Regional analysis of convective heavy rain events in the German State of Hesse

Perschke, Manuel; Schmalz, Britta; Ruiz Rodriguez, Ernesto

doi:https://doi.org/10.5194/egusphere-2023-1907

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https://doi.org/10.5194/egusphere-2023-1907

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30 Aug 2023

| 30 Aug 2023

Regional analysis of convective heavy rain events in the German State of Hesse

Manuel Perschke, Britta Schmalz, and Ernesto Ruiz Rodriguez

Abstract. The convective heavy precipitation events, which occur primarily in the summer months, cannot be recorded representatively by ground-based precipitation stations due to their frequently small spatial extent, short life span and high rapidly changing intensity. The radar network of the German Weather Service, on the other hand, records area-wide, spatiotemporally highly resolved precipitation information that enables comprehensive identification of precipitation objects. In this study, a method for the identification, description and classification of convective precipitation objects considering a flood-relevant event extent is presented. Assuming an orographic independence of the events in the Central European low mountain range, the German State of Hesse is chosen as representative study area. Considering the spatial and temporal extent of the identified events, the most extreme expression is selected and independence is ensured. With the assignment of an authoritative duration for the intensive main rainfall phase, an extensive collection of heavy precipitation objects results. The results show a characteristic event length of 15 to 60 minutes; longer durations are underrepresented and exhibit inhomogeneous extreme value behavior. Statistically, the generated samples can be well represented and classified by the generalized extreme value distribution. The evaluation allows us to make a regional characterization of convective heavy precipitation.

Received: 21 Aug 2023 – Discussion started: 30 Aug 2023

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Manuel Perschke, Britta Schmalz, and Ernesto Ruiz Rodriguez

Status: closed

CC1: 'Comment on egusphere-2023-1907', Mathias Raschke, 01 Sep 2023

The explanations of the statistics are not convincing.
The generalized extreme value distribution should be applied for block maxima or block minima according to extreme value statistics (Coles 2001). One of the Burr distributions (Berilant et al. 2004) is probably a suitable distribution model that is flexible enough.
The presented KS test and the corresponding critical value apply to the fully specified distribution. This is not a simply "defined" distribution, but a fully known distribution. The critical value mentioned applies (alpha 5%) to large sample sizes. When the author applies this test to a distribution model with estimated parameters (using the same sample), the critical values are smaller for the same level of significance. This must be taken into account. Otherwise the application makes no sense. For example, distributions with more parameters would be preferred by the test. The error of erroneously rejected models would also be smaller than defined by the significance level.
The same applies to the AD test. Is the same critical value considered for the Gumbel distribution and the generalized extreme value distribution? I doubt that the same critical value applies to every extreme value index of the generalized extreme value distribution. The reference Ahmad et al. (1988) may contain incorrect results. It is not accepted by extreme value statistics and theory (e.g. not mentioned by Beirlant et al. 2004).
Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. Springer.
Beirlant, J., Goegebeur, Y. et al. (2004) Statistics of Extremes: Theory and Applications. Wiley.

Citation: https://doi.org/10.5194/egusphere-2023-1907-CC1
RC1:
'Comment on egusphere-2023-1907', Benjamin Poschlod, 01 Sep 2023
General comment
The authors present a methodology to identify and categorize spatio-temporal independent short-duration rainfall events from radar data over the state of Hesse (Germany). Based on the categorization into different event durations, they apply extreme value theory to derive return levels between 15 min and 45 min. The structure of the manuscript does not follow the common scientific order (see major comments) and the description is unclear at many parts (see minor comments). Hence, it is very difficult to follow. The methodology is statistically not convincing to me (see major and minor comments). Furthermore, the authors fail to show the added value of their method. The research question(s) of this study remains unclear to me. Even though I acknowledge the effort, which has been taken, I cannot support the publication and would recommend a rejection in the current version of the manuscript. In case that the editor decides for a revision, I hope that my following comments can be addressed.
Major comments:
The introduction section lacks references/justification for some statements (L22-28; L42-54).

Why is this study only focussing on the state Hesse? Is there any physical explanation or data restriction?

The structure of the article does not follow the common scientific structure (Introduction -> Data -> Methods -> Results -> Discussion -> Conclusion). I would not insist to always strictly follow this structure. However, here a closer orientation towards this guideline is needed to enhance the readability.

Section 2.2 should be revised accordingly; it is not clear how Fig. 2 is generated (what are “independent convective events”?).

Section 2.3.1 is really hard to follow. I know that the description of such multidimensional algorithm is generally not easy – however in the current state, I could not follow a lot of parts.

The combination of thresholds and monthly Block Maxima, which are then again pooled for whole Hesse and the hydrological summer is not appropriate for the application of the GEV.

The “discussion” section 3.3 is totally insufficient. There is no interpretation of the results, no comparison to existing data sets (e.g. KOSTRA 2020) or methods: what would be different, if a GEV, Gumbel, or the SMEV (Marra et al., 2019: https://doi.org/10.1016/j.advwatres.2019.04.002) is fitted to each grid cell of RADKLIM separately? The SMEV framework is found to work also with low sample sizes. Hence, it is not clear, what added value this methodology provides.

Further, the discussion of uncertainty lacks major sources of uncertainty (internal climate variability, dependence on the areal extent of the study area, unproven assumption of orographic independence, arbitrary choice of the duration characteristics).

