Unexpected limitation of tropical cyclone genesis by subsurface tropical central-north Pacific during El Niño

The vast tropical Pacific is home to the majority of tropical cyclones (TCs) which threaten the rim countries every year. The TC genesis is nourished by warm sea surface temperatures (SSTs). During El Niño, the western Pacific warm pool extends eastward. However, the number of TCs does not increase significantly with the expanding warm pool and it remains comparable between El Niño and La Niña. Here, we show that the subsurface heat content change counteracts the favorable SSTs in the tropical central-north Pacific. Due to the anomalous positive wind stress curl, the 26 °C isotherm shoals during El Niño over this region and the heat content diminishes in the tropical central-north Pacific, even though warm SST anomalies prevail. This negative correlation between SST and 26 °C isotherm depth anomalies is opposite to the positive correlation in the tropical eastern and western Pacific. This is critical because quantifying the dynamics of the subsurface ocean provides insight into TC genesis. The trend in TC genesis continues to be debated. Future projections must account for the net effect of the surface-subsurface dynamics on TCs, especially given the expected El Niño-like pattern over the tropical Pacific under global warming.

#1 On the problem with G function derivation and inferences of contributions from D26. Unlike the formulation of maximum potential intensity (MPI) of TC, the G function and its dependance on a bunch a variables in all three papers (26,27,28) were empirical and not based on the solid dynamical and physical constrains. Murakami and Wang (ref. #27) found the original formula by K. A. Emanuel, D. S. Nolan (2004, ref #26) was problematic, although it has been used in the research community by many. M. Zhang,L. Zhou,D. Chen,C. Wang (ref # 28) further developed two new forms for G functions, trying to combine different combinations for atmospheric and ocean variables to fit the TC genesis data. The four forms of G functions of these three paper are all very different, all works well or some extent in term of fitting. But, this is a "big" problem for attributions to tell apart about what are factors "cause" the variations in G! Here I give a mathematical proof to demonstrate that using the two different forms of G function in Ref #2 which has two co-authors appear to be the co-authors of this manuscript as well. One is so-called oceanic G function which used in this manuscript, I will denote it as G-o. The other they refereed it as atmospheric and oceanic G function, denoted G-ao. These two G functions as quite different but have shared considerations for the dependences of D26. Let me simply rewrite them into the following form: G=G_o=F_1 X^i, G=G_ao=F_2 X^j Here X=D26 /80 is what they have used. F1 and F2 are different functions which depends on a bunch of different variables and can be found from equation 3 and 4 of the ref#28. If we wish to attribute how variations in G is partitioned among changes due to ∆X and ∆F1, or ∆X and ∆F2, we have the following formulations ∆G=(iG ̅ )/(X ) ̅ ∆X+X ̅i ∆F1, ∆G=(jG ̅ )/(X ) ̅ ∆X+X ̅j ∆F2 Here I uesd the fact G ̅ =(F1) ̅ X ̅i=(F2) ̅ X ̅j by definition. In ref #27, they found that i=0.25, j=0.13. Please note the ∆X is the same and G ̅ /(X ) ̅ is the same, but two formulas will give almost a factor 2 difference in terms of contributions from D26 to ∆G. In other words, I give a mathematical prove here that the estimated contribution from D26 will be cut into half if the authors use the equation 4 instead of ref#28. Mathematically, this problem of indetermination comes from the fact that predictors are not uncorrelated. But more fundamentally, it comes from the lack of physical constrains on the forms of G function, a problem not solved even by the best TC dynamist, like Prof. Emanual. Anyone can propose his new versions by fitting the data, but the fact we have a rather small sample set of TC genesis data set will not give a solid answer until a breakthrough is made with a theory for GPI, which is not in sight. Dynamically, I do not see a strong argument why a small changes in D26 in the regions with 28.5-29C warm surface water as shown in Fig.4D&E will matter that much for TC genesis. How strongly a pre-TC depression can be affected by subsurface at 80m bellow? As it is unlikely a pre-TC depression can be strongly affected by the deep water, I am skeptical about this X factor for GPI. The indeterminacy as shown above using the results in ref#28 lends support to my point as well. My objection points to an essential weakness of the work. #2 There is a shift of pattern TC genesis in the central to western north Pacific as shown In Fig.2, But this shift can be more likely due to shift in vertical wind-shear patterns rather than due to D26. Surface wind patterns shown in Fig.5A would indicate a change in vertical shear in the region about 5-15N and in the so-called green and yellow box which may have different contributions to G function variations. If the authors formulated the G function with considerations of vertical shear instead of D26, the changes in G function will be attributed to something else other than D26. Thus the inference draw from G functional analysis are nonunique. The hypothesis about importance of D26 has to be further supported such as by CGCM simulations to demonstrate that D26 really matters.
#3 The authors tends to stress " The negative correlation between warm SST anomalies and shallower 26C isotherm depth is opposite to the current understanding for ENSO dynamics" . But this has little to do with ENSO dynamics. The difference in green and yellow box in terms of tsub and SST is more related to the difference in heat flux due to wind evaporations, which can become clear if one adds the wind pattern in Fig.5A onto the summer climatology wind, at least to my eyeballing estimations.
I do not role out completely the role of subsurface ocean in GPI. But I provide my assessments to convince the authors that they need to provide direct evidence to prove (or falsify) the hypothesis that the D26 matters for GPI. The empirical Gs are not adequate and easily misleading as I can see into it. As I personally know the authors well, I am signing this negative but otherwise constructive review ( with an interesting mathematical analysis which potentially can be a useful tool itself for the authors to use). REVIEWER COMMENTS</B>

