Historical Floods of the Danube River in View of Climate Change
Research article
Stevan Prohaska^{1}, Pavla Pekarova^{2}, Aleksandra Ilić^{3}
^{1} „Jaroslav Černi“, Institute for the Development of Water Resources, Belgrade, Serbia; E-mail:
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^{2} Institute of Hydrology, Academy of Sciences of Slovakia, Bratislava; E-mail:
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^{3} Faculty of Civil Engineering and Architecture, University of Niš, Serbia; E-mail:
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Abstract
This paper presents the results of a statistical-stochastic analysis of a series of historical floods along the Danube River, registered in a period of more than 1000 years from 1012 until today. Relying on the historical floods estimating method, this period of over a thousand years can be divided into three characteristic subperiods: the Middle Ages – floods estimated based on archival material; period 1501–1820 – floods estimated based on high water traces and the period from 1821 until today – floods estimated based on official data provided by hydrometeorological services. Using all available data on historical floods, the basic statistical-stochastic analysis was performed, and the results of the analysis were linked to the data, which, according to different scenarios of climate change, are expected for the considered Danube sector.
Keywords: historical flood, climate change, statistical-stochastic analysis, archive data, traces of high water.
Introduction
Floods belong to extreme natural phenomena, which often occur on many world rivers as well as in the Danube basin. The first evidence of recorded floods on the Danube dates back to 1012.
The aim of this paper is to “draw closer” the results of research of the occurrence of historical floods to the wider professional public of our region from the Middle Ages to the present, which were thoroughly analysed in the project:
The “Flood Regime of The Rivers in the Danube River Basin” which, through the Regional Cooperation of the Danubian countries within the International Hydrological Program IHP UNESCO, is carried out by the Slovakia National Committee for IHP UNESCO at the Institute of Hydrology of the Slovakia Academy of Sciences. The project coordinator is Dr. Pavla Pekarova from the Institute of Hydrology. Representatives of the following national committees of the Danube countries participate in the project’s realization: Germany, Austria, the Czech Republic, Slovakia, Hungary, Serbia and Slovenia. The project contains ten chapters with different executives from the countries participating in the project (Pekarova et al., 2018). Representatives of participating countries provide the necessary hydrometeorological data for all chapters.
Available Hydrometeorological and Other Data on Historical Floods
Data on phenomena of historical floods in the Danube basin in the past exist in various historical archives and documents starting from 1012. In Fig. 1 the Danube River basin with water gauge profiles is shown.
Many scientists in the Danubian countries have dealt with various written traces and reports. Much of this information was mostly original records of registered floods, newspaper reports, chronicles, official letters, books, maps of flood zones, and photographs. Original records (manuscripts) generally contain a brief description of the flood event, usually the time of the occurrence of the flood and the reached river levels. Locations commonly mentioned in the upper Danube basin are Passau, Linz, Mauthausen, Grain, Ybbs, Melk, Krems and Hainburg on the Danube. These historical records cover the period up to 1501.
According to Kresser (1957) and Horvatova (2003), the oldest recorded flood of the Danube is from 1012. The other floods occurred periodically and, according to documents and historical analogues, appeared in the following years: 1210, 1344, 1402, 1466, 1490, 1499 1501, 1526, 1572, 1594, 1598, 1670, 1682, 1721, 1787, 1809, 1876, 1897, 1899, 1954, 1965, 2002. According to Kresser (1957), the largest flood of the Danube occurred in 1501, when maximum flow of 12000m^{3}/s was estimated in Linz and 14000 m^{3}/s in Stein Krems.
Figure 1: The Danube River basin with water gauge profiles.
Floods in the Middle Ages from 1012 to 1500
Medieval floods of the Danube between the Austrian-Slovakian-Hungarian border was most detailed described by Kiss (2011) in his doctoral dissertation. The largest floods were marked by summer floods from: 1012, 1235, 1316, 1402, 1414, 1432 and 1490, which can be seen in Figure 2.
Figure 2: Floods on the upper Danube from 1000 to 1500 according to Kiss (2011): red - summer floods, blue - winter floods.
In general, it can be said that the 15th century is known for the appearance of significant floods in the Danube River basin.
Floods in the Period from 1501 to 1820
There are many recorded traces of high waters on historical buildings in Germany and Austria in the period after 1500 (Kiss and Laszlovszky, 2013). These are buildings in the cities directly adjacent to the Danube, such as Vilshofen, Passau, Linz, Mauthausen, Ybbs, Melk, Emmersdorf on the Danube, Durnstein, Spitz, Stein-Krems, Hainburg and Budapest. These traces were the basis for the reconstruction of the Danube water level, which enabled the understanding of the significance of individual floods and their mutual comparison and ranking. It should be said that these data must be carefully considered, since Danube morphology has changed over the centuries. Also, many historic buildings have been reconstructed in the meantime, so the issue of the correct transmission of the recorded traces of high waters can be debatable. Therefore, other archival materials were used for accurate description of these floods.
