Distinct responses of tropical cyclone activity to spatio-uniform and nonuniform SST warming patterns

Most previous studies have reported a decrease in global tropical cyclone (TC) genesis frequency (TCGF) under anthropogenic warming. However, little attention has been drawn to the influence of sea surface temperature (SST) warming patterns on TCGF changes. Here, we investigate the impacts of three distinct SST warming patterns on global TCGF: uniform SST warming, nonuniform (El Niño-like) SST warming, and a combination of both. Results show that spatio-uniform SST warming has a limited impact on global TCGF, instead redistributing the TC genesis locations. Conversely, nonuniform SST warming significantly suppresses global TCGF. The combined warming produces a similar decrease in TCGF to nonuniform warming albeit with differences in spatial distribution. This indicates the dominant role of nonuniform SST warming in affecting TCGF and highlights the nonlinearity of the process. Further analysis shows that these differences in TCGF primarily stem from the distinct responses of tropical circulations to the three warming patterns.


Introduction
Among the various tropical cyclone (TC) metrics, TC genesis frequency (TCGF) remains poorly understood under climate change, with conflicting projections in previous studies (Emanuel 2018, Knutson et al 2020, Sobel et al 2021).Although the majority of climate models have projected a decrease in TCGF under global warming (GW; Sugi et al 2009, Murakami et al 2012, Yoshida et al 2017), other studies have indicated an increase (Emanuel 2013, Park et al 2017).Therefore, future change in TCGF has low-to-medium confidence (Knutson et al 2020) and thus deserves further study.
Although the physical mechanism responsible for TCGF changes under GW remains unclear (e.g.Knutson et al 2020), two hypotheses have been commonly used to explain reduced global TCGF under GW: the upward mass flux hypothesis and the saturation deficit hypothesis (Sugi et al 2015, Knutson et al 2020).In the upward mass flux hypothesis, the reduction of global TCGF is attributed to the decreased upward mass flux at midtroposphere in the tropics, resulting from increased atmospheric stability (Sugi et al 2002(Sugi et al , 2012)).Saturation deficit represents the shortfall between the actual water vapor content in the air and the amount required for the air to become saturated at its current temperature.In the saturation deficit hypothesis, a warmer climate may reduce TCGF by increasing saturation deficit in the lower troposphere, leading to enhanced moisture divergence and atmospheric stability (Emanuel et al 2008, Emanuel 2010).
Sea surface temperature (SST) stands as a pivotal factor influencing TC activity under GW (Walsh et al 2016, Knutson et al 2020).Some previous studies have focused on the influence of uniform SST warming on TCGF without considering warming patterns (Sugi et al 2015, Zhao et al 2023).However, TC activity may be sensitive to different SST warming patterns (Zhao et al 2009, Murakami et al 2012, Knutson et al 2015).Zhao et al (2020) have shown that TCGF over the Western North Pacific (WNP) and the North Atlantic (NA) responds differently to El Niño-and La Niñalike warming patterns.Hsieh et al (2022) pointed out that different warming patterns have diverse impacts on the formation of TC seeds, further influencing TCGF.It therefore suggests that both spatio-uniform and nonuniform SST warming play important roles in affecting TCGF.However, it remains unknown whether these two warming patterns play distinct roles in TC activity and which one contributes more significantly.
In this study, we aim to provide a comprehensive and quantitative analysis of the distinct effects of uniform and nonuniform SST warming on TCGF, as well as their nonlinearity resulting from their combined influence.By utilizing the high-resolution atmospheric general circulation model (HiRAM-C180), we find that uniform SST warming generates a dipole pattern of spatial changes in TCGF across most basins, while having limited impact on the total number of TCs.Conversely, nonuniform SST warming results in a prominent reduction in global TCGF.These findings offer valuable insights into understanding and projecting future TC changes under global warming.