Minor comments:
L24/25: Sentence unclear; „change behaviour” – behaviour under climate change? Or which change?
L50 I’d avoid the term “stationary” in this context as it is more often used in a statistical sense
L68-75: Could be shortened
L81/82: Please specify the duration and area size of the data gap
L83: Why is this called “Previous studies”?
L87: Why is the natural area Central European low mountain sill introduced? Is there any later reference to this natural area? The central part of this area is covered with RADKLIM data; so why do you constrain your study to administrative boundaries of Hesse?
L89: Are the alpine foothills extending that far north? I would not say so.
L91/Fig1: The elevation legend is very hard to read. Is “-217” correct? Please revise the legend. Please remove the scale (not necessary, and depending on screen size).
L98: grid cells could be replaced by km²? 95% percentile: do 9 to 100 grid cells refer to the inner 95% (2.5% to 97.5%)?
L106: Naming the subsection “Orographic independence” is very misleading, as we see strong orographic dependence for the frequency of events.
L110/Fig. 2: Fig. 2a: You refer to “Flechtdorf” in the text; please add that as label to the map. Fig. 2b: Same as for Fig. 1: Please provide a more readable legend of elevation.
L114: “that potentially convection occurs more frequently at higher altitude”; I cannot read that from Kirshbaum et al. (2018). It is rather the slope than absolute altitude.
L117-119: How do you decide that 60 min events are less dependent on orography than 15 min and 30 min? Can you quantify that by e.g. correlation measures of elevation/slope and event count?
L121-124: Then you can also use a measure (see comment above) to quantify the lower dependence of event count on orography for the higher threshold of 15 mm/h. However, I still see a strong pattern of the event count above 15 mm/h for Großer Feldberg, Wasserkuppe, and Vogelsberg.
L133-135: “the disturbing influence of inhomogeneities – as described in the introduction – on the statistical analysis can be reduced”; I guess you refer to L60/61: “the strong inhomogeneity could be attributed to the short observation period and the single occurrence of local extreme events”. How exactly can spatial aggregation of radar data reduce this? Can you prove this?
L153ff: “the partial series of the target cell and its neighboring cells” – from Table 1, I understand that the partial series of the target cell is used, and the same timestamps of the neighboring cells are then investigated. In the current state of the text, it sounds as the partial series (max. 1000 events) of the target cell and the partial series (max. 1000 events) of the neighboring cells are merged. Please revise this paragraph to be more precise.
L154/155: You refer the sizes (3x3 and 5x5) to the one-hour sizes by Lengfeld et al. (2022). Why are your events forced to be rectangular? Lengfeld et al. (2022) allow for any connected shape.
L174-176: I cannot follow, please revise. (with the Table 2 as example I get, how it works, but the sentence is not understandable for me). Further, can you justify the values of > 10 % or 5 mm intensity change per additional 15 min? Have you checked the sensitivity of the later results to this arbitrary threshold?
L185-189: I cannot follow at all. Please revise. Check the suitability of the term “clustering” for your methodology.
L190-197: Due to the previous lack of understanding, I cannot follow.
L199-213: As far as I can follow, you first apply a threshold, which all events under consideration need to exceed. In a second step, you apply a block maxima sampling for each month separately, to “avoid that the influence of extreme years or months takes an over-representative part of the data collective”. However, at the end you pool all sampled events again in one pot (one for each duration). From my understanding, you would have to generate different GEV/Gumbel models for each month, if you use monthly block maxima as sampling strategy (see e.g. Coles, 2001: https://doi.org/10.1007/978-1-4471-3675-0).
L208: What is “a non-overlapping monthly interval in the hydrological summer season – May till October”?
L289: “The results of the previous studies (Sect. 2.2) have shown that no sufficient number of extreme events can be identified for a duration greater than 90 minutes.” Where in Sect. 2.2 or which previous studies have shown that?
L291/Fig 4: Please increase label font, add grid lines, write proper legend labels.
L298: Are these statistical outliers or physically plausible measurements?
L300ff: To what degree is the behaviour of the different durations (15 min to 90 min in Fig. 4) sensitive to your selection of characteristic duration in L175?
L328: Why do you want to “achieve” temporal coverage? If the climate in Hesse does not favour 60-min extreme rainfall in October, there is no need to force your sampling strategy to include such events.
Isn’t this coverage also dependent on the size of your study area? And should that be the case?
L335/Fig 7: The dot sizes of the markers should be comparable between a) and b). I would recommend to form more senseful classes (e.g. according to the occurrence probability of an event) instead of quintiles.
L342-344: Can you provide any quantitative proof for this assumption?
L360: Fig. 8: I recommend the same y-axis scaling for a) and b) for better comparability. Bigger labels increase readability.

The highest empirical value for a) is plotted at ~110 years. Sample size should be roughly 70 according to Fig. 5. The highest empirical value for b) is plotted at ~42 years. Sample size should be roughly 65 according to Fig. 5. Seems not correct.
Furthermore, I’d expect confidence intervals for the GEV and Gumbel fits.
L392-420: The Conclusion is mainly a summary.
Citation: https://doi.org/10.5194/egusphere-2023-1907-RC1
- AC1:
  'Reply on RC1', Manuel Perschke, 17 Nov 2023
  To the reviewer, I would like to thank you on behalf of all the authors for the detailed and very helpful assessment of this work. To begin with, I would like to briefly explain the research objectives of this thesis, as these were obviously not formulated concisely enough.
  Due to the statistically short recording period of the radar network and the rarity and small-scale nature of convective heavy precipitation events, a regional sampling approach is chosen here. This means that the events are identified over the entire observation area and the most extreme manifestation over the path of the convective rain cell. The characteristic duration is defined for the intensive main rainfall phase with a constant precipitation rate of at least 20 mm/h.
  A more in-depth comparison with existing extreme value statistics (KOSTRA, RADKLIM) is refrained from in this paper, as the type of analysis is conceptually very different. In particular, the scope of the sample should be mentioned here, as the event identification in this study does not refer to precipitation stations or individual cells with a limited area of validity.
  Individual aspects of the report that require additional explanation are discussed below:
  The spatial restriction to the area of Hesse can be justified by the processing effort of the input data: From a meteorological point of view, there is no reason to define fixed boundaries in the natural area under consideration. From the point of view of engineering hydrology, the consideration of specific catchment areas based on regionally representative samples is desirable in the context of precipitation-runoff models.
  
