Using CMIP6 model projections, Denissen et al evaluate the co-occurrence of increasing trends in extreme temperature and increasing trends in ELI, a water-limitation metric. They find that these trends co-occur in many regions of the world especially in transitional and more energy limited regions. Therefore, more energy-limited locations are becoming more water-limited and experiencing more temperature extremes. This study is well done, carefully written, and concise which is always appreciated. I advocate for the use of ELI here which captures soil moisture and its nonlinear relation to energy fluxes. I find ELI to be a more direct variable to evaluate the questions here than soil moisture alone – something the authors could highlight more because it is a big strength compared to previous work.

My main criticism is the removal of many dryland regions, which I think are important for the message. I study the water, carbon, and energy cycles of these dry regions, including the influence of vegetation on the surface energy balance (for example, https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.16455; no expectation to cite). I am concerned that many of these regions are not fully included in the study and could bias overarching conclusions since they can respond so differently (see my #1 comment below). Nevertheless, I think it is a great study and ask the authors to consider several points.

-Andrew Feldman

Main Comments

1) I find the condition in L114-115 to remove pixels at <0.5 m2/m2 of LAI is quite restrictive and removes many drylands, including the Sahel, most of China, and nearly all of Australia. These are key water limited regions to remove, especially in the context of heatwaves where these regions may be most vulnerable. Drylands have been deemed an important part of the climate system. Dryland vegetation also plays a critical role in the surface energy balance. See some studies here (with no expectation to cite) where meaningful dryland vegetation energy balance studies were conducted with different results from expectations:

https://www.science.org/doi/10.1126/science.abm9684

https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.16455

I suggest using a less restrictive condition. Or be very clear motivating why such a strict condition is used here to remove these dry places.

2) In support of this study, I think a huge advantage of this study is the use of ELI rather than soil moisture alone. This point is not clear in the study and I think it is one of the main points to make up front on why this complements existing literature so well. Most studies typically evaluate the question of how the land surface influences temperature extremes with soil moisture. However, because soil moisture is nonlinearily related to energy fluxes, it limits soil moisture’s use to evaluate temperature by itself. A more important variable that captures this nonlinearity and soil moisture variability simultaneously is how water-limited versus energy limited a location is. ELI is one nice way to capture this (my variable of choice is time spent in the water-limited regime). I suggest making this over point clearer throughout.

3) Language and bias of thinking throughout seems to be about how ELI is influencing excess temperatures and that the direction of causality is from ELI to excess temperature. For example, see lines 275-276. Following that, it is nicely stated that this correlative analysis does not mean causality. However, I do suggest also noting in the discussion or elsewhere how excess temperature can influence ELI. This might help complete the loop on that discussion since I think the feedback in the opposite direction of heatwaves on ELI is also just as interesting and valuable. In other words, the authors might be limiting themselves in influencing the reader to think about ELI influencing on temperature extremes, when the other way around can give insights about sustaining heatwaves.

4) Figure 3 is really neat. I think it could be a better facilitated display of results in Fig. 3 and lines 231-247 if the nonlinear ET-soil moisture (and maybe also ET-SWin) relationships are discussed/displayed more prominently. I think the authors are making claims about how EF is insensitive to water in energy limited regions and might become even insensitive at lower soil moisture in water-limited places. These would be better supported if the Budyko framework and/or EF-soil moisture relationships are introduced before these other points are made about Figure 3.

5) This is a “devil’s advocate” position, but something I worry about in studies using models to learn about land-atmosphere interactions is how much model biases in the relationships between soil moisture and energy fluxes (here EF) cause errors in results such as those presented here. I always look at CMIP or reanalysis based results and hope that ensemble means teach us emergent behavior of the land surface, rather than only give us back the potentially flawed relationship between soil moisture and EF that some models might have. This study is valuable in presenting the model results and also adds the dimension that projections can be made, which is not directly possible with observations. However, at least in the discussion, I suggest advocating for the main figures being reproduced in an observation-based study to test whether these model behaviors are reproduced in nature. For example, Figure 1c can be reproduced with satellite soil moisture and LST (or gridded air temperature) to give further support for the results here.

6) There are many figures in the SI that are discussed extensively in the results. For example, Figure S6 about ET in lines 164-174 and Figure S8 in lines 198-211. I suggest moving them to the main text if they are pivotal parts of the manuscript.

Specific Comments

L12: note that the use of ecosystem (assuming both soil+vegetation) and vegetation are mentioned here which is making it unclear what the paper is about (is it only vegetation or soil+vegetation?). Potentially define what you mean by ecosystem here.

L70: The “|” symbol indicates conditioning in mathematics/probability. It is unclear how it is being used in the correlation function “cor(Ta’|SWin’,ET’).” It sounds like the correlation is either between Ta and ET or Ta and SWin based on line 75. Therefore, I think the “|” symbol is being used to somehow indicate this potential alternation in the metric. However, one can also interpret that notation as the correlation of Ta’ with ET’ while conditioning (or binning) Ta’ on SWin’. Can the authors be clearer about this notation? I know L85 says to refer to another study for details of ELI, but details like this should be shared here for completeness.

L95, Table 1: It might be worth noting what the difference in r1/r2 and f1/f2 mean since not all are the same in that column.

L114-115: The LAI condition at 0.5 m2/m2 might be overly restrictive and remove many drylands from the analysis that are important facets of the global climate.

L115: Central Africa? Do you mean East Africa?

L118: It should be the sum of radiative components minus the ground heat flux (G) (or Rn-G).

L150-152: This statement is tough to follow. This is only referring to the second term on the right side of Equation 1 or the energy limited component of ELI? I was thinking that water-limitation should be a big component in the tropics (but it looks like water-limitation is not considered in Fig. S1)

L157-158: It could be the other way around where temperature extremes contribute to increasing ELI.

L158-L160: With removal of many drylands and some opposing results in these locations (see my comment 1), it would be worth discussing further what physical processes cause these regions to differ.

Dear authors,

All my comments can be found in a separate pdf file.

Best,

Dominik