Observational data
In this study, we obtained the TC best-track data from two sources: the Shanghai Typhoon Institute of the China Meteorological Administration (CMA-STI, Ying et al 2014) for the WNP, and the National Hurricane Center (NHC, Landsea and Franklin 2013) for the NA and other basins, covering the period 1980-2009. The period 1980-2009 was considered because only the SST data before 2010 were available in the HiRAM-C180 model.Here, we defined the TC genesis location as the point where a TC first reaches tropical storm intensity (with maximum sustained 10 m wind speed V max ⩾ 17.2 m s −1 or 35 knots).TCGF was counted once if a TC formed within a grid box.In addition, we used the observed monthly mean SST data from the Met Office Hadley Centre Sea Ice and Sea Surface Temperature dataset, covering the same period (Rayner et al 2003).

HiRAM model and experiments
We used the HiRAM-C180 model to conduct numerical experiments and examine the responses of TCGF and TC track density (TCTD) across the seven basins (supplementary figure S1) to three different warming patterns.The HiRAM-C180 was developed by the geophysical fluid dynamics laboratory (GFDL), with the details in (Zhao et al 2009).Previous studies have demonstrated that the HiRAM-C180 is capable of well reproducing the spatial distribution of the observed TC genesis and tracks (Zhao et al 2009(Zhao et al , 2020(Zhao et al , 2023)).
The model simulations were conducted from January 1980 to December 2009.It should be mentioned that we have examined the atmospheric response to the warming SST and found that the process is very rapid in the HiRAM-C180.Hence, we did not consider the effect of the ocean-atmosphere adjustment in the model.The control (CTRL) experiment used the observed monthly mean SST as the boundary condition to simulate the present climate (figure 1(a)).Three future runs were conducted by adding different SST warming modes to the observed monthly mean SSTs.The first run, referred to as the Uniform 2 K run, incorporated a spatio-uniform warming pattern of 2 K to the SST in the CTRL experiment (figure 1(b)).The second run, known as the Pattern 2 K run, utilized an El Niño-like warming pattern derived from the multimodel ensemble mean of 21 CMIP6 models (Eyring et al 2016, supplementary table S1) under the 1pctCO2 experiment (figure 1(c)) added to the SST in the CTRL experiment.Finally, the Total 4 K run encompassed a total warming pattern consisting of the SST in the CTRL experiment, a spatio-Uniform 2 K warming, and an El Niño-like warming pattern (figure 1(d)).
Note that although the SST perturbation in the Total 4 K run is a linear superposition of the Uniform 2 K and the Pattern 2 K runs, their effects on TCGF (circulation) are nonlinear.See the calculation of nonliear effect in supplementary text S1.Here, the 6-hourly outputs from HiRAM are utilized to detect TC vortices.The TC detection algorithm was obtained from the GFDL website (www.gfdl.noaa.gov/tstorms/)(supplementary text S2).In general, the CTRL run reasonably reproduced the climatology and interannual variability of TCGF and TCTD in compared to observation (the comparisons in the WNP and the NA are shown in supplementary figure S2).

