographic variations (Schreck et al. 2012; Payne and Methven 2012; McTaggart-Cowan et al. 2008, 2015).
The analysis of the distributions of relative SST and potential intensity show greater differences between genesis events and the seasonal environment than the distributions of absolute SST. The distributions of the vertical difference in equivalent potential temperature and of the potential intensity have the greatest conditional probability of genesis, and these large probabilities of genesis occur at the largest observed environmental values. The conditional PDFs for δθe and PI are bimodal and also have a local maxima for lower environmental values, which supports the use of multivariate genesis indices that are distinct and advantageous compared to these thermodynamic variables in isolation. The characteristics of these other thermodynamic variables is consistent with the preference for their use in the construction of recent genesis potential indices over local SST.
The main conclusions of this study are as follows:
The canonical global SST “threshold” for TC genesis of 26°C then arises from averaging between climatological cold and warm ocean basins, with the NA basin accounting for the cold genesis events, and WP and SP accounting for warm genesis events.
The conditional probability of genesis given a MDR SST typically spans the range of MDR SST and has smooth variations (Fig. 3), suggesting that there are not abrupt threshold changes in the conditional probability of genesis as SST increases.
The conditional probability of genesis given a MDR SST does not increase for SSTs warmer than the TC season mean SST, except in the EP (Fig. 3).
In contrast to absolute SST, relative SST and potential intensity have distinct probability distributions during TC genesis events compared to the TC season climatology (Table 1).
The absence of a global SST threshold for TC genesis and the broad conditional distribution of TC genesis given environmental SST in observations indicate that observations of the present climate do not offer an expectation for the relationship between TC genesis and SST warming from anthropogenic climate change. For example, if the conditional probability distribution of SST at TC genesis had a shape that favored warm SST, one might expect an increase of TC genesis with climate change. The analysis presented here shows that this is not the case. Observations of SST at TC genesis across ocean basins, where interbasin differences are similar to those of the environment, and observations of the long-term trend, where there is a significant warming that is similar to that of the environment (Defforge and Merlis 2017), are broadly consistent with the view that SST at genesis is a record of the TC genesis environment rather than an integral variable in determining TC genesis.
We are grateful for the support of the Stephen and Anastasia Mysak Graduate Fellowship (C.D.) and the support of NSERC Discovery Grant (T.M.). The sea surface temperature data used in this study were acquired from NOAA’s daily Optimum Interpolation Sea Surface Temperature (https://www.ncdc.noaa.gov/oisst). We acknowledge NOAA for providing the OISST dataset and the IBTrACS database (http://www.ncdc.noaa.gov/ibtracs). We also thank the Global Modeling and Assimilation Office (GMAO) and the GES DISC for the dissemination of MERRA (http://disc.sci.gsfc.nasa.gov/daac-bin/DataHoldings.pl). We thank Kerry Emanuel for providing the code to compute potential intensity (ftp://texmex.mit.edu/pub/emanuel/TCMAX/) and Suzana Camargo, Ron McTaggart-Cowan, and three anonymous reviewers for helpful feedback.
Definition of Main Development Regions and Analysis of Sensitivity
For each basin, the MDR is defined as the smallest area such that 75% of the TC genesis events have developed within the area and during the TC season. Here, we compare this to analogously defined MDRs that include 65% and 85% of the TC genesis events and MDR defined using simple latitude–longitude bounds (Defforge and Merlis 2017) to assess the sensitivity of results to basin definition.
Figures A1 and A2 show the probability distribution of SSTG and SSTS, respectively, in each basin and in the global mean for the four different MDR definitions. For each basin, the four PDFs corresponding to the four MDR definitions are quite close to each other, indicating that the results presented in the main text are not sensitive to the MDR definition.
Method of Calculation of the Vertical Difference in Equivalent Potential Temperature
The difference between midtroposphere and near-surface equivalent potential temperature is a measure of the convective instability of the atmosphere. This metric is similar to the instability index used in several studies (Raymond et al. 2011). The lower level is taken as the surface air (at 1000 hPa) and the midtroposphere level is 500 hPa. This choice is justified by top row of Figure B1, which shows the vertical profile of equivalent potential temperature at genesis for 20 TCs in each basin and the average over these 20 events (red). The 20 TCs examined here are selected such that the probability distribution of SSTG for these 20 events coarsely samples the SSTG probability distribution of the corresponding basin. Figure B1 shows that, for all the basins, the 500-hPa level (dashed line) is close to the minimum in equivalent potential temperature in the midtroposphere. Consequently, the difference between θe,G at 500 hPa and near the surface generally reflects the convective instability of the atmosphere at TC genesis.
The bottom row of Figure B1 shows the 20-day time series of δθe at the location of genesis of 20 TCs in each basin. As the time of TC genesis approaches, δθe increases, peaks the day of genesis (indicated by the vertical dashed line), and then decreases. Consequently, the effect of the TC itself (local increase of δθe) may start to be substantial 2 days before genesis. However, the intensity of TCs within reanalyses, particularly MERRA, are generally too weak (Murakami 2014; Hodges et al. 2017), and the associated θe anomaly of the TC itself would likely also be underestimated. To examine the environmental condition and not attempt to probe the inflow layer of an existing TC, the values of equivalent potential temperature are averaged over the 3 days preceding genesis (from day −3 to day −1) at the grid point corresponding to the genesis location.
We note that the observations taken during the PREDICT field campaign had weaker vertical differences in θe for two developing hurricanes than one tropical storm that weakened (Smith and Montgomery 2012). This is not necessarily inconsistent with our analysis, as we find larger magnitude of δθe for TC genesis than for the TC season environment, which includes many more events than just nondeveloping disturbances and weakening tropical storms. In addition, the individual time series in the bottom row of Fig. B1 show a variety of temporal behavior of δθe for TC genesis events. This suggests it is difficult to draw general conclusions about the role of vertical differences in θe in TC development from a small sample of events.
Method of Bootstrapping for Percentile Values
The statistical samples studied here are quite small (less than 1000 TCs in each basin), so a method of bootstrapping is used to determine the confidence interval of the percentile values (Efron and Tibshirani 1994).
The basic principle of bootstrapping is to create a large number B of samples of the same size as the initial distribution, using random sampling with replacement. For each of these B bootstrap samples, the value of the statistic of interest T is computed to obtain a sampling distribution of T. The 95% confidence interval for T corresponds to the 2.5th and 97.5th quantiles of the B replications of T.
In our study, the initial sample for each basin is the distribution of the SST at TC genesis, for all the TCs observed during the 33-yr analysis period. The statistics of interest are the values of all the percentiles of these distributions. We obtained an estimate of the 95% confidence interval for these statistics using the bootstrapping method with B = 10 000. The values of the SSTG percentiles and the confidence intervals obtained with bootstrapping are shown in Fig. 2b.