  The application of the GEV was chosen on the basis of existing studies on extreme value analysis (Fischer & Schumann 2018). The applicability of the GEV model under the existing sample creation is checked for your reference and alternative distribution models (GPD, SMEV) are tested.
  
  To describe the orographic dependence of the identified events, the Pearson correlation of the number of events (threshold value 15 mm/h) was determined via the mean altitude of the place of occurrence. In addition, the correlation for precipitation rate and altitude was carried out. In both cases, there is no correlation between the variables with r < ±0.1.
  
  Figure 1 shows that, despite the not insignificant correlation, clustering occurs in certain regions (at all altitudes), which can be attributed to the climatologically short period of observations. Nevertheless, hotspots can be seen on the Großer Feldberg (Taunus), Vogelsberg and Neunkircher Höhe (Odenwald). This could be an indication that convective and orographic precipitation cannot simply be separated by a threshold value.
  
  The purpose of aggregating neighboring cells (9 or 25) is to represent event quantities for a specific catchment area size. For hydrological engineering questions, the reference to a specific area is often important. The recording of the "real" form of the events is not provided for in this evaluation due to its complexity. For this purpose, a detailed evaluation of the life cycle and movement patterns of convective precipitation cells is planned in a follow-up study based on the identified event focal points.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1907-AC1
CC2: 'Comment on egusphere-2023-1907', Mathias Raschke, 03 Sep 2023

Expanding my criticism: goodness-of-fit tests are not designed to compare the performance of statistical models. There are (for example) information criteria for this purpose (Akaike 1974, Schwarz 1978).
Akaike, H. (1974), "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Schwarz, Gideon E. (1978), "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.

Citation: https://doi.org/10.5194/egusphere-2023-1907-CC2
RC2:
'Comment on egusphere-2023-1907', Anonymous Referee #2, 12 Sep 2023
The manuscript deals with the identification of short-term heavy rainfall events from radar precipitation data. The authors present a method to determine precipitation events with durations between 15 and 90 minutes and test different extreme value probability distribution to describe the collection of events.
The study fits in the scope of NHESS, however, in the current state the manuscript is hard to follow and lacks a clear structure, a clear formulation of the research goals and a profound discussion of the results also in relation to other studies. Therefore, I would not recommend publishing the manuscript in the current from. Substantial changes should be made to the structure and content of the manuscript before it could be published in NHESS. I’d be happy to discuss my suggestions with the authors in the open discussion and clear up possible misunderstandings.

Major comments:

A major concern is the structure of the manuscript. In the introduction information on previous work on the topic and other approaches to identify extreme precipitation is missing. The second section (Methodology) is a mixture of a description of the dataset, previous work and a description of the method. For better readability I recommend to split this section into a data and a method section. The part about previous studies (2.2) is not clear to me. As far as I understand, this is work that has been done by the authors but not been published. Therefore, I would recommend moving this part to the results section, going into more detail here and support some of the statement with additional figures to make it easier for the reader to understand the results presented here. Section 3 presents the results, but a discussion and interpretation of the results is missing. For more detail see the Minor Comments below.

The description of the method is unclear and a bit hard to follow. I recommend to add more detail to the description.

A comparison to other existing methods and datasets is completely missing. E.g. how do the calculated precipitation amounts in Figure 8 fit the values from KOSTRA DWD2020? The authors mention CatRaRE, that also includes precipitation events with 1 hour duration. A comparison with in this study identified hourly precipitation events would be interesting (total number, time and location of occurrence, spatial distribution over Hesse, etc.).

A mayor assumption in this study is the orographic independence of the convective events in Hesse (section 2.2.2). From figure 2, however, this independence is not obvious to me and should be proven with a statistical analysis.

The figures in section 3 should be revised. The legends, axis labels and ticks are hard to read and should be larger and lines could also be a bit thicker.