Results
Figure 2 shows the simulated changes in TCGF over the seven oceanic basins in response to the three SST warming patterns and the nonlinear effect, respectively, with the number of TCGF for each basin shown in supplementary figure S3.In the Uniform 2 K run, there is a negligible change in global number of TCs relative to the CTRL run.This is reflected by a limited reduction in TCGF over the WNP, the NA, the North Indian Ocean (NI), and the South Indian Ocean (SI), and a modest increase over the eastern North Pacific (ENP) and Southwest Pacific (SP).TCGF remains relatively constant over the South Atlantic (SA).However, there is a notable spatial difference in TCGF compared to the CTRL run, displaying a distinct dipole distribution in most basins.For instance,   S4), and these changes can also be reflected in the shifts of TC genesis locations (supplementary table S2).
The ratios of TCGF changes in the three warming experiments relative to the CTRL run are −0.6%,−12.0% and −11.9%, respectively, suggesting a rough linear relationship between them.However, there is still a significant nonlinear response in terms of the spatial distribution of TCGF changes between the Pattern 2 K and the Total 4 K runs.The nonlinear effect exhibits a moderate dipole distribution in TCGF changes across most basins, but with the pattern nearly opposite to that in the Uniform 2 K run (figure 2(d)).This suggests that the nonlinear effect can offset the impact of global warming on TCGF to some degree.
To gain insight into the different impacts of three warming patterns on TCGF, we examine changes in the large-scale environment associated with TC activity in response to the different warming patterns (figure 3).This includes the low-level winds, SLP, mid-level relative humidity (RH) and vertical velocity, and vertical wind shear (VWS) defined as the vector difference of the horizontal winds between 200 and 850 hPa, as well as 850-hPa vertical vorticity shown in supplementary figure S5.Among these, the mid-level RH is a thermodynamic factor, and others are large-scale atmospheric dynamical factors.Note that these simulated differences in the large-scale environment were averaged over June-November in the Northern Hemisphere and December-May in the Southern Hemisphere.
In general, westerly anomalies dominate over the equatorial Pacific, while easterly anomalies prevail over the equatorial Atlantic and Indian Ocean (figure 3(a)).In response to the Uniform 2 K SST warming, anomalous cyclonic circulation, high mid-level RH, and increased upward motion over the western parts of WNP and ENP (figures 3(c) and (d)), favor TC genesis in those regions.Conversely, a dry mid-level atmosphere and anomalous descending motion associated with northerly anomalies contribute to a decrease in TCGF over the eastern parts of the WNP and ENP (figure 2(a)).Over the South Pacific, anomalies in the LLW, RH, and vertical velocity show a zonal dipole structure, with anomalous cyclonic circulation, positive RH, and upward motion east of 180 • , and anomalous anticyclonic circulation, and low RH and descending motion west of 180 • (figures 3(a), (c) and (d)).This pattern is favorable for the dipole pattern of TCGF.VWS is more favorable for TCGF in NI and less favorable in SI (figure 3(b)).As for the NA, TCGF is generally suppressed (figure 2(a)) due to tropical easterly anomalies (figure 3(a)), although mid-level RH is conductive to TC genesis over this basin.Consequently, Uniform 2 K warming leads to an insignificant global TCGF change but redistributes TC genesis locations across individual basins.
In sharp contrast, the Pattern 2 K run reveals the dominance of anomalous low-level anticyclonic circulation and positive SLP, as well as anomalous negative RH and descending motion across most of the WNP and the Southern Hemisphere (figures 3(e) and (h)), unfavorable for TCGF in those regions.Increased VWS and descending motion over the NA (figures 3(e) and (f)) also suppress TC genesis in that basin (figure 2(b)).Over the ENP, there are low-level cyclonic anomalies, increased RH and upward motion, all promoting ENP TC genesis (figure 3(g)).For the NI and SI, VWS plays a crucial role in TC genesis, with reduced VWS contributing to more NI TCGF and increased VWS to less SI TCGF.These changes in large-scale environment closely resemble those induced by El Niño events (Chan and Liu 2004, Camargo et al 2007, Zhao et al 2020), suggesting that nonuniform warming significantly affects both global and regional TC geneses.
The spatial changes in large-scale environment in the response to Total 4 K warming exhibit similarities to those in the Pattern 2 K but with larger magnitude anomalies (figures 3(i)-(l)), contributing to similar changes in TCGF in these two runs.Considering the linear response of TCGF to warming SST, the differences in TCGF between the Total 4 K and Pattern 2 K runs should align with the TCGF change in the Uniform 2 K run.However, there exists clear nonlinearity.The differences in large-scale thermodynamic and dynamic factors (figures 3(m)-(p)) between the Total 4 K and Pattern 2 K runs are generally opposite to those in the Uniform 2 K run, which also explains slightly higher number of TCs in the Total 4 K run relative to Pattern 2 K run.It implies that there is nonlinear relationship between TCGF and circulation responses to SST warming, consistent with previous studies (Zhao et al 2023).
