1. Introduction
Genesis potential indices (GPIs) are commonly used to explain the climatology of tropical cyclone activity on Earth from a small number of large-scale environmental parameters (Camargo and Wing 2016; Sobel et al. 2021). They have been employed to explain the observed mean-state climatology of tropical cyclogenesis (Gray 1979; Camargo et al. 2007a) as well as climatological variability induced by modes of climate variability on seasonal time scales, such as El Niño–Southern Oscillation (ENSO; Gray 1979; Camargo et al. 2007b) and the Atlantic Meridional Mode (Patricola et al. 2014), and subseasonal time scales, such as the Madden–Julian oscillation (Camargo et al. 2009; Klotzbach and Oliver 2015; Wang and Moon 2017). GPIs have also been used to explain forced variations in tropical cyclone activity, such as due to volcanic eruptions (Pausata and Camargo 2019), paleoclimatic changes in orbital forcing (Korty et al. 2012) and continental land surface properties (Pausata et al. 2017), and due to increasing greenhouse gases in the modern and future climate (Camargo 2013; Korty et al. 2017; Emanuel 2021b).
Most GPIs contain two essential components, one dynamic and one thermodynamic, intended to capture the known physics required for the development and maintenance of a tropical cyclone. The dynamic component represents background rotation and is commonly represented by the lower-tropospheric (e.g., 850 hPa) absolute vorticity. Recent work has further argued for the inclusion of the low-level absolute vorticity gradient to represent the propensity to generate seed disturbances that precede genesis (Tory et al. 2018; Hsieh et al. 2020). The thermodynamic component represents the energetic potential of the atmosphere to support a tropical cyclone and is commonly defined by the maximum potential intensity (Bister and Emanuel 2002), the bulk deep-tropospheric (e.g., 850–200 hPa) wind shear, and a measure of the dryness of the midtroposphere. Potential intensity captures the base thermodynamic potential of an atmospheric column and extends to any climate state (Ramsay and Sobel 2011; Korty et al. 2012, 2017), thereby avoiding any tethering to present-day global temperatures (Wehner et al. 2015; Tory and Dare 2015). The latter two terms together represent the import of environmental dry air into the storm’s inner core induced by the interaction of the vortex with background vertical wind shear (Tang and Emanuel 2012). These parameters are then combined together jointly (Hoogewind et al. 2020), in a simple multiplicative fashion, allowing for different weighting exponents (Emanuel and Nolan 2004; Emanuel 2021b; Tory et al. 2018) or in a Poisson framework (Tippett et al. 2011). The dynamical GPI of Wang and Murakami (2020) deviates slightly from this structure by including an additional dynamical dependence on the meridional shear of the zonal wind specifically in the Southern Hemisphere and no explicit dependency on potential intensity or SST. Moreover, the midtropospheric vertical velocity has been proposed as an additional factor that measures seed activity (Held and Zhao 2008; Hsieh et al. 2020). These variations in parameters and the functional form for combining these parameters into an index reflect our lack of a proper theory for tropical cyclogenesis (Sobel et al. 2021), which fuels ongoing debate over the appropriate spatial and temporal scales for their use in explaining tropical cyclone variability (Mei et al. 2019; Cavicchia et al. 2023). While most GPIs were developed globally, some GPIs were especially designed for specific tropical cyclone (TC) basins, with the argument that genesis processes are different across basins (e.g., Bruyère et al. 2012; Meng and Garner 2023). Recently, machine learning methods have started to be used to develop alternative GPIs (Fu et al. 2023; Ascenso et al. 2023).
Ultimately, many GPIs share the same dynamic component (low-level absolute vorticity) and share a common structure for the thermodynamic component: They start from the potential intensity and then modify it based on the known effects of wind shear (negative) and environmental moisture (positive). Of these two factors, the representation of environmental midlevel moisture has caused the greatest consternation, with choices spanning relative humidity, saturation deficit, and normalized entropy deficit as detailed in section 3 below. This choice has significant consequences in projections of future TC genesis with warming: relative humidity and normalized entropy deficit yield an increase and saturation deficit yields a decrease (Camargo et al. 2014; C.-Y. Lee et al. 2020; Lee et al. 2023; Emanuel 2021b). This degree of epistemic uncertainty translates to very large uncertainty in how tropical cyclone activity will change under future warming, including a lack of consensus on the sign of the change in storm counts (Knutson et al. 2020; Camargo et al. 2023).