Minor comments:
p.1, l.16: The authors state that that they get an extensive collection of heavy precipitation objects. However, in the analyses carried out in the manuscript durations of 75 and 90 minutes and later also 60 minutes were excluded because of the insufficient number of events. How does that correspond?
p.2, first paragraph: References are missing that support the statements here.
p.2, l.40: Here the reference is Knist et al, 2018. In the reference list at the end of the manuscript, the year of publishing is 2020. Please revise.
p.2, l.45-47: Please add a reference here.
p.2.l.50: The authors highlight that radar data is necessary to represent the track of convective cells, but in this study this is not taken into account either.
p.3, l.55: A reference to the RADKLIM RW dataset is missing. It is listed in the reference list, but not referred to here (or anywhere else in the manuscript).
p.3, l.62ff.: A paragraph about previous work in the field is missing (other approaches to determine heavy precipitation events and statistics, e.g. KOSTRA, SMEV, CatRaRE, etc.).
p.3, l.65: A reference to the RADKLIM YW dataset is missing.
p.3, l.81: Figure 2 is referenced before Figure 1 in the text. The figures should appear in the manuscript in the order they are mentioned in the text.
p.4, section 2.2: the name “previous studies” is misleading
p.4, l.97-105: Are those studies done by the authors? If so, more detail would be desirable. Otherwise a reference is missing.
p.5, l.108-110: The authors should describe subfigures a) and b) before they describe subfigures c) and d).
p.6, l. 115: It is not clear to me at this point of the manuscript how independency of the events is defined. Please, add some more details here.
p.6, l. 119: It is not obvious to me from Figure 2c that the occurrence of maxima becomes detached from the orography with increasing duration.
p.7, l.157: Why do the local maxima have to occur in all the 8, respectively 24 cells? Doesn’t that filter out the very local convective maxima that the authors want to study? Especially 25 km² is quite a large area for a convective cell.
p.8, Table 1: It would be easier to name the cell either 580828 or 645/327 throughout the whole table and manuscript.
p.9, l. 175: In Table 2 the relative change to the next lower duration is given, not to the initial value per 15 minutes. Is there a reason for the threshold of 10% and 5 mm? Why not taking the duration with the largest change compared the next lower/higher duration?
p.9, l.183-189: It is not clear to me how the clustering works if the neighbouring cells have extreme events with different durations.
p.10, l.203: How are the values computed. The general warning criteria for heavy precipitation of the DWD are given for 1 and 6 hours only. And why do the authors use the same value for 60, 75 and 90 minutes, but different ones for 15, 30 and 45 minutes? Shouldn’t there be different values for each duration?
p.10, l.211: The use of block maxima is not clear to me. If the authors want to investigate the most extreme events and have already ensured for independency of the events, I don’t see the necessity to use block maxima and exclude heavier rainfall events that occurred in an extreme year.
p.10, l.216: KOSTRA-DWD-2020 uses a different method that will be described in an updated version of the DWA-Worksheet 531. The older version of KOSTRA (e.g. KOSTRA-DWD-2010R) are based on the DWA-Worksheet-531, 2017
p.13, l.287-288: Add a reference here, please.
p.13, l.289-290: It is not clear to me which previous studies have shown that no sufficient numbers of extreme events can be identified for duration greater than 90 minutes. How many events were identified and what is considered a sufficient number?
p.13, Figure 4 and l.294-306: Due to the chosen method, the precipitation amount for events with 60 minutes duration is larger than for 75 minutes duration. For 90 minutes it is even lower. From a scientific point of view it doesn’t really make sense that the precipitation amount in 60 minutes should be larger than in 90 minutes, as the 60 minutes should be included in the 90 minutes. How would the results change if the authors investigate each duration independently? Please, clarify and discuss this issue in more detail.
p.15, l.332: I don’t understand, where the associated precipitation totals are shown.
p.16, l.345: What does “some events” mean? How many of the events are identified in both aggregated levels? By visually comparing the maps in Figure 7, I guess it is quite a large fraction.
p.17, Table 4: Please use AD and MAD as it is done throughout the manuscript in this table instead of A² and AU².
p.18,.l. 375: Please, clarify what is meant by “assumed”. How is the plausibility of the criteria tested?
p.18, l.382-390: This should be shifted to the data section.
Citation: https://doi.org/10.5194/egusphere-2023-1907-RC2
- AC2:
  'Reply on RC2', Manuel Perschke, 17 Nov 2023
  To the reviewer, I would like to thank you on behalf of all the authors for the detailed and very helpful assessment of this work. To begin with, I would like to briefly explain the research objectives of this thesis, as these were obviously not formulated concisely enough.
  Due to the statistically short recording period of the radar network and the rarity and small-scale nature of convective heavy precipitation events, a regional sampling approach is chosen here. This means that the events are identified over the entire observation area and the most extreme manifestation over the path of the convective rain cell. The characteristic duration is defined for the intensive main rainfall phase with a constant precipitation rate of at least 20 mm/h.
  A more in-depth comparison with existing extreme value statistics (KOSTRA, RADKLIM) is refrained from in this paper, as the type of analysis is conceptually very different. In particular, the scope of the sample should be mentioned here, as the event identification in this study does not refer to precipitation stations or individual cells with a limited area of validity.
  Individual aspects of the report that require additional explanation are discussed below:
  The comparison with the CatRaRE dataset was carried out independently of this work. However, the data set only has a minimum temporal resolution of one hour, which is why a detailed description of the results was omitted. The characteristics of the events were not directly comparable due to the different temporal resolution and identification methods. The timestamp and localization of the 1-hour events from CatRaRE largely coincide with the events identified in this study.
  
  To describe the orographic dependence of the identified events, the Pearson correlation of the number of events (threshold value 15 mm/h) was determined via the mean altitude of the place of occurrence. In addition, the correlation for precipitation rate and altitude was carried out. In both cases, there is no correlation between the variables with r < ±0.1.
  
  Figure 1 shows that, despite the not insignificant correlation, clustering occurs in certain regions (at all altitudes), which can be attributed to the climatologically short period of observations. Nevertheless, hotspots can be seen on the Feldberg, Vogelsberg and Neunkircher Höhe. This could be an indication that convective and orographic precipitation cannot simply be separated by a threshold value.
  
  For the definition of the characteristic duration, a rate of change of 10 % to the previous value with a precipitation rate of at least 20 mm/h was selected. The value of 10 % proved to be stable in order to ensure sufficient intensity of the core event. A strict choice of the largest change between the individual duration levels would have the disadvantage that (runoff)-relevant partial quantities would not be taken into account.
  
  The purpose of clustering over the entire study area is to establish the connection between the duration-classified cell-related events. This allows the movement patterns of the precipitation cells to be recorded. Over the life cycle of a precipitation cell, different characteristics of the duration and intensity of an event can arise locally. The most extreme manifestation of an event is included in the sample.
  
