the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Oct 2026
Seasonal trends and spatial variability of precipitation extremes in Berlin-Brandenburg, Germany, from 1981 to 2025
Abstract. Precipitation extremes have caused substantial damage in the Berlin-Brandenburg region in recent decades. This study assesses seasonal trends and spatial variability in daily precipitation return levels for 2-, 5-, and 10-year return periods between 1981 and 2025. We use a peaks-over-threshold approach and a non-stationary Generalised Pareto Distribution with a time-dependent scale parameter. The analysis is based on observations from 223 rain-gauge stations operated by the German Meteorological Service (DWD) and the 2 km Central Europe Refined analysis version 2 (CER), a dynamically downscaled product based on the ERA5 atmospheric reanalysis. CER-based return levels show contrasting seasonal patterns: spring return levels decline across nearly the entire domain by up to approximately 20 %, while summer return levels show the largest absolute increases, averaging spatially approximately 5–10 mm d-1 (+14–15 %), depending on the return period. Summer increases are also spatially more heterogeneous than in other seasons. Autumn return levels increase by up to 19 % across the analysed return periods, whereas winter changes remain weak. The DWD and CER datasets show consistent directions of change, although the CER underestimates the magnitude of summer increases relative to DWD. In some locations, the 2025 2-year summer return level approaches the magnitude of the 5-year return level estimated for 1981, highlighting the relevance of non-stationary return levels for regional risk assessment and future infrastructure planning.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Natural Hazards and Earth System Sciences.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 16 Nov 2026)
- RC1: 'Comment on egusphere-2026-5231', Anonymous Referee #1, 21 Oct 2026 reply
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RC2: 'Comment on egusphere-2026-5231', Anonymous Referee #2, 26 Oct 2026
reply
In the manuscript “Seasonal trends and spatial variability of precipitation extremes in Berlin-Brandenburg, Germany, from 1981 to 2025” the authors examine changes in seasonal daily precipitation return levels (2-, 5-, 10-year) across Berlin-Brandenburg in the period 1981-2025 using DWD station observations and the gridded high-resolution CER dataset within a non-stationary POT-GPD framework. The findings demonstrate that the spatial variability of return levels, alongside their temporal shifts, is strongly season-dependent. Spring return levels decline across nearly the entire CER domain, summer values exhibit the most pronounced increases, autumn shows a relatively coherent positive trend, whereas winter changes remain modest and spatially heterogeneous. Furthermore, the high consistency in the direction of change across seasons and return levels between the DWD and CER datasets reinforces the robustness of the identified seasonal patterns.
I can confidently state that the paper is highly compelling and well-structured. The introduction includes a comprehensive analysis and overview of the topic and a clear description of the objectives. The methodology is well explained and the approach is clearly presented, allowing readers potentially to replicate the entire procedure. The results are accurately analysed and discussed and the interpretations are sound and justified by the data.
Overall, the manuscript exhibits two major strengths. First, the methodological framework is rigorous and well-elaborated, meticulously accounting for several critical factors (threshold selection, temporal declustering, model evaluation, and uncertainty estimation). Second, the findings carry significant practical and theoretical impact, offering valuable insights to the field.
That being said, a few aspects require further clarification and elaboration to enhance the overall rigor and quality of the manuscript.
1) The study relies on a non-stationary POT-GPD framework for the extreme value analysis. While this choice is methodologically sound, the manuscript would benefit from a more comprehensive literature review (for instance, in the Introduction) regarding alternative modeling paradigms (parametric and non-parametric). Specifically, the authors should discuss competing methodologies, outlining their respective strengths and limitations. Expanding on these alternatives would significantly strengthen the theoretical justification behind their methodological approach.
2) Section “2.3.2 Reanalysis-based data”: Regarding the CER gridded precipitation dataset, at lines 134-135 the authors state that “the evaluation of monthly, seasonal and annual precipitation products is given in Bart et al. (2025)”. However, since the current study relies on daily data, it would be highly beneficial to perform (or explicitly include, if already performed) a comparison between the DWD stations and their nearest CER grid cells at the daily time resolution.