Recently, Komacek et al. (2020) derived an analytic expression for the ventilated potential intensity in the context of understanding the potential for tropical cyclone activity on tidally locked exoplanets. Their expression is derived directly from the foundational theory for how dry air ventilation acts to reduce the traditional potential intensity below its nominal (ventilation free) value (Tang and Emanuel 2010). The effects of ventilation are captured by a single quantity known as the ventilation index, which depends specifically on the normalized entropy deficit and is known to be a very useful predictor for both genesis and intensification rate in nature (Tang and Emanuel 2012). The ventilation index motivates the GPI of Emanuel (2010), employed in Emanuel (2021b), in which the normalized entropy deficit, vertical wind shear, and potential intensity are taken as separate predictors. An alternative and more direct approach, though, would be to use the theoretical prediction for the ventilated potential intensity itself, thereby integrating all three thermodynamic terms together into a single parameter that is fully rooted in a successful theory for tropical cyclone energetics. This approach has the opportunity to greatly simplify existing genesis parameters and reduce the degrees of freedom of our genesis parameters and their wide range of outcomes. Moreover, a simpler GPI may yield insights into the genesis process that can better link our GPIs to a broader theory for genesis. Indeed, Komacek et al. (2020) defined TC genesis favorability by combining the ventilated potential intensity with the 850-hPa absolute vorticity, and Garcia et al. (2024) found that this combination can successfully predict genesis regions from explicitly simulated TCs in idealized high-resolution exoplanet simulations. This approach has yet to be applied to Earth, which is the focus of our work here.
This work examines the use of a ventilated potential intensity in GPI formulations. Our aim is to demonstrate a novel and simpler approach to representing the thermodynamic component of genesis potential relative to existing versions and explore its climatological applications. Specifically, we aim to answer the following questions:
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What is the climatological distribution of the ventilated potential intensity?
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To what extent can a GPI be simplified when using the ventilated potential intensity?
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How well does this simplified GPI capture the climatology of tropical cyclogenesis, including its seasonal cycle and ENSO?
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How do the results compare to existing GPI formulations with comparable formulations, including changes in future projections?
We answer these questions via historical tropical cyclone genesis data and environmental data from reanalysis and future climate change projection simulations. For the final question regarding climate change, our hypothesis is that a GPI based on the ventilated potential intensity should predict an increase in TC genesis with warming as was found in Emanuel (2021b) given their shared theoretical basis.
Section 2 revisits the basic theory of the ventilated potential intensity. Section 3 describes the data and methods. Section 4 presents the results. Section 5 summarizes key results and discusses avenues of future work.
2. Theory
a. Ventilated potential intensity
We begin with a brief rederivation of the ventilated potential intensity (vPI) initially developed in Komacek et al. (2020), whose final form was simplified in Garcia et al. (2024). The solution is visualized in Fig. 1.
vPI as a fraction of the standard (ventilation free) PI (y axis; nondimensional), plotted as a function of the VI (x axis; nondimensional). The analytic solution (red) is given by Eqs. (5) and (6). The numerical solution to Eq. (4) is shown in black, with stable equilibrium in solid and unstable equilibrium in dashed. The VImax is the maximum VI value that yields a nonzero vPI, which is set here to VImax = 0.145, following Hoogewind et al. (2020).
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
As can be seen in Fig. 1, a major conceptual benefit of vPI is that this quantity cuts off sharply to zero at the threshold value of VI (VImax). This property allows for sharper cutoffs in genesis regions, which is consistent with past research showing how, at sufficiently high values of the ventilation index, genesis becomes highly unlikely and existing TCs decay rapidly (Tang and Emanuel 2012; Tang and Camargo 2014; Hoogewind et al. 2020). This behavior may be valuable given the propensity for existing GPIs to be too gradual in the climatological transition from favorable to unfavorable regions which we confirm in our results below.
Similar to the standard potential intensity, vPI may be readily calculated from a vertical profile of temperature and moisture and a sea surface temperature and pressure. This quantity will be calculated at every gridpoint in reanalysis fields and climate model simulations as described below.
b. GPI with ventilated potential intensity (GPIυ)
We choose the power-law form, as the behavior of the power law and Poisson formulations are very similar. Figure 2a compares the observed and predicted dependence of the number of TCs per year on vPI × ηc. For the range of values greater than 1.5 × 10−3, which represents the vast majority of all TCs (note the log scale on the y axis; TC frequency at this threshold is approximately 1/20 of the peak), the two models are nearly identical. For smaller values, they diverge and Poisson is the better model, as the observed dependence in the log-linear plot of Fig. 2a is nearly linear, consistent with the exponential dependence of the Poisson model that is also linear (a power-law model is linear in a log–log space). However, this departure at small values of vPI × ηc is associated with regions/times on Earth that have very few TCs at all: small values of vPI ≤ 40 m s−1 (Fig. 2b), corresponding to regions on Earth that cannot support TCs at a reasonable intensity, and ηc < 1.25 (Fig. 2c), corresponding to very low equivalent latitudes of <5° where storm formation is very rare (Chavas and Reed 2019). Hence, for practical purposes, the power law formulation [Eq. (8)] and Poisson formulation [Eq. (9)] are equivalent.1 This close equivalence between the two forms has not, to our knowledge, been addressed in the past literature despite both forms being consistently used in different GPI formulations (Emanuel and Nolan 2004; Tippett et al. 2011). Their mathematical similarity over the range of predictor values relevant to the vast majority of TCs on Earth may explain why both formulations perform similarly in practice.