  The purpose of aggregating neighboring cells (9 or 25) is to represent event quantities for a specific catchment area size. The reference to a specific area is often important for hydrological engineering issues. The information on the very local maxima of the individual cells is also documented in the results data set from 2.3.1 (see Table 1).
  
  Citation: https://doi.org/10.5194/egusphere-2023-1907-AC2

Status: closed

CC1: 'Comment on egusphere-2023-1907', Mathias Raschke, 01 Sep 2023

The explanations of the statistics are not convincing.
The generalized extreme value distribution should be applied for block maxima or block minima according to extreme value statistics (Coles 2001). One of the Burr distributions (Berilant et al. 2004) is probably a suitable distribution model that is flexible enough.
The presented KS test and the corresponding critical value apply to the fully specified distribution. This is not a simply "defined" distribution, but a fully known distribution. The critical value mentioned applies (alpha 5%) to large sample sizes. When the author applies this test to a distribution model with estimated parameters (using the same sample), the critical values are smaller for the same level of significance. This must be taken into account. Otherwise the application makes no sense. For example, distributions with more parameters would be preferred by the test. The error of erroneously rejected models would also be smaller than defined by the significance level.
The same applies to the AD test. Is the same critical value considered for the Gumbel distribution and the generalized extreme value distribution? I doubt that the same critical value applies to every extreme value index of the generalized extreme value distribution. The reference Ahmad et al. (1988) may contain incorrect results. It is not accepted by extreme value statistics and theory (e.g. not mentioned by Beirlant et al. 2004).
Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. Springer.
Beirlant, J., Goegebeur, Y. et al. (2004) Statistics of Extremes: Theory and Applications. Wiley.

Citation: https://doi.org/10.5194/egusphere-2023-1907-CC1
RC1:
'Comment on egusphere-2023-1907', Benjamin Poschlod, 01 Sep 2023
General comment
The authors present a methodology to identify and categorize spatio-temporal independent short-duration rainfall events from radar data over the state of Hesse (Germany). Based on the categorization into different event durations, they apply extreme value theory to derive return levels between 15 min and 45 min. The structure of the manuscript does not follow the common scientific order (see major comments) and the description is unclear at many parts (see minor comments). Hence, it is very difficult to follow. The methodology is statistically not convincing to me (see major and minor comments). Furthermore, the authors fail to show the added value of their method. The research question(s) of this study remains unclear to me. Even though I acknowledge the effort, which has been taken, I cannot support the publication and would recommend a rejection in the current version of the manuscript. In case that the editor decides for a revision, I hope that my following comments can be addressed.
Major comments:
The introduction section lacks references/justification for some statements (L22-28; L42-54).

Why is this study only focussing on the state Hesse? Is there any physical explanation or data restriction?

The structure of the article does not follow the common scientific structure (Introduction -> Data -> Methods -> Results -> Discussion -> Conclusion). I would not insist to always strictly follow this structure. However, here a closer orientation towards this guideline is needed to enhance the readability.

Section 2.2 should be revised accordingly; it is not clear how Fig. 2 is generated (what are “independent convective events”?).

Section 2.3.1 is really hard to follow. I know that the description of such multidimensional algorithm is generally not easy – however in the current state, I could not follow a lot of parts.

The combination of thresholds and monthly Block Maxima, which are then again pooled for whole Hesse and the hydrological summer is not appropriate for the application of the GEV.

The “discussion” section 3.3 is totally insufficient. There is no interpretation of the results, no comparison to existing data sets (e.g. KOSTRA 2020) or methods: what would be different, if a GEV, Gumbel, or the SMEV (Marra et al., 2019: https://doi.org/10.1016/j.advwatres.2019.04.002) is fitted to each grid cell of RADKLIM separately? The SMEV framework is found to work also with low sample sizes. Hence, it is not clear, what added value this methodology provides.

Further, the discussion of uncertainty lacks major sources of uncertainty (internal climate variability, dependence on the areal extent of the study area, unproven assumption of orographic independence, arbitrary choice of the duration characteristics).

