The authors investigate the precipitation event occurred in July 2021 in western Germany by means of the weather extremity index (WEI) and the cross-scale WEI (xWEI) with the updated RADKLIM product (estimations of WEI and xWEI for this event were already performed, but not including the year 2021, as it was still not available). They highlight that, when including the year 2021 in the estimation of GEV parameters, the ranking of the event changes for what concerns the WEI but is always the most extreme when looking at the xWEI. This finding points out the relevance of considering multiple spatial and temporal scales, as they might be crucial for defining the extremeness of rainfall events.

The event object of the study is surely of high interest, given the consequences it caused in Germany and western Europe, and the paper emphasizes the need of updating the way through which we study rainfall events and determine their characteristics. Therefore, I think that this communication is worth publication, after some minor revisions and clarifications. As a general comment, the paper is well written and mostly easy to follow, analyses are sound, and methods and results clearly presented in most of the cases. Please find a few remarks below.

L3: firstly, the sentence “both rely….GEV parameters” might not be clear to everybody (I am putting myself in the shoes of someone not completely within the topic). Secondly, from how it is written it seems that the GEV distribution is the only one that can be used for the estimation of return periods of extreme events, which is not the case. I would suggest trying to make this sentence clearer and include some details about the link between return period and GEV parameters when you introduce the WEI in the main text.

L26: even if the authors claim that the WEI is increasingly used in the community (I guess they mean the meteorological one), for someone that is not within it the information reported about the WEI (229 log(yr)km) at this point of the paper is not straightforward to understand. The definition of WEI is indeed provided only at L60. I would therefore suggest trying to insert this number into a context and explain briefly what the extremity index is and how it is computed (or at least what variables are considered) such that a broader audience can have a feeling of what this number means.

L57-66: see my comment on L3.

L69-74: writing explicitly the formula through which the xWEI is computed would be helpful.

Figures.

Figures are not color-blind friendly, please consider change color scaled such that everyone can appreciate differences and color meanings.

Figures 2: do the gray lines represent the WEI of the July 2021 event? If yes, it should be specified somewhere. Moreover, I would rather representing it as a point (with different markers/colors depending on the RADKLIM product used to compute it).

This is an interesting and relevant study about a major rain event in July 2021 in Germany. Overall, the paper is in good shape. The previous reviewer already made some good points. Below, I would like to add a few of my own.

Main point of criticism: I only found one major issue that needs to be addressed before publication, which is the lack of a proper uncertainty assessment. The authors could and should do more to quantify the uncertainty on the estimated return periods in the GEV, and how this uncertainty propagates to the WEI and xWEI. These are very important issues given the short available data record and the fact that the differences between the top 5 events aren’t that large.

Additional, general comments:

1) On the usefulness and need to rank extremes: I see value in studying extremes and their characteristics. However, I also wonder how useful it is to rank extremes over a given range of scales. Who needs such a ranking? And what can you really learn from a ranking that keeps changing over time as more data get available? Also, wouldn't such a ranking strongly depend on the lower/upper bounds for the calculation of xWEI?

Suggestion: add some discussion about the practical usefulness of ranking extremes and the scientific/practical limitations of the approach.

2) Alternative approaches: One limitation of WEI and xWEI is that they do not really tell us anything about how extreme an event was relative to others. Furthermore, the metrics involve the fitting of a GEV model, which comes with large uncertainty. Perhaps a different metric or different way of quantifying relative extremeness across scales should/could be considered?

Suggestion: add a few words about possible, alternative approaches to WEI and xWEI.

3) Temporal structure: Some information about the temporal structure of the July 2021 event would help the reader understand why this event was extreme over multiple scales, and how the water was distributed over time.

Suggestion: show a time series and/or give some information about peak rainfall rates, intermittency and standard deviation of rainfall rate over time for a fixed location. Fig1 covers the spatial aspect but there is no information about the time aspect so far.

4) Stationarity assumption: There is an implicit stationarity assumption behind the whole study that should be mentioned.