Dependence of observations (blue), GPIυ (red), and GPIvent,Pois on (a) vPI × ηc, (b) vPI, and (c) ηc. Plots are displayed as log linear, such that an exponential (Poisson) dependence will be linear. Abscissa values are separated into 20 bins (equal numbers of values).
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
Given their similar practical performance, for the remainder of our study, we utilize the power-law model of Eq. (8). Indeed, all of our results below are nearly indistinguishable if the Poisson formulation is used instead. Additionally, the power-law formulation has important intuitive and physical appeal. First and foremost, the quantity vPI × ηc has units of acceleration (m s−2), which might be interpreted as analogous to an intensification rate. Second, past theoretical work has argued that vertical velocity w scales directly with the potential intensity (Khairoutdinov and Emanuel 2013) in a tropical cyclone, in which case this quantity behaves like wη, i.e., a vortex stretching, which is the lone vorticity source term in the vorticity equation proposed as a genesis framework by Hsieh et al. (2020). This interpretation also aligns at least qualitatively with the importance of the overall updraft mass flux in setting regions of significant convective activity and precursor seed disturbances (Held and Zhao 2008; Hsieh et al. 2020). The exponent represents a strong sensitivity of genesis to this quantity, but its magnitude lacks any obvious physical explanation. Nonetheless, this GPI formulation is simpler and may take an important step closer to linking the GPI to a physical theory of genesis; further discussion is provided in section 5 below.
3. Data and methods
Global historical 6-hourly tropical cyclone genesis data are taken from the IBTrACS data archive (Knapp et al. 2010). Environmental parameters are calculated from monthly mean ERA5 reanalysis fields (Hersbach et al. 2020). The horizontal grid spacing of ERA5 is 0.25°, and all fields were interpolated to a 2° horizontal spacing. For both datasets, we analyze the period 1981–2020.
For historical climate model simulation data, we use monthly surface and pressure-level data for 1981–2014 from 45 phase 6 of the Coupled Model Intercomparison Project (CMIP6) model historical simulations (Eyring et al. 2016). For future climate simulation projections, we use data from the ssp245, ssp370, and ssp585 scenarios and analyze each for the periods 2021–40 (near term), 2041–60 (medium term), and 2071–2100 (long term). All model data were interpolated to a common 2° horizontal spacing. For each model and scenario, all ensembles which had all required output fields for all variables were considered. The ensemble mean of each model was calculated using all the ensembles available before calculating the multimodel mean for each scenario. Note that the number of models available differed across future scenarios, as well as the number of ensembles. When the differences between future and current scenarios are calculated, the models in the historical scenario matched those in each of the future scenarios. Table 1 lists the models and the number of ensembles in each scenario as well as the papers that describe each of these models.
The CMIP6 models, number of ensembles per scenario, and references.
Note that we use coarse resolution data to provide a simple consistent grid across all datasets that is also more manageable for storage. We have tested the derivation of the genesis indices in high-resolution reanalysis datasets, and for consistency, we would also need to calculate the genesis density on the same grid, which is a very noisy field at this resolution, which leads to problems when doing the statistical fit. Furthermore, for our study, we are interested at the larger scales, so variations on scales smaller than 2° are not central to our analyses. These quantities generally do not vary too strongly on these short spatial scales, so coarsening the grid will smooth features but will not change the qualitative outcome.
We first calculate historical tropical cyclogenesis rates using the IBTrACS dataset across all major basins globally as our observational baseline for the period 1981–2020. The eastern Pacific basin is defined as all storms east of 180°. Each storm is counted only once based on its genesis location when the storm first reaches 35 kt (1 kt ≈ 0.51 m s−1). We calculate our new GPI as well as existing commonly used GPIs from environmental data in ERA5 reanalysis for comparison against one another and against observed genesis rates. We then calculate our new GPI in CMIP6 historical and future simulations to examine future changes under global warming. Note that the CMIP6 historical simulations in the CMIP6 models end in 2014. Therefore, when calculating the historical climatology, we used the closest full decades to the observational climatology 1981–2010. When considering changes between present and future simulations, we considered the last 30 years of the twentieth century (1971–2000) and the last 30 years of the twenty-first century (2071–2100).