Reviewer #1
The authors addressed most of my concerns. I am happy to recommend for its publication.
I do have two more suggestions.
As I am especial happy to see they indeed dogged into some existing high resolutions simulations to provide some modeling evidence about the potential effect of D26 on TC genesis ( The author used a data fitted empirical function G for TC genesis to infer the role of subsurface temperature measured by the depth (D26) of T=26C surface. I found some serious issues in their approach and reasoning to reach their conclusions. Thereby I cannot recommend this paper for considerations for publication in NC.
#1 On the problem with G function derivation and inferences of contributions from D26.
Unlike the formulation of maximum potential intensity (MPI) of TC, the G function and its dependences on a bunch a variables in all three papers (26,27,28) were empirical and not based on the solid dynamical and physical constrains. Murakami and Wang (ref. #27) found the original formula by K. A. Emanuel, D. S. Nolan (2004, ref #26) was problematic, although it has been used in the research community by many. M. Zhang,L. Zhou,D. Chen,C. Wang (ref # 28) further developed two new forms for G functions, trying to combine different combinations for atmospheric and ocean variables to fit the TC genesis data. The four forms of G functions of these three paper are all very different, all works well or some extent in term of fitting. But, this is a "big" problem for attributions to tall apart about what are factors "cause" the variations in G! Here I give a mathematical proof to demonstrate that using the two different forms of G function in Ref #2 which has two co-authors appear to be the co-authors of this manuscript as well. One is so-called oceanic G function which used in this manuscript, I will denote it as G-o. The other they refereed it as atmospheric and oceanic G function, denoted G-ao. These two G functions as quite different but have shared considerations for the dependences of D26.
Let me simply rewrite them into the following form: Here X=D26 /80 is what they have used. F1 and F2 are different functions which depends on a bunch of different variables and can be found from equation 3 and 4 of the ref#28. If we wish to attribute how variations in G is partitioned among changes due to ∆ ∆ 1, or ∆ ∆ 2, we have the following formulations Here I uesd the fact ̅ = 1 0000 0 # = 2 0000 0 & . In ref #27, they found that i=0.25, j=0.13. Please note the ∆ is the same and ' ̅ ) + is the same, but two formulas will give almost a factor 2 difference in terms of contributions from D26 to ∆ . In other words, I give a mathematical prove here that the estimated contribution from D26 will be cut into half if the authors use the equation 4 instead of ref#28.
Mathematically, this problem of indetermination comes from the fact that predictors are not uncorrelated. But more fundamentally, it comes from the lack of physical constrains on the forms of G function, a problem not solved even by the best TC dynamist, like Prof. Emanual. Anyone can propose his new versions by fitting the data, but the fact we have a rather small sample set of TC genesis data set will not give a solid answer until a breakthrough is made with a theory for GPI, which is not in sight.
Dynamically, I do not see a strong argument why a small changes in D26 in the regions with 28.5-29C warm surface water as shown in Fig.4D&E will matter that much for TC genesis. How strongly a pre-TC depression can be affected by subsurface at 80m bellow? As it is unlikely a pre-TC depression can be strongly affected by the deep water, I am skeptical about this X factor for GPI. The indeterminacy as shown above using the results in ref#28 lends support to my point as well. My objection points to an essential weakness of the work.
#2 There is a shift of pattern TC genesis in the central to western north Pacific as shown In Fig.2, But this shift can be more likely due to shift in vertical wind-shear patterns rather than due to D26. Surface wind patterns shown in Fig.5A would indicate a change in vertical shear in the region about 5-15N and in the so-called green and yellow box which may have different contributions to G function variations. If the authors formulated the G function with considerations of vertical shear instead of D26, the changes in G function will be attributed to something else other than D26. Thus, the inference draw from G functional analysis are nonunique. The hypothesis about importance of D26 must be further supported such as by CGCM simulations to demonstrate that D26 really matters.
#3 The authors tend to stress " The negative correlation between warm SST anomalies and shallower 26C isotherm depth is opposite to the current understanding for ENSO dynamics". But this has little to do with ENSO dynamics. The difference in green and yellow box in terms of tsub and SST is more related to the difference in heat flux due to wind evaporations, which can become clear if one adds the wind pattern in Fig.5A onto the summer climatology wind, at least to my eyeballing estimations.
I do not role out completely the role of subsurface ocean in GPI. But I provide my assessments to convince the authors that they need to provide direct evidence to prove (or falsify) the hypothesis that the D26 matters for GPI. The empirical Gs are not adequate and easily misleading as I can see into it. As I personally know the authors well, I am signing this negative but otherwise constructive review (with an interesting mathematical analysis which potentially can be a useful tool itself for the authors to use). In this study, the authors highlight a counterintuitive relationship between the potential TC genesis in the Central North Pacific and the phase of ENSO. Whereas the warm El Niño phase is characterized by an extension of the warm pool and warmer surface anomalies in the Centralnorth Pacific, the depth of the isoT26C is actually shallower (due to increased Ekman suction in relation with the large scale wind stress anomalies associated with the North Pacific subtropical high) making the heat content lower and counteracting the favorable sea surface environment for TC activity which leads to a suppression of TC genesis in this region. While the idea and proposed mechanism are interesting, I think the conclusion is a bit overstated. The authors claimed a suppression, whereas it is merely a reduction of the TC genesis potential. This study is well written and has the potential for publication in Nature Communication but would require more convincing analysis or a shift in focus beforehand.