Suggestion: Clearly mention the assumptions underlying your approach and the consequences they could have on the calculation of return values and (x)WEI. To reassure readers, I suggest you check whether there a trend in the precipitation extremes data over time. You can check this by fitting alternative GEV models with time-dependent shape or scale parameters and applying model selection based on likelihood ratio tests or AIC.

5) Equation 1:

Eq.1 Please provide units for all quantities (A, T and E).

Eq.1 what does the index i represent? The text does not say. Same for the index t.

Eq.1 please use ln() instead of log() to avoid ambiguity about the base of the logarithm.

6) Table 1:

Table 1: please provide units for WEI and xWEI

Table 1: I struggle to understand what you mean by “Duration”. The caption says that the “Duration” is the timescale at which the maximum extremity was reached. But there are only two values (24h and 48h) for 5 events. I would have expected each event to have a peak at a different time scale. More generally, I think it would be useful to clarify what you consider to be an “event” and what the difference is between the “Duration” and the length of an “event”. For example, is the average precipitation depth calculated at the event scale or over the duration indicated in the table?

Table 1: it would be useful to indicate the change in WEI and xWEI for the other events as well. I understand that you are primarily interested in the changes for the July 2021 event. However, I also think that it’s important to convey a general sense of how sensitive the WEI and xWEI metrics are to the inclusion/exclusion of particular year of data.

7) Min/Max bounds for integration: Section 3: For the calculation of WEI and xWEI, please clearly state the minimum/maximum bounds you took for integrating over the duration and area.

8) Other minor things:

l.87 The term "characteristic" duration was not properly defined.

l.103: I don't understand why the July 2021 could be considered a compound event. Please justify.

According to Leonard et al. (2014), "A compound event is an extreme impact that depends on multiple statistically dependent variables or events". According to Zhang et al. (2021), compound extremes are defined as 1) two or more extreme events occurring simultaneously or successively, 2) combinations of extreme events with underlying conditions that amplify the impact and 3) a combination of events that are not extreme individually but lead to an extreme event or impact when combined.

In the case of the July 2021 event, I do not see why this event should be labeled as “compound”. It just appears to have been extreme over multiple spatial and temporal scales at the same time. Please elaborate!

References:

- Leonard, M., Westra, S., Phatak, A., Lambert, M., van den Hurk, B., McInnes, K., et al. (2014a). A Compound Event Framework for Understanding Extreme Impacts. Wires Clim. Change 5, 113–128. doi:10.1002/wcc.252

- Zhang W, Luo M, Gao S, Chen W, Hari V and Khouakhi A (2021) Compound Hydrometeorological Extremes: Drivers, Mechanisms and Methods. Front. Earth Sci. 9:673495. doi: 10.3389/feart.2021.673495

Authors present the extremeness of the precipitation event in July 2021 in Germany using a pair of indices, based on the spatial evaluation of the return periods of precipitation totals for variously long time windows. They compare this event with four other cases from the period 2001 - 2021, focusing primarily on the change in the extremity index values caused by the inclusion of the year 2021 in the evaluation of return periods.

I consider the presented communication to be a suitable addition to the paper recently published by two of the authors (Voit and Heistermann, 2022). In addition, the text opens an interesting question of changes in the rarity-based evaluation of weather events due to the extension of the time series by years, during which an extreme event occurred in a certain part of the considered territory.

Many relevant comments have already been done by both previous reviewers. Thus, I only add several minor comments:

• The two WEI values are not obvious in Fig. 2. Moreover, they are labeled as “realtime” and “climatological” which is not the main factor of the difference as authors state at l. 66-67.
• Significant decrease in both WEI and xWEI values when including the year 2021 proofs that the presented estimation of return periods is not very robust. It is natural because of the rather short length of the data series. Nevertheless, because this is the main concern of the communication, a short sensitivity analysis could be done, e.g. by the “leave-one-out” technic.
• The unique impacts of July 2021 were not only because of the precipitation event itself but partly also due to the enhanced soil moisture at its beginning. In my opinion, this fact should be more stressed in the discussion.

Technical comments:

• line 80: adding the word “even” into the sentence (“are even less pronounced”) would make it more clear in my opinion;
• line 84: I suggest to add “respectively” at the end of the sentence.