Analyses of seasonal and annual maximum daily discharge records for central Europe
Research highlights
► Analyses of maximum daily discharge records for 55 stations in central Europe. ► Abrupt changes are responsible for violations of the stationarity assumption. ► Step changes linked to anthropogenic effects (construction of dams, river works). ► It is difficult to detect a climate change signal in these flood peak records. ► The results of this study suggest that these records exhibit a heavy tail behavior.
Introduction
Under human-induced climate warming scenarios (Intergovernmental Panel on Climate Change, 2007), results from various studies point to an acceleration of the hydrologic cycle (e.g., Allen and Ingram, 2002, Voss et al., 2002, Held and Soden, 2006), with large impacts on the occurrence of extreme events, such as droughts and floods (e.g., Voss et al., 2002, Milly et al., 2002, Milly et al., 2005, Christensen and Christensen, 2003; consult Blöschl and Montanari (2010) and references therein for a recent discussion about this issue). Recently, Milly et al. (2008) wrote that “stationarity is dead,” “cannot be revived,” and cannot be assumed, not even as a mere working hypothesis, in a modern design and management of hydraulic structures. Moreover, probable human-induced global climate change scenarios point to the demise of this assumption, and make searching for alternative solutions that would allow us to live, design, and manage structures in a “non-stationary” world, as well as pursuing the best adaptation strategies, unavoidable (Milly et al., 2008).
Over the past decade, a series of large flood events has affected central Europe, with a large toll in terms of fatalities and economic damage (e.g., Engel, 1997, Becker and Grünewld, 2003, Kundzewicz et al., 2005b, Kreibich et al., 2009). Moreover, several modeling studies suggest an increase in flood risk over this area under a warmer climate (e.g., Kwadijk and Rotmans, 1995, Middelkoop et al., 2001, Allamano et al., 2009, Dankers and Feyen, 2008, Dankers and Feyen, 2009, Hurkmans et al., 2010, te Linde et al., 2010). The use of historical observations is an important tool for obtaining a clearer understanding of what the future will hold (e.g., Blöschl and Montanari, 2010).
In this study, we investigate the validity of the stationarity assumption in the flood peak record over part of central Europe (including Germany, Switzerland, Czech Republic, and Slovakia). We focus on 55 stations with a record of at least 75 years of daily discharge (data obtained from the Global Runoff Data Centre, Federal Institute of Hydrology, Koblenz, Germany). A time series is considered stationary if it is invariant under temporal translations (Brillinger, 2001), meaning that it is free of slow and abrupt changes and periodicities (Salas, 1993). For an in-depth discussion on stationarity in hydrology, consult Matalas, 1997, Koutsoyiannis, 2006.
Different studies have examined flood peak records over central Europe, with contradicting results. Mudelsee et al., 2003, Mudelsee et al., 2004 studied long time series of the Elbe and Oder Rivers (eastern Germany), finding a decrease in winter flood occurrence and no trends for summer flood occurrence. For 48 catchments in Switzerland, Birsan et al. (2005) found a tendency towards increasing trends in annual streamflow. These increases were mostly driven by increases in winter and spring streamflow. Kundzewicz et al. (2005a) analyzed 70 stations over Europe and found that 11 of them showed statistically significant increasing trends and nine decreasing trends (see Svensson et al. (2005) for similar analyses using peak-over-threshold series). Wang et al. (2005) analyzed annual maximum flow series for 12 rivers in western Europe over the 20th century and found that two of them had a statistically significant increasing trend, while one of them a decreasing trend. Pekarova et al. (2006) analyzed annual runoff series for 18 major European rivers without finding any long-term trends. Petrow and Merz (2008) found mostly upward trends in flood peaks in Germany over the period 1951–2002 and ascribed these results to climate changes. Generally increasing trends in Germany were found by Petrow et al. (2009) as well. Moreover, seasonal analyses highlighted how these changes were larger during the winter than the summer. Schmocker-Fackel and Naef (2010b) examined 83 stations in Switzerland and found that 42% of them exhibited a statistically significant trend for a period starting before 1960 and ending after 2000, while the percentage of statistically significant decreasing trends was much smaller.
Temporal changes in the flood peak records have been generally investigated only by performing trend analysis. However, these catchments have undergone profound changes related, for instance, to the construction of dams, river training (e.g., straightening, diversion, meander cut-off), and changes in land use/land cover (e.g., Dynesius and Nilsson, 1994, Bronstert et al., 1995, van der Ploeg et al., 1999, Belz et al., 2001, De Roo et al., 2001, Disse and Engel, 2001, Helms et al., 2002, Lammersen et al., 2002, Robinson et al., 2003, Herget et al., 2005, Pinter et al., 2006a, Pinter et al., 2006b, Socher et al., 2008). If unaccounted for, these changes could have a large impact on the outcome of analyses of the temporal non-stationarities (e.g., Villarini et al., 2009a). Following Villarini et al. (2009a), we will perform both change-point and monotonic trend analysis (similar to the “downward” approach in Blöschl et al. (2007)). Abrupt changes, both in mean and variance, can be associated with both climatic (e.g., shifts in climate regimes; e.g., Potter, 1976, Hare and Mantua, 2000, Alley et al., 2003, Swanson and Tsonis, 2009) and anthropogenic effects (e.g., construction of dams and systems of reservoirs, changes in land use/land cover and agricultural practice, stream gage relocation; e.g., Potter, 1979, Villarini et al., 2009a). The main difference between abrupt and slowly varying changes is that when a trend is detected, it is likely to continue in the future, while the presence of a change-point indicates the shift from one regime to another, and the status is likely to remain the same until a new regime shift occurs. Step changes in the mean and variance of the flood peak records are tested using the non-parametric Pettitt test (Pettitt, 1979), while the presence of monotonic trends is tested using the Mann-Kendall and Spearman tests. Similar to Villarini et al. (2009a), we will first perform change-point analysis. If no statistically significant change-point in mean is detected, then we perform trend analysis on the entire record. On the other hand, if we detect a statistically significant change-point in mean, then we will split the record into two sub-series (before and after the change-point) and perform trend analysis on each of the two sub-series separately. When examining the data for the presence of increasing or decreasing trends, different results were obtained depending on whether we focus on seasonal or annual blocks. For this reason, besides considering maximum daily discharge time series for blocks of one year, we will also consider four additional seasonal blocks (winter, spring, summer, and fall). In this way, the existence of any seasonal changes in the flood peak record can be assessed.