Fei-Fei Jin
Major comments: 1/ Figure 2C displays actually an increase in TC genesis during El Nino phases compared to La Nina's. In addition, I wonder if the unchanged TC number between the 2 phases of ENSO shown in their figure 1 comes from the choice of their averaging region (not clearly specified by the way, but which, I assume, encompasses the whole warm pool) that integrates the reduction of TC number around the Philippines and the increase between 140 and 170W and lead to an overall similar number of TC during both ENSO phases. What if this figure was done using the region delineated by their yellow dashed box, would the increase in TC genesis during El Niño remain insignificant? 2/ Maybe the authors could explore more the limitation in increase/reduction of potential TC genesis during El Niño/La Niña phases compared to climatological/neutral ENSO conditions? For instance, the figure 2 of Lin et al. (2020) shows a limited increase/reduction in TC activity during El Niño/La Niña in the Central North Pacific compared to the westernmost part of the basin that might come from the proposed competing mechanism between SST and heat content: -A limitation in TC genesis in that region during El Nino despite positive SST anomalies due to the shoaling of D26 -the opposite during La Nina due to a reduction of SST anomalies but an increase in heat content 3/ Also, why not extending the analysis to the entire central Pacific (i.e. until 150ºW, the usual definition of the Central North Pacific TC basin)? 4/ Knowing that the heat content is more influential on TC intensification than genesis, I wonder if these results would be changed (even maybe strengthened) if the authors used an index accounting for TC intensity (the Accumulated Cyclone Energy for instance, Bell et al 2000Bell et al , 2004 as compared to an index of TC genesis or limited their analysis to the occurrence of major TC (Category 3 and above) in this region?

Minor comments:
Reference 13 is not the best suited Line 42: I thought the term had been coined "hiatus" Line 53: Phase not flavor 1

Responses to Reviewers
We greatly appreciate the insightful comments, and the very specific and valuable suggestions provided by the two reviewers. The manuscript is revised accordingly, and we hope that the revisions are satisfactory to the reviewers.