4. Results
We begin first with the climatology of our new genesis potential index GPIυ and its components, including the vPI. We then compare GPIυ with existing GPIs. Finally, we examine how GPIυ changes in the future in CMIP6 future climate projection simulations.
a. Climatology of vPI, GPIυ
1) Annual climatology
The annual-mean climatology of the components of GPIυ is shown in Fig. 3. The traditional PI (Fig. 3a) takes higher values broadly over the equatorial and western portions of the global tropical oceans and decreases gradually moving poleward and eastward within each basin. The transition from PI to the ventilated potential intensity vPI is mediated by the deleterious effects of the ventilation index [Fig. 3b; Eq. (5)]. The regions of lowest ventilation (i.e., smaller values of VI), which are favorable for TCs, are also found in the same general regions as where potential intensity is high. The resulting distribution of vPI (Fig. 3c) is a qualitatively similar pattern to PI but with a much sharper transition from high values, primarily over the western North and South Pacific Ocean and the near-equatorial Indian Ocean and North Atlantic Ocean, to very low values moving poleward and eastward from those regions. In the regions of highest PI over the equatorial western Pacific Ocean, the ventilation index is very small, and hence, there is very little reduction in vPI relative to PI. In contrast, moving poleward and eastward within each basin, particularly the North and South Atlantic and Pacific basins, the ventilation index increases substantially, and thus, there is a sharp reduction in vPI, decreasing rapidly toward zero as the ventilation index approaches its maximum value that allows a positive vPI. Hence, vPI yields a much more refined geographic region capable of supporting tropical cyclones than PI.
Maps of annual-mean climatology of (a) PI, (b) VI, (c) vPI, and (d) 850-hPa clipped absolute vorticity ηc. Data from ERA5 1981–2020.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
The distribution of clipped absolute vorticity (Fig. 3d) is largely zonal in structure with values monotonically increasing moving poleward, reflecting the dominant contribution of f, up to the cut-off value above which it is held constant. The lone notable large-scale deviation is over the Indian Ocean and Maritime Continent in the western Pacific, where the absolute vorticity is relatively large owing to a significant time-mean relative vorticity contribution from a quasi-stationary cyclonic circulation. This equatorial region is characterized by relatively high values of both absolute vorticity and ventilated potential intensity, and indeed, it coincides with tropical cyclone formation closer to the equator than anywhere else in the world (Lu et al. 2021; Chavas and Reed 2019).
The annual-mean climatology of GPIυ and observed genesis density is shown in Fig. 4. The spatial distribution of GPIυ (Fig. 4a) aligns well with that of historical genesis density (Fig. 4b), capturing the key regions of tropical cyclogenesis globally. GPIυ is largest over the tropical western North Pacific south of 20°N between 120° and 150°E, as well as over relatively narrow latitudinal bands (10°–15°N) in the south Indian and western South Pacific basins west of 170°W. In the eastern North Pacific, which is known to have the highest genesis density in the world, GPIυ is also relatively large though not as large as the aforementioned regions. In the North Atlantic basin, GPIυ is largest over the Gulf of Mexico and western Caribbean, though it is overall smaller in magnitude than the other basins. Finally, a small region with modest values of GPIυ is found in the western South Atlantic off the coast of Brazil, consistent with the infrequent and weak tropical cyclones that form in this subregion but not elsewhere in the basin (Pezza and Simmonds 2005; Evans and Braun 2012; Gozzo et al. 2014). Our new genesis index captures the gross meridional structure of genesis (Fig. 4c), including the greater meridional extent of genesis in the Northern Hemisphere. However, GPIυ predicts that genesis within the tropics, particularly its peak amplitude, ought to be nearly symmetric between the Northern and Southern Hemispheres, in contrast to the nearly doubled peak genesis density in the Northern Hemisphere relative to the Southern Hemisphere. This is a problem common to existing GPIs as well as shown below.
Maps of annual-mean (a) GPIV (function of vPI), (b) observed genesis density (yr−1) 1981–2020, and (c) zonal mean genesis per latitude in observations and integrated GPIV.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
2) Annual cycle
The seasonal-mean climatologies of GPIυ for August–October (ASO) and January–March (JFM), which correspond to the peak 3-month periods of TC activity in each hemisphere, and observed genesis densities for each season are shown in Fig. 5. Similar to the annual mean, GPIυ captures the spatial pattern of TC activity in the peak season of each hemisphere. It also successfully captures the rare occurrence of genesis events in the opposite hemisphere, with low but nonzero values over the tropical south Indian and southwestern Pacific basins in boreal summer and over the tropical north Indian Ocean and northwestern Pacific in austral summer.
Maps of seasonal-mean GPIV and observed genesis density (yr−1) 1981–2020 for (a),(b) boreal summer (ASO) and (c),(d) austral summer (JFM). Seasonal values are simply the sum of the GPI over the season, averaged across years.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
The annual cycle climatologies of monthly GPIυ and observed genesis count within each basin are shown in Fig. 6. Overall, GPIυ does reasonably well in reproducing the annual cycle of genesis across all basins and globally. It does very well in the south Indian (Fig. 6a) and South Pacific (Fig. 6c), as well as in Australia (Fig. 6b) and the North Atlantic (Fig. 6g) though with slight underestimation of genesis counts during the peak months. There is a stronger underestimation of genesis throughout the primary TC season of approximately 20%–30% in the western North Pacific (Fig. 6e) and ∼30%–70% in the eastern North Pacific (Fig. 6f). These low-biased basins drive the overall underestimation of genesis count in the Northern Hemisphere noted above and that shows up globally (Fig. 6g).
