Changes in event soil moisture-temperature coupling can intensify very extreme heat beyond expectations

Domain: earth_science
Published: 2025-01-16
Editorial outcome: major_revision

Abstract
The most disastrous heatwaves are very extreme events with return periods of hundreds of years, but traditionally, climate research has focussed on moderate extreme events occurring every couple of years or even several times within a year. Here, we use three Earth System Model large ensembles to assess whether very extreme heat events respond differently to global warming than moderate extreme events. We find that the warming signal of very extreme heat can be amplified or dampened substantially compared to moderate extremes. This modulation is detectable already in mid-century projections. In the mid-latitudes, it can be explained by changes in event soil moisture-temperature coupling during the hottest day of the year. The changes depend on the interplay of present soil moisture and coupling during heat events as well as projected precipitation changes. This mechanism is robust across models, albeit with large spatial uncertainties. Our findings are highly relevant for climate risk assessments and adaptation planning.

Introduction
Extreme events are becoming more severe1. This holds in particular for heat extremes: rising mean temperatures increase the severity, frequency and duration of heatwaves. These changes may additionally be modulated by circulation changes and land-atmosphere feedbacks2. It is well known that in regions of increasing soil moisture-temperature coupling, temperature variability is amplified such that extreme heat responds stronger to climate change than average temperatures2–5.

Attribution studies have found an influence of anthropogenic climate change on a large number of recent heat extremes, including the devastating events in Canada in 20216, Northern India in 20227 and the Western Mediterranean in 20238. Such disastrous heatwaves are very rare events with return periods of hundreds of years even in present climate, and among the most severe events ever recorded9,10. The rareness of these events is not well represented by the typical analyses conducted in climate change studies until recently: widely used extreme event indicators11 consider events occurring once a year or more often, and even analyses explicitly quantifying return levels typically select return periods of only 20 years or below12,13. This choice may often be motivated by the limited availability of long time series to robustly estimate very extreme events, both from observations and models. A large fraction of our knowledge about extreme events is therefore based on the study of moderate extreme events, and applying this knowledge to statements about changes in very extreme events therefore tacitly assumes that the latter respond in a similar way to climate change than the former.

Over recent years, researchers have therefore started to study very extreme or record breaking events with return periods of hundred years or beyond, focusing on the analysis of individual events14–16 or investigating multi-model projections17–20. None of these studies, however, has investigated whether and to what extent very extreme heat events may respond differently to climate change compared to moderate extreme events. Ignoring such differences would have dramatic consequences for climate risk assessments, as projections and attribution statements would misrepresent the influence of climate change on the most impactful events.

There is evidence for exactly such differential climate change signals of moderate and very extreme heat events. While most studies investigate the role of land-atmosphere coupling for seasonal mean conditions2,21,22, the coupling has been shown to be particularly relevant for intense heat events14,23–25. In fact, the strength of land-atmosphere coupling is not constant but varies with weather26,27. Hence, episodic coupling during extreme heat events, in the following referred to as event coupling, may be different—stronger or weaker—from seasonal mean coupling, and trends in event coupling may be different from trends in seasonal mean soil moisture-temperature coupling.

The generation of multiple single model initial conditions large ensembles (SMILES) over the last decade28 offers new possibilities to sample many extreme events19,29, and thus to robustly study also very extreme events.

Here, we employ three different SMILES to assess to what extent changes in very extreme heat events differ from changes in moderate heat extremes, and to identify the underlying mechanisms. For our analysis, we consider daily maximum temperatures TX. Extremes of TX are a well-established heat index4,19,30 and a useful proxy for heatwaves, as the hottest temperatures typically build up during long heatwaves31,32. We represent mean temperature conditions as the summer (annual in the Tropics) average of TX, moderate extremes as discussed above by the 2-year return levels of TX, and very extreme events by their 200-year return level. In the following we refer to these indicators as mean, moderate extreme and very extreme heat.

The choice of 200 years balances the need to consider, on the one hand, the most extreme events, but on the other hand allows sampling several such events with a SMILE, and thus to gain robust statistics without having to extrapolate and thus potentially create statistical artefacts. We have chosen the three SMILES available offering daily data for characterising the underlying processes while providing a sufficient number of ensemble members. We refer to these as the MPI, CSIRO and MIROC SMILES. For details on the methodology see the Methods section.

The spatial patterns of return level changes differ substantially between the models considered. To avoid smoothing out physical effects, we therefore consider each model separately as a plausible and physically self-consistent storyline of future changes33,34.

Results
Projected changes in moderate and very extreme heat
The spatial patterns of moderate extreme and very extreme heat over land are mainly controlled by latitude, continentality and elevation, and strongly resemble the pattern of the corresponding means (Fig. 1a, c and e for the MPI SMILE, and Table 1, pattern correlations above 0.97). Their climatic changes, however, are markedly different (panels b, d and f). Change patterns in the 2-year return level closely resemble those in mean TX (pattern correlations between 0.80 and 0.90 depending on the model, Table 1), although the amplitude of changes is stronger in many regions. This amplification is consistent with previous findings2. But change patterns in mean and moderately extreme temperatures are much weaker correlated with spatial patterns of changes in the very extreme heat (pattern correlations between 0.02 and 0.56). Major regions of strong changes are substantially shifted: for instance, while strong changes in 2-year return levels can be found over the Great Plains of North America, the strongest changes in 200-year return levels over North America can be found several hundred kilometers further east. Similarly, the strongest changes in 2-year return levels over Eurasia can be found along a band ranging from the Balkans and the coast of the Black Sea to central Asia. The strongest changes in the 200-year return levels, however, are shifted northward, starting in Central Europe. Patterns in changes of very extreme heat are essentially uncorrelated with changes in the mean (for two models, and only weakly correlated for one model; pattern correlations between 0.02 and 0.40).

The orthogonality of the change patterns is highlighted by considering the differences between the changes in 200-year and 2-year return levels: over distinct regions, very extreme heat respond differently to climate change compared to moderate extreme events. Pronounced dipole-like patterns emerge for all considered models, but the spatial patterns are markedly different between different models (Fig. 2a, c and e; maps for further return periods are shown in Supplementary Fig. S3). For instance, the MPI SMILE shows a strong amplification of changes in the 200-year return levels over Eastern North America and a band ranging from France via Eastern Europe into Central Asia. Here, the changes in 200-year return levels are often some 4 K stronger than those in 2-year return levels. In contrast, over the North American Great Plains and a band from the Balkans into Mongolia, the changes in the very extreme heat are typically 2–3 K weaker than those in moderate extremes. Also the other two SMILES show distinct patterns of regionally amplified and dampened responses of very extreme heat, albeit with substantially displaced spatial features. These differences highlight large uncertainties in the representation of changes in very extreme heat events.