Reply:
We agree with the reviewer that the GPIs "were empirical". Nevertheless, nature is so complex that existing theories on the dynamical control on TC genesis are still not satisfactory. 25 Otherwise, empirical methods such as GPIs would not have been developed, if the theories were adequate. The reviewer has also acknowledged that the GPIs, particularly the one by Emanuel and Nolan (2004), have been widely applied and many useful conclusions have been drawn (such as Emanuel 2013;Lavender et al. 2018;Zhao et al. 2020;Yang et al. 2021). Moreover, the GPIs have 2 also been used to quantify the influences of various physical features on tropical cyclones (TCs), 30 such as in Patricola et al. (2016), Cao et al. (2021), Fu et al. (2021), and Murakami (2022).
Therefore, although the dynamical and physical bases for GPIs are still a grand scientific challenge, they have demonstrated applicability and usefulness for exploring the interactions between TCs and the environment. We humbly submit that the science of improving GPIs and advancing the process and predictive understandings of TCs based on both dynamical and statistical approaches 35 can proceed hand-in-hand and complementarily. It is also true that " Murakami and Wang (ref # 27) found the original formula by Emanuel and Nolan (2004, ref # 26) was problematic". Murakami and Wang (2010) pointed out that the "upward motion was not fully taken into account in the original GPI [the one in Emanuel and Nolan (2004)]". They made an improvement "by explicitly incorporating the following vertical motion term" and proposed another GPI in Eq. (2) in their paper. The modification in Murakami 55 and Wang (2010) was also made on an empirical basis, rather than a solid dynamical basis.
However, the results in Murakami and Wang (2010) indicated that "the impact of remote dynamical forcing (on TCs) is greater than that of local thermodynamical forcing" in the western North Atlantic. Hence, this is a good example that an empirical GPI promoted our understandings in the environmental impacts on TCs. 60 3 In addition, although GPIo proposed in Zhang et al. (2016) presented the empirical relations between the TC genesis numbers and different environmental variables, the variables were not selected randomly or artificially. The details of the selection are: 1. All variables were selected based on previous process studies, which had already unveiled the dynamical relations between each variable and TCs. 65 2. GPIo was obtained with a recursive regression algorithm. The flowchart is shown in Fig. R1.
The algorithm guaranteed that, statistically, (1) the inclusion of any new variable from the candidate pool cannot improve GPIo; (2) the removal of any variable from GPIo would significantly deteriorate the performance of GPIo. Therefore, GPIo does have an implicit dynamical basis and is not totally empirical. It is unique, as long as the large candidate pool 70 remains the same. See more technical details in Zhang et al. (2016).
3. The GPIs are a statistical proxy for the TC dynamics in nature. Although no dynamics were considered explicitly when creating GPIs, all GPIs reflect the dynamical constraints which are intrinsic to the TC system and life cycle. That is probably why, as the reviewer stated, "all (four GPIs) work well to some extent in terms of fitting". In Murakami and Wang (2010), it 75 was also claimed that the "upward motion was not fully taken into account in the original GPI, although the relative humidity term may reflect it to some degree". In the response to a following comment, we will show that the same conclusions about the impacts of 26 on TC genesis numbers can be drawn when using both GPIo and GPIao, which have different forms.

80
Overall, an item f is added in the Methods section in the revised manuscript, which briefly summarizes the above explanations.

Figure R1
Flowchart of the regression algorithm which was used to obtained GPIo in Zhang et al. (2016). It begins with a null model (no variables). When a candidate variable Xi is added to the 85 GPI (denoted with Y), an F-test is performed to determine whether the inclusion would significantly improve the GPI, i.e., increase the match between GPI and observations. If yes, the variable Xi is kept in GPI, otherwise it is removed. Note that for each step, the F-test is not only performed to the new variable Xi but the test is also performed to all variables which are already selected. As a result, any variable which could not contribute significantly to the improvement of 90 GPI would be returned to the candidate pool. This is a recursive process. The regression process stops when no new variable can be included into the GPI and no variable can be removed from the GPI. Therefore, the final GPI does not depend on the order of feeding the variables into the regression system. Anyone can propose his new versions by fitting the data, but the fact we have a rather small sample set of TC genesis data set will not give a solid answer until a breakthrough is made with a theory for GPI, which is not in sight.

Reply:
We appreciate the reviewer's effort in providing a detailed mathematical proof to verify our 120 results. To the best of our understanding, the key concern that the reviewer raised is whether our current conclusions depend on the specific form of the GPI. With the following analyses, it is shown that the two different GPIs in Zhang et al. (2016) yield consistent conclusions.
Firstly, we agree with the reviewer that the variables in any GPI are not independent from each other. This was clarified in Murakami and Wang (2010) as well, as noted in the above 125 response. As a result, the specific form of a variable (such as 26 ) may change in different GPIs, after different variables are selected. This is also a reflection of the intrinsic inter-dependence of different variables. One can create a GPI with orthogonal variables by applying the Gram-Schmidt process (Ford 2015), but it would render difficult the physical interpretations.
6 Secondly, we found that the mathematical processes in the comment need to be modified. 130 Following the symbols used in the comment, one has ��� is the climatological mean of , which is different from � (i.e., � to the ith power). The difference between ̅ and ̅ is neglected, which was also assumed by the reviewer. However, 135 because , are dependent on X. Hence, the following two equations in the comments, i.e.,

#3 Dynamically, I do not see a strong argument why a small change in
in the regions with 28.5-29C warm surface water as shown in Fig.4D&E will matter that much for TC genesis. How strongly a pre-TC depression can be affected by subsurface at 80m bellow? As 155 it is unlikely a pre-TC depression can be strongly affected by the deep water, I am skeptical about this X factor for GPI. The indeterminacy as shown above using the results in ref#28 lends support to my point as well. My objection points to an essential weakness of the work.