3) To further enhance the statistical rigor and overall robustness of the study, the authors might consider complementing the analysis outlined in Point 4 (Temporal Trends) of the conceptual workflow (in Figure 1) with formal non-parametric trend detection tests. Specifically, applying the Mann-Kendall test alongside Sen’s slope estimator to the quantile time series would allow for a rigorous assessment of statistical significance and rate of change associated with any detected upward or downward trends. Such an analysis could be systematically performed across all DWD station-season and CER grid cell-season combination. Furthermore, from a spatial perspective, it would be highly informative to provide spatial mapping that illustrates: the spatial distribution of stations and grid cells categorized by trend behavior (statistically significant increasing, decreasing, or no trend); the spatial pattern of trend magnitudes as estimated by Sen’s slope. Although including these new analyses is not strictly necessary, it would certainly add value and relevance to the paper.
4) Line 227: The assertion that “the GPD underestimates the most extreme observations” represents a major point that deserves deeper reflection. The authors are encouraged to discuss the underlying causes of this limitation, examining whether it is attributable to the specific distribution family, the parameter estimation approach, or other aspects of the modeling procedure.
5) There is an inconsistency regarding the formula used to calculate the statistical metric (Δqp) for the differences in seasonal return levels. Specifically, the equation applied to compute the values reported in Tables 1 and 2 (and stated in their captions) differs from the one presented in Equation 4 (line 206) of Section “2.4.4. Return-level estimation”. The authors are kindly requested to clarify which formula was actually used for the analysis, explain the rationale behind this methodological choice, and ensure full consistency throughout the manuscript.
Minor comments:
1) Lines 22-23: The statement “Statistical analyses suggest […] 100-year return levels.” should be backed by appropriate references.
2) Figure 1 (right panel): The legends identifying the curves in the three subplots lack sufficient clarity. In particular, although the curves are shown as solid, dashed, and dotted in the plots, they all appear solid in the legends. Therefore, the authors are requested to improve the overall legibility of the figure (potentially using distinct colors for the three curves).
3) Lines 156-157: There is an inconsistency referring to Figure 1 (right panel). The callout for σ should correspond to the top subplot, while ξ should correspond to the middle subplot. Therefore, at line 156, replace “see Fig. 1, middle right” with “see Fig. 1, top right”; while at line 157, replace “see Fig. 1, top right” with “see Fig. 1, middle right”.
4) Line 438: Replace “magnitude of the changes differ” with “magnitude of the changes differs”.
Citation: https://doi.org/10.5194/egusphere-2026-5231-RC2 -
RC3: 'Comment on egusphere-2026-5231', Anonymous Referee #3, 26 Oct 2026
reply
General Comment
The manuscript investigates trends in daily precipitation using a non-stationary extreme value analysis on an observational and a reanalysis dataset. The analyses are clearly presented and well structured. The results are well organized and sufficiently detailed.
Overall, I found the presented research interesting and scientifically sounding, albeit lacking of innovation and of a clear added value over the existing scientific literature. This can be ascribed to three major drawbacks:
1) The study is titled “…precipitation extremes” but it is focused on daily precipitation at relatively low return periods. Analyses on extremes are generally focused on sub-daily scale, so I would suggest to be more upfront about the choice to focus on daily values. As for the return periods, I understand the reasoning behind the choice, but it seems a lost opportunity to ignore larger values (50 years?) given the introduction of a theoretical fitting, which is usually done exactly to avoid such limitations. The T = 2 years, in particular, barely qualifies as extreme.
2) There is a limited clarity on the added value of this research over the existing literature. Some results confirm outcomes of other studies mentioned in the introduction, but the role of the non-stationary analysis, over other parametric or non-parametric trend analyses, is not sufficiently underlined.
3) A big emphasis is given on the inclusion of the reanalysis dataset, but the added value of this dataset over the ground data is non sufficiently detailed. Some inconsistencies were observed, but not further elaborated, and the spatial analysis is very limited in scope. What are the patterns observed on the gridded data not possible to observe on the rain gauges?