The role of changes in event soil moisture-temperature coupling
Soil moisture-temperature coupling plays a key role in the amplification of extreme temperatures2,35: in an energy limited regime, soil moisture values are so high that evaporation is dominated by the available energy and not limited by soil moisture. In a dry regime, soil moisture and thus evaporation are low. In both cases, the coupling between temperature and soil moisture is weak. In a transitional regime, soil moisture limits evapotranspiration, but is sufficiently high to generate a coupling: decreasing soil moisture in turn decreases evaporation, thereby increases sensible heat fluxes and ultimately temperature35. Increases in the summer coupling strength therefore amplify temperature variability such that heat extremes typically warm stronger than mean temperatures in a warming climate2–4,21,36. The SMILES we consider reproduce the present-day coupling strength (highest values in the lower mid-latitudes and subtropics, Supplementary Fig. S4) as well as the amplifications of changes in moderate extreme events (e.g., over the Americas, Europe and Southern Africa, Supplementary Fig. S5) found in previous studies2,4, although with strong displacements in spatial patterns across individual models.

While research so far has focused on quantifying the change of soil moisture-temperature coupling in a climatological sense, there is evidence that the coupling is particularly relevant for very severe heat events14,23–25. In fact, it has recently been highlighted that land-atmosphere coupling varies with weather26, and climate in many locations is composed of days with and without active coupling27. We argue that this event character of land-atmosphere coupling is particularly relevant for heatwaves. During heatwaves soil moisture typically decreases over time, such that the coupling may change from an energy limited regime into a transitional regime, or from a transitional regime into a dry regime. Thus, we hypothesise that the coupling strength for the hottest days of the year is different from summer mean coupling.

We therefore specifically analyse event coupling between annual maxima TXX of daily maximum temperatures and latent heat fluxes at the occurrence days of these maxima (see Methods section for details). Projected changes in this event coupling, in particular in the mid-latitudes, closely follow the patterns of differences in the changes of very and moderate extreme events (Fig. 2b, d and e). Increases in event coupling strength amplify the climate change signal of the very extreme heat events, decreases dampen them. The robustness of the effect across models corroborates that changes in event soil moisture-temperature coupling are indeed an important physical mechanism for modulations of changes in very extreme heat.

Changes in event coupling during heat events behave differently compared to summer mean coupling (see Methods section for definitions). While both exhibit broadly similar zonal mean behaviour (Fig. 3a), the regional patterns may differ substantially (see Supplementary Fig. S4 and the discussion of spatial patterns of driving processes in the following section). Also projected changes between mean and event coupling differ substantially (Fig. 3b, compare also Fig. 2, right column). While models more or less agree on changes in mean coupling, uncertainties in event coupling changes are substantial and differ even in sign. The role of changes in event coupling for amplifying changes in very extreme heat is strongest in the mid-latitudes. There, it explains some 40% of the differential changes in extreme return levels (Fig. 3c), while its role is insignificant in the Tropics and high latitudes.

Driving processes
Seneviratne et al.35 have presented a conceptual model to explain changes in seasonal soil moisture-temperature coupling. They argue that a drying in an energy limited regime leads to enhanced variability (e.g., in Europe), whereas further drying in a transitional regime leads to reduced variability (e.g., in the southeast US). Apart from studies on land surface influences37 and decadal SST variability38, further research on the causes of coupling changes is sparse.

Here, we transfer Seneviratne’s model to event coupling, and expand it to situations of increasing soil moisture (Fig. 4). Based on this model, we identify potentially relevant hydrometeorological drivers and their changes. We hypothesise that regional differences in changing coupling strength are mainly caused by changes in soil moisture during heat events. As discussed above, three regimes exist: weak coupling for both low and high soil moisture values, and strong coupling in a transitional regime of medium soil moisture values. Thus soil moisture-temperature coupling increases when soil moisture values increase from dry to a transitional regime, or decrease from wet to a transitional regime. Vice versa, soil moisture-temperature coupling decreases when soil moisture values decrease to dry, or increase to wet conditions. Such changes can be caused by both changes in rainfall amounts as well as by increases in evapotranspiration, caused by changes mainly in temperature.

Regions of strong changes in event coupling strength and thus strong amplification or dampening of changes in very extreme heat (Fig. 2a, b for MPI model) coincide with regions of intermediate to high event coupling strength in present climate (Fig. 5a for MPI model). Yet event soil moisture values in present climate vary strongly across these regions (panel b). Where soil moisture values are high, but decrease in a warming climate (panel c), coupling strength increases—see Central Europe and the Eastern US as prominent examples. But also when soil moisture values are low and increase in a warming climate, such as in Central Africa, the coupling strength increases. In contrast, when soil moisture values are already low and further decrease (such as in the Balkans and US Great Plains), and when soil moisture values are relative high and further increase in a warming climate (e.g., around Beijing), the coupling strength decreases (see also Fig. 4). These changes in soil moisture can, to a large extent, be explained by changes in summer precipitation patterns (panel d).

These findings highlight the role of planetary-scaled dynamic and thermodynamic changes in modulating changes in soil moisture coupling and thus changes in very extreme heat: the overall poleward shift of summer precipitation can be explained by a poleward shift of the summer jet streams and the accompanying storm tracks39,40. Regionally, processes such as changes in the frequency of atmospheric ridges in the western United States and Canada during summer41,42, or changes in the land-sea temperature contrast and lapse rate over the Mediterranean43 affect changes in summer precipitation patterns. In some continental regions, of course, soil moisture-precipitation coupling may play an additional role35.

The subtle interplay between event coupling strength and event soil moisture values in present climate, as well as changes in soil moisture, and the role of atmospheric dynamics explain the large uncertainty in the projections of very extreme heat across the different considered models: a small displacement in the patterns of one of these variables may have strong implications for changes of the coupling strength and may even revert the sign of these changes.