Reply:
We appreciate the reviewer for raising the essential issue whether the variation at the 26ºC 160 isotherm can have an impact on "a pre-TC depression". Below, we present some observational evidence and confirm that such impact exists in nature, and it is consistent with current dynamical understandings.
Genesis Potential Index (GPI) sets up a bridge between various environment variables and the potential for TC genesis over a large region (such as the northwestern Pacific in this study). 165 Therefore, the projection of TC genesis variation under climate change is different from the prediction of an individual TC genesis potential.
GPI is usually applied with low-frequency data, such as monthly data. The reviewer is correct that SST is critical for the genesis of an individual TC. Nevertheless, for the potential of TC genesis, the regional mean SST is not the only oceanic contributor. Instead, a deeper 26 provides a 170 favorable environment and a higher probability for TC genesis. Gray (1979) argued that "other conditions being favorable and remaining constant, seasonal tropical cyclone genesis frequency should be directly related to the magnitude of ocean thermal energy E", and "thermal potential may also be thought as the potential for Cb (Cumulonimbus) convection." Hence, he used "ocean thermal energy" instead of SST as the key parameter for TC genesis, because the ocean provides 175 energy for TC genesis and the 2-D SST does not contain mass or energy (re-emphasized in Gray 1998, ref #24 in the manuscript). In a very recent paper, Emanuel (2022) confirmed again that "the annual mean frequency of tropical cyclones depends on climate parameters, such as the specified ocean mixed layer depth". Therefore, for the potential genesis of TCs, the thermal energy in the upper ocean (which is represented with 26 ) can play a non-negligible role. 180 Moreover, in many tropical regions, SST is a good proxy for ocean thermal energy, since it has a good correlation with 26 as shown in Fig. 4B of the manuscript. Nevertheless, such an 8 assumption does not hold for the central-north Pacific (yellow box in Figs. 3 and 4A of the manuscript). The opposite relations between SST and 26 in the western north Pacific and the central-north Pacific was highlighted in this study ( Fig. 4B and 4C). As a result, SST alone is no 185 longer a good representation of the ocean thermal energy, and 26 is found to be a necessary supplement in this situation.
Practically, the dependence of TC genesis numbers on 26 can be seen from Fig. R3. For example, when � is between 29ºC and 30ºC, the TC genesis numbers increase significantly when The drag coefficient has a large uncertainty at high wind speeds and it varies from basin to basin. Kara et al. (2007)  Overall, both in the physical and statistical analyses, 26 tends to have a significant impact 210 on TC genesis. It is possible that this impact may not be universal. Nevertheless, the contrast in TC genesis numbers between El Niño and La Niña over the northwestern Pacific is very evident, which is the motivation of this study. We also agree with the reviewer that the dynamic bonds between the ocean subsurface and TC genesis are far from obvious. Much more dedicated work is required in the future for a better understanding of the observations (Fig. R3). 215 In the revised manuscript, Fig. R3 is added as the new Fig. S1. Reply: We agree with the reviewer that the vertical wind shear is usually important for TC genesis, 230 and it has been proven to play a key role in modulating TC genesis during ENSO, especially in the Atlantic Ocean (Camargo et al. 2007, i.e., ref # 19).
Although the vertical wind shear was not explicitly included in GPIo (not predetermined but selected by the regression algorithm; Fig. R1), it does not mean that the effect of vertical wind shear was excluded. The reviewer is correct that the effect of vertical wind shear was represented 235 by other variables that were already included in GPIo. In fact, SST is the highly related one, rather than 26 . SST is shown to be a key parameter in controlling the vertical wind shear (Latif et al. 2007). As Fig. R4A shows, the pattern of the changes in the vertical wind shear from La Niña to El Niño is close to that of � (Fig. 3A in the manuscript). This is further supported by Fig. R4B.
There are significantly negative correlations between the vertical wind shear and � , except for the 240 upper-left corner of the green box. Note that strong vertical wind shear is unfavorable for TC genesis. Thus, the impact of vertical wind shear and � on TC genesis is positively correlated. In other words, the impact of vertical wind shear can be largely represented by the � term in GPI.
That's probably why the vertical wind shear was not included in any of GPIo and GPIao in Zhang et al. (2016). Besides, the vertical wind shear is relatively less important for TC genesis in the 245 Pacific than in the Atlantic (Camargo et al. 2007, i.e., ref # 19;Fu et al. 2012;Peng et al. 2012).
As Fig. R5 shows, the climatological wind shear is less than 10 m/s over most northwestern Pacific Ocean, which cannot prevent the TC genesis (Bracken and Bosart 2000). That is another reason that the vertical wind shear was not selected into the GPI developed for the northwestern Pacific.
In summary, the effect of vertical wind shear was not really excluded in this study. It is 250 implicitly represented since its impact is closely related to that of � , but there is no evidence that the impact of 26 can be represented by the vertical wind shear.
The above explanations are briefly summarized on Lines 69-72 in the revised manuscript.

