Present and future European heat wave magnitudes: climatologies, trends, and their associated uncertainties in GCM-RCM model Chains by Lin et al. 

General comments

Lin et al. used dynamical downscaling to analyse heatwaves based on simulations carried out with regional climate models (RCMs) from the Euro-CORDEX programme. A particularly relevant topic of this paper is that the authors investigated if there is any added value in the representation of heat waves in the RCMs compared to the driving GCMs. It is an interesting topic definitely worth pursuing.

A general remark is that all researchers discussing evaluation and use of GCM results on regional scales ought to read the paper by Deser et al (2012; DOI:10.1038/nclimate1562), and citing it in a study like this thus should be required. The findings of Deser et al. suggest that the small number of GCMs selected here is insufficient for a proper analysis of future outlooks and model evaluation, due to pronounced chaotic regional variability on decadal scales.

The regional climate modelling community also still seems to exhibit a ‘silo thinking’ behaviour, and in order to try to make som progress in the general thinking about downscaling, I would urge that this paper by Lin et al. also includes work based on empirical-statistical downscaling (ESD). Many papers on RCMs ignore ESD, which becomes invisible and under-appreciated, and this unfortunately seems to create an attitude that RCMs suffice - hence many of the climate services in Europe do not consider ESD. I suspect most people working with RCMs don’t read the literature on ESD, but I think there are benefits from consolidating the two approaches - in particular when it comes to the evaluation of RCMs. There are also a few examples of ESD applied to heatwave statistics that merit a mention in the context of this paper (e.g. DOI:10.5194/ascmo-4-37-2018). Nevertheless, ignoring ESD is a weakness, although Lin et al. give a good summary of the limitations of RCMs. RCMs and ESD make use of different sets of assumptions and have different strengths and weaknesses independent of each other, and hence a combination of the two makes the results more robust. 

Often the most severe effects of heatwaves are connected with night-time temperatures not cooling off. It is therefore also of interest to use a heatwave index based on daily minimum temperatures and not the daily maximum. The most pronounced temperature trends also are those of the nights.

It would be interesting to see the statistical distribution of yearly HWMId values - are they normally distributed? (E.g. is the central limit theorem valid for this statistic aggregated over Europe?) One way to evaluate the models is to compare their statistical distributions (e.g. Kolmogorov-Smirnov Test). 

I was a bit surprised by Fig.1 that seems to indicate more heatwave activity in the Nordic countries and less further south on the continent. This also seems to be the case for EOBS and ERAINT - does that mean that perhaps HWMId doesn’t represent the typical heatwave reported by the news headlines? It’s defined in terms of local variability (IQR) and autocorrelation - and not on any threshold value, as far as I read this paper. At least, this warrants some comments.

Does the result that all RCMs show less agreement with E-OBS in RMSE and r compared to that of ERA-Interim suggest that these RCMs don’t add value to that of the global model? Or could it be differences in heat fluxes, cloudiness and topography of the driving and nested models? Perhapst the model domain is so large that the RCMs generate their own dynamics within the interior of their lateral boundaries? Or have they involved spectral nudging to avoid that? See e.g. DOI:10.1007/s00382-022-06219-y (it’s also a useful paper to discuss in this context). These questions certainly merit some discussion. The results are nevertheless useful and interesting as they suggest that differences between the RCMs matter. 

I’m not sure that I understand Table 4 and the use of MBE, RMSE and correlation for results derived from GCMs since we don’t expect the GCMs to be synonymous with the real world and hence no correlation with observed heatwaves. The only way to evaluate the downscaled results from GCMs is through statistical properties such as statistical distributions and parameters. But perhaps Table 4 shows the correlation in space rather than over time? If so, this ought to be explained more explicitly and clearly. Also if the appearance of the number of heatwaves more or less follows a random process, then we’d expect that it over a given period will follow a Poisson distribution - this can be assumed to be true for both models and the real world. Then the number of observed heatwaves can be compared to a statistical distribution of corresponding number of heatwaves based on the model ensemble by assuming a Poisson distribution (this works if the ensemble is considerably greater than 30 independent runs). Is this possible, or does the HWMId statistic suffice? Also, so-called ‘common Empirical Orthogonal Functions’ can be used to compare spatial structures and the covariance structures in different data sets - it’s an elegant maths-based approach that is surprisingly uncommon. However, this is more general and not specific for a small selection of extreme events. But regarding my comment on Fig 1, I’m a bit unsure what HWMId really represents. Perhaps it also may be of relevance here to mention that one indicator of trends in extremes, including an increasing severity of heatwaves, can also involve an analysis of record-breaking events. There is some literature on this subject connected to climate change.