We further analyzed the spatial distribution of the genesis potential index (GPI) developed by Emanuel and Nolan (2004) (hereafter 'ENGPI') and a new dynamic GPI (hereafter 'DGPI') developed by Wang and Murakami (2020) (supplementary text S3).It is clear that the DGPI well reproduced the distribution of simulated TCGF under each warming pattern, including the dipole pattern of TCGF changes in different basins in the Uniform 2 K run and the consistent decrease/increase of TCGF in the Pattern 2 K run (supplementary figure S6).In contrast, the ENGPI demonstrated a good skill of TCGF-reproducing only in the ENP, while in other basins where TCGF decreases, the ENGPI unexpectedly shows a consistent increase.This could be attributed to the significant increase in MPI (the key factor in ENGPI), which correlates with the rising SST.This strongly suggests that dynamic conditions play the more important role in affecting TC genesis under GW than thermodynamic conditions (Camargo et al 2014).
A question naturally arises as to how the uniform and nonuniform warming patterns affect local thermodynamic and dynamic conditions, especially dynamic conditions, thereby influencing TCGF changes.To address this issue, we further examine the changes in velocity potential and the associated divergent wind at 200 hPa, as well as precipitation, in response to the different warming patterns (figure 4).In the Uniform 2 K run, an upper-level convergence pattern is found over the western parts of the Northern and Southern Pacific, centered over land, while an upper-level divergence pattern covers the tropical regions in the eastern Pacific and the Atlantic simultaneously (figure 4(a)).In contrast, the Pattern 2 K run displays an eastward shift in the upper-level convergence/divergence anomalies over the Pacific (figure 4(d)), as a result that the convergence center moves from land to the ocean, and the divergence center over the tropical eastern Pacific shifts northeastwards.These changes can be attributed to the spatial distribution of simulated precipitation anomalies, which indicates shift in the location of heat source from the WNP to the central Pacific, and from the ENP near 120 • W to east of 120 • W (figures 4(b), (c), (e) and (f)), respectively.As a result, Pattern 2 K run experiences a stronger anomalous anticyclonic circulation in the lower atmosphere and sinking motion in most regions of the WNP and the Southern Pacific, leading to a significant decrease in TCGF compared to the Uniform 2 K run.At the same time, the shift in the upper-level divergence center over the tropical eastern Pacific associated with heat source causes increased anomalous cyclonic circulation in the lower atmosphere and ascending motion over the main TC genesis region of the ENP, favorable for more TCs over there.Over the NA, upper-level divergence weakens in the Pattern 2 K run, leading to decreased RH and increased VWS, and thus a decrease in TCGF.The responses in upper-level circulation and atmospheric heat source to the Total 4 K run have a similar spatial distribution to the Pattern 2 K run, but with a larger magnitude in values (figures 4(g)-(i)).In terms of nonlinearity, changes in the upper-level circulation and precipitation are generally opposite to those in the Pattern 2 K run, slightly offsetting the impacts of warming on TCGF (figures 4(j)-(l)).
To further investigate the underlying mechanisms behind the TCGF changes in a warmer climate, we turn our attention to the land-sea thermal contrast (Li and Yanai 1996) and Lindzen-Nigam model (Lindzen and Nigam 1987), as well as two hypotheses: the upward mass flux hypothesis (Sugi et al 2012) and the saturation deficit hypothesis (Emanuel et al 2008, Emanuel 2010), as mentioned in the Introduction.Under the uniform SST warming without considering the zonal SST gradient, the circulation changes are primarily driven by the land-sea thermal contrast, resulting in the anticyclonic (cyclonic) anomaly in the lower troposphere over land (ocean) (figure 3(a)).The circulation patterns tend to cause a distinct dipole distribution of TCGF anomalies across most basins (figure 2(a)).In contrast, according to the Lindzen-Nigam model, a nonuniform SST warming pattern with zonal SST gradients tends to induce eastward-extensive changes in tropical low-level winds (supplementary figure S7), leading to more uniform and significant changes in TCGF across basins.As for the two hypotheses, table 1 shows the tropical mean stability, precipitation rate, upward mass flux, and saturation deficit in the four experimental scenarios (see their definitions in supplementary text S4).In the Uniform 2 K run, there is an increase in atmospheric stability and saturation deficit, followed by a decrease in upward mass flux.Particularly, these changes are more pronounced over land (see figures 3 and 4), leading to a slight decrease in TCGF compared to the CTRL run.In the Pattern 2 K experiment, atmospheric stability increases at a faster rate, followed by a significant decrease in upward mass flux, although saturation deficit remains the same as in the Uniform 2 K run.Consequently, there is a significant decrease in TCGF compared to the CTRL run.These changes are consistent with the upward mass flux hypothesis and the saturation deficit hypothesis.Interestingly, the TCGF changes in the Total 4 K experiment closely resemble those in the Pattern 2 K experiment, despite the larger change ratio of upward mass flux and saturation deficit in the former.These responses are also consistent with the behavior of the large-scale environment, as shown above (figures 3 and 4).We speculate that this might be associated with the impact of the nonreality, which partially offsets the role of the SST warming in reducing TCGF.