Reply:
We agree that the conclusions in this study require further verifications by CGCM. 265 Firstly, we evaluated the simulated relations between 26 and � in 20 CMIP6 models and 10 CMIP6 HighResMIP (Roberts et al. 2020) models. As shown in Fig. 4C of the manuscript, 26 and � have a negative correlation in the central-north Pacific in observations. This is reproduced with a black bar in Figs. R6 and R7. In 20 CMIP6 models (Fig. R6), 12 models produce positive correlations, and 8 models capture the negative correlations. The lowest negative correlation 270 coefficient is -0.22 from CESM2, which is still much weaker than the observation (~ -0.4). In 10 CMIP6 HighResMIP models (Fig. R7), only two models, i.e., EC-Earth3P-HR and ECMWF-IFS-HR, reproduce negative correlations albeit correlations close to zero. Therefore, it can be concluded that the relation between 26 and � over the central-north Pacific is a common bias in model simulations. 275 Secondly, we examine the dependence of TC genesis on 26 using the products from 10 CMIP6 HighResMIP models. As Fig. R8 shows, a larger correlation coefficient between 26 and SST over the central-north Pacific leads to an increase of TC genesis number during El Niño compared with that during La Niña. In the 10 CMIP6 HighResMIP models, the simulated SSTs increase over the central-north Pacific during El Niño as expected. Thus, a shallow 26 (i.e., a 12 weak positive correlation between 26 and SST) can reduce the tendency of increase in TC genesis number during El Niño, which lend supports to the conclusions in this study.
In fact, at present, only a few global climate models can resolve and reproduce TCs (such as Zhao et al. 2009). It is common that a CGCM produces fewer TCs than in observations (Camargo 2013). Actually, the reason why GPIs are practically useful is partly due to the limited reproduction 285 of TCs in contemporary climate models. Therefore, current conclusions are but the first critical step and serve as a call for more dedicated verifications with high-resolution CGCMs in the future.
The information about HighResMIP is added on Lines 151-152 in the revised manuscript.

#6 The authors tends to stress "The negative correlation between warm SST anomalies and shallower 26C isotherm depth is opposite to the current understanding for ENSO dynamics" . 305
But this has little to do with ENSO dynamics. The difference in green and yellow box in terms of Tsub and SST is more related to the difference in heat flux due to wind evaporations, which can become clear if one adds the wind pattern in Fig. 5A onto the summer climatology wind, at least to my eyeballing estimations.

Reply: 310
The relation between SST and thermocline depth is a key component in ENSO dynamics. For example, in the recharge-discharge theory (Jin 1997), SST in the eastern Pacific ( ) was represented by (Eq. 2.4 in Jin 1997) where ℎ is the thermocline depth and is the surface wind stress. A deep ℎ leads to a warm 315 anomaly of . In this study, the contrast between Figs. 4B and 4C in the manuscript indicated that the relation between 26 (similar to the thermocline depth) and SST was different from the one in the eastern Pacific. Note that the negative correlation between 26 and SST occurs over the central-north Pacific, which is beyond the two boxes prescribed in the classical recharge-discharge theory. 320 The relations between the simulated ENSO and the 26 -� correlation in the central-north Pacific are examined using 20 CMIP6 models. The simulated ENSO is evaluated with the CLIVAR 2020 ENSO Metrics Package (Planton et al. 2021). The package was developed by PCMDI, IPSL/LOCEAN, and NOAA. One metric is the τx-SSH feedback, i.e., the regression slope of sea surface height (SSH) anomalies (as a proxy for subsurface temperature) in the Niño3 region onto 325 the zonal wind stress ( ) anomalies in the Niño4 region. The feedback is the ocean-atmospheric branch of the Bjerknes feedback as defined in Planton et al. (2021), connecting the trade wind anomalies and the subsurface temperature anomalies in the eastern equatorial Pacific. Such feedback is generally weaker in CMIP6 models than that in the observation. The ENSO simulations are evaluated by the score, 330 where is the regression coefficient in simulations; is the regression coefficient in observations.
The score actually measures the difference between simulations and observations, normalized by 15 the observations. A model has a better simulation of the feedback, if the score approaches zero.
Therefore, this score is also a metric for ENSO simulations. The score for the simulated relation 335 between 26 and � over the central-north Pacific is similarly defined.
The relations between the 26 -� score and the ENSO simulations in CMIP6 models are shown in Fig. R9. The x-axis shows the score (Eq. R3) for the regression between 26 and � over the central-north Pacific (yellow box in the manuscript) in the models. The y-axis shows the score in Eq. R3 for ENSO simulations. The significantly positive regression coefficient in Fig. R9  340 indicates that a better simulation of the 26 -� relation over the central-north Pacific is accompanied with a better ENSO simulation in CMIP6 models.
Overall, as the reviewer states, the dynamic implication of the negative correlation between 26 and � over the central-north Pacific to ENSO is not fully explored in this study. Further dynamical research is desired, but it is beyond the scope of current study. 345