(a)–(g) Monthly mean new GPIV and storm count by basin and (h) the sum across all basins globally. For (h), the sum is slightly smaller than the true global count because a small number of genesis events occur outside of basin boundaries.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
3) ENSO
GPIs are known to skillfully represent the variability in TC activity related to ENSO (e.g., Camargo et al. 2007b). Maps of composite differences of GPIυ and observed genesis density between El Niño and La Niña events for JFM and ASO are shown in Fig. 7 for the period 1950–2020. In El Niño events, GPIυ is reduced over the tropical Atlantic, particularly through the western half of the main development region where most TCs form, while it is modestly enhanced over the subtropical North Atlantic. Meanwhile, GPIυ is enhanced throughout most of the eastern North Pacific; this shift in genesis between the North Atlantic and east Pacific is a well-documented response to ENSO (Camargo et al. 2007b). Additionally, GPIυ is larger across most of the central and western tropical North Pacific, with smaller reductions in the far western tropical and subtropical Pacific. For the Southern Hemisphere, GPIυ is enhanced over the tropical western South Pacific to the east of New Zealand, while it is reduced over the tropical eastern south Indian Ocean to the west of southern Indonesia and northern Australia. The pattern of changes in observed genesis is quite similar to that of GPI, indicating that genesis does indeed closely track GPI in the context of ENSO variability. The pattern of changes in GPI in each season is broadly similar across all GPIs (supplemental Fig. 1 in the online supplemental material).
Difference between El Niño and La Niña events for the period 1950–2020 for (a) GPIυ in ASO and (b) GPIυ in JFM, as well as for (c) observed genesis in ASO and (d) observed genesis in JFM. Hatching in (a) and (b) indicates that the difference is statistically significant at the 95% confidence level.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
4) Dependence on common physical variables
Finally, we provide a deeper analysis of the performance of GPIυ within each basin by examining how well it captures the observed dependence of TC genesis on related physical parameters in Fig. 8: 200–850 hPa vertical wind shear (Fig. 8a), vPI (Fig. 8b), and saturation deficit (Fig. 8c). This analysis complements the analysis of the spatial and temporal variations in the previous sections by now testing the dependence on physical parameters themselves across their full range of observed values. The dependence of observed genesis count on each physical parameter is shown in Fig. 8 (blue curves), which displays the ranges of parameter values that are most important for TC activity on Earth: most TCs form with low vertical wind shear (left column), high ventilated potential intensity (middle column), and moderate saturation deficit (right column). The dependence of GPIυ is also shown (red curves) for direct comparison.
Dependence of observations (blue) and GPIυ (red) on 850–200-hPa vertical shear, PI, and SD by basin. Data were binned into 20 percentile intervals (0–100th percentile, in increments of 5%), and the average values of the observations and GPIυ were calculated for each bin.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
In the North Atlantic, south Indian, and Australian basins, the dependence for GPIυ closely matches the dependence for observed genesis count on all three parameters. The dependence of GPIυ is biased low across all three variables in the eastern North Pacific and the western North Pacific. In the former, the bias is concentrated in the most favorable environments (high vPI, low shear); in the latter, the bias is more diffuse spread across all types of environments. GPIυ is biased high across all three variables in the South Pacific basins, primarily concentrated in the most favorable environments. Meanwhile, in the north Indian basin, the biases are mixed, though with a high bias at low vertical shear and high vPI. Hence, overall our GPIυ is capturing these physical dependencies well, but the weaker-than-observed dependence in the North Pacific indicates an important gap not captured by our genesis potential index. The broad low biases in the Northern Hemisphere and high biases in the Southern Hemisphere reflect how GPIυ does not capture the hemispheric asymmetry in genesis found in observations (Fig. 4c). Why the bias structure differs between the eastern and western North Pacific basins is unclear, but it could be relevant to explaining biases in GPIυ relative to observations within each basin.
b. Comparison with existing GPIs
The annual-mean climatology of GPIυ and the other four GPI formulations are shown in Fig. 9, with seasonal climatologies shown in Fig. 10. Observed genesis density (smoothed) is also included in these figures, whose spatial pattern across the tropics is generally well captured by the GPIs as expected. The overall spatial distribution of GPIυ is quite similar to the other formulations. The differences between GPIυ and existing GPIs are not obviously larger than among the existing GPI formulations. Note that the combination of shear and relative humidity or saturation deficit in existing GPIs serve to greatly reduce GPI over the marginal parts of the ocean basins in a similar manner as our vPI does in a single parameter. Ultimately, we are not arguing that our spatial distribution of GPIυ is superior to the others, but rather that it performs comparably well to the others with fewer parameters and more firmly grounded in tropical cyclone physics.