The most rapid warming in northern Europe is during winter, but maximum daily temperatures are highest in summer, and it’s only summer that defines HWMId? (L348)

The point about ‘cascade of uncertainty’ is a myth and forgets that each step of analysis also introduces new information (or constraints) in addition to uncertainty. It’s only sensible with several model stages as long as we introduce more information than uncertainty for each step (see e.g. DOI:10.1038/NCLIMATE3393). In fact, downscaling can be considered as an act of adding new information to that already provided by GCMs: information about how local geography influences the local climate (as in this case) and information about how local climates depend on the ambient large-scale conditions and teleconnections that the GCMs skillfully reproduce. 

In summary, the tiny sample of GCMs in this study severely limits the application of these results and there were some points which were unclear and needed elaboration, as pointed out above. One way to improve this is to extend the ensemble of GCMs to the whole of CMIP5 (CMIP6?), and then compare those three selected here in this study with the larger set of GCMs. There are also some issues that merit more discussion, as mentioned above. I also think it’s useful to discuss other definitions of heatwaves than HWMId, even if this paper focuses on just this fairly established indicator. Furthermore, it’s important to consider ways to connect these results with what can be delivered by ESD (e.g. much larger ensembles than Euro-CORDEX), and in general I suggest that papers on downscaling that ignore one of these strategies do not merit publication.

Details:

L52 “hace” is misspelt.

Fig. 2 caption: ‘Scott’s rule’ needs a reference.

L.188: Missing “there” in “shows a similar pattern to the ensemble mean (first row of Fig. 5) but exists considerable differences in the spread (second row Fig. 5) of the RCM ensembles”?

This paper analyses the historical occurrence and future projections of heat waves in Europe using simulations from four RCMs driven a) by ERA-Interim and b) by three different GCMs. Heat waves are identified by the Heat Wave Magnitude Index daily (HWMId). The paper finds that RCMs generally reproduce well observed heat wave patterns when driven by ERA-Interim. When using historical simulations driven by GCMs, the (statistical) agreement with observations gets a bit weaker. Future projections reveal increasing heat wave magnitudes throughout Europe but with differing patterns for GCMs and RCMs. This implies that RCM patterns are not only determined by the driving GCM model, but the physical parameterization of RCMs plays an important role as well. Uncertainties of future projections are due to both GCMs and RCMs.

The paper is well structured and generally it is easy to follow the argumentation. Some parts would need a more concise language to be better understandable. The paper mostly focuses on analysing the contributions of RCMs and GCMs to the HWMId patterns, but also includes some statements about impacts. For the latter, I would suggest using a different approach (e.g. focusing on warming levels instead of time periods) due to the usage of the high-emissions scenario RCP8.5, as this scenario does not include any climate mitigation efforts and thus likely overestimated impacts at the end of the century.

General remarks:

• Some parts of the result section would benefit from a revision of the language to make the paper easier understandable. Arguments are sometimes rather hard to follow, especially in the parts focusing on the analysis to which extent RCMs and GCMs are responsible for a certain HWMId pattern (e.g. lines 170-194). I would recommend formulating the text in a more concise way and try to keep the same terms throughout the paper to facilitate reading.
• In the results section, the coverage of certain topics is sometimes split (e.g. a table relating to a certain figure is described at a different place than the figure). I would suggest restructuring the results such that each topic is only described/discussed once (i.e. table and figure at the same time). This would make it easier for the reader to follow the argumentation. In the specific remarks I mention some examples for text that could be merged.
• The paper mentions several times that HWMId rises in an “exponential-like” rate. However, the paper provides no figure or analysis that shows such an exponential increase. I would thus recommend to include a time series plot showing this behaviour. Further, I am not sure if “exponential-like” is the right term: Either the increase is indeed exponentially, or it follows a different functional form.
• The study currently uses a matrix of 4 RCMs x 3 GCMs. To my knowledge, even a larger matrix of GCMs and RCMs with full RCM/GCM coverage would be available. Is there any reason why only 4x3 models were used? Have the models been specifically selected?

Specific remarks:

• There are some typos and small mistakes in the manuscript that I do not list here. I would recommend to carefully read the manuscript again and correct them.
• Line 5: I would specify the observations (i.e. E-OBS)
• Line 6: Higher resolution compared to what?
• Line 8: What does “satisfactory way” mean? How is this determined?
• Abstract: I think it would be nice to finish the abstract with one or two sentences describing the implications of this study.
• Line 22: Weren’t also other Scandinavian countries in addition to Sweden affected by the 2018 heatwave?
• Lines 23-24: Heatwaves can also affect agricultural productions or cause forest dieback (due to lack of water or insects). Might be worth to mention this here as well.
• Lines 54-59: I think some more argumentation would be good to explain why HWMId is used (instead of other heat wave indicators)?
• Lines 76-77: From the original publication of HWMId (Russo et al., 2015) I understand that Tmax,ref,25p and Tmax,ref,75p are calculated based on the annual maximum temperature distributions at a certain gridpoint (i.e., 30 values per grid point). It seems that in your study, the total summer distribution was used. This should be checked to make sure the calculation agrees with Russo et al.
• Line 80: Remove “is calculated” at end of sentence.
• Line 88: Can you briefly mention why focusing only on RCP8.5?
• Line 101-103: This sentence regarding the different reference periods sounds a bit complicated. As I understand, when RCMs are driven by ERA-Interim the reference period is 1989-2008, and when driven by GCMs it is 1990-2010. Maybe it could be explained like this?
• Line 106: At which step were the data remapped? Before or after calculating HWMId? And were the data remapped to the ERA-Interim or E-OBS grid? And what about remapping of ERA-Interim or E-OBS?
• Line 110: I am not sure “effective precipitation” is the right term here, as it would also include runoff. Maybe just use P-E? Alternatively, sometimes “net surface water budget” is used.
• Line 132: Which RCM simulations?
• Lines 139-140: Would be better to include this in the paragraph of lines 117-127.
• Lines 143-144: I guess this is due to the fact that RCMs are driven by ERA-Interim and not E-OBS.
• Lines 147-151: I would remove this here and only mention it when the respective figures or tables are discussed (see general remark).
• Lines 155-156: The improvement seems to depend strongly on the model. E.g. RCA4 has a relatively weak pattern correlation in Table 4.
• Lines 163-166: Combine with lines 152-156.
• Lines 172: I would not necessarily call this “error”. Maybe the term “error” could even be removed here.
• Lines 174-175: I do not fully understand this. Could this be rephrased to make it better understandable?
• Line 193: “are not“ instead of “would not be”
• Line 199: Where does the manuscript contain the information that there is no difference according to the spatial r?
• Lines 201-202: Something is missing in this sentence after “the driving”.
• Line 215: “Observed” refers to E-OBS, right? If yes, I think it is best to mention it explicitly.
• Line 222: What is meant by “simulations”?
• Line 243: Better performance in terms of what?
• Lines 249-255: In your study, HWMId is already studied in detail, so I am wondering if you could extend the analysis a bit more to the mentioned events. And what would be the benefit of such a detailed analysis (keeping in mind the other CORDEX evaluations that have been carried out already)?
• Line 269: How exactly does this study show added value? What does this refer to exactly?
• Line 273: How does this statement relate to line 263?
• Line 275: Again, what is the added value referred to here?
• Line 286: RCP8.5 is a high-emission scenario and thus, it is unlikely that the future climate will be as projected by the scenario. Thus, statements about the impacts should be made carefully when using RCP8.5. One option would be to use warming levels instead of time periods, if statements about impacts are made.
• Line 288: I would remove “with a strong probability”. Also, what is meant by “on the alarm on”?
• Lines 292-294 & lines 301-302: I think that missing plant-physiological effects in RCMs might also contribute to the difference between RCMs and GCMs (Schwingshackl et al., 2019; https://doi.org/10.1088/1748-9326/ab4949). I am aware that the suggestion to include more papers is always delicate (in particular, if the paper is written by the reviewer). My future review will not depend on the inclusion of this paper.
• Lines 310-328: This paragraph seems rather speculative to me, as it does not include any clear causal links, but remains mostly on comparing patterns. I would suggest to either extend this analysis of potential drivers or to shorten it.
• Lines 327-329: This sentence seems rather vague. I think it might be better to highlight which open questions arising from your study would be worth to be analysed by future studies.
• Line 335: I am not sure I would expect an exact match with ERA-Interim, given that it only provides the boundary conditions.
• Line 341: The exponential-like increase is not shown in the paper. I would suggest to include a figure showing it (see general remark).
• Line 343: What exactly does “relatively more moderate rising trend” mean?
• Lines 346-347: As mentioned above, I am not really convinced by the analysis regarding the impact of drying trends on HWMId. Thus, this statement currently seems not convincing to me.
• Line 348: Which figure does this refer to?

Remarks about figures and tables:

• Figure 2: I think a time series plot for the different datasets would be easier to understand than the current Figure 2a. Moreover, I am not sure the distributions in 2b are really needed. I personally find them hard to interpret. Another option would be to replace the violin plots by PDFs.
• Figure 3: The red rectangle is hard to see. A different colour (e.g. blue) might be better.
• Table 2: If I understand correctly, this table refers to Figure 1. I would try to highlight this better because it is not instantly clear to me (same for other tables that are connected to certain figures).
• Figure 4 ff: I find the greyish colormap rather hard to read. Maybe choose a different one? Or adjust the limits?
• Figure 10: I think this figure is too busy to understand. And the skewness is hardly visible to me from the violin plots. As above, I would suggest showing PDFs instead of violin plots as they are probably easier to interpret, and potentially also make the skewness visible more clearly.