Methods
Climate model simulations
To sample very rare extreme events and to obtain robust estimates of 200-year return levels, we employ all available SMILES providing the required variables at a daily resolution50. These are 51 (present) and 30 (future) realisations of the MPI-ESM1-2-LR (1.8° horizontal resolution in the atmosphere) of the Max Planck Institute of Meteorology50, 32 (present) and 40 (future) realisations of the ACCESS-ESM1-5 (1.88° × 1.25°) developed by an Australian consortium51, and 50 (present and future) realisations of the MIROC6 (1.4°) developed by the Japanese team MIROC52. For future projections we have considered the worst-case scenario SSP5-8.5 because it represents a high signal-to-noise ratio and is available for all models providing the relevant data.

We consider three 25-year periods representing present climate (1990–2014), near future (2036–2060), and the end of the century (2076–2100).

Temperature return levels
For the temperature analyses, we have considered daily maximum temperatures TX. For mean changes, we calculated summer means (June to August in the Northern Hemisphere, December to February in the Southern Hemisphere, annual means in the Tropics, i.e., between 20° S and 20° N). Moderate extreme events have been represented by 2-year return levels, very extreme events by 200-year return levels. Return levels have been estimated from a Generalised Extreme Value distribution, fitted to annual maxima TXX of daily maximum temperatures. Note that the return levels are not based on block maxima from a single model arising under the same forcings. We therefore combined block maxima from all ensemble members. Over a 25-year period, the total number of maxima entering the fits is thus 25 times the number of ensemble members for a given model. For instance, for the MPI SMILE we had 30 × 25 = 750 maxima in the future period. For comparison, we estimated return levels as averages across the results for individual ensemble members. The results are based on analysis in individual ensemble members (shown as grey lines in Fig. 7). These return levels are calculated from 25 maxima.

Coupling strength
We calculate seasonal mean coupling strength as the summer (annual in the Tropics) correlation of 7-day running mean surface latent heat flux (a measure of evapotranspiration) and daily maximum temperature. This approach loosely follows the widely-used definition from the GLACE project2. To speed up computations, we calculate these correlations separately for each ensemble member and subsequently average.

Event soil moisture-temperature coupling during heat events is measured correspondingly as the correlation between all (over a 25-year period and all ensemble members) annual maxima of Tx and surface latent heat flux on the occurrence days of the annual maxima in Tx. The changes in event coupling strength are calculated on the days of all annual maxima of Tx and thus do not consider any information about the severity of the events. These changes, therefore, cannot be an effect but only a cause of the differential temperature changes.

Uncertainty assessment
Climate response uncertainties have been considered as comprehensively as currently possible by using three different SMILES. The role of sampling uncertainty is relatively small because the SMILES provide many ensemble members to robustly estimate most relationships. Thus all significance tests (apart from where pattern correlations are considered) have a very high sensitivity given the high number of data points (25 years × number of ensemble members), i.e., also small changes emerge as significiant. To assess the relevance of derived changes, we therefore compare projected changes with interannual variability where the latter can meaningfully be defined. For changes in temperature (Fig. 1 second column) and soil moisture (Fig. 5c), 100% of interannual variability have been considered as threshold. Because of the lower signal-to-noise ratio, for precipitation changes the threshold has been chosen as 25% of interannual variability (Fig. 5d).

The significance of differences in return level changes (Fig. 2 first column and Fig. 6) has been assessed as follows. First, we derived standard errors sdp,f of present-day and future 200 and 2-year return levels zp,f from their respective maximum likelihood estimates. From these, we calculated the standard error sdΔp,f of differences in return level changes (rlf200 - rlp200) - (rlf2 - rlp2). We then conducted a significance test for zero difference under the assumption that

(rlf200 - rlp200) - (rlf2 - rlp2)
-----------------------------------
sdΔp,f

is approximately standard normal distributed. Similarily, we have derived 95% confidence intervals of return levels and their changes from the return level standard errors (Fig. 7).

The significance of the coupling strength (Fig. 5a) has been assessed based on the assumption that

t = r * sqrt(n-2) / sqrt(1-r^2)

follows a t-distribution with n–2 degrees of freedom. In a similar vein, changes in coupling strength (i.e., correlation, Fig. 2 second column) have been assessed for signficance53. First we transformed the correlations rp,f in present and future climate using the Fisher z-transformation as

zp,f = 0.5 * ln(1+rp,f / 1-rp,f)

and derived standard errors as

sezp - zf = sqrt(1 / (np-3) + 1 / (nf-3))

We then conducted the significance test assuming that the test statistic

zf - zp
-------
sezp - zf

is approximately standard normal distributed.

For the latitudinal dependencies, i.e., zonal averages across latitudinal bands, the effective number of spatial degrees of freedom has been estimated as54

Neff = 2 * mu^2 / sd^2

where mu and sd are sample mean and standard deviation of the field average E of the squared grid box time series xt,i

E = 1/N * sum(xt,i^2)

with i=1...N grid boxes. For seasonal mean and event properties we have considered Neff of seasonal mean Tx and annual maxima Txx, respectively. Neff depends on both the spatial correlations and the number of land grid boxes in a considered latitudinal band.

For the zonal means of coupling strength, we have first derived approximate grid box 95% confidence intervals for invididual realisations from standard errors of the grid box correlations, approximated as55

sd = sqrt(1-r^2 / n-3)

We then derived confidence intervals for the average across the full ensemble and the latitudinal band, accounting for the effective number of degrees of freedom (Fig. 3a). From these, we have further derived corresponding confidence intervals for the changes in coupling strength (Fig. 3b). For the latitudinally dependent pattern correlation we have assessed the significance in the same way as for the coupling strength, but accounting for the effective number of degrees of freedom (Fig. 3c).