Annual mean climatology for the period 1981–2020 for (a) GPIV, (b) Emanuel’s original index (GPIE04), (c) Emanuel’s 2010 index (GPIE10), (d) TCGI-CRH, and (e) TCGI-SD for the ERA5 reanalysis regridded to a 2° × 2° grid. Emanuel’s indices were normalized to match the other indices. Values below 5 × 10−3 are set to zero (white). All indices integrate globally to a value of 84.625 yr−1. Observed genesis density is overlaid (contours, with interval 0.04 yr−1 from 0.01 to 0.27; smoothed once with a kernel density smoother to reduce noise).
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
As in Fig. 9, but for the seasonal mean climatology in ASO and JFM for (a),(b) GPIV, (c),(d) GPIE04, (e),(f) GPIE10, (g),(h) TCGI-CRH, and (i),(j) TCGI-SD.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
The annual cycle climatologies comparing GPIυ to the other GPI formulations within each basin and globally are shown in Fig. 11. Clearly, all GPI formulations successfully capture the main regions of TC activity globally, but the relative magnitudes between basins differ. Our GPIυ falls somewhere in between the Emanuel GPIs, which tend to show the highest values in the east Pacific and smaller values in the west Pacific (and mixed outcomes in the North Atlantic), and the TCGIs, which show the highest values in the west Pacific, moderate values in the east Pacific, and lower values in the North Atlantic. Across GPIs, the two based on either the normalized entropy deficit (E10) or the saturation deficit (TCGI-SD) tend to show higher magnitudes over the North Atlantic relative to the east Pacific, an outcome that is also evident in our GPIυ in line with their shared physical foundation. All GPIs are low-biased in the west Pacific and east Pacific though this bias is smaller for the two TCGIs, the reason for which is unknown. Ultimately, though, none are conclusively better or worse than the others. However, our GPIυ is more parsimonious in form than the others and rooted more strongly in tropical cyclone physics and hence may provide clear guidance on the representing the free-tropospheric moisture variable and its impact on the spatial distribution of GPIs in their existing formulations.
Annual cycle of all indices (lines: GPIV in blue, GPIE04 in orange, GPIE10 in yellow, TCGI-CRH in purple, and TCGI-SD in green) and observations (gray bars) in different basins and the sum of all basins.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
c. Future projections in CMIP6
Finally, we examine future projected changes in GPIυ from the CMIP6 multimodel ensemble. We begin first with the multimodel mean historical climatology of PI, vPI, and GPIυ in Fig. 12. The spatial distribution closely aligns with that found in reanalysis in Fig. 4. Accounting for ventilation in the potential intensity again yields a much more refined geographic distribution of environments favorable for TCs. The distribution of GPIυ aligns with the key regions of TC activity, with a broader region of very small values extending into higher latitudes relative to ERA5 owing to model biases and the smoothing that arises from averaging over many ensembles and models in those regions.
Historical (1981–2010) multimodel mean annual climatology for 45 CMIP6 models for (a) PI, (b) vPI, and (c) GPIV (bottom).
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
Figure 13 displays the differences in the multimodel mean climatology of PI, vPI, ηc, and GPIυ for ssp245, ssp370, and ssp585 between the end of the 21C (2071–2100) and the end of the 20C (1971–2000). Basin-integrated changes in GPIυ are shown in Table 2. Globally, there is a consistent broad increase in GPIυ across all basins (fourth column), with the magnitude increasing with increasing warming across scenarios while maintaining a very similar spatial pattern (rows). The eastern and central North Pacific, subtropical North Atlantic, and south Indian Ocean Basins are regions of the largest increase, with the subtropical western North Pacific showing slightly weaker increases. Changes in GPIυ are driven almost entirely by changes in vPI (second column), particularly at higher latitudes, with increases of 5–15 m s−1 in the aforementioned regions. Because the absolute vorticity ηc is capped at 3.7 × 10−5 s−1, which corresponds to an equivalent Coriolis latitude of approximately 15°, and this term is generally dominated by f, changes in its impact are effectively limited to within the deep tropics (third column). Changes in ηc within the deep tropics have a very small impact on GPIυ with the exception of a slight increase in the near-equatorial eastern North Pacific basin and a slight decrease in the near-equatorial north Indian Basin, the latter offset by an increase in vPI. Changes in vPI broadly follow the changes in PI (left column), particularly the increase in both poleward of 20°N. However, within the tropics, there are regions where the two diverge, particularly the western Atlantic and Pacific basins and central south Indian Basins where vPI decreases despite an increase in PI. Note that there is a strong decrease in mean vPI in the central South Pacific and tropical western Atlantic, yet GPIυ decreases only slightly in the former while remaining relatively constant in the latter, with GPIυ still consistently increasing in the Atlantic basin as a whole (Table 2). This outcome highlights that GPIυ is a nonlinear combination of vPI and ηc, and hence, mean changes in GPIυ may not always neatly follow mean changes in the individual components.
