General comment:

The authors present a two-fold study, which 1) modifies an existing micro-canonical disaggregation method to include temperature classes as covariate, and 2) applies this disaggregation on climate projections for future rainfall. The study area extends over Germany, where 45 locations are presented. Overall, the manuscript is well structured and the figures are clear. The method is relevant for impact modellers. However, I have major concerns regarding the disaggregation setup (daily to 5-min) and the investigated climate model ensemble.

Major comments:

• The first part of the introduction (L29-63), which deals with climate modelling and scenarios, and section 2.2 have imprecise or uncommon vocabulary in several places (some are noted in the minor comments). This might confuse the reader and should be adapted.
• In the introduction, the availability of sub-daily precipitation data from EURO-CORDEX is not correctly described. Here (https://doi.org/10.24381/cds.bc91edc3), 3-hourly data from many simulations are available. However, also the hourly resolution is often stored at the local model institute, but might be accessed only upon request (as e.g. by Berg et al., 2019: https://doi.org/10.5194/nhess-19-957-2019 ). At the same spatial resolution, the CRCM5-LE provides 50 members of hourly precipitation data (Leduc et al., 2019: https://doi.org/10.1175/JAMC-D-18-0021.1). Hence, I’d argue that the “main task” for rainfall disaggregation features the disaggregation from hourly to e.g. 5-min resolution. The relative error of the overall disaggregation (Tables 5 & 7) and of 2-year return levels (Figs. 5 & 7) could be possibly lowered by disaggregation from hourly to 5-min resolution instead of daily to 5-min. Hence, I strongly recommend to apply the disaggregation from 3-hourly or hourly to 5-min resolution.
• The choice of the climate model ensemble (“DWD core ensemble”) at daily temporal and 0.11° spatial resolution does not represent the “state-of-science”. 0.11° simulations are available at 3-hourly and hourly resolution (see comment above). Furthermore, for the representation of convection and short-duration rainfall extremes, higher-resolution set-ups (“convection-permitting”) are found to be beneficial (Coppola et al., 2021: https://doi.org/10.1007/s00382-018-4521-8; Purr et al., 2021: https://doi.org/10.1002/joc.7012).
  
  The possible post-processing (downscaling? bias-adjustment?) of the climate model data is totally unclear. Neither the article nor the provided reference (Delalane, 2021) does provide the necessary information. Convection-permitting simulations would be available for Germany from the German Weather Service (journal article: Rybka et al., 2022: https://doi.org/10.1127/metz/2022/1147 ; data: https://dx.doi.org/10.5676/DWD/HOKLISIM_V2022.01; https://esgf.dwd.de/projects/dwd-cps/cps-hist-v2022-01; https://esgf.dwd.de/projects/dwd-cps/cps-scen-v2022-01 ).  

• The discussion section only discusses projected increases of sub-daily extreme rainfall and its temperature scaling compared to three other studies. However, the disaggregation procedure and its performance compared to other approaches is not discussed. Pui et al. (2012) follow that the method of fragments (MoF) outperforms a micro-canonical cascade model. The systematic underestimation of the wet spell duration (Table 5) is also found by Pui et al. for the cascade model, whereas MoF can reproduce this rainfall characteristic (see also Poschlod et al., 2018: https://doi.org/10.1175/JHM-D-18-0132.1 for a comparison to convection-permitting climate model performance). The authors should at least discuss these drawbacks and elaborate on the advantages of a cascade model versus the MoF or other disaggregation approaches (e.g. Zhao et al., 2021: https://doi.org/10.1016/j.jhydrol.2021.126461 ).
  
  Furthermore, general uncertainties of the whole workflow need to be discussed: 1) The applied climate models have model biases. They parameterize convective processes. 2) What happens for temperature values under e.g. RCP8.5 LTF, which are outside the range of observed reference temperatures? 3) more generally: this empirical disaggregation method is calibrated on reference climate, but applied on strongly altered climate. This should be acknowledged from my perspective.