In my opinion, the manuscript present some compelling researches, which would benefit from a strengthen emphasis on the key outcomes and a more detailed analysis of the spatial patterns in the two datasets, before publication.
Minor Comments
Title: better emphasize the daily scale and the focus on non-stationary analysis.
L32-42. What is the attempted new contribution of your research over these consolidated results?
L43-50. Following the results, is this limitation addressed by the reanalysis used here? Is there any region where the ground data are not able to capture spatial patterns in the reanalysis?
L64. How are these improvements connected to local convection? Discuss in the framework of the role of convection-permitting models at daily scale
L80. Is this period long enough to talk about trend? Wouldn’t non-stationarity a better fit?
L84. This sentence gives the impression that the parameterization derived on the stations was used on the gridded data. Please reword to avoid confusion.
L85. Compare should mean also in term of spatial patterns, not only at point scale
L93. It should be briefly clarified why the non stationarity is accounted only in the scale parameter.
L109. Please add also seasonal values, as seasonality is a major focus of the study.
L173-176. I would move this to the results section.
L179. Is this referring to the avg. on all stations? Clarify. Also, is there any difference in the variability between seasons?
L187. Any sensitivity analysis on this choice?
Fig. 3. I would adjust the y-axis to make the plot more readable. In the histogram, add mean and std to better connect to the text. Add info on number of events per season and its variability among sites.
L201. Better clarify how the threshold exceedance rate is calculated (lambda=n/N?), the obtained value and the hypothesis of Poisson process.
L211-212. This has been already stated in the previous section. Also, it is not clear how 908 procedures are obtained (223x4?).
228-229. These results also differ by station. How many are very different? Are they systematically located in a specific regions
L237. How is the LRT applied? Is the temporal dependency considered an extra parameter? Like 3 (standard gpd) vs. 4 for non-stationary? Is this a correct application of LRT?
Fig. 4 it would help to show also the stationary value.
L253. Is this result correct? They both seem closer to 25% from fig. 6.
L265. Only in some seasons. Please clarify.
L282. This inversion seems the major outcome of this analysis. However, the figure focuses more on the comparison between dwd and cer. Maybe the results can be presented differently.
L288. Is this the right figure to refer here?
L288. “Near-equal share”. I would not call 60/40 near equal
Fig. 7. The color are a little difficult to distinguish
L293-321. Are those patterns substantially different than the ones in dwd?
L323-324. Large number tends to have large variability. What about relative changes? It seems to me that % changes are rather similar for the different percentiles
Fig. 9. You should mention the similarities with the other quantiles reported in the appendix
L328. Spatial coherence in the patterns between the two datasets should be better reported. In general, the spatial analysis is very limited and mostly qualitative.
L352-357. These usually justify specific years and not systematically trends. Any evidence on how these can cause different trends in different regions?
L361. This is usually associated to sub-daily more than daily (see Haslinger et al., 2025: Nature, over Austria)
L407. This is a key point that should be better emphasized. Any sign of discontinuities that can suggest temporal fluctuations rather than trends?
L432-433. This result is not clearly highlighted anywhere in the main plots
Citation: https://doi.org/10.5194/egusphere-2026-5231-RC3
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- 1
This study looks at 2, 5, and 10-year daily rainfall return levels in two separate historical datasets, one set of stations, the other a high-resolution gridded reanalysis. Standard “Peak Over Threshold” theory is applied, especially the generalized Pareto distribution (GPD) fits to the threshold exceedances. From a methodological perspective, the main original element in this work is the use of a time-dependent scale parameter in the GPD function fits: this in turn allows the estimation of trends in the size of the return levels over the observational period (Figs. 4, 7-9). Those trends are statistically robust and physically credible. From a climatological perspective, the value of this work is primarily in the results shown for the Brandenburg region of eastern Germany, and especially how they vary according to season. Some aspects of this work (e.g., Fig. 5) also serve as model validation tests.
Overall, the work is interesting and thorough, the methods used are appropriate (if perhaps more elaborate than strictly required), the details provided are sufficient for a reader to understand what was done, and the writing is good. But rather than give two thumbs up, I’m giving just 1.9 or so, since as a reviewer I’m trying to see how this could be improved, and I do think there are a few minor ways that this could be done.