Differences between the CMIP6 multimodel mean (Northern Hemisphere for ASO, Southern Hemisphere for JFM) at the end of the twenty-first century (2071–2100) and at the end of the twentieth century (1971–2000) for (a),(e),(i) PI, (b),(f),(j) vPI, (c),(g),(k) ηc × 105, and (d),(h),(l) GPIV × 103 for three different future scenarios: (top) ssp245 (40 models), (middle) ssp370 (36 models), and (bottom) ssp585 (45 models). Statistically significant differences among the multimodel ensemble based on the Kolmogorov–Smirnov test at the 95% level are marked with a circle.
Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0186.1
Percentage changes of the mean GPIυ in the tropics in different basins, Southern Hemisphere basins in JFM, Northern Hemisphere basins in ASO for three periods: 2021–40 (P1), 2041–60 (P2), and 2071–2100 (P3). Also shown are the estimated multimodel mean global mean surface temperature increases (TS) at the midpoint of each period (2030, 2050, and 2085).
Comparing results across scenarios and time periods, the response is quantitatively very similar between ssp245 and ssp370, with only a slightly higher increase across basins in the latter by the end of the century owing to the stronger global warming by that period. The patterns exhibit similar localized regions of statistically significant increases in the Northern Hemisphere subtropics (Fig. 13d vs Fig. 13h). The basin-wide response magnitude within each basin scales closely with global-mean warming (Table 2), with the largest responses by the end of the twenty-first century when warming is strongest. The signal of increasing GPIυ at higher latitudes in the subtropical North Atlantic and North Pacific emerges by the end of the century across all scenarios, but it becomes much more pronounced in both hemispheres only in ssp585, corresponding to the greatest magnitude of warming. The end-of-century ssp585 scenario exhibits a substantially larger jump in GPIυ relative to the global-mean warming, with percentage increases in GPIυ nearly double that of ssp370 despite a global-mean warming only 20% larger (4.9°C vs 4.0°C). Recall that ssp245 is the closest analog to our current emissions trajectory, with ssp370 representing a reasonable high-end scenario that is considered more plausible than ssp585 (Pielke et al. 2022).
Overall, our results indicate that the global environment becomes very gradually more favorable for tropical cyclones in general (as measured by vPI) and for genesis in particular (as measured by GPIυ), though these changes are relatively modest for current plausible scenarios through the end of 2100. The first signal to emerge is an increase in higher-latitude genesis as the warming magnitude increases, whether due to higher emissions or more time at lower emissions, which is consistent with recent poleward trends in TC activity, in particular in the western North Pacific (Kossin et al. 2014; Daloz and Camargo 2018; Studholme et al. 2022), as well as future projections (Kossin et al. 2016); however, there could be some compensating effects due to higher-latitude environmental characteristics (Lin et al. 2023). Furthermore, recent trends in TC frequency have been decreasing globally (Klotzbach et al. 2020). Long-term estimates of trends in TC frequency have been a source of significant debate in the scientific community, given the uncertainty of the data presatellite era and the multiple methods used to make such estimates leading to contrasting results (Vecchi et al. 2021; Emanuel 2021a; Chand et al. 2022; Emanuel 2024; Chand et al. 2024.
Our new GPI using the ventilated potential intensity predicts a modest increase in TC genesis with warming, consistent with the predictions from the GPI of Emanuel (2021b) based on the normalized entropy deficit, which is the closest GPI cousin to ours. It is also consistent with GPIs that use either midlevel relative humidity or column relative humidity but not column saturation deficit, which might not be expected on intuitive grounds. Hence, this speaks to the importance of using physical parameters that fully exploit our underlying theory, as the precise nature of its influence appears to determine its influence in a warming climate.
At the same time, our new GPI is again not a closed theory, and hence, the above also further emphasizes the intrinsic uncertainty associated with GPIs of any form as proxies for tropical cyclogenesis. Indeed, GCM-based projections tend to show a broad decrease in global tropical cyclone count (Knutson et al. 2020) similar to recent observed global trends (Klotzbach et al. 2022; Chand et al. 2022), though GCMs may project an increase at sufficiently high model resolution (Vecchi et al. 2019) and are otherwise known to be strongly sensitive to internal model parameters (Zarzycki 2022). Clearly, the details of explicit TC representation are important, an issue that our GPI cannot resolve by definition. Moreover, it is important to acknowledge ongoing uncertainties in both historical tropical cyclone data and reanalysis data used to train our GPI, and perhaps more importantly in climate models whose future projections for a more El Niño–like pattern are currently sharply at odds with the recent La Niña–like trend (Seager et al. 2019; Sobel et al. 2023). Given the relatively modest increases in our GPI with warming, these changes may certainly be viewed as well within the combined error bars of our estimation of the current climate and projection of future climate. As such, our work may help settle the debate regarding the treatment of moisture within a GPI, but it cannot conclusively settle the broader debate about whether genesis itself will change with warming.