All signficance tests have been conducted with a significance level α=0.05.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper investigates the differential impacts of climate change on moderate and very extreme heat events using large\nensembles. It finds that very extreme heat events, with return periods of 200 years, respond differently to climate change\ncompared to moderate heat events, largely due to changes in soil moisture-temperature coupling during heat events. The\nstudy highlights significant regional variations and uncertainties in these changes, emphasizing the need for improved\nclimate risk assessments and adaptation planning.\nThe paper would benefit from a more detailed explanation of the methodology, particularly the calculation of soil moisture-\ntemperature coupling and return periods, to enhance clarity and reproducibility.\n1. My major concern is about the method to calculate return period.\nThe authors combine all the ensemble realizations (30) and have one return period (30x25=750). I think each simulation\nshould be treated independently and separately when calculating the return period. Each simulation is independent and not\na continuous 750-year simulations. I suggest calculating the return periods for each simulation and analyze the mean and\nvariance of those return periods across all simulations. For example, the variances could be used for statical significance of\nFigure 2. As shown in Figure7, the return value differences can be very different across ensemble members.\nPlease provide some literatures if the method is commonly used.\n2.The method of calculating coupling strength is unclear. Specifically (1) Is it correlation between Tx and latent heat or soil\nmoisture? Is the seasonal cycle removed? Please provide equation and examples for positive/negative coupling. How Tx-\nET strength relate to soil moisture-temperature coupling for general audiences of Nature Communications (i.e., why not\ndirectly use soil moisture-tempearature). (2) For correlation across maximum temperature in each year, I think the naming\n“event” coupling is misleading. It seems more like cross-events relationships.\n3.What’s the definition of “total soil moisture content” (Figure 5 b,c)? Is it root-zone soil moisture or total soil moisture in all\nsoil layers? Does deep soil moisture reflect to the occurrence atmospheric surface conditions, or does it reflect to the\nprevious day-to-season weather or hydrological changes (ice, groundwater).\n4.Additionally, addressing the regional uncertainties and providing more context on the implications for climate risk\nassessments and adaptation strategies would strengthen the overall impact and relevance of the findings.\nMinor comments\n1.Please ensure consistent use of return time(s) or period(s), also return value(s) or level(s).\n2.Please specify the raw spatial resolution of the models and the regridded resolution used in this study.\n3.Please make sure refer to figures, and tables, including supplementary information explicitly in the context.\n4.Line 87 Project changes “of”-> in\n5.For figure 3, please add labels for x- y- axes to the plots for clarity.\n6.Line 270-272 realisations-> realizations?\n7.Line 278: For the warm-season means, how about area in non-tropics?\n8.Check if Txx is a typo of Tx.", "reviewer_2": "Title: Changes in event soil moisture-temperature coupling can intensify very extreme heat beyond expectations\nIn this article, the authors use climate model simulations from large ensemble runs to assess heat extremes with large return\nperiods of 200 years relative to heat extremes with shorter return periods of 2-years. Then, they explore the source of the\ndifferences between the events with a 2-year return interval vs. events with a 200-year return interval, finding that soil\nmoisture-temperature coupling plays a key role.\nOverall, I think this is a very interesting study, and the methods are straightforward and justifiable. I have some suggestions\nthat I recommend the authors address prior to publication, as outlined below:\nMajor comments\n[1] I think it would be nice to more explicitly describe what constitutes an extreme event using return periods. I question\nwhether a 2-year event is considered “extreme”, as it seems more like normal, frequent event. Is an event with a 2-year\ninterval really a “moderate” extreme event? Furthermore, why do the authors choose to compare a 2-year event to 200-year\nevents? Why not along a gradient of return periods? Analyzing just the end points seems like a missed opportunity.\n[2] L135-145, I am a bit confused how moving from a transitional to dry regime would dampen a heatwave. Even though the\ncoupling is strongest in transitional regimes, this does not imply that heatwaves are amplified in transitional regimes, right? If\na transitional regime, for example, became water-limited, all the available energy would go to sensible heat, heating the\nsurface and increasing near-surface air temperature more than if there was any soil moisture available. It might benefit the\npaper to think about the distinction between transitional regimes in space vs. time. Also, it could be interesting to include a\nconceptual figure using example data showing how event coupling is calculated in the SI.\n[3] It is unclear what is considered the “warm season”, and if seasonality during the warm season affects the coupling\nstrength, i.e. is the seasonality driven by seasonality or daily anomalies?\n[4] Figure 4, The arrows below the conceptual figure are confusing. Do the arrows correspond with the conceptual figure\nabove? More importantly, though, I am not sure this figure adds much to the paper, as the information seems to be easily\ndescribed in text.\nMinor comments\n[1] Introduction: I think the readability would improve if the one sentence paragraphs in the introduction were incorporated\ninto larger paragraph.\n[2] has to have\n[3] L61, These seem more like the key results, not your hypothesis.\n[4] L84, “of our results” should be more specific\n[5] L85, check grammar\n[6] The language in the last four paragraphs feels too casual and vague, “good news”, “bad news”, “huge model\nuncertainties”, “But still”.", "reviewer_3": "This manuscript explores the different responses of extreme heat events and moderate extreme events in climate change\nthrough various SMILES, and how changes in soil moisture temperature coupling affect these extreme events. The author\nhas reached consistent conclusions on different models, providing profound insights into the response to extremely extreme\nheat events. However, I believe there is room for further improvement in the content. I suggest considering this manuscript,\nbut it requires some modifications.\nL73: Warm season is not clearly defined in the text, which specific months is it?\nL80: Why use these three large sample models? Have you considered other large sample models? The physical process\nsimulations between different models are inconsistent and may result in inconsistent results.\nL88: The article does not explain why SSP585 is used to continue the results of the model after 2014. Will the response of\nextreme heat events to soil moisture temperature coupling be inconsistent under lower emission scenarios? Furthermore, I\nbelieve that the period representing the 'present' should be chosen to be 2024 or 2023, rather than 2014 when the Historical\nscenario ends. The SSP scenario can be used to extend the subsequent years. And, there is no uncertainty-related\ninformation in the graph, do all grid results have a high level of confidence? I hope the author takes into account the issue of\nuncertainty when analyzing.\nL94: To characterize the correlation between two variables, confidence analysis should be added instead of just presenting\ncorrelation data. In addition, almost all the data in the article does not include uncertainty ranges, which has caused me\ngreat concern.\nL134: What conclusions did the seasonal average coupling strength of these models reproduce from previous studies?