Conclusions and discussion
In this study, we revealed the impacts of spatiouniform and nonuniform SST warming patterns on global and regional TCGFs.We find that spatiouniform SST warming primarily influences TC genesis locations, while nonuniform warming pattern exerts a more pronounced impact on global TC activity, resulting in a decrease of −12.0%compared to a mere −0.6% for uniform warming.However, despite the overall decrease in global TC numbers in a warmer climate, TCGFs vary across different ocean basins.TCGFs over the WNP, the NA, and the SI experience a decreasing trend, while those over the ENP shows an increase.In addition, the spatial distributions of TCGFs also exhibit a non-linear feature with a dipole-like pattern in most ocean basins.Furthermore, environmental factors associated with TC activity vary by ocean basins and warming modes, with dynamic factors playing a major role in the WNP and the NA, while thermodynamic factors dominate in the ENP.Changes in the Walker circulation and tropical Pacific heat sources, induced by the warming modes, drive changes in local large-scale environment in different ocean basins, either promoting or inhibiting TC genesis.
The mechanisms can be also explained by landsea thermal contrast and Lindzen-Nigam model, as well as the upward mass flux hypothesis and the saturation deficit hypothesis.In the case of nonuniform warming, zonal SST gradients tends to force eastward-extensive changes in tropical lowlevel winds based on the Lindzen-Nigam model.As such, there is an increase in atmospheric stability and saturation deficit, followed by a decrease in upward mass flux, leading to a significant decrease in TCGF compared to the CTRL run.Conversely, under the uniform SST warming, the circulation changes are primarily driven by land-sea thermal contrast.Atmospheric stability increases at a slower rate with the center over land, leading to a minimal change in TCGF compared to the CTRL run.The TCGF changes in the Total 4 K experiment are very similar to those in the Pattern 2 K experiment, which might be due to the impacts of nonlinearity.Hsieh et al (2022) have indicated that the model spread in TCs is correlated with that in seeds.In this sense, TC seeds could vary across different SST warming patterns, which contributes to TCGF changes to some degree.Thus, we have also explored the changes in TC seeds in different experiments (supplementary figure S8).Here, TC seeds were defined following Zhao et al (2023).As expected, TC seeds exhibit consistent changes with TCGF, highlighting the connection between them.Nevertheless, to what extent TC seeds influence TCGF, and whether the mechanisms affecting TC seeds are notably different from those affecting TCGF merit further investigation in future.
To validate the robustness of our results, we examined the output data from different models under the CMIP6 and the database for policy decision making for future climate change (d4PDF), and found that the results generally correspond with our simulations conducted using the HiRAM-C180 model (supplementary figures S9 and S10).In addition, we acknowledge that there may be more warming scenarios than just uniform or SST-pattern considered in this study.Here, we chose the uniform 2 K SST warming scenario to represent a relatively simplified, evenly distributed warming pattern, which has been a common approach in climate modeling and has served as a baseline for understanding the impact of warming on TCs.We included the non-uniform (El Niño-like) SST warming scenario to investigate the effects of a more realistic, spatially heterogeneous warming pattern that often occurs in the real world.Although limited warming scenarios were considered in this study, these findings enhance our understanding of the complex relationship between GW and TCs, with important implications for predicting future TCs under climate change.

