The paper introduces the "cross-scale weather extremity index" (xWEI) as an extension and complement of WEI, aiming at integrating extremeness of an event over significant spatio-temporal scales.

The authors manage to convince the reader that xWEI provides complementary information to WEI, and that it is not just a duplicate of it but rather an extension of it. The two indices are of course quite related (see Fig. 5). Nonetheless, Sec. 4.2.2 shows a good example where the two indices differ and explain the reasons (Fig. 7, which shows a pronounced peak which determines WEI but has less influence on xWEI). The database of extreme events used (over Germany) is numerous enough to support the authors conclusions. xWEI is well described and a good number of examples are presented. The choices of the authors on the configurations adopted to obtain the examples are well motivated and generally well described. The same is for the computation of GEV parameters. In Sec 4.3, the authors discuss the sensitivity of xWEI to the implementation choices and that is an important factor.

In my case, after reading the article, a general question that remains is the following. The motivation that leads to the definition of WEI is quite clear, we can say -simplifying a lot- that WEI takes the "maximum of maximums" to classify an extreme event. On the other hand, xWEI is somewhat closer to an average WEI across spatio-temporal scales. In this sense, the final xWEI ranking of events might not differ from one obtained using simpler metrics, such as the total precipitation amount integrated over the same spatial scales (e.g. upscale the amounts on coarser grids, by averaging, then integrate). 

The message I would like to convey is that it might be worth showing that the index is more informative than coarser/simpler quantifications. In fact, among important users of indices like xWEI there are the providers of climate services. For them, it is quite important that the information delivered conveys an immediate message to the final user. In this sense, a ranking of the events based on e.g. rainfall intensity, rainfall duration, or return period/probability of exceedance may be more appealing. For future research, I suggest you focus also on the comparison against ranking of extreme events based on simpler indicators. It would be interesting to understand the additional information content of xWEI in terms of correlation with registered damages after a catastrophic event, for instance.

My advice to the Editor is to publish the paper after the authors have addressed the comments that follow. The comments mostly deal with the presentation of the work.

Major comments:

• Title. You may consider to add “quantifying extremeness of precipitation across scales using the cross-scale weather extremity index xWEI”
• Abstract. The abstract can be shortened significantly. Try to be short and snappy. For instance, your first 12 lines could be rephrased as (what follows is just an example) “Quantifying the extremeness of a heavy precipitation event is important to classify it. The impact of an event depends on its spatial extent and duration, many indices neglect at least one of these aspects. The weather extremity index (WEI) quantifies the extremeness of an event and identifies the spatial and temporal scale at which the event was most extreme. However, the WEI does not account for the fact that an event can be extreme simultaneously at various spatial and temporal scales. To better understand and detect the compound nature of precipitation events, we suggest to complement the original WEI, and refer to this complement as the "cross-scale weather extremity index" (xWEI). xWEI does not aim to detect the spatio-temporal scale of maximum extremeness, instead it integrates extremeness over relevant scales.”
• Sec. 2.1. Line 118. When you write that “RADKLIM provides a promising dataset for climatological application”, do you mean that it is consistent in time? Can you be a bit more specific?
• Sec. 3.2. I like your idea of using an example to introduce the WEI. However, I think that: i) you should better describe the initial configuration of your example. At line 174, before “Starting with the pixel…” you may consider adding something like ”we will refer to the following example, shown in figure 1, let's consider an event as follows …”; ii) the definition of the area A is a critical point of the procedure that you discuss again in Sec. 4.3.1, I think that you should let the reader know that you are going to discuss further this point and introduce a reference to Sec 4.3.1 within Sec 3.2. In general, try to create better links between related sections.
• Sec 3.3. The ratio behind the definition of xWEI is explained in a clear way. I do not completely understand why you need to interpolate the WEI value onto a regular grid (Fig. 2c). It looks to me that one may sum all the areas of the colored curves in Fig 2b and that’s it. Since Fig 2b should include all the durations that a user may be interested in, I do not see the risk of overemphasising long durations. Could you add something more on this point?
• Fig 2a. If this is the same as Fig. 1d, then I think you should write it explicitly somewhere in the caption.

Minor comments/typos (search for the text in the document):

• “xWEI in top of WEI” -> “xWEI on top of WEI”
• “Complimentary” -> “complementary”

The authors present a cross-scale weather extremity index (xWEI) which is an extension of the original weather extremity index (WEI). They compare the values of both indices for 100+1 events in Germany over a period of 20 years.

I consider the introduction of xWEI as a complement to WEI to be useful, as it adds another dimension to the methodology for assessing the extremity of precipitation events. While the authors point out the different settings for calculating the two indices, I consider the settings they use to be appropriate, especially the use of ln(t) instead of t when integrating E_tA values. I also appreciate the study of the sensitivity of the WEI to the method of determining GEV parameters and especially the discussion of the settings of both indices that may affect the values.

The paper brings new insights, it is well structured, of reasonable length, the authors argue logically and discuss the results. I recommend its publication in NHESS after addressing the following comments.

Comments on the content:

The authors analyzed 100+1 events with extra high WEI values and determined the xWEI for these events. While I do not suppose that there could be an event with a very high xWEI and yet a WEI so low that it would not belong to the 101 events analyzed, the authors should check this possibility.

An important parameter is not only the size of the considered area, but also its shape. The authors should mention this aspect in the article, because the affected area is often elongated in one direction compared to a square. It is also not clear from the paper how the authors dealt with the situation where the core of the event was located at the German border and the 200x200 km square extended beyond the area covered by the data.

The authors note that the NI/Jul2017 event ranked higher than SN/Aug2002 in the WEI, but offer no explanation (Figure 4 does not include NI/Jul2017). Could the reason be the state-border effect, where SN/Aug2002 significantly affected also the neighboring Czech Republic (Müller et al., 2015)?

Formal comments:

In my opinion, flash- or pluvial floods are mainly related to infiltration excess (line 40) while saturation excess is more typical in case of large-scale fluvial floods (e.g., Rogger et al., 2013).

If the form of the short names of HPEs is your choice, I suggest to replace “NI” by “LS” which seems to be more intuitive in English.

Date formats should be unified, compare e.g. beginnings of both case studies.

I recommend expanding the beginning of Figure 6 and Figure 7 captions so that they are not just short names of the events. On the other hand, in my opinion, the interpretation of the two pictures does not belong in the captions, its place is in the text.

Typos:

line 35: In “…Prein et al. (2017), state…”, the comma is redundant.

line 310: The second acronym “WEI” should probably by replaced by “xWEI”.

line 257: As in the previous line, it would be good to mention also the short name of the event in the brackets.

References:

Rogger, M., Viglione, A., Derx, J., Blöschl, G., 2013. Quantifying effects of catchments storage thresholds on step changes in the flood frequency curve.

Müller, M., Kašpar, M., Valeriánová, A., Crhová, L., Holtanová, E., Gvoždíková, B., 2015. Novel indices for the comparison of precipitation extremes and floods: an example from the Czech territory. Hydrol. Earth Syst. Sci., 19, 4641–4652.