\nThere is no necessary explanation for Figure S3, making it difficult for readers to understand its meaning.\nL140: This is very counterintuitive. Humidity should always have a restraining effect on temperature drop, as it reduces the\nevaporative cooling effect on the surface, leading to an increase in temperature. Although the strength of land-atmosphere\ncoupling decreases, the temperature should be increasing. I hope the author can provide clearer explanations.\nL146: As above, the uncertainty range should be added to the graph, and the time representing \"now\" should be selected as\n2024 or 2023. Furthermore, perhaps adding a sliding sequence of global averages over a 25-year window would be more\nconvincing. This can also demonstrate the robustness of the research results on a temporal scale.\nL183: Given that the author compares the changes in coupling strength here, I believe that a spatial distribution map of the\nchanges in coupling strength should be added to the figure, even though it has already appeared in Figure 2."}, "author_response": "Response to Reviewer Comments\nWe thank all reviewers for their encouraging and constructive comments. We addressed all these\ncomments. Please find below a summary of the main changes as well as detailed one-by-one\nresponses to all points raised by the reviewers.\nMajor changes:\n• Most importantly, we added a comprehensive uncertainty analysis. Note that we had\nassessed model uncertainties by considering the three available SMILES to the extent\ncurrently possible (see the discussion below on available SMILES). Our new analysis\naddresses sampling uncertainty and internal variability, i.e., the statistical robustness of our\nresults. Please note that the 50-member ensemble provides sufficiently many data points to\nrobustly estimate high return levels (as was already assessed for selected locations in Figure\n7), changes and correlations. In fact, in some cases, significance tests would not have been\nvery meaningful as even small changes were highly significant. In these cases we used an\nassessment of changes relative to interannual variability. In other cases we conducted\nsignificance tests or calculated confidence intervals. To explain these assessments, we added\na long subsection to the Methods section and brief explanations in the relevant figure\ncaptions.\n• We expanded the analyses to more return periods between 2 and 200 years. For selected\nlocations, we presented such an analysis already in Figure 7, but we now added maps of\nreturn level change differences (compared to 2-year return level changes) for 5, 10, 20, 50\nand 100 years. These 15 panels have been added to the supplementary information, new\nFigure S3.\n• We found a bug in the calculation of summer mean coupling strength. As a result we needed\nto correct panels (a) and (b) in Figure 3 as well as Figure S5 and the corresponding\ndiscussion in the text. The patterns of significant summer mean coupling shifted a bit\npolewards, which is even more consistent with results from other studies. These changes did\nnot affect our main results as these are related to changes in very extreme heat and event\ncoupling.\n• We reorganised, rephrased and expanded the discussion section to accommodate for the\nreviewer’s concerns. Additionally, we sharpened the text in some cases by replacing words\nor rephrasing individual statements. These changes are all highlighted in the document with\ntrack changes.\nIn the following, all line numbers refer to the document with track changes.\nReviewer #1\nThe paper would benefit from a more detailed explanation of the methodology, particularly\nthe calculation of soil moisture-temperature coupling and return periods, to enhance clarity\nand reproducibility.\nWe addressed these points now in more depth in the Methods section.\n1. My major concern is about the method to calculate return period.\nThe authors combine all the ensemble realizations (30) and have one return period\n(30x25=750). I think each simulation should be treated independently and separately when\ncalculating the return period. Each simulation is independent and not a continuous 750-\nyear simulations. I suggest calculating the return periods for each simulation and analyze\nthe mean and variance of those return periods across all simulations. For example, the\nvariances could be used for statical significance of Figure 2. As shown in Figure7, the\nreturn value differences can be very different across ensemble members.\nPlease provide some literatures if the method is commonly used.\nNote that a return level is a property of the climate system, not a property of a single realisation.\nReturn value estimates from individual realisations might be rather different, depending on the\ninternal variability, but this is an expression of sampling uncertainty and not indicating that the\nunderlying population (or true) return levels would differ from sample to sample. They depend only\non the underlying state-of-the climate system, i.e., the forcing.\nIn practice, one only has individual realisations to estimate return levels, therefore our approach\nmight seem somewhat unintuitive. But in fact it is fully rooted in extreme value theory and an\nelegant and natural way to estimate return levels (note that there is not much literature yet on using\nSMILES for such applications; Suarez-Gutierrez et al. (Clim. Dynam. 2020) do not precisely\nexplain how their estimation is implemented, and Bevacqua et al. (Nat. Commun. 2023) follow the\napproach suggested by the reviewer).\nExtreme value theory deals with limiting distributions for infinitely long block lengths (Coles,\n2001). Using, e.g., annual blocks is a mere practical approximation because of the limited length of\navailable time series and the need to sample many maxima. The assumption underlying the\nestimation from finite blocks is that the length is sufficiently high and that the block maxima can be\nassumed to be sampled from the same distribution. This is the case for blocks from different initial\ncondition simulations with identical forcings. There is no theoretical argument against this\nassumption.\nOur approach also allows for the estimation of uncertainty estimates in a natural way following\nstandard statistical theory. Assuming normally distributed uncertainties, one can, by Gaussian error\npropagation of the standard errors of the GEV parameters, derive approximate 95% confidence\nintervals (Coles, 2001). An alternative, more sophisticated approach, would be based on the profile\nlikelihood (Coles, 2001).\nTo demonstrate the validity of our approach, we compare it to the procedure suggested by the\nreviewer (see Figure below). The results are virtually indistinguishable (Only in locations where the\nGEV does not properly describe the data, likely because of implausible numerical values in single\nensemble members, the method suggested by the reviewer smoothes out the misfit for a single\nmember by averaging over all members).\nWe prefer using our approach as it estimates the GEV parameters in one go from the full ensemble\nand is the natural choice when considering extreme value theory.\nFigure: Comparison of different\napproaches to calculate\ndifferences in 200- and 2-year\nreturn level changes simulated by\nthe MPI SMILE. Top: return\nlevels estimated as means over all\nensemble members (the\nreviewer’s approach). Bottom:\nreturn levels estimated from the\nfull ensemble (our approach). The\nbottom panel corresponds to\nFigure 2 (a) in the paper.\n2. The method of calculating coupling strength is unclear. Specifically (1) Is it correlation\nbetween Tx and latent heat or soil moisture? Is the seasonal cycle removed? Please provide\nequation and examples for positive/negative coupling. How Tx-ET strength relate to soil\nmoisture-temperature coupling for general audiences of Nature Communications (i.e., why\nnot directly use soil moisture-tempearature).