Summary

The objective of this article is to propose a novel methodology for quantifying the emergence of statistically significant compound events and then apply this approach to extreme temperature and drought conditions across Europe estimated using ERA5 reanalysis. The authors define a Period of Emergence to quantify whether the probability that the dependence between compound events is temporarily statistically significant (Period of Emergence) or permanently statistically significant (Time of Emergence; an existing method within time series analysis). They then compare these probabilities under two assumptions: that the dependence structure between compound hazards does not change over time, and that this dependence structure does change over time. Finally, they quantify the relative contribution of each component (the drought index, the temperature index, and their dependence structure) to the Time of Emergence and Period of Emergence over time. They compare findings across five regions in Europe. They make an R package available for researchers to conduct similar analyses on any compound event pair. They explore the impact of two signals on the Time of Emergence and Period of Emergence for compound event probability. One, in black, is the probability of compound event if we take the dependence structure between temperature and drought to be constant over time. The other, in blue, is the probability of compound event if we take the dependence structure between temperature and drought to change over time. When either signal temporarily exceeds a confidence interval of noise, call it a period of emergence. When either signal permanently exceeds a confidence interval of noise, call it a time of emergence. Note that the signal is weakened under the assumption of constant dependence structure and is strengthened under the assumption of changing dependence structure.  

Overall, this manuscript is well-written and provides a compelling argument for the inclusion of this novel methodology into compound event research. They find that a statistically significant compound event signal emerges earlier in time than previously recognized when 1) the dependence structure is allowed to change over time and 2) a period of emergence is quantified. They quantify how the contribution to these compound events has changed over time, allowing for regional and location-specific applications to compound events. This research contributes to the field of compound and multi-hazard research because it expands our definition of compound events using a novel statistical approach that can be readily applied to any event pair. The manuscript follows a logical structure and identifies potential approaches for future research that would enable more than two hazards to be simultaneously analyzed for their time-varying dependence. There are few clarifying, structural, and editorial changes needed prior to accepting this manuscript. Comments and suggestions are provided below and organized into major and minor.

Major comments

• Generally lacking helpful descriptions of each figure, see minor comments for suggestions.
• Section 5.1 – I’m missing a takeaway from this section. What do we now understand if we consider period of emergence and / or changing dependence structure between compound events. Simply that some areas are more at risk of compound hazard than previously expected? That more compound events can be attributed to a dependence structure or when a period of emergence is considered? How does this affect researchers and exposed communities? How can researchers, insurance providers, community planners, etc. use the results of this study to improve outcomes from future compound events? Can we link this kind of analysis with research exploring the drivers of compound events?
• Section 5.2 – how would your analysis change if you considered aggregating your indices at different temporal resolutions? Ie. daily, weekly, monthly max values? Min values? What is the sensitivity of your analysis to your chosen variables and chosen resolutions? Would the application of this method to climate model simulations affect the confidence interval of noise?

Minor comments

Line

• 55 needs a citation for ‘most damaging impacts’.
• 60-61 explain why covariance matrix is not appropriate for CE.
• Paragraph starting on 48 is very difficult to follow, consider rewriting from line 55 to the end, potentially break up into a few paragraphs, remove excessive detail and streamline.
  • I missed the explanation as to why a gaussian assumption of the dependence between variables is not appropriate for compound extremes.
• 254 componen is missing a t; perhaps remove ‘even’ before ‘negative’, or find another way to highlight this otherwise counterintuitive statement.
• 271 Perhaps outline this argument as a counterfactual. When I first read this section, I thought your argument was that it is safe to assume that dependence can be kept constant. But I see that you are setting up the argument that this assumption is invalidated through this modeling framework and that you indeed have similar findings to Wang et al., 2021 in the prior sentence.
• 289 please elaborate on the line ‘not considering the dependence evolution would advance the signal emergence’. Does this suggest that signal emergence occurs earlier in the record under the assumption of constant dependence? I think rewording this sentence could provide needed clarity.
• 415 please include something like (78% of the grid points observe a time of emergence prior to the end of the temporal record) for clarity.
• 420 for my own interest, do any points experience a period of emergence, but then return to within the noise confidence interval? If so, where do those locations occur?
• Table 2. Please elaborate on this description. Include units, describe each of the four contributions, etc.
• Figure 1. It would be helpful to visualize the signal prior to smoothing. Is that possible to include in a figure or even in the supplement?
• Figure 2. Explain what the difference between the red and black arrows is. Is it appropriate to compare regions of different spatial scales, covering different proportions of land and ocean area?
• Figure 3. Are you able to show with different colors / hatch marks the four cases where white color is? It’s currently difficult to decipher what white means across the region. It would also be helpful to give a short summary of your interpretation of this figure.
• Figure 4. It would also be helpful to give a short summary of your interpretation of this figure.
• Figure 9. It would also be helpful to give a short summary of your interpretation of this figure.