Minor comments:
L24/25: Sentence unclear; „change behaviour” – behaviour under climate change? Or which change?
L50 I’d avoid the term “stationary” in this context as it is more often used in a statistical sense
L68-75: Could be shortened
L81/82: Please specify the duration and area size of the data gap
L83: Why is this called “Previous studies”?
L87: Why is the natural area Central European low mountain sill introduced? Is there any later reference to this natural area? The central part of this area is covered with RADKLIM data; so why do you constrain your study to administrative boundaries of Hesse?
L89: Are the alpine foothills extending that far north? I would not say so.
L91/Fig1: The elevation legend is very hard to read. Is “-217” correct? Please revise the legend. Please remove the scale (not necessary, and depending on screen size).
L98: grid cells could be replaced by km²? 95% percentile: do 9 to 100 grid cells refer to the inner 95% (2.5% to 97.5%)?
L106: Naming the subsection “Orographic independence” is very misleading, as we see strong orographic dependence for the frequency of events.
L110/Fig. 2: Fig. 2a: You refer to “Flechtdorf” in the text; please add that as label to the map. Fig. 2b: Same as for Fig. 1: Please provide a more readable legend of elevation.
L114: “that potentially convection occurs more frequently at higher altitude”; I cannot read that from Kirshbaum et al. (2018). It is rather the slope than absolute altitude.
L117-119: How do you decide that 60 min events are less dependent on orography than 15 min and 30 min? Can you quantify that by e.g. correlation measures of elevation/slope and event count?
L121-124: Then you can also use a measure (see comment above) to quantify the lower dependence of event count on orography for the higher threshold of 15 mm/h. However, I still see a strong pattern of the event count above 15 mm/h for Großer Feldberg, Wasserkuppe, and Vogelsberg.
L133-135: “the disturbing influence of inhomogeneities – as described in the introduction – on the statistical analysis can be reduced”; I guess you refer to L60/61: “the strong inhomogeneity could be attributed to the short observation period and the single occurrence of local extreme events”. How exactly can spatial aggregation of radar data reduce this? Can you prove this?
L153ff: “the partial series of the target cell and its neighboring cells” – from Table 1, I understand that the partial series of the target cell is used, and the same timestamps of the neighboring cells are then investigated. In the current state of the text, it sounds as the partial series (max. 1000 events) of the target cell and the partial series (max. 1000 events) of the neighboring cells are merged. Please revise this paragraph to be more precise.
L154/155: You refer the sizes (3x3 and 5x5) to the one-hour sizes by Lengfeld et al. (2022). Why are your events forced to be rectangular? Lengfeld et al. (2022) allow for any connected shape.
L174-176: I cannot follow, please revise. (with the Table 2 as example I get, how it works, but the sentence is not understandable for me). Further, can you justify the values of > 10 % or 5 mm intensity change per additional 15 min? Have you checked the sensitivity of the later results to this arbitrary threshold?
L185-189: I cannot follow at all. Please revise. Check the suitability of the term “clustering” for your methodology.
L190-197: Due to the previous lack of understanding, I cannot follow.
L199-213: As far as I can follow, you first apply a threshold, which all events under consideration need to exceed. In a second step, you apply a block maxima sampling for each month separately, to “avoid that the influence of extreme years or months takes an over-representative part of the data collective”. However, at the end you pool all sampled events again in one pot (one for each duration). From my understanding, you would have to generate different GEV/Gumbel models for each month, if you use monthly block maxima as sampling strategy (see e.g. Coles, 2001: https://doi.org/10.1007/978-1-4471-3675-0).
L208: What is “a non-overlapping monthly interval in the hydrological summer season – May till October”?
L289: “The results of the previous studies (Sect. 2.2) have shown that no sufficient number of extreme events can be identified for a duration greater than 90 minutes.” Where in Sect. 2.2 or which previous studies have shown that?
L291/Fig 4: Please increase label font, add grid lines, write proper legend labels.
L298: Are these statistical outliers or physically plausible measurements?
L300ff: To what degree is the behaviour of the different durations (15 min to 90 min in Fig. 4) sensitive to your selection of characteristic duration in L175?
L328: Why do you want to “achieve” temporal coverage? If the climate in Hesse does not favour 60-min extreme rainfall in October, there is no need to force your sampling strategy to include such events.
Isn’t this coverage also dependent on the size of your study area? And should that be the case?
L335/Fig 7: The dot sizes of the markers should be comparable between a) and b). I would recommend to form more senseful classes (e.g. according to the occurrence probability of an event) instead of quintiles.
L342-344: Can you provide any quantitative proof for this assumption?
L360: Fig. 8: I recommend the same y-axis scaling for a) and b) for better comparability. Bigger labels increase readability.

The highest empirical value for a) is plotted at ~110 years. Sample size should be roughly 70 according to Fig. 5. The highest empirical value for b) is plotted at ~42 years. Sample size should be roughly 65 according to Fig. 5. Seems not correct.
Furthermore, I’d expect confidence intervals for the GEV and Gumbel fits.
L392-420: The Conclusion is mainly a summary.
Citation: https://doi.org/10.5194/egusphere-2023-1907-RC1
- AC1:
  'Reply on RC1', Manuel Perschke, 17 Nov 2023
  To the reviewer, I would like to thank you on behalf of all the authors for the detailed and very helpful assessment of this work. To begin with, I would like to briefly explain the research objectives of this thesis, as these were obviously not formulated concisely enough.
  Due to the statistically short recording period of the radar network and the rarity and small-scale nature of convective heavy precipitation events, a regional sampling approach is chosen here. This means that the events are identified over the entire observation area and the most extreme manifestation over the path of the convective rain cell. The characteristic duration is defined for the intensive main rainfall phase with a constant precipitation rate of at least 20 mm/h.
  A more in-depth comparison with existing extreme value statistics (KOSTRA, RADKLIM) is refrained from in this paper, as the type of analysis is conceptually very different. In particular, the scope of the sample should be mentioned here, as the event identification in this study does not refer to precipitation stations or individual cells with a limited area of validity.
  Individual aspects of the report that require additional explanation are discussed below:
  The spatial restriction to the area of Hesse can be justified by the processing effort of the input data: From a meteorological point of view, there is no reason to define fixed boundaries in the natural area under consideration. From the point of view of engineering hydrology, the consideration of specific catchment areas based on regionally representative samples is desirable in the context of precipitation-runoff models.
  
  The application of the GEV was chosen on the basis of existing studies on extreme value analysis (Fischer & Schumann 2018). The applicability of the GEV model under the existing sample creation is checked for your reference and alternative distribution models (GPD, SMEV) are tested.
  
  To describe the orographic dependence of the identified events, the Pearson correlation of the number of events (threshold value 15 mm/h) was determined via the mean altitude of the place of occurrence. In addition, the correlation for precipitation rate and altitude was carried out. In both cases, there is no correlation between the variables with r < ±0.1.
  