\nWe are sorry for the confusion about the method of calculating coupling strength as the description\nin the main text is not consistent with the actual version as explained in the Methods section. It is\nthe correlation between latent heat flux and daily maximum temperature. We have corrected this in\nthe main text.\nWe compared calculations based on this definition with soil moisture based calculations. The results\nare qualitatively very similar. As in the literature, the coupling strength is usually derived based on\nlatent-heat flux and temperature, we decided to follow this definition.\nFor seasonal mean coupling, we consider averages across the summer season in the Extra-Tropics\nand the whole year in the Tropics (within 20° North/South). Note that we have replaced “warm\nseason” by “summer”. For the event coupling we consider values on the hottest day of the year.\n(2) For correlation across maximum temperature in each year, I think the naming “event”\ncoupling is misleading. It seems more like cross-events relationships.\nWe have actually been thinking a lot about an appropriate terminology and agree that “event\ncoupling” is not perfect. But we are afraid that “cross-event” may be misunderstood as well (e.g. as\ntemperature vs. latent heat flux). Our rationale for choosing the term was to distinguish it from\nseasonal means and to highlight that it considers specific events, namely the hottest day of a year.\nAnother term we had in mind was “episodic”, but we were not happy either. We therefore finally\ndecided to keep the term “event coupling”.\n3.What’s the definition of “total soil moisture content” (Figure 5 b,c)? Is it root-zone soil\nmoisture or total soil moisture in all soil layers? Does deep soil moisture reflect to the\noccurrence atmospheric surface conditions, or does it reflect to the previous day-to-season\nweather or hydrological changes (ice, groundwater).\nTotal soil moisture content is defined as the sum across all soil layers in the land surface model of\nthe corresponding Earth System Model. We did not assess how fast soil moisture responds to\natmospheric drivers at different depths, but the fact that seasonal mean precipitation is a driver of\ncoupling changes suggests that the total event coupling depends on a long integration of\natmospheric variability, i.e., is affected by soil moisture in considerable depth. Note that standard\nclimate models do not represent groundwater.\n4.Additionally, addressing the regional uncertainties and providing more context on the\nimplications for climate risk assessments and adaptation strategies would strengthen the\noverall impact and relevance of the findings.\nThank you for this suggestion. We have now added several discussion points related to climate risk\nin the 3rd and 2nd last paragraphs of the discussion. These include a likely lack of preparedness (in\nthe paragraph “But the concerning finding…”), suggestions for better sampling or reducing\nuncertainties and a discussion of how regional statements following the precautionary principle can\nstill be made based on the physical drivers we identified (in the end of the paragraph\n“Unfortunately, our assessment…”).\n1.Please ensure consistent use of return time(s) or period(s), also return value(s) or level(s).\nWe have changed to a consistent use of return period and return level.\n2.Please specify the raw spatial resolution of the models and the regridded resolution used\nin this study.\nWe have added this information in the Methods section. Note that all results are presented on the\nnative resolution of each model (because we did not combine information across models, but\nconsidered each model as a self consistent storyline).\n3.Please make sure refer to figures, and tables, including supplementary information\nexplicitly in the context.\nWe checked that we refer now to each figure and table in the main text or relevant figure caption in\nthe main manuscript. A reference to figure S4 (now S5) was missing and has been added.\n4.Line 87 Project changes “of”-> in\nWe have corrected this.\n5.For figure 3, please add labels for x- y- axes to the plots for clarity.\nWe added labels.\n6.Line 270-272 realisations-> realizations?\nWe decided to use British English. This may be adjusted by the copy editors.\n7.Line 278: For the warm-season means, how about area in non-tropics?\nWe made this point clearer and changed the notation. We replaced “warm season” by “summer”,\nadded definitions (JJA in the NH, DJF in the SH). We also added that we consider the whole year in\nthe Tropics (20° North to 20° South).\n8.Check if Txx is a typo of Tx.\nThank you for spotting this. Txx is the variable name for the annual maximum of Tx. We actually\navoided using Txx in the text (and rather referred to annual maxima of Tx). We now explicitly\nintroduce this notation in the methods section and the main text.\nReviewer #2\nOverall, I think this is a very interesting study, and the methods are straightforward and\njustifiable. I have some suggestions that I recommend the authors address prior to\npublication, as outlined below:\nWe thank the reviewer for their positive assessment. We are confident that we have addressed all the\nreviewer’s concerns.\n[1] I think it would be nice to more explicitly describe what constitutes an extreme event\nusing return periods. I question whether a 2-year event is considered “extreme”, as it seems\nmore like normal, frequent event. Is an event with a 2-year interval really a “moderate”\nextreme event? Furthermore, why do the authors choose to compare a 2-year event to 200-\nyear events? Why not along a gradient of return periods? Analyzing just the end points\nseems like a missed opportunity.\nWe agree with the reviewer that a 2-year event is not really an extreme event – this is a key point of\nour paper. Early in the introduction we discuss the mismatch between impactful events, which often\nhave return periods of hundreds of years, and the typically considered extreme event indicators\nwhich often refer to events happening even several times per year (e.g. the 95th percentile of daily\nvalues is exceeded every 20 days on average, even the 99th percentile is exceeded some 3-4 times\nper year). We chose the 2-year return period to address such events. When introducing 2-year events\nas moderate extremes, we refer to the preceding discussion on standard extreme event indicators\n(page 2, line 74).\nWe agree with the reviewer that considering a continuum of return periods would add valuable\ninformation. In fact, figure 7 shows such a continuum for two selected locations. Additionally, we\nnow added additional figures for 5, 10, 20, 50 and 100-year events. Given the huge number of\npanels, we had to move these plots to the supplementary information, Figure S3.\n[2] L135-145, I am a bit confused how moving from a transitional to dry regime would\ndampen a heatwave. Even though the coupling is strongest in transitional regimes, this does\nnot imply that heatwaves are amplified in transitional regimes, right? If a transitional\nregime, for example, became water-limited, all the available energy would go to sensible\nheat, heating the surface and increasing near-surface air temperature more than if there was\nany soil moisture available.\nWe thank the reviewer for spotting this issue. Of course, drying out reduces latent heat fluxes,\nincreases sensible heat fluxes, and thereby increases the maximum temperature during a heatwave,\nas during the transition from a transitional to a dry (water-limited) regime. The point we actually\nwanted to make was rather about the amount of amplification during the heatwave, not absolute\ntemperatures. We deleted the corresponding statements from the manuscript.\nIt might benefit the paper to think about the distinction between transitional regimes in\nspace vs. time.\nWe are not quite sure we correctly understand the reviewer’s comment.