| 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.
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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 .