Figure R9
Association between the 26 -� relation over the central-north Pacific and the ENSO simulation in 20 CMIP6 models. The x-axis shows the scores for simulated 26 -� relation. The y-axis shows the scores for ENSO simulations. Both scores are defined in Eq. R3. The correlation coefficient is significant at the 99% confidence level. 350 I do not role out completely the role of subsurface ocean in GPI. But I provide my assessments to convince the authors that they need to provide direct evidence to prove (or falsify) the hypothesis that the matters for GPI. The empirical Gs are not adequate and easily misleading as I can see into it. As I personally know the authors well, I am signing this 355 negative but otherwise constructive review (with an interesting mathematical analysis which potentially can be a useful tool itself for the authors to use).

Reply:
We are happy that the reviewer agrees that the subsurface ocean can play a role in TC genesis.
In the above responses and the revised manuscript, we added much more direct evidence to verify 360 the hypothesis that the 26 matters for TC genesis. We would like to emphasize that most evidence does not depend on the GPI. Instead, they are obtained from observations, such as Figs. 1, 4, 5, S1, S3, S5 in the revised manuscript. The GPI is only a quantitative tool, whose results are consistent with the observations. Therefore, we believe our conclusions capture the intrinsic properties of TC genesis in nature. 365 We truly appreciate the reviewer for his time, honest evaluation, mathematical analysis, and the very insightful comments. We hope that he finds our responses and revisions acceptable and complete.

Reviewer #2 (Remarks to the Author): 370
In this study, the authors highlight a counterintuitive relationship between the potential TC This result is consistent with many previous studies, such as Wang and Chan (2002). Combining the two regions, the TC genesis numbers show no significant differences between El Niño and La Niña over the tropical northwestern Pacific, as shown in Fig. 1B in the manuscript. years is 25.13. However, the p-value is 0.5334, which indicates that the TC genesis increase during El Niño is not statistically significant. It is also true that "TC frequency during CP El Niño years 425 is also above normal". The mean annual TC number of 6 CP El Niño years is 29.33, and the mean annual TC number of 57 years  is 26.96. But the increase is still not significant, since the p-value is 0.3798. Therefore, current conclusion based on Fig. 1B in the manuscript is consistent with the results in Lin et al. (2020).  There are two reasons for the domain selection.
First, GPI is a statistical constraint between various environmental variables and the TC genesis number. The statistical relation varies with regions. Particularly, GPIo was created for the northwestern Pacific Ocean (Zhang et al. 2016) and it performs well in this region. Such regional 450 dependence of GPI is systematically described in Raavi and Walsh (2020). For example, vertical wind shear is important for TC genesis in the North Atlantic, but not as important as other parameters in the western North Pacific Peng et al. 2012). Overall, GPIo is an appropriate GPI for the northwestern Pacific, but might not work for the eastern tropical Pacific.
Second, as shown in Fig. R13, most TCs that are generated to the west of 150ºW travel to the 455 west, leaving a trail of devastation over eastern Asia. While most TCs generated to the east of 150ºW travel to the east and have impacts on the Americas. Hence, practically, it is meaningful and useful to explore the slow variation of TC genesis separately between the northwestern and the eastern Pacific Ocean. Figure 1B in the manuscript can be reproduced to the west of 150ºW, following the reviewer's suggestion. The results are consistent with the original figure, since TC 460 genesis numbers between 170ºW and 150ºW are small (Fig. R13).
More information is added to item a in the Methods section.