This manuscript by Schmutz et al introduces a new framework within which to consider the emergence of hot and dry compound events over Europe and North Africa. Building on the extant concept of Time of Emergence (ToE), the authors introduce a Period of Emergence (PoE) which generalizes the ToE to include emergence [above/below the natural variability] that does not last until the end of the analyzed time period. The authors claim that this allows better characterization of the resulting signal by analyzing the number and duration(s) of PoE events in the time record. Further development of the framework allows the authors to introduce a budget-type analysis examining the role that the individual components (temperature and drought) play in this emergence, as well as their combination and interactions. To demonstrate this framework, the authors use the ERA5 reanalysis dataset to look for changes in compound events in Europe and North Africa between 1950 and 2023.

General Comments

Overall, this manuscript lays out the foundations for the scientific gap addressed well and rightly highlights the myriad of ways in which heatwaves, droughts, and their co-occurrence affect human life, society, and the environment at large. More detail could be included about the data used, which I have outlined further below. As the main novelty within this manuscript, the methods and underlying reasoning are laid out in a comprehensive manner, including reference to finding the analysis code online.  Areas where the authors include slightly less technical language to summarize the steps they've made are appreciated and add accessibility to the manuscript beyond those who are primarily statistical modelers. The resulting analysis is also quite comprehensive, although there might be a slight dependence on supplemental figures through this section (although I appreciate the authors transparency in sharing all figures associated with the analysis!). I have some reservations, mainly about the underlying data and assumptions of some of the analysis, outlined below in my specific comments, and followed by technical corrections. While a full exploration of the issues raised in the specific comments would entail additional reanalysis that the authors could choose to pursue, I believe that a more complete explanation of their choices as to the data in the manuscript would also be sufficient.

Specific Comments 

1.) When attempting to understand the framework and analysis methods in the paper, perhaps I overlooked it, but it is unclear to me how exactly the monthly temperature and SPEI data is handled within the framework - how the three data points become one for the year, for example. More clarification on this process would help to make the transition from the data introduction to the analysis products clearer.

2.) Further explanation for the choice of using monthly maximum temperatures would help to provide context for the results. Although maximum temperatures are certainly important and crucial to identifying impactful heat wave events, increases in minimum temperatures can also play a significant role, especially in thinking about mortality applications of this type of analysis. Are similar results achieved for substituting in the monthly maximum of the daily average temperature for example? Additionally, how is the analysis affected by use of monthly aggregated temperatures versus weekly for example, especially in terms of using a single point in time to represent the month?

3.) While understanding that the authors are somewhat boxed in given the ERA5 dataset limitations in time, I'm concerned about the reference period for emergence only being from 1950-1969. How does this choice affect the results afterwards? Use of only a two-decade period may lend itself to an underestimation or transposition of where the natural variability in the system lies, depending on if/how that period was itself anomalous - which then cascades downstream by affecting the ToE and PoE thresholds. Have the authors considered longer reference periods or other time slices as their periods of reference? 

Regardless, along this line, the detection and definition of multiyear to multi-decadal oscillations strikes me as both an issue that plagues the reference period as well as an intriguing potential application of the PoE method to climate data analysis.

4.) Similarly, does a different selection for the preceding time period of SPEI (other than 6 months, perhaps 3 or 4) have a significant effect on the results? If so, this could also enlighten differences as to the effect that winter versus spring moisture amounts have on these CEs.

Technical Comments

Generally, there are some verb tense disagreements, but these are simple enough to fix up.

115 - ressources --> resources

117 - Additional "Drought" included in the PDSI acronym

119 - It is made clear late that "this indicator" is the SPEI, but it might be good to specifically mention it here, as it is indirectly referenced twice in a row.

262 - an other --> another