Figure 1 .
Figure 1.Input SSTs of the four GFDL-HIRAM experiments.(a) observation sea surface temperature (SST in K) during 1980-2009; (b) spatio-uniform warming with SST changing 2 K at 1-degree interval when comparing with the observation; (c) SST change with an El Niño-like warming pattern at 1-degree interval when comparing with the observation; (d) the sum of Uniform 2 K warming and El Niño-like warming pattern at 1-degree interval when comparing with the observation.

Figure 2 .
Figure 2. The simulated differences in TCGF under different experiments.(a) The simulated differences between the Uniform 2 K and CTRL runs, (b) the differences between the Pattern 2 K and CTRL runs, (c) the differences between the Total 4 K and CTRL runs and (d) the differences from the nonlinearity.The black dots represent area where the difference is statistically significant above 90% confidence level based on Student's t test.

Figure 3 .
Figure 3.The large-scale environmental factors differences under different experiments.Changes in spatial patterns of (a), (e), (i) and (m)) low-level wind (LLW in m s −1 ; arrow) and sea level pressure (SLP in hPa; shaded), (b), (f), (j) and (n) vertical wind shear between 200 and 850 hPa (VWS in m s −1 ), (c), (g), (k) and (o) 500 hPa relative humidity (RH in %), and (d), (h), (l) and (p) 500 hPa vertical velocity (Omega in Pa s −1 ) in response to the spatio-uniform warming, El Niño-like warming pattern and total warming pattern.The simulated differences were averaged over June-November in the Northern Hemisphere and December-May in the Southern Hemisphere during 1980-2009.(a)-(d) The simulated differences between the Uniform 2 K and CTRL runs, (e)-(h) the differences between the Pattern 2 K and CTRL runs, (i)-(l) the differences between the Total 4 K and CTRL runs and (m)-(p) the differences from the nonlinearity.The shading in (a), (e), (i), (m) and gray dots in others represent areas where the difference is statistically significant above 90% confidence level based on Student's t test.

Figure 4 .
Figure 4.The velocity potential, divergent wind and surface precipitation differences under different experiments.Changes in spatial patterns of velocity potential (VP in 10 6 m 2 s −1 ; shaded) and divergent wind (m s −1 ; arrow) at 200 hPa (a), (d), (g) and (j) and surface precipitation (Pr in kg m −2 d −1 ) in JJASON (b), (e), (h), and (k) and DJFMAM (c), (f), (I) and (l) in response to the spatio-uniform warming, El Niño-like warming pattern and total warming pattern.(a)-(c) The simulated differences between the Uniform 2 K and CTRL runs, (d)-(f) the differences between the Pattern 2 K and CTRL runs, (g)-(i) the differences between the Total 4 K and CTRL runs and (j)-(l) the differences from the nonlinearity.The white slashes in (a), (d), (g), (j) and gray dots in others represent areas where the difference is statistically significant above 90% confidence level based on Student's t test.

Table 1 .
Annual mean TCGF and TC-related tropical mean (30 • N-30 • S) environmental quantities for CTRL, Uniform 2 K, Pattern 2 K and Total 4 K experiments.