5. Conclusions
This work has developed a novel genesis potential index that depends on a single parameter given by the product of the ventilated potential intensity and the clipped absolute vorticity. The ventilated potential intensity represents the thermodynamic favorability of an environment for supporting a tropical cyclone by explicitly incorporating the detrimental effect of the shear-induced entrainment of midlevel low-entropy environmental air on the potential intensity and is taken directly from existing ventilation theory, which has been shown to successfully explain tropical cyclone genesis and intensity change in nature. The ventilated potential intensity helps clarify the choice of midlevel environmental moisture term, as its strong physical basis contrasts with other choices, such as midlevel relative humidity or column saturation deficit, that are reasonable but chosen arbitrarily and can yield conflicting outcomes. This quantity was first developed in recent work to understand tropical cyclogenesis on tidally locked exoplanets, but it had yet to be applied to Earth. The new GPI presented here is more parsimonious than existing indices and performs comparably well in reproducing the climatological distribution of tropical cyclone activity and its covariability with ENSO. When applied to CMIP6 projections, the new GPI predicts that environments globally will become gradually more favorable for TC activity (as measured by the ventilated potential intensity) and genesis (GPI) with warming. However, significant changes emerge only under relatively strong warming and principally at higher latitudes outside of the tropics. This qualitative outcome is consistent with the projected increases found by Emanuel (2021b) using a GPI that takes the normalized entropy deficit as its environmental moisture predictor, whose formulation is motivated by the same underlying theory that we have used explicitly in creating our new GPI presented here. Hence, our results emphasize the importance of employing parameters whose form is fully rooted in theory. Our findings should help resolve the debate over the treatment of the moisture term in a GPI and the implication of this choice for how TC genesis may change with warming. However, this outcome is in contrast to the decreasing trend in TC count in the recent historical record (Klotzbach et al. 2022; Chand et al. 2022), as well as projections of most GCMs (though GCM uncertainties remain large). Hence, if frequency indeed decreases with warming, our results argue that opposing processes or feedbacks must exist that more than offset the expected enhancement of genesis by a more favorable environment as represented by our GPI.
Indeed, it is important to emphasize that genesis potential indices, including our own, remain semiempirical proxies for TC genesis that carry intrinsic uncertainty in extrapolating to future climate states owing to the nature of their formulation in the absence of a complete theory for genesis. We ultimately must assume that the relationships between actual genesis and any GPI estimated from the historical record extend to a future climate, which may not be true (Murakami et al. 2013). Given these circumstances, it is arguably more imperative to choose parameters that are most strongly grounded in tropical cyclone physics, which are not intrinsically tied to our present-day climate. The core parameter in our new GPI is given by the simple product of the ventilated potential intensity, which is the fundamental thermodynamic ingredient for the energetics of the TC, and the absolute vorticity, which is the fundamental dynamic ingredient for the rotation of the TC. This joint parameter has units of acceleration, which could plausibly be interpreted as analogous to an intensification rate. Hence, this parameter carries deep intuitive physical appeal as a crude representation of the growth rate of a weak initial disturbance. Why the parameter should be taken to the fifth power has no intuitive explanation, though, and instead is an indication of how this remains well short of a theory for genesis. Instead, our new GPI may perhaps be viewed as the most refined possible representation of two necessary (but not sufficient) ingredients for tropical cyclogenesis: energy and rotation. Clearly, localized and sustained upward motion in the form of a “seed” is also a necessary condition (Merlis et al. 2013; Sugi et al. 2020; Hsieh et al. 2020; Zhang et al. 2021; Yoshida and Ishikawa 2013; Ritchie and Holland 1999), whose absence in GPIs likely explains why they struggle to predict changes in TC genesis on subclimatological time scales (Cavicchia et al. 2023). Our GPI provides no further insight on this matter relative to previous iterations. However, the physical simplicity and parsimony of our version may provide a useful step toward a broader theory of genesis that is skillful in predictions across all time scales, including future climate change.
Mathematically, power law and exponential functions are very similar so long as the range of their shared predictor is not too large. A power law is given by log(y) = log(a1) + a2 log(x′), while an exponential is given by log(y) = log(b1) + b2x′, where x′ = x − x0 is the departure from the y-weighted mean value x0 to which both models are fit. The difference is strictly log(x′) vs x′ on the right-hand sides. Substituting in the Taylor series approximation
Acknowledgments.
D. R. C. was supported by NSF AGS Grant 1945113. S. J. C. was supported by NSF Grants AGS 20-43142, 22-17618, 22-44918, and NOAA Grants NA21OAR4310345 and NA22OAR4310610.
Data availability statement.
IBTrACS data are publicly available from the National Center for Environmental Information website at https://www.ncei.noaa.gov/products/international-best-track-archive. ERA5 reanalysis data are publicly available from the European Center for Medium-Range Weather Forecasts Copernicus Climate Data Store at https://cds.climate.copernicus.eu/. Coupled Model Intercomparison Project version 6 model simulation data are publicly available at https://aims2.llnl.gov/search/cmip6/. Data for this work are publicly available via the Purdue University Research Repository (PURR) at https://doi.org/doi:10.4231/7N7B-2494 (Chavas 2025).
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