Reply:
We appreciate the reviewer's very helpful and feasible suggestion. We fully agree that "the heat content is more influential on TC intensification than genesis". It will be very interesting to quantitatively explore such an impact on TC intensity. 475 Following the reviewer's suggestion, we computed the accumulated cyclone energy (ACE), which is shown in Fig. R14. There is a significantly positive correlation between ONI and ACE. ACE depends both on TC frequency and TC intensity as well as TC duration. During El Niño, more TCs are born over the central Pacific, although the total TC genesis numbers do not increase (based on current results in the manuscript). Therefore, the TCs tend to have more time to intensify 480 over the ocean before landing over eastern Asia. As a result, more cyclone energy can be accumulated. Hence, the increase of ACE during El Niño shown in Fig. R14 has no conflict with the conclusions in the manuscript. Moreover, we also counted TCs in the categories from 1 to 5 22 (Fig. R15). More intensive TCs occur during El Niño than during La Niña, which is consistent with the changes in ACE (Fig. R14) and the findings in Camargo and Sobel (2005). 485 Existing studies have confirmed that the subsurface ocean environments have important influences on TC intensity. Lin et al. (2013) modified the potential intensity index by replacing SST with depth-averaged ocean temperature to quantify the role of subsurface temperature on TC's intensity. Zheng et al. (2015) unveiled the unfavorable oceanic impacts during El Niño. Particularly, according to Huang et al. (2015). It is likely that 26 can have a non-negligible impact on TC 490 intensity. However, in order to quantify such an impact, an index for TC intensity needs to be created following the algorithm shown in Fig. R1 (see Zhang et al. 2016 for more details). In this way, all variables which may be influential on TC intensity will be considered, and an index for TC intensity is created with the recursive regression method. Based on our current dynamical understanding , it is highly probable that 26 would be selected as a variable 495 in the new index. Then, the impact of 26 on TC intensity in an ocean basin can be quantitatively estimated. One can see that this is a separate though related study from the current one. We will complete that in the future and report the results separately.
This issue is addressed at the end of the manuscript by saying "our results do not exclude the possibility that super typhoons may increase in number, since more TCs tend to be generated over 500 the tropical central Pacific and can have a longer lifetime to grow over the warm ocean".

Figure R14
The same as Fig. 1B in the manuscript but for the accumulated cyclone energy (ACE).
The unit is 10 5 m 2 /s 2 . The correlation coefficient is significant at the 99% confidence level. 505 23 Figure R15 The monthly mean TC numbers of Category 1 to 5 during La Niña, Neutral, and El Niño conditions.

Reference 13 is not the best suited
Reply: Ref #13 is replaced with Chapter "Impact of El Niño on Weather and Climate Extremes" from the book "El Niño Southern Oscillation in a Changing Climate" (Goddard and Gershunov 2020).

515
Line 42: I thought the term had been coined "hiatus" Reply: "global warming pause" has been replaced with "hiatus".
Line 53: Phase not flavor 520 Reply: Here we intended to say different types of ENSO, such as the CP El Niño and the EP El Niño.
In the revised manuscript, "flavor" is replaced with "type".

Response:
Following the reviewer's suggestion, Fig. A1 is produced using the ten HighResMIP climate models. In agreement with Fig. 3D in the main text which is based on observations, Fig. A1 shows 15 a nontrivial and negative impact of 26 on TC genesis numbers, including the central-north Pacific (the yellow box). Nevertheless, the negative impact of 26 in the yellow box is confined to the lower panel, instead of the whole box as in Fig. 3D. The discrepancy is likely to be largely attributable to the inadequate performance of the HighResMIP models in reproducing the relationship between 26 and ̅ as shown in Fig. R7 in the previous response. Such model 20 deficiencies are not surprising and yet important to report. Figure A1 is included as the Supplementary Fig. S7A in the revised manuscript. mine is beyond question as it clearly shown in Fig. R2. I urge the authors to include this information in the extend figures so that readers will be aware with this caveat, which leaves door open for someone to go further to find ways to eliminate this uncertainty. Figure R2 in the previous response is added in the revised manuscript as Supplementary Fig.  35 S8. Moreover, we also reproduce Fig. A1, which is obtained with the HighResMIP model outputs, using GPIoa. The results are shown in Fig. A2, which is included as Supplementary Fig. S7B in the revised manuscript. We hope that the quantitative uncertainties due to different GPIs are clearly seen with the new Supplementary Figs. S7 and S8.  [Comment 4] As for the relevance of the math behind the use of GPIocean to assess the dominant role of D26 in controlling the TC genesis in the tropical central north Pacific, I leave it to Prof.

Response:
Jin's expert appreciation. 100 We thank the reviewer for the specific and insightful suggestions again.