Synopsis:

The study by Lin et al. investigates present and future heat wave magnitudes over Europe with RCMs of the Euro-Cordex ensemble. It is found that for present climate conditions, the RCMs are able to capture most of the observed spatial and temporal features of heat wave magnitudes. A central finding in my view is that the uncertainty in a simulated future change of heat wave magnitudes can be attributed almost equally to the difference in model physics and to the driving data. In general I am positive about the work. Still, I raise some issues below which concern the processes behind the observed signals and the choice of evaluation metrics. Further, there are numerous typos in the manuscript which I do not list here. These should be corrected prior to resubmission.

Major:

1) Processes behind climate change signals: I very much appreciate that the authors investigate the link of changes in HWMId to processes of the climate system. However, an important component is missing in my view which is the representation of blocking. It is well known that blocking is an important driver of heat waves in Europe and that the representation of blocking over Europe represents an important challenge to climate models (e.g., Masato et al. 2013). To complete the analysis, I therefore suggest either quantifying blocking biases or at least putting the results of this work in the context of studies that have already investigated blocking in CMIP5 models. The availability of open source code should simplify such an analysis (e.g. https://github.com/jlpscampos/Blocking_Index2d).

2) I understand that the models are evaluated in terms of the MBE, RMSE and Pearson correlation coefficient. However, are the HWMId values normally distributed so that the central limit theorem is valid? Accordingly, I suggest to also evaluate the statistical distributions of the models. 

l. 7: The conclusion that "RCMs can reveal spatial features of HWMId associated with small-scale processes" is place quite prominently in the abstract. However, after reading the manuscript it is neither entirely clear to which spatial features the authors are referring to, nor have the small-scale processes been named explicitly. Also what is meant with small-scale process? This is rather colloquial terminology and it would be good to specify explictly. Are you referring to processes on the meso-scale or processes that are parametrized. Please clarify.

l. 10: The term "expontential-like" is used frequently? However, I am not sure what "expotential-like" means. Either a rise is exponential or it is not. Therefore, I suggest to rethink the terminology used here.

l. 24: I guess you mean "marine heat waves" instead of "maritime heat waves".

l. 26: Is it on purpose to using the terminology "warm spell" here?

l. 48: Perhaps write explicitly "differently then GCMs".

l. 52: "have" instead of "hace".

l. 80: delete "is calculated" at the end of sentence.

l. 84: What is the reasoning for only using a subset? Please explain.

l. 88: Please give reasons why you selected RCP8.5.

l. 98: Do you mean "to ERA-Interim" instead of "the ERA-Interim"?

l. 109: Please clarify this sentence/make it more concise. Also, please specify the processes you are thinking of. To the reader it may not be immediately clear which processes you are referring to.  

l. 114: You may want to delete "the following questions" since i) and ii) are not actually formulated as questions.

l. 122: The way the results are presented it is difficult to directly see the differences "of some local features". Therefore, I suggest to revise the figures by showing differences between the RCM results and E-Obs (or ERA-Interim). This would help the reader to spot differences directly. Also, it would be good to name the "local features" explicitly. Are these local features related to land-sea contrasts, the direct effect of topography on temperature, etc?

l. 124: Delete "only" before "focusing".

l. 128: What is the area of the spatial average? Please provide this information somewhere in the text.

l. 161: As for l. 122: In my view, it would easier to follow the discussion if differences between RCM/GCM results and E-Obs were shown. Also, please mention explicitly where the GCMs "miss out both in detailed structure and amplitude". In its current form it is left to the reader to spot these deficiencies.

l. 182: "of" instead of "in".

l. 187: Please split this sentence in two sentences as it is hard to follow the explanation. Also, there is a word missing between "but" and "exists".

l. 200: Please provide a "not shown" as the reader may otherwise try to find the spread information in a Figure.

l. 279: What exactly is meant with the quite general term "orographic effects"? How are they differently represented in the RCMs? Some explanation would be helpful here.

l. 295: This sentence is overly complicated in my view (2x "is expected"). Please revise this sentence.

l. 335: It would be good to mention explicitly the "room for improvement". The interpretation should not be left to the reader.

l. 344: Do you have any insights on what is leading to the weaker drying trend in the RCMs?

l. 349: "Plays" instead of "play".

l. 354: Also here, what is meant with the term "orographic effects"? Are you thinking of the treatment of sub-grid orography? Please specify?

References:

Masato, G., Hoskins, B. J., & Woollings, T. (2013). Winter and Summer Northern Hemisphere Blocking in CMIP5 Models, Journal of Climate, 26(18), 7044-7059. Retrieved Jun 7, 2022, from https://journals.ametsoc.org/view/journals/clim/26/18/jcli-d-12-00466.1.xml