  Figure 1 shows that, despite the not insignificant correlation, clustering occurs in certain regions (at all altitudes), which can be attributed to the climatologically short period of observations. Nevertheless, hotspots can be seen on the Großer Feldberg (Taunus), Vogelsberg and Neunkircher Höhe (Odenwald). This could be an indication that convective and orographic precipitation cannot simply be separated by a threshold value.
  
  The purpose of aggregating neighboring cells (9 or 25) is to represent event quantities for a specific catchment area size. For hydrological engineering questions, the reference to a specific area is often important. The recording of the "real" form of the events is not provided for in this evaluation due to its complexity. For this purpose, a detailed evaluation of the life cycle and movement patterns of convective precipitation cells is planned in a follow-up study based on the identified event focal points.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1907-AC1
CC2: 'Comment on egusphere-2023-1907', Mathias Raschke, 03 Sep 2023

Expanding my criticism: goodness-of-fit tests are not designed to compare the performance of statistical models. There are (for example) information criteria for this purpose (Akaike 1974, Schwarz 1978).
Akaike, H. (1974), "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Schwarz, Gideon E. (1978), "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.

Citation: https://doi.org/10.5194/egusphere-2023-1907-CC2
RC2:
'Comment on egusphere-2023-1907', Anonymous Referee #2, 12 Sep 2023
The manuscript deals with the identification of short-term heavy rainfall events from radar precipitation data. The authors present a method to determine precipitation events with durations between 15 and 90 minutes and test different extreme value probability distribution to describe the collection of events.
The study fits in the scope of NHESS, however, in the current state the manuscript is hard to follow and lacks a clear structure, a clear formulation of the research goals and a profound discussion of the results also in relation to other studies. Therefore, I would not recommend publishing the manuscript in the current from. Substantial changes should be made to the structure and content of the manuscript before it could be published in NHESS. I’d be happy to discuss my suggestions with the authors in the open discussion and clear up possible misunderstandings.

Major comments:

A major concern is the structure of the manuscript. In the introduction information on previous work on the topic and other approaches to identify extreme precipitation is missing. The second section (Methodology) is a mixture of a description of the dataset, previous work and a description of the method. For better readability I recommend to split this section into a data and a method section. The part about previous studies (2.2) is not clear to me. As far as I understand, this is work that has been done by the authors but not been published. Therefore, I would recommend moving this part to the results section, going into more detail here and support some of the statement with additional figures to make it easier for the reader to understand the results presented here. Section 3 presents the results, but a discussion and interpretation of the results is missing. For more detail see the Minor Comments below.

The description of the method is unclear and a bit hard to follow. I recommend to add more detail to the description.

A comparison to other existing methods and datasets is completely missing. E.g. how do the calculated precipitation amounts in Figure 8 fit the values from KOSTRA DWD2020? The authors mention CatRaRE, that also includes precipitation events with 1 hour duration. A comparison with in this study identified hourly precipitation events would be interesting (total number, time and location of occurrence, spatial distribution over Hesse, etc.).

A mayor assumption in this study is the orographic independence of the convective events in Hesse (section 2.2.2). From figure 2, however, this independence is not obvious to me and should be proven with a statistical analysis.

The figures in section 3 should be revised. The legends, axis labels and ticks are hard to read and should be larger and lines could also be a bit thicker.

