Review on “Global relevance of atmospheric and land surface drivers for hot temperature extremes” by Yigit Uckan and colleagues.

The manuscript investigates different atmospheric and land surface drivers of hot extremes on two time-scales in the period 2001-2020. The authors find geopotential height to be by far the most important driver of 1 day events, while for longer 7 day events land surface drivers become more important. 

The manuscript is well written and well organized and supported by meaningful figures. The topic covered is a timely one and nicely supplements the existing literature, for example, a recent study by Röthlisberger et al. (2023; 10.1038/s41561-023-01126-1) which the authors should consider discussing as it investigates a very similar question but using a quite different approach for atmospheric drivers. 

While I do not have any major comments, I see several open questions that should be addressed before publication: 

- independence of the variables used as drivers: This is briefly discussed buy should be quantified in some way, in particular to show that atmospheric and land surface drivers are indeed independent as assumed by the authors (line 186).

- effect of analogue quality: What role does the ‘closeness’ of the found analogues to the observed event have on the results and could this influence, e.g., the differences in 1 day and 7 day events (as it might be harder to find good analogues for 7 day events)?

- the metric ‘degree of relevance’ and its interpretation is not quite clear to me as mentioned in the specific comments below

- the discussion of changes due to climate change (3.3) is very short could benefit from some more analysis and contexualization. In particular since the two time periods investigated are quite short, I’m wondering if any of the effects are statistically significant.

Minor comments

Given that the manuscript is well organized and written this is not a large issue but the authors could consider focusing data section (2.1) better. Currently it reads like a mixture of data and method section, with sentences like: “In addition, we compute the geopotential height differences at 500 hPa pressure level for each grid cell with respect to the values in adjacent grid cells in the northern, eastern, southern and western directions.” 

line 79: Could the authors elaborate why the use only 2001-2020?

table 1: some of these drivers are probably quite correlated (e.g. GPH and surface radiation), could the authors comment on how this might influence the analysis and interpretation of the results?

90: “For the 7-day time scale we apply a moving average” Could the authors state the window size explicitly here? (I’m guessing its 7 days?)

91: “For each type we select the three hottest events” 

I’m assuming the authors refer to the 1 day and 7 day events here? However, this is not really clear form the context of the last few sentences.

To make sure I understand correctly: for the 1 day events these would be 3 individual days and for the 7 day event three 7 day periods?

In general I think this section might benefit from a concrete example. I’m not a 100% sure I understood the approach. 

For example: for the 1 day events, this would give 3 individual days which are all separated by at least 15 days? Meaning if there’s a 7 day heatwave only the hottest day of it would be selected for the 1 day event?

Its also never mentioned if this is done on an annual basis (as seems to be indicated in figure 1) or for the entire dataset at once. 

Figure 1:

-  could mention that “Hottest Period x” does also refer to a single day in the case of 1 day events?

- increase font size

“2.5 Effect of the increasing trend” For me ‘increasing’ indicates an acceleration of a trend (which is already a change measure) so it is probably not what the authors want to say here? ‘increasing number’ or ‘positive trend’ instead?

Figure 2: 

- the authors could consider using ‘more different’ colors to make the separation of the different drivers easier? In particular, for the separated view in figure A1 it is almost impossible to really separate drivers due to the chosen colormaps.

- it could also be interesting to compare these results to the work from Roethlisberger et al. 2023 (10.1038/s41561-023-01126-1) at least for the atmospheric drivers?

153: could this be partly due to the fact that it is (presumably) harder to find good analogues for 7 day events for GPH compared to 1 day events and hence the temperature anomaly is less pronounced for the 7 day case?

186: “Furthermore, our main goal is to disentangle land surface and atmospheric drivers of hot extremes which are not expected to be strongly related to each other.”  As commented earlier: could the authors quantify the cross-dependence of the drivers is some way?

192: another limitation might be the quality of the analogues, which seems to be crucial for the quantification of the contribution?

Figure 4: “The degree of relevance is computed as the ratio between the respective analogue temperature anomalies and the observed temperature anomalies during hot extremes.” This could be explained in a bit more details in the methods section? For example: this seems to mean that the degrees of relevance from different drivers can sum up to more than 100% percent, right? 

203: “While EVI is the most relevant driver of hot extremes in more areas at longer time scales (Fig. 2), we find in the main driving variables of hot extremes summarized across climate classes that it also exhibits a higher relevance in these areas but also in other areas where other variables are even more important”

This sentence is somewhat convoluted.

200-210: This section reads a bit strange in general and seems to make the same point over and over?