\nIn the classical literature (e.g. Seneviratne et al., 2010), soil moisture temperature coupling was\nimplicitly assumed to be constant in time. In this context, the term “transitional” refers to a state\nwith intermediate soil moisture values (low enough not to be energy limited, high enough to allow\nfor coupling). The temporal aspect of coupling strength (and therefore possible regime changes in\ntime) as discussed recently by Hsu & Dirmeyer (2023) is a key starting point for our paper as\ndiscussed above. Our main aim is to assess long term climatic changes in the coupling strength on\nthe hottest days of a year.\nSpatial aspects could also be discussed from two perspectives: we present the spatial patterns of\ncoupling regimes and how they change in a warming climate. Another perspective could be to\ndiscuss “spatial transitions” as e.g. the spatial propagation of soil moisture drought during\nindividual events. This aspect, however, is beyond the scope of our paper and merits separate\nstudies. Given the limited space, we therefore decided not to mention this point.\nRelated to this discussion, note that the term “transition” here refers to two issues: (1) in the\ntraditional concept, the “intermediate” regime where coupling is possible; and (2) to the transition\nbetween regimes. Given this new notion of regime transitions, the former, older, term “transitional”\nappears to be somewhat misleading. We decided to still use it, as it is common in the literature, and\ninstead replaced the verb “transition” (as from wet to transitional) by “change” in the text.\nAlso, it could be interesting to include a conceptual figure using example data showing how\nevent coupling is calculated in the SI.\nWe now better explain the calculation of event coupling in the methods section. As the actual\ncalculation as the correlation of Txx and LH (at the occurrence day of Txx) is rather simple, we\nbelieve it is not necessary to include an example calculation or an additional conceptual figure.\n[3] It is unclear what is considered the “warm season”, and if seasonality during the warm\nseason affects the coupling strength, i.e. is the seasonality driven by seasonality or daily\nanomalies?\nWe replaced “warm season” with “summer” with the additional explanation that we use annual\nvalues (means, maxima) in the Tropics. It is likely that seasonality during the summer influences the\ncoupling strength, as the warmest values would cluster in a certain time of the year and the typical\nprecipitation during that day would again depend on the time of the year. This seasonal dependence,\nhowever, does not have any implications for our methodology as the choice of the maximum values\nwithin a year intrinsically accounts for this seasonality. We agree, however, that understanding how\nmuch day-to-day variability and seasonality affect the timing of the hottest day in a year for a given\nregion would be an interesting study in itself.\n[4] Figure 4, The arrows below the conceptual figure are confusing. Do the arrows\ncorrespond with the conceptual figure above? More importantly, though, I am not sure this\nfigure adds much to the paper, as the information seems to be easily described in text.\nWe actually believe the visualisation strength of the figure lies in the combination of the three\nregimes with the arrows. The arrows are consistent with the conceptual figure and describe changes\nin coupling regimes from present to future climate. We clarified this in the figure itself and added to\nthe figure caption that these 4 examples are discussed in the main text (in the discussion of Figure\n5). The Eastern US were not mentioned in the text, so we added them. Vice versa, we added a\nreference to Figure 4 (the conceptual figure) when discussing the examples in the text. We thought\nabout adding circles or crosses at these locations in the maps, but decided against this as such icons\nwould either be hardly visible or hide too much information in the figures.\n[1] Introduction: I think the readability would improve if the one sentence paragraphs in the\nintroduction were incorporated into larger paragraph.\nWe combined paragraphs accordingly.\n[2] has to have\nWe changed this.\n[3] L61, These seem more like the key results, not your hypothesis.\nWe agree that these points emerge as our key results based on the analyses presented in the study.\nHowever, in the introduction we present these as hypotheses to motivate the study.\n[4] L84, “of our results” should be more specific\nWe specified this in the text (and added also that storylines are physically self-consistent).\n[5] L85, check grammar\nWe added the missing “we”.\n[6] The language in the last four paragraphs feels too casual and vague, “good news”,\n“bad news”, “huge model uncertainties”, “But still”.\nWe adjusted the language.\nIt appears that there is code to create each figure. There is no README file describing each\nfile, though.\nWe replaced the old code with the new one generating the uncertainty analysis and also added a\nREADME file describing the indicidual scripts. Note that there is one file that executes all files and\nproduces all figures.\nReviewer #3\nL73: Warm season is not clearly defined in the text, which specific months is it?\nWe replaced “warm season” by “summer”, i.e., JJA in the NH and DJF in the SH, with a remark\nthat we considered the whole year in the Tropics.\nL80: Why use these three large sample models? Have you considered other large sample\nmodels? The physical process simulations between different models are inconsistent and\nmay result in inconsistent results.\nWe wanted to analyse as many SMILES as possible. For our analyses we chose all SMILES that\nprovided the required variables at a daily resolution for a common (medium or high-emission)\nscenario. For comparison, Olonscheck et al. (2023) provide an overview of available CMIP6-based\nSMILES: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2023MS003790. Most of these\nseven ensembles did not provide the required data. We specified this more explicitly in the methods\nsection.\nL88: The article does not explain why SSP585 is used to continue the results of the model\nafter 2014. Will the response of extreme heat events to soil moisture temperature coupling be\ninconsistent under lower emission scenarios?\nAs indicated above, the choice was more or less enforced by the available ensembles. An alternative\nwould have been the SSP1-2.6, but we considered this being too optimistic given our focus on\nclimate risks (and thus the need to explore at least medium-high emission scenarios). We are of\ncourse aware of the fact that SSP5-85 is a very pessimistic worst-case scenario. Therefore we also\nconsidered mid-century projections (Figure 6), where SSP5-85 is still close to other scenarios. The\nfact that the same pattern as shown for the end of the century emerges, demonstrates that our results\nare also relevant for both lower emission scenarios and mid-term projections. This has been\nexplicitly stated already in the initial submission (page 6, line 232 – we slightly rephrased the\nstatement).\nFurthermore, I believe that the period representing the 'present' should be chosen to be\n2024 or 2023, rather than 2014 when the Historical scenario ends. The SSP scenario can be\nused to extend the subsequent years.\nOur intention was not to provide an assessment relative to exactly present climate, but to\ndemonstrate the physical effect and its relevance. For this purpose, the choice of reference (as well\nas future) periods is somewhat irrelevant as long as it considers (a) a range with a strong signal\nrepresenting high-emissions and/or long-term changes and (b) a range with a moderate signal\nrepresenting medium emissions and/or mid-term term changes. We therefore decided to keep the\nreferences period. We considered renaming this period “historical” or “recent”, but found both\nterms potentially misleading (historical implying a distant past, recent implying the last couple of\nyears).\nAnd, there is no uncertainty-related information in the graph, do all grid results have a high\nlevel of confidence? I hope the author takes into account the issue of uncertainty when\nanalyzing.