Minor comments:

L30: "predicted" --> "projected"

L35: How does disaggregation of daily rainfall relate to question 9: 'How do flood-rich and drought-rich periods arise, are they changing, and if so why?'? Can you elaborate on that?

L39: RCP are emission scenarios not “climate scenarios”.

L40: IPCC 6^th AR and the “state-of-science” in CMIP6 applied scenarios, which combine Shared Socioeconomic Pathways (SSPs) and the RCPs (Riahi et al., 2017: https://doi.org/10.1016/j.gloenvcha.2016.05.009). EURO-CORDEX is driven by CMIP5. Please clarify in this paragraph.

L41: Please rephrase: GCMs do not model RCP scenarios, as the emissions are provided as part of the external forcing to the GCMs.

L91-104: Here, you already introduce quite specific features of the cascade model in order to discuss the parameter reduction. However, the reader does not know about the parameters beforehand. I’d recommend to shift this paragraph to Sect. 3.2.

L127: Updated reference to Köppen-Geiger climates is available from Beck et al., 2018: https://doi.org/10.1038/sdata.2018.214

L132: The sentence is not well connected; first you describe the overall climatology and then jump to availability of temperature data. I’d recommend to reorganize 2.1 into paragraphs on 1) climatology of Germany, 2) station data, 3) radar data.

L139 / Fig. 1: Please provide a readable legend for elevation.

L162: The spatial resolution is described in the abstract (5km, L17), but misses here. How is the spatial downscaling from 0.11° to 5km carried out? Are the data bias-adjusted? Is drizzle considered/removed?

L174ff.: The explanation of the cascade model should be rearranged. A general explanation of the working principle of a cascade model is missing. In L183, you mention the model parameters are scale-dependent without having introduced the model parameters (only the parameter b; parameters are fully introduced in L204 for the first time). The paragraph should be revised and understandable by a reader without pre-knowledge about the cascade model.

L209: How sensitive is the resulting disaggregation to the choice of the volume class threshold (q=0.998)? Are there any “jumps” in the resulting rainfall frequency/intensity around the q=0.998? I would like to see a figure of resulting sorted rainfall intensities of different durations above q=0.99.  

L232: Can you additionally provide a measure of the intra-event similarity for all 45 locations?

L238/Tab 3: V index seems not correct.

L252ff: As the temperature-dependent cascade model performs better only for rainfall extremes (see Tab. 7, Fig. 6 and 7), the dependence could only be introduced for the volume class V₂? In Section 3.3, the temperature dependence is estimated for temperature classes at 5°C steps, for all rainfall intensities > 0 mm / 5 min. However, the temperature dependence is expected to be different for different rainfall generating mechanisms (stratiform vs. convective), which are associated with different rainfall intensities.

L270: What are the advantages of the DWA approach over the well-established extreme value theory approaches, such as peak-over-threshold sampling and Generalized Pareto distribution fit (Davison and Smith, 1990: Davison, A. C. and Smith, R. L.: Models for exceedances over high thresholds, J. Roy. Stat. Soc., 52, 393–442, 1990)?

L279: Rainfall characteristics should be already introduced and defined in Section 3.4. How are wet spell duration, dry spell duration, and wet spell amount defined?

L359: “scatter” means variance or inter-quartile range?

L470 / L604: The article in the references (L604: https://doi.org/10.5194/essd-13-983-2021) describes the evaluation of sub-daily extreme precipitation compared to observational products, whereas the article in the text (L470: https://doi.org/10.1088/1748-9326/ac0849) investigates future projections and temperature scaling of extreme rainfall.

Review of 'Estimation of future rainfall extreme values by temperature-dependent

disaggregation of climate model data' by Ebers et al.