As general comments, I would describe this work as something of a statistical sledgehammer used to crack a climatological nut, where simpler methods might have produced comparable results. Given that powerful statistical tool, however, it is only used very conservatively. Let me explain…
This work focuses on the “exceedance” or GPD aspect of POT theory, while somewhat neglecting the “number count” or Poisson process element of it. The only mention of the “number count” aspect that I could see was in the “threshold exceedance rate” factor P(X>u) in the text following Eq. (3). The paper develops quite an elaborate analysis focusing on return levels for 2, 5, and 10-year return periods involving time-varying scale parameters in GPD fits to exceedance data for each station. I wonder whether a simple “number count” trend analysis over the 45 years might have yielded much the same essential information? (See e.g., O’Brien et al, 2026, in reference list below).
The research questions (R1 and R2, l.80-81) could (conceivably) be re-phrased to ask “how have intense rainfall days changed over time, and how do they vary spatially?” If instead of 2, 5, and 10-year return levels (requiring the elaborate POT/GPD approach), the variables of interest were “days with more than X mm precipitation” (X=20, 30, 40, etc.), those days could be very simply counted (and subsequently plotted) in either dataset. I suppose engineers do like to use 5- and 10-year return levels, but climatologically, saying that “the number of 20 mm days will increase by Y%” is much the same as saying that “2-year return levels will increase by Z%” (as in rightmost column of Fig. 9) – but much simpler to estimate (being just a count, like a climate index).
Given that the analysis of exceedances leads to smooth GPD functions, the authors use these very conservatively by looking only at events no larger than the 10-year return level. This is despite having 45 years of observations, and even though much of the appeal of POT theory with its asymptotic GPD fits to limited data is that it can estimate return levels for return periods longer than the observational period. The authors say (l.408) that their “results should not be extrapolated directly to longer return periods”. The word “directly” is key here, but given that GPD distributions extend to return levels beyond the observed data, I would expect that the results could be extrapolated at least indirectly to longer return periods. I suppose the time-dependent scale parameter requires the “direct” qualification; but how else, in a changing climate, can the size of the 50-year or 100-year event be measured at all? I would say, by thinking in probabilities (e.g., p=0.01) instead of return times in years.
I don’t expect the authors to change what they did given those comments by me; I'm just suggesting that in this context, alternative approaches were possible.
Specific points (some trivial, some more about style than substance, and not all requiring a response; I see the vertical “banding” in Fig. 5 as the main unresolved issue here):
In the many references to Coles (2001) here, it would help if the specific chapter or section of that book were provided as well. (I’m just reminded of references I’ve seen to “IPCC (2021)”, which aren’t much help in finding the relevant place in a 4,000 page report). The methods in Coles (2001) are supported by several more recent studies (e.g., Hosseinzadehltalaei et al., 2020).
p.1, l.23: Is there any reference to back up the claim that “Statistical analyses suggest that the observed intensities exceeded the corresponding 100-year return levels”?
p.2, l.26: A recent reference relevant to the choice between Block Maxima and Peak Over Threshold approaches might be Bücher and Zhou, (2021) – see reference list below.
p.2, l.41: This is just a personal style preference, but I would delete “It is important to note that”, and simply start with “These previous investigations…”.
p.2, l.52: The sentence about radar data here is something of a strawman argument (i.e., only raised in order to be knocked down again), and could be deleted as not really relevant.
Fig. 1: While the 3 different curves in each panel here are either solid, dashed, or dotted, those distinctions are not apparent in the “legends” shown, where they all look solid, to my eye at least. Since this figure is only likely to be reduced in size in any final publication, they authors might consider making it easier to associate each curve with its particular parameter size, or sign. Using 3 different colours within each panel would do the trick.
p.5, l.120,121: No need for the space between “75” and “%”; “75%” is more standard, as far as I know.
Section 2.4.1: Somewhere in here it would be worthwhile to mention that the GPD fits are applied to each station (or grid point) separately (or not…). This would complement the emphasis on temporal variability, to clarify that e.g., a “constant shape parameter” is constant over time, but not space. At least, that’s my understanding, but it would help to either confirm or correct it.
