the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Interannual variations in the seasonal cycle of extreme precipitation in Germany and the response to climate change
Madlen Peter
Henning W. Rust
Uwe Ulbrich
Abstract. Annual maxima of daily precipitation sums can be typically described well with a stationary generalized extreme value (GEV) distribution. In many regions of the world, such a description does also work well for monthly maxima for a given month of the year. However, the description of seasonal and interannual variations requires the use of non-stationary models. Therefore in this paper we propose a non-stationary modelling strategy applied to long time series from rain gauges in Germany. Seasonal variations in the GEV parameters are modelled with a series of harmonic functions and interannual variations with higher ordered orthogonal polynomials. By including interactions between the terms, we allow for the seasonal cycle to change with time. Frequently, the shape parameter ξ of the GEV is estimated as a constant value also in otherwise instationary models. Here, we allow for seasonal-interannual variations and find that this is benefical. A suitable model for each time series is selected with a step-wise forward regression method using the Bayesian Information Criterion (BIC). A cross-validated verification with the Quantile Skill Score (QSS) and its decomposition reveals a performance gain of seasonal-interannual varying return levels with respect to a model allowing for seasonal variations only. Some evidence can be found that the impact of climate change on extreme precipitation in Germany can be detected, whereas changes are regionally very different. In general an increase of return levels is more prevalent than a decrease. The median of the extreme precipitation distribution (2-year return level) generally increases during spring and autumn and is shifted to later times in the year, heavy precipitation (100-year return level) rises mainly in summer and occurs earlier in the year.
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Madlen Peter et al.
Status: final response (author comments only)
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RC1: 'Comment on nhess-2023-62', Anonymous Referee #1, 03 Jul 2023
This manuscript presents an analysis of the seasonal and interannual variations of extreme precipitation at stations in Germany, employing a non-stationary block maxima approach. Additionally, it investigates the impact of climate change on the seasonal cycle of extreme precipitation in Germany, which is a crucial topic in climate change research. The paper is well-structured and complemented by visually appealing figures. However, there are several issues that require attention and improvement before this work can be considered for publication.
Main comments:
- For introduction, according to the objective of the paper, it is important to address what previous studies have specifically accomplished, identify the existing gap or problem in the research, and emphasize why this problem is of significant concern. It is crucial to provide clarity on these aspects before describing the approach or research you intend to use in your study. For example, the third paragraph of the introduction discusses previous analyses conducted on extreme precipitation in Germany across different seasons. “Analyses of extreme precipitation in Germany for different seasons has already been done (Zolina et al., 2008; Łupikasza, 2017; Fischer et al., 2018; Zeder and Fischer, 2020; Ulrich et al., 2021).” More details of what previous studies have done are needed before you introduce the two main new aspects you will do in this study. In addition, the second question is “RQ2 How important is a flexible shape parameter to reflect recorded variations?”. However, you did not add any descriptions or previous studies about shape parameter in the introduction. Therefore, My suggestion is to rewrite the introduction.
- For method: return level, the return period T can be written as T=μ/(1-p), where, p is the non-exceedance probability. μ is the mean interarrival time between two successive events, which is defined as one divided by the number extreme events per year. When considering annual maxima, μ corresponds to 1 year. However, in your study, when calculating the return period T, are we utilizing the annual or monthly maximum or non-exceedance probabilities? If we are using the monthly maximum time series or non-exceedance probabilities, μ should not be equal to 1.
- In addition, when applying the GEV to the monthly maximum, if two extreme events occur on the last day of the month and the first day of the next month, these two events are often treated as a single individual event. When applying the GEV to non-exceedance probabilities, precipitation occurrences are highly clustered in time and space. Therefore, the independence of the extreme values should be taken into account prior to modeling.
- The fitted return period distribution may exhibit uncertainties due to the limited sample size of the data. The short time period of the datasets may introduce uncertainty in the distribution model fitting. Therefore, for the question “RQ1: Can a model with interannual variations better represent the observations than a seasonal-only model?” how can you distinguish the difference or bias from the uncertainty in distribution model fitting or from the model with or without interannual variations? As shown in the paper “the total QSS for different non-exceedance probabilities (return periods). Skill is positive but small<= 2%, increasing with non-exceedance probability (return period).” The larger bias for higher return period is very likely caused by large uncertainties for higher return period in model fitting.
Other comments:
- Lines 21-25: Please maintain consistency in the usage of terminology such as 'heavy rain' or 'heavy precipitation' throughout the entire
- Line 77-79, “The four stations Krümmel (1899-01-01 until 2021-12-31), Mühlhausen / Oberpfalz-Weiherdorf (1931-01-01 until 2021-12-31), Rain am Lech (1899-01-01 until 2021-12-31) and Wesertal-Lippoldsberg (1931-01-01 until 2021-12-31) are highlighted in Fig. 1 and will be discussed exemplarily in this study”. Why do you choose these four stations? It would be beneficial to include a brief introduction explaining the reasons behind selecting these stations. Although you provide more details about the stepwise selection process in Section 4.1, adding an introductory explanation would provide context for the readers.
- The sample size of the data in model fitting. For example, for figure 7 and figure 8, the GEV was applied to each station, especially for each month of each station, how many extreme values (sample) are you collected for each station for each month? Are the number of samples enough for distribution model fitting?
- Figure 12, it is better to add a,b,c,d into the each figure.
- In Section 7, "Impact of climate change on the seasonality of extreme precipitation," it is important to note that the trend of the time series is significantly influenced by the chosen start year. Although the study mentions comparing the time period from 1941 to 2021, where all stations have data, the start year appears to be different in Figure 15. Could you please provide further clarification on the discrepancy?
- In section 7, the return period was calculated for each station for each year? is the sample size enough for model fitting?
Citation: https://doi.org/10.5194/nhess-2023-62-RC1 - AC1: 'Reply on RC1', Madlen Peter, 31 Aug 2023
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RC2: 'Comment on nhess-2023-62', Theano Iliopoulou, 20 Jul 2023
- AC2: 'Reply on RC2', Madlen Peter, 31 Aug 2023
Madlen Peter et al.
Madlen Peter et al.
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