The study analyzes a set of 45 sub-hourly rainfall stations, uniformly distributed

over Germany, with respect to the occurrence of rainfall extremes. Future projections of

corresponding quantities are obtained from an existing micro-canonical cascade model

(Müller and Habelandt 2018) that is extended to include temperature as a covariate. The

resulting model parameters are reduced in two directions, one by assuming scaling behavior

across the relevant time scales, and one by assuming certain intra-event symmetries; this

reduces the number of parameters from 144 to 40.

The so optimized disaggregation is then applied to 6 GCM/RCM model simulations, each

driven by a modest (RCP4.5) and by a pessimistic (RCP8.5) emission scenario.

The main results are:

– disaggregation performance with respect to key quantities (e.g. intensity) is improved

by using T dependence

– in the near future, changes in the intensity of extreme (2y) events are moderate

– in the long term, expecially for RCP8.5, changes are +12% without and +21% with T

dependence.

It is also reported, but not discussed much, that core statistics such as wet spell

duration or rainfall intensity deviate considerably for the disaggregation model, with

relative errors of -22% and 23%, respectively.

Major comments:

As they are posed, the three research questions of the study

i) Is there a temperature-dependency of sub-daily rainfall extreme values?

ii) How can the temperature-dependency be integrated in the cascade model parameters for

temporal rainfall disaggregation?

iii) How will rainfall extreme values change in the future?

are not new. iii) is a core topic of IPCC since more than two decades, i) belongs to the

folklore at least since the seminal Lenderink and Meijgaard (2008) paper, and the more

specific point ii) has already been addressed e.g. by Bürger et al. (2019). To become

publishable, the study evidently needs to re-formulate its goals decisively. One options

is to dive more deeply into the strong biases (see above) and their dependence on

parameterization. It is not clear, for example, why one should have parameter reduction at

all (apart of course from the general validity of Occam's razor). Another is to emphasize

more clearly the regional structure (the 45 stations) of the main results.

Another weakness is the uncritical and un-adjusted use of climate models, whose biases

confound the disaggregation bias. What are the biases? Which models have which bias? And

where? On this background, are relative projections (e.g. +21% intensity) still

reliable and have added value?

Specific comments:

l. 40: developments --> evolutions

l. 40: but IPCC AR6 uses SSPs

l. 76-78: I don't understand this argument.

l. 82: Kelvin units are "K" not "k".

l. 94: note that already Olsson (1998) uses parameter reduction (by averaging over several

levels).

l. 108: All central questions have been addressed in previous work already:

   i) has populated the scientific debate at least since the seminal paper by Lenderink

   and Meijgaard (2008) and does not really fit as a core research question.

   ii) has been thoroughly addressed by the Bürger et al. papers.

   iii) is probably one of the most addressed questions in climate research of the past 3

   decades or so.

l. 148: It is not clear to me why you used the YW data at all, and not just stick to the

station data?

l. 159: 'climate scenario' and 'climate emission' inadequate

l. 164: there is a big resolution gap between the 50km/12.5km resolution of EURO-CORDEX

and the 5km of the DWD. Please explain!

l. 172: Since for the main part a branching number of b=2 is used, it is unclear how the

cascade model is different from the Olsson model.

l. 184: Why 'unbounded'?

l. 186: You may consider putting this at the beginning near l. 174

l. 193: The relative fraction definition does not make sense as it stands.

l. 195: Is it uniform, or U-shaped? – How does it look?

l. 211: This sentence is awkward, and seems to bring back the confusion about the target

quantity.

l. 218: How does your implementation compare to e.g. Bürger et al. (2019) and Pons et al.

(2022) who also aim at parsimonious implementation of temperature dependency? How do the

12 parameters of (an updated version of) the original cascade model of Olsson (Willems and

Olsson, 2012) compare to the 40 parameters from your S1-P1 implementation?

l. 228: event-connecting systematic is an awkward term.

l. 228-230: This should be removed. Unless being unity, the probabilities do not imply

anything about the connectedness of the disaggregated events.

Table 4: This should go to the results section (# of T classes)

Section 3.4: Consider removing this as NHESS readers are most likely familiar with the

basic statistics.