\nIn our context, the most relevant uncertainties are climate response uncertainty and forcing\nuncertainty (see IPCC AR6 WG1 Chapter 1, Chen et al., 2021 for definitions). Both have been\ncovered by (a) comparing different climate models and (b) by comparing two projection horizons\n(mid/end-of century). Note that, for climate response uncertainty, we deliberately decided NOT to\npresent multi-model ensemble means as the identified spatial patterns were qualitatively so different\nthat averaging would not have made any sense. Instead, as discussed in the introduction, we\nconsidered each model independently as a plausible physically self-consistent storyline (Shepherd\net al., 2018, and IPCC AR6 WG1, Chapter 10, Doblas-Reyes et al.).\nThe third source of uncertainty, internal variability and thus sampling, is of much lower relevance\nas we use SMILES with many realisations. However, we agree with the reviewer that it is not a\npriori clear how robust our estimates of high return levels actually are, even when based on\nSMILES. We thus assessed the sampling uncertainties and role of internal variability for our results\nin the revision.\nHere we would like to highlight an important point. Given the high number of ensemble members,\nthere is a danger that even tiny changes or differences are significant, highlighting that significant\nresults are not necessarily relevant when the sample size is large enough (The famous statistician\nFisher summarised this dilemma as “All Null hypotheses are wrong”). In fact we found exactly this\nresult for most of the aspects considered. Therefore, we decided to deliberately avoid significance\ntests where possible and rather asked the question “Are the detected differences/changes relevant?”.\nWe considered “relevant” as being large compared to a chosen fraction of interannual variability.\nFor some aspects, however, we did consider significance tests as interannual variability could not\neasily be defined. These are (1) the coupling strength in present climate; (2) the changes in coupling\nstrength; and (3) differences in changes of return values. We added a new sub-section to the\nmethods section to discuss and explain these issues in depth, brief explanations in the discussions of\nthe results, and short statements in the corresponding figure captions.\nL94: To characterize the correlation between two variables, confidence analysis should be\nadded instead of just presenting correlation data. In addition, almost all the data in the\narticle does not include uncertainty ranges, which has caused me great concern.\nAs discussed above, we added significance tests. Our key results are all highly significant.\nL134: What conclusions did the seasonal average coupling strength of these models\nreproduce from previous studies? There is no necessary explanation for Figure S3, making it\ndifficult for readers to understand its meaning.\nWe added brief explanations to the text and the caption of Figure S3 (now S4, we also refer to S5\nnow) and refer to two relevant papers. We also make it clear now that S5 refers to the amplification\nof changes in moderate extremes, and state that the actual spatial patterns are displaced across\nmodels (something which is typically hidden in the multi model mean plots of other studies).\nL140: This is very counterintuitive. Humidity should always have a restraining effect on\ntemperature drop, as it reduces the evaporative cooling effect on the surface, leading to an\nincrease in temperature. Although the strength of land-atmosphere coupling decreases, the\ntemperature should be increasing. I hope the author can provide clearer explanations.\nWe thank the reviewer for spotting this issue. Of course, drying out reduces latent heat fluxes,\nincreases sensible heat fluxes, and thereby increases the maximum temperature during a heatwave,\nas during the transition from a transitional to a dry (water-limited) regime. The point we actually\nwanted to make was rather about the amount of amplification during the heatwave, not absolute\ntemperatures. We deleted the corresponding statements from the manuscript.\nL146: As above, the uncertainty range should be added to the graph, and the time\nrepresenting \"now\" should be selected as 2024 or 2023. Furthermore, perhaps adding a\nsliding sequence of global averages over a 25-year window would be more\nconvincing. This can also demonstrate the robustness of the research results on a temporal scale.\nWe added confidence intervals to the figure. Note that these confidence intervals are deliberately\nchosen as conservative upper bounds: The estimation of the degrees of freedom of zonal averages\nover land areas is not trivial, so we assumed that for each latitude we had only one data point. The\ntrue confidence intervals are thus much narrower, depending on the landmass and spatial\ndependencies at any given latitudinal band.\nAs discussed above, we decided not to change the reference period. The spatial patterns are highly\nregional, such that a global average sliding sequence would average out all interesting features.\nL183: Given that the author compares the changes in coupling strength here, I believe that a\nspatial distribution map of the changes in coupling strength should be added to the figure,\neven though it has already appeared in Figure 2\nWe are afraid that repeating this information would be difficult. Adding contour lines to panel (c)\nwould make this map overloaded with information. We additionally double checked with the editor\nthat Nature Communications would not allow repeating figure panels."}, {"round": 2, "reviewer_comments": {"reviewer_2": "The authors have thoroughly addressed my concerns.", "reviewer_3": "Thanks for the authors to address my comments. It looks much better than the previous version.There are two further ones:\n1)I appreciate the author's description of the GEV for calculting the 2-year and 200 year return periods. As another reviewer\npointed out, it may be inappropriate to label the events with a 2-year recurrence interval as \"moderate\" extreme events. But\nfrom my perspective, I believe that a 200 year recurrence interval event as an \"extremely\" strong high-temperature event is\nmore inappropriate because it rarely occurs. Is it meaningful to study it?\n2)Further， it seems that there may be too many Figures for Nature Communications (usually 4-5 charts), and the\n“Introduction” part of the MS is a bit too long."}, "author_response": "Response to remaining Reviewer Comments\nReviewer #3\n1)I appreciate the author's description of the GEV for calculting the 2-year and 200 year\nreturn periods. As another reviewer pointed out, it may be inappropriate to label the events\nwith a 2-year recurrence interval as \"moderate\" extreme events. But from my perspective, I\nbelieve that a 200 year recurrence interval event as an \"extremely\" strong high-temperature\nevent is more inappropriate because it rarely occurs. Is it meaningful to study it?\nAs discussed in the introduction of our manuscript, the highest impacts typically arise from very\nrare exteme events such as in the European heatwave from 2003, the Russian heatwave from 2010\nor the Pacific North West heatwave from 2021. For climate risk assessments, these events are\ntherefore highly relevant. In fact, it has been prominently argued that climate risk assessments\nshould also address the highest risks (e.g. Weaver et al., Env. Res. Lett., 2017; Sutton, Bull. Amer.\nMeteorol. Soc., 2019). Studying how these events change in a warming climate is thus important.\nCurrently, research on such events is limited, and assessments are typically built on the assumption\nthat very extreme events change similar to moderate extremes. Here, we demonstrate that this\nassumption is wrong for large regions of the globe.\n2)Further, it seems that there may be too many Figures for Nature Communications\n(usually 4-5 charts), and the “Introduction” part of the MS is a bit too long.\nWe double checked that the number of display items and the length of the introduction are in line\nwith Nature Communications formatting requirements. Nevertheless, we slightly shortened the\nintroduction."}]

Decision letter