“Notably, the relevance of EVI increases with the time scale, in contrast to that of geopotential height, probably due to the longer memory of land surface variables compared to the atmospheric variables”

“This finding highlight that the land surface generally affects hot extremes at longer time scales, as opposed to the more immediate influence of atmospheric drivers.”

“This is related to the fact that land surface effects such as evaporative cooling or shading are comparatively smaller but more persistent.”

“they are more influential at longer time scales and for hot extremes that build up during a time period without major changes in weather and air masses at a given location”

215: “Moreover we calculate the sum of the degree of relevance of the three most influential variables at each grid cell (Fig. A5). This shows which part of the observed hot temperature anomalies can be explained with our approach” I think I might misunderstand something here (see also my earlier comment on this). The temperature anomalies from the analogues of different drivers could sum up to more than the observed anomaly, right? So I’m not sure about the interpretation of this.

Figure 5: set the maximum of the y-axis to ~.4 to avoid large empty spaces? 

I’d like to see some kind of significance measure for these changes. It seems like apart from EF, none of them are significant even though the authors seem to indicate the opposite in line 233: “At the same time, the relevance of geopotential height, radiation and wind slightly decrease.”

247: “This finding underscores the significant role of atmospheric blocking mechanisms in the formation of hot extremes” I would assume that most positive GPH anomalies are not blocks even at mid latitudes? In particular on a time-scale of 1 day? 

The paper shows an interesting study that teases out how different potential drivers for extreme heat emerge at time scales. The shorter (1-day) time scales are effectively a proxy of the “initial condition” forecast problem, from the atmospheric perspective, in weather prediction, and the strong role of circulation features bears that out. At longer time scales, the “boundary conditions” (i.e., land surface) emerges as an important factor. It brings to mind the point being made in the “infamous” figure used widely in the subseasonal-to-seasonal community (https://www.weather.gov/sti/stimodeling_s2sreport).

The main weakness of the manuscript is a lack of sufficient detail in the description of the methods - I believe this can be easily addressed. The main weakness of the study, as it weakens the conclusions, is the lack of significance testing of the trend analysis. I realize it is not applicable to all the methods shown, but certainly the part of the research comparing changes from the first to second decade of this century could be tested (see specific comments). Otherwise, I think the study has strong merit, and the manuscript can be published after some revisions described below.

General comments:

1. An idea that emerges from this work is validation of the long-held notion that it is circulation features such as stationary ridges that initiate heatwaves (this is clearly stated in a couple of places), but that the land-atmosphere feedbacks (via surface drying and warming – much work by D. Miralles and colleagues on this) can both amplify and prolong heatwaves. The second aspect, prolonging heatwaves, is particularly well demonstrated by this study, and should be emphasized more in the abstract and conclusions, in my opinion. It comes from the novelty of the way a range of timescales has been investigated.
2. Another conclusion that I reached from reading this paper, based on the clear role of EVI (and EF, which is related to canopy conductance that itself links to vegetation carbon uptake and plant processes that regulate that), but that is not made by the authors, is that the results advocate for the inclusion of vegetation phenology in forecast models of weather and subseasonal climate. It is a bit “connecting the dots”, but these relationships are arising from processes that are not a part of any operational forecast model (i.e., not parameterized in their land surface schemes), and are even absent from many CMIP models. In the final paragraph of the conclusions, you should point to operational prediction models specifically.
3. Regarding land surface drivers for hot extremes, the literature review is quite short and Euro-centric for a paper with “global” in the title. There are other highly relevant citations in the recent literature that should be noted; a few I am quite familiar with: https://doi.org/10.1029/2020AV000283, https://doi.org/10.1175/JCLI-D-20-0440.1, https://doi.org/10.1175/JCLI-D-22-0447.1, https://doi.org/10.1029/2023WR036490.

Specific comments:

1. L65: It took a while for me to realize that by “height differences” you mean horizontal gradients, relevant to the geostrophic wind relationship. In atmospheric thermodynamics, the term “height differences” is typically applied with respect to the hypsometric relationship, i.e., the vertical distance or “thickness” between two pressure levels, which relates to the mean virtual temperature of the layer between. To avoid confusion, you should replace “height differences” with “horizontal height gradients”, or just be explicit that this is a proxy for the geostrophic wind (you could label this as “Advection” here and in Figures 2, 5, A1, A6, A7).
2. §2.1: It is stated that daily data (shortest time scale) are used. Are these based at each point on the local time, or all on 0000UTC as the day boundary? If the latter, then for about half of the world, what you call “one day” actually spans two days with respect to important diurnal phase of drivers like net radiation and evaporative fraction. Please clarify and/or justify the choice.
3. L70-71: This is the first time either “X-BASE” or “ERA5” are mentioned (before Table 1 is cited). They should be defined or described here, or else moved after Table 1.
4. Table 1, EF: How is EF calculated from X-BASE? To my knowledge, the publicly released data does not contain this variable, nor the necessary data to calculate it (i.e., there is no sensible heat flux field). That renders this part of the study unreproducible by others.
5. L92: How are the warm seasons defined? There are a number of approaches, as there are strong latitudinal (and more complex) determinants. Are the same number of months used everywhere, or are only very cold months avoided (a temperature threshold)?
6. Figure 1: This is an important figure, but it not clear and the descriptions in the text do not fully clarify the workflow, especially for part (c). In the caption, it should explicitly say “see text for details”.
7. L100: Please give more description of the definition of “similar” (i.e., please do not rely solely on a reference to Yiou et al. 2007). Is it based on RMSE? Is some normalization applied? Perhaps it is best to include equations.
8. L103: This is not entirely clear – do you mean that the center of the window is on the calendar date (month and day) applied across all years?
9. §2.4: As noted above, this description is very fuzzy. I do not follow the process. Again, perhaps equations or pseudocode is needed. I would not be able to reproduce this methodology based on the description.
10. L114-115: This is, of course, a linear assumption, that the drivers can be considered separately. This point is acknowledged later as a possible drawback, but it would be good to state that here – this is where some readers will begin to have this question in their minds.
11. L120: Should “both” be replaced with “each of the”?
12. Figures 2, 4, A1, A5, A7: It is difficult to tell the grey from some of the pale blue shades – they have very similar luminance. Additionally, the monochrome palettes in Figures 4 and A5 make them somewhat hard to read. It appears that you are trying to be considerate of colorblind readers – using a cubehelix palette in these two figures would improve clarity for all.
13. L142-143: Please move this final sentence of the paragraph up to become the 2^nd sentence (right after Fig. 2 is mentioned).
14. L154-163: This is methodology: it should be explained in §2, not with the results. Additionally, how the Random Forest method is applied must be explained in sufficient detail such that a reader could hope to reproduce it.
15. L168: Replace “mostly just” with “barely”.
16. Figures 3, A3, A4, A8: Aside from aridity=1.0, which has a special meaning in the Budyko framework, the other boundaries for the bins do not necessarily need to be chosen because they are round numbers or evenly spaced. If instead you had chosen boundaries on each axis that contained approximately equal numbers of grid cells, you may arrive at a more robust and clear result with fewer dependencies on varying sample sizes. But I would suggest keeping a boundary for aridity at 1.0.
17. L181-192: I appreciate this paragraph. If you are interested in pursuing this further, you might consider using an approach based in information theory, which has the advantage of also being nonparametric. There are also ways to quantify nonlinearity and parameter interaction (see: https://doi.org/10.1002/2016WR020218, https://doi.org/10.1002/2016WR020216, https://doi.org/10.1029/2020WR028179).
18. L190: I think the independence of different data sources could be looked upon as a strength, not a weakness, of this research. When patterns emerge across datasets with different algorithms, or not all from one model, it gives more credence to the results.
19. L205: Replace “highlight” with “highlights”.
20. Figure 5: The result is not compelling unless statistical significance of these differences between decades can be established. Fortunately, that is straightforward. A very robust test is a bootstrap approach where the 20 years are randomly split into 2 sets of 10 and the “degree of relevance” calculation is repeated many times (say 1000 times; C(20,10) = 184756, so no problem with oversampling). Then find where the particular case of 2001-2010 versus 2011-2020 falls in the larger distribution… that is your p-value. Otherwise, we don’t know if the EF changes are meaningful.
21. L245: Drop the word “wide” – it’s not very appropriate.
22. L246: You say “particularly at the 500 hPa level” but the results for other levels were never quantified, save for squinting at all the similar shades of color in Figure A1. A Table (A1, perhaps?) should be included with the complete quantifications (for all factors in each decade – as Figure A7 is also difficult to read).
23. L267: Here you are talking about trends, but you do not use the word “trend”. It would be clearer if you did.
24. Figure A2: Please expand the acronym “SHAP”.
25. Figure A7: I suggest for the bottom 2 panels, only color the grid cells where a change has occurred. Leave the unchanged cells blank.
26. Figure A8: Presumably there is a bit of movement of some grid cells between bins from one decade to the next. Are you considering that here, or are the 2m temperature and aridity still based on the 20-year climatology? Also, here again, a bootstrap statistical test can tell which bins have significant changes (or perhaps use color to indicate p-value).