Table 5: For intensity, an 25% error in the mean and 50% error in stddev is quite

something. Are future projections reliable given such errors?

Figure 4: Are you only counting events on wet days in all cases?

l. 327: Are you describing here the exponential dependence?

l. 330: If you only analyze wet days in Fig. 4, it may well be that the total number of

high rainfall events does not occur at the highest temperatures.

Fig. 6: While the modeling error is certainly interesting, I would have found it more

illuminating to have Fig. 4 repeated with T dependence (overlayed). Could that be done?

l. 411: Is it justified to apply the daily climate models data uncorrected?

l. 487: The term 'physical extension' should be avoided and replaced with, e.g., 'physically

inspired extension' or similar.

l. 514: Fortran code can be shared like any other code. So please consider sharing the code as well.

References:

Willems, P. and Olsson, J. (Eds.): Impacts of Climate Change on Rainfall Extremes and

Urban Drainage Systems, IWA Publishing, 2012.

Bürger, G., Pfister, A., and Bronstert, A.: Temperature-driven rise in extreme sub-hourly

rainfall, Journal of Climate, 32, 7597–7609, 2019.

Pons, V., Benestad, R., Sivertsen, E., Muthanna, T. M., and Bertrand-Krajewski, J.-L.:

Forecasting green roof detention performance by temporal downscaling of precipitation

time-series projections, Hydrology and Earth System Sciences, 26, 2855–2874,

https://doi.org/10.5194/hess-26-2855-2022, 2022.

The authors use cascade modelling to disaggregate RCM rainfall at 45 locations in Germany from 1-day to 5-min resolution, in order to estimate future changes in short-duration extremes. The model is first developed and calibrated using observations. In this procedure some reduction of parameters is attained and a temperature dependency is implemented. The model is then applied to three 30-year periods of RCM ensemble output at the same 45 locations and future changes are estimated.

The challenge of estimating future changes in short-duration rainfall extremes indeed deserves to be tackled, by different complementary approaches, one of which is combining dynamical and statistical downscaling techniques as done here. The paper is quite clear, the calculations seem well performed and everything is reasonably well presented. Still there are several deficiencies that need to be resolved before publication, in my opinion.

First of all, I agree with the criticism provided by Reviewers 1 and 2. Main issues here are, in my opinion (partly copied from previous reviews):

-    daily temporal and 0.11° spatial resolution does not represent the “state-of-science”;

-    the impact of the (substantial) biases in precipitation from these RCMs is not assessed;

-    the research questions are poorly formulated.

I also share the rest of the concerns raised by Reveiwers 1 and 2 and thus I do not need to repeat them here. In addition I have the following comments.

General:

-    Some parts (mainly in the introduction and methods sections) are overly wordy, as also commented by the other reviewers, and more or less repeat what is found in other papers on this topic. I suggest to keep it more compacts (but still stand-alone, of course) and refer to other papers for more information, when need.

-    It would be interesting to see the difference between data dissagregated from the YW data and RCM data in the C20 period, respectively. Even if the periods differ they supposedly represent present climate and one wonders about the realism in the RCM-based disaggregation.

-    The Conclusions is in my opinion a Summary. Conclusions need more of…well, conclusions; what do the results mean in a broader context, how can they be used, what research remains, etc.

Specific:

-    L51: Berne et al. needs a year.

-    145: To have just one dry time step (i.e. 5 dry minutes) separating wet spells is very unusually short, which also make the wet spells very short (around 20 min) and small (around 0.5 mm). I recommend a separation of hours to really encapsulate the full events. Maybe this is one reason for the quite weak performance in terms of spell durations (Table 6).

-     L167: Here NTF is written as 2051-2070, later in the paper it is 2021-2050 (e.g Fig. 8). Which is correct?

-    L194: Which f(x) is used here?

-    L379: od -> of

-    L385: Delete the first “temperature”.