In section 2.4.2, allowing the threshold values to vary with location effectively turns the threshold into another adjustable parameter (which it need not be) and potentially reduces the generality or interpretability of the analysis overall. I doubt that it matters very much though: e.g., Benito et al. (2023) found that varying the threshold in their POT analyses made no fundamental difference to their results, and I would expect the same to apply here.
Section 2.4.3: While this section is about temporal declustering, is there any comparable effort made for spatial declustering, i.e., to avoid the same event being counted several times at several adjacent stations, and so guarantee spatial independence? In Fig. 2b, spatial separation between stations appears to be < 5 km for quite a few of them, which in itself raises the issue of spatial independence.
Fig. 4 is a very nice figure insofar as it has a lot of information content, even if just for a single station, showing all the raw data (black points) along with the modelled quantile time-dependence and uncertainty levels. The trends shown are visually obvious and so quite persuasive. The slopes in Fig. 4 are also consistent with Figs. 6 and 7.
Section 2.5.1: The observation with respect to Fig. 5 that “the GPD underestimates the most extreme observations” is consistent with similar findings by Jewson et al. (2025), and may be an artifact of the Maximum Likelihood fitting method, that gives equal weight to every exceedance event but in practise may give too little weight to data points at the extreme end of the tail, where data is most scarce but most “interesting”, and arguably ought to be most influential in determining the GPD parameters.
The vertical banding in Fig. 5 is indeed curious. However, the suggestion in this section that the upper tail is “constrained across stations, likely governed by the estimated shape parameter ξ” doesn’t seem like an adequate – or at least an accurate - explanation, given that ξ is allowed to be different across stations, as is σ. In principle, the upper tail is no more constrained by the GPD fits than the empirical observations are. Perhaps there is some very weak suggestion of clustering of ξ in Fig. 3, but not enough to explain the banding in Fig. 5. Of course, what counts for the banding in Fig. 5 is the overall GPD function, i.e., the combination of shape and scale parameters. That “discrete clustering of extreme events across many stations at similar modelled quantile values” could be a consequence of the fact that in absolute terms, i.e., in mm/day, most stations record no really extreme events at all, and so the GPD fits to those fall into one or two “clusters”, while the GPD fits to stations with genuine extreme events fall into one or two other “clusters”. Even so, the banding is still strange. Otherwise, all I can think of is that it might somehow be a consequence of the finite 45-year observing period, but that too is just idle speculation on my part. It may take displaying the data in various different formats (e.g., exceedance histograms) to figure it out. Currently this is something of a "ragged edge"; it would be nice to tidy it up, if at all possible.
Section 4.2: This section is very worthwhile even though necessarily speculative.
Optional extra references:
Benito, S., López-Martín, C. & Navarro, M.Á. (2023). Assessing the importance of the choice threshold in quantifying market risk under the POT approach (EVT). Risk Manag 25, 6 . https://doi.org/10.1057/s41283-022-00106-w.
Bücher, A. and C. Zhou, (2021). A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach. Statistics of Science, Vol. 36, No. 3, 360-378, https://doi.org/10.1214/20-STS795 .
Hosseinzadehtalaei, P., Tabari, H. and Willems, P., (2020). Climate change impact on short-duration extreme precipitation and intensity–duration–frequency curves over Europe. Journal of Hydrology, 590, p.125249.
Jewson, S., Sweeting, T., and Jewson, L. (2025). Reducing reliability bias in assessments of extreme weather risk using calibrating priors, Adv. Stat. Clim. Meteorol. Oceanogr., 11, 1–22, https://doi.org/10.5194/ascmo-11-1-2025 .
O’Brien, E., Wang, J., Ryan, P., Nolan, P., Mateus, C. (2026), A depth-duration-frequency model for analysis of extreme precipitation events, with application to past and projected future climates in Ireland. Weather and Climate Extremes, Vol. 51, 100862, ISSN 2212-0947, https://doi.org/10.1016/j.wace.2026.100862 .