The upper tail and scaling properties of the flood peak distributions are examined by means of the Generalized Extreme Value (GEV) distribution (e.g., Coles, 2001), which is widely used when working with hydrologic extremes (e.g., Stedinger and Lu, 1995, Hosking and Wallis, 1996, Katz et al., 2002). It represents the limiting distribution resulting from maxima of identically distributed and independent or weakly dependent random variables (Leadbetter, 1983). It has three parameters (location, scale, and shape), with the shape parameter that is related to the upper tail of the distribution. For the eastern US, Villarini and Smith (2010) showed that the upper tail properties of the flood peak distribution exhibited large spatial variability, with the tropical cyclones responsible for large values of the shape parameter over large areas. Similar analyses for summertime convective systems over the central US were performed by Villarini et al. (in press). We also examine the dependence of the location, scale, and shape parameters of the GEV distribution on drainage area. Previous studies found that the location and scale parameters exhibit a power law behaviour when plotted as a function of drainage area (e.g., Morrison and Smith, 2002, Northrop, 2004, Lima and Lall, 2010, Villarini and Smith, 2010, Villarini et al., in press), while the shape parameter showed a decreasing linear behaviour in the log-linear domain (the larger the catchment, the lighter the tail; Villarini and Smith, 2010, Villarini et al., in press). The results of these analyses provide additional evidence about the upper tail properties of the flood peak distribution for different regions of the world. Moreover, they would help identifying the presence of possible general relations between the parameters of the GEV distribution and drainage area.
The paper is organized as follows. In the next section we describe the data and provide a brief description of the change-point and trend tests, and the GEV distribution. Section 3 describes the results of our analyses. In Section 4 we summarize major conclusions of this work and discuss future research.
Section snippets
Data
We use daily averaged discharge data from 55 stations over central Europe (Germany, Switzerland, Czech Republic, and Slovakia) with a record of at least 75 years (Fig. 1). There are 32 stations in Germany, 13 in Switzerland, six in the Czech Republic, and four in Slovakia. Daily discharge time series were provided by the Global Runoff Data Centre (GRDC). We perform analyses on both annual and seasonal (winter, spring, summer, and fall) maximum daily discharge records. These time series cover
Stationarity
In this section we examine the validity of the stationarity assumption by testing the time series of annual maximum daily discharge for the presence of change-points and monotonic trends. As a preliminary step, we checked the validity of the independence assumption by examining whether the lag-1 correlation was significantly different from zero. For ten stations we found that the lag-1 was statistically different from zero. The violation of the independence assumption would affect the
Conclusions
We analyzed daily discharge measurements from 55 streamflow stations with a record of at least 75 years over central Europe (including Germany, Switzerland, Czech Republic, and Slovakia). The main findings of this study can be summarized as follows:
- 1.
There is a marked seasonality in annual maximum daily discharge over this area. In the western part of this region, the largest frequencies of annual maximum discharge values are concentrated during the winter months. During spring, the areas with
Acknowledgments
This research was funded by the Willis Research Network. We acknowledge the Global Runoff Data Centre (Federal Institute of Hydrology, Koblenz, Germany) for providing the daily river flow data. The river network data were obtained from the Catchment Characterisation and Modelling (CCM) River and Catchment Database, version 2.1 (CCM2). We thank Dr. Attilio Castellarin and an anonymous reviewer for useful comments and suggestions.
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2021, Science of the Total EnvironmentCitation Excerpt :Streamflow means (see, e.g., Small et al., 2006; Markonis et al., 2018b; Papacharalampous et al., 2019a; Papacharalampous and Tyralis, 2020). Floods and streamflow maxima (see, e.g., Villarini et al., 2011; Mallakpour and Villarini, 2015; Archfield et al., 2016; Berghuijs et al., 2016; Slater and Villarini, 2016; Villarini, 2016; Berghuijs et al., 2017; Blöschl et al., 2017; Do et al., 2017; Slater and Villarini, 2017; Steirou et al., 2017; Hall and Blöschl, 2018; Berghuijs et al., 2019a, 2019b; Bertola et al., 2020; Blöschl et al., 2019b; Iliopoulou et al., 2019; Steirou et al., 2019; Tyralis et al., 2019c; Brunner et al., 2020; Do et al., 2020; Kemter et al., 2020; Perdios and Langousis, 2020; Stein et al., 2020; see also the overviews by Hall et al., 2014; Blöschl et al., 2015; Zaghloul et al., 2020). Droughts and low flows (see, e.g., Tongal et al., 2013; Van Loon et al., 2014; Hanel et al., 2018; Markonis et al., 2018a; Iliopoulou et al., 2019).
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