Minor comments:
p.1, l.16: The authors state that that they get an extensive collection of heavy precipitation objects. However, in the analyses carried out in the manuscript durations of 75 and 90 minutes and later also 60 minutes were excluded because of the insufficient number of events. How does that correspond?
p.2, first paragraph: References are missing that support the statements here.
p.2, l.40: Here the reference is Knist et al, 2018. In the reference list at the end of the manuscript, the year of publishing is 2020. Please revise.
p.2, l.45-47: Please add a reference here.
p.2.l.50: The authors highlight that radar data is necessary to represent the track of convective cells, but in this study this is not taken into account either.
p.3, l.55: A reference to the RADKLIM RW dataset is missing. It is listed in the reference list, but not referred to here (or anywhere else in the manuscript).
p.3, l.62ff.: A paragraph about previous work in the field is missing (other approaches to determine heavy precipitation events and statistics, e.g. KOSTRA, SMEV, CatRaRE, etc.).
p.3, l.65: A reference to the RADKLIM YW dataset is missing.
p.3, l.81: Figure 2 is referenced before Figure 1 in the text. The figures should appear in the manuscript in the order they are mentioned in the text.
p.4, section 2.2: the name “previous studies” is misleading
p.4, l.97-105: Are those studies done by the authors? If so, more detail would be desirable. Otherwise a reference is missing.
p.5, l.108-110: The authors should describe subfigures a) and b) before they describe subfigures c) and d).
p.6, l. 115: It is not clear to me at this point of the manuscript how independency of the events is defined. Please, add some more details here.
p.6, l. 119: It is not obvious to me from Figure 2c that the occurrence of maxima becomes detached from the orography with increasing duration.
p.7, l.157: Why do the local maxima have to occur in all the 8, respectively 24 cells? Doesn’t that filter out the very local convective maxima that the authors want to study? Especially 25 km² is quite a large area for a convective cell.
p.8, Table 1: It would be easier to name the cell either 580828 or 645/327 throughout the whole table and manuscript.
p.9, l. 175: In Table 2 the relative change to the next lower duration is given, not to the initial value per 15 minutes. Is there a reason for the threshold of 10% and 5 mm? Why not taking the duration with the largest change compared the next lower/higher duration?
p.9, l.183-189: It is not clear to me how the clustering works if the neighbouring cells have extreme events with different durations.
p.10, l.203: How are the values computed. The general warning criteria for heavy precipitation of the DWD are given for 1 and 6 hours only. And why do the authors use the same value for 60, 75 and 90 minutes, but different ones for 15, 30 and 45 minutes? Shouldn’t there be different values for each duration?
p.10, l.211: The use of block maxima is not clear to me. If the authors want to investigate the most extreme events and have already ensured for independency of the events, I don’t see the necessity to use block maxima and exclude heavier rainfall events that occurred in an extreme year.
p.10, l.216: KOSTRA-DWD-2020 uses a different method that will be described in an updated version of the DWA-Worksheet 531. The older version of KOSTRA (e.g. KOSTRA-DWD-2010R) are based on the DWA-Worksheet-531, 2017
p.13, l.287-288: Add a reference here, please.
p.13, l.289-290: It is not clear to me which previous studies have shown that no sufficient numbers of extreme events can be identified for duration greater than 90 minutes. How many events were identified and what is considered a sufficient number?
p.13, Figure 4 and l.294-306: Due to the chosen method, the precipitation amount for events with 60 minutes duration is larger than for 75 minutes duration. For 90 minutes it is even lower. From a scientific point of view it doesn’t really make sense that the precipitation amount in 60 minutes should be larger than in 90 minutes, as the 60 minutes should be included in the 90 minutes. How would the results change if the authors investigate each duration independently? Please, clarify and discuss this issue in more detail.
p.15, l.332: I don’t understand, where the associated precipitation totals are shown.
p.16, l.345: What does “some events” mean? How many of the events are identified in both aggregated levels? By visually comparing the maps in Figure 7, I guess it is quite a large fraction.
p.17, Table 4: Please use AD and MAD as it is done throughout the manuscript in this table instead of A² and AU².
p.18,.l. 375: Please, clarify what is meant by “assumed”. How is the plausibility of the criteria tested?
p.18, l.382-390: This should be shifted to the data section.
Citation: https://doi.org/10.5194/egusphere-2023-1907-RC2
- AC2:
  'Reply on RC2', Manuel Perschke, 17 Nov 2023
  To the reviewer, I would like to thank you on behalf of all the authors for the detailed and very helpful assessment of this work. To begin with, I would like to briefly explain the research objectives of this thesis, as these were obviously not formulated concisely enough.
  Due to the statistically short recording period of the radar network and the rarity and small-scale nature of convective heavy precipitation events, a regional sampling approach is chosen here. This means that the events are identified over the entire observation area and the most extreme manifestation over the path of the convective rain cell. The characteristic duration is defined for the intensive main rainfall phase with a constant precipitation rate of at least 20 mm/h.
  A more in-depth comparison with existing extreme value statistics (KOSTRA, RADKLIM) is refrained from in this paper, as the type of analysis is conceptually very different. In particular, the scope of the sample should be mentioned here, as the event identification in this study does not refer to precipitation stations or individual cells with a limited area of validity.
  Individual aspects of the report that require additional explanation are discussed below:
  The comparison with the CatRaRE dataset was carried out independently of this work. However, the data set only has a minimum temporal resolution of one hour, which is why a detailed description of the results was omitted. The characteristics of the events were not directly comparable due to the different temporal resolution and identification methods. The timestamp and localization of the 1-hour events from CatRaRE largely coincide with the events identified in this study.
  
  To describe the orographic dependence of the identified events, the Pearson correlation of the number of events (threshold value 15 mm/h) was determined via the mean altitude of the place of occurrence. In addition, the correlation for precipitation rate and altitude was carried out. In both cases, there is no correlation between the variables with r < ±0.1.
  
  Figure 1 shows that, despite the not insignificant correlation, clustering occurs in certain regions (at all altitudes), which can be attributed to the climatologically short period of observations. Nevertheless, hotspots can be seen on the Feldberg, Vogelsberg and Neunkircher Höhe. This could be an indication that convective and orographic precipitation cannot simply be separated by a threshold value.
  
  For the definition of the characteristic duration, a rate of change of 10 % to the previous value with a precipitation rate of at least 20 mm/h was selected. The value of 10 % proved to be stable in order to ensure sufficient intensity of the core event. A strict choice of the largest change between the individual duration levels would have the disadvantage that (runoff)-relevant partial quantities would not be taken into account.
  
  The purpose of clustering over the entire study area is to establish the connection between the duration-classified cell-related events. This allows the movement patterns of the precipitation cells to be recorded. Over the life cycle of a precipitation cell, different characteristics of the duration and intensity of an event can arise locally. The most extreme manifestation of an event is included in the sample.
  
  The purpose of aggregating neighboring cells (9 or 25) is to represent event quantities for a specific catchment area size. The reference to a specific area is often important for hydrological engineering issues. The information on the very local maxima of the individual cells is also documented in the results data set from 2.3.1 (see Table 1).
  
  Citation: https://doi.org/10.5194/egusphere-2023-1907-AC2

Manuel Perschke, Britta Schmalz, and Ernesto Ruiz Rodriguez

Data sets

Spatiotemporally independent heavy precipitation events for the state of Hesse (Germany) Manuel Perschke, Britta Schmalz, and Ernesto Ruiz Rodriguez https://doi.org/10.5281/zenodo.8131633

Manuel Perschke, Britta Schmalz, and Ernesto Ruiz Rodriguez

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Short summary

With climate change, an increase in extreme summer precipitation is predicted in Central Europe. The location, time and intensity of these events can only be predicted to a limited extent or at short notice, which makes preventive measures by municipalities and citizens even more important. A regional classification of the events and their most intense phases helps to develop adequate protection strategies against the negative impacts of heavy precipitation, such as flash floods.


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