The largest flood, which is relatively reliably marked at several historic buildings along the Danube, appeared at the sector between Passau and Bratislava in 1501 (Kresser, 1957; Rohr, 2005). As already mentioned, the estimated peak of the flood wave was 12000m^{3}/s in Linz and 14000m^{3}/s in Vienna. During this period, maximum flows were recorded at Ybbs exceeding 11000m^{3}/s, as summer waves in June 1682 and October 1787, as well as the “rain” wave on March 2nd, 1862. Figure 3 shows all reconstructed flood peaks of flood waves registered on the Danube in the period 1501-1876 in the sector from Kienstock to Bratislava. Red signifies summer flood waves and blue winter flood waves. From 1876 on the same graph, the maximum annual flows of the Danube river near Bratislava obtained from the base of the hydrometeorological Service of Slovakia were applied.
Figure 3: Floods at the Danube in the period 1501–1876 at Kienstock-Bratislava sector.
Floods in the Period 1821 to 2013
In the last fifteen years, several significant floods appeared in the Danube Basin, in the upper Danube in June 2013 and in August 2002, and in the central and lower Danube in the period March-April 2006.
The highest maximum annual flows in the upper Danube were recorded in Krems / Kienstock: 11900m^{3}/s in 2013, 11306m^{3}/s in 2002 and 11200m^{3}/s in 1899. In Bratislava, the maximum annual flow was in 1899. At the Danube Delta, according to Bondar and Panin (2001), the maximum annual flow was estimated at 20940m^{3}/s during the July 1897 flood.
The Statistical-Stohastic Character of Multi-Year Series of Historical Floods Along the Danube River
Available Time Series
In addition to the historical maximum flows shown in Figs. 2 and 3, gauge data at the following hydrological stations along the Danube River: Berg, Ingolstadt, Regensburg, Hofkirchen, Achleiten, Wien, Bratislava, Bezdan, Bogojevo, Pančevo and Orsava were needed for statistical-stohastic analysis.
The available multi-year data enabled the formation of two types of time series for the statistical-stochastic analysis:
- Series of maximum annual flows;
- Coupled series of maximum annual flows (Qmax) and maximum volumes (W_{max}) – (Q_{max}∩W_{max})
Series of maximum annual flows can be formed at all of the above mentioned hydrological stations, for the periods from the beginning of the station operation to date. However, for the upper Danube sector, it is possible to combine series of historical floods from the first recorded flood (from 1012) to the present. The problem is that the data of the Middle Ages, due to the manner of registration and collection, are insufficiently reliable, so, in order to obtain a time series as long as possible, a unique series was formed by simply merging series of historical floods from 1501 and series of registered maximum annual flows of the Danube near Bratislava, as shown in Figure 3.
The coupled series of maximum annual flows and maximum volumes - (Q_{max} ∩W_{max}) were formed on the basis of gauged flow data at all of these hydrological stations.
Criteria for Historical Floods Selection
The basic parameters for the historical flood definition are combined (simultaneous) values of the maximum ordinates of the hydrograph and the volume of the flood wave, which are essentially random variables, which follow to the two-dimensional law of distribution probability. According to the criterion, the “historical flood” is the flood where values of the basic parameters of the hydrograph: the maximum ordinate of the hydrogram Qmax (m3/s) and the volume of the flood wave W_{max} (106 m^{3}) are above the probability of exceedance (Prohaska and Ilić, 2017):
P(Q_{max} ∩ W_{max}) ≤ P {Q_{max} ≥ q_{max,p}) ∩ (W_{max} ≥ w_{max,p})} = p = 1.0% (1)
The PROIL model (Ilić et al., 2017) is used to define the two-dimensional law of distribution (coincidence) i.e. the probability of exceedance.
In Figs. 4 and 5 are the results of the model PROIL presented grafically, for h.s. Achleiten in the Upper Danube and Bezdan in the Middle Danube.
For all hidrological stations, considered in this paper, return periods of flood events which exceed probability P{(Q_{max}≥q_{max,P})∩(W_{max}≥w_{max,P})}≥1.0% were estimated. The results are shown in Table 1.
Figure 4: Coincedence of flood hydrograph parameters of the Danube River at h.s. Achleiten with estimated return period of the biggest gauged flood in 2013.
Figure 5: Coincedence of flood hydrograph parameters of the Danube River at h.s. Bezdan with estimated return period of the biggest gauged flood in 1965.
Table 1: Estimated return periods of historical floods registrated along the Danube River reach from h. s. Berg to h. s. Orsova.
Estimation Methodology of Character of Multi-Year Historical Floods Series Along the Danube River from the Climate Change Point of View
Regarding flooding in river basins, most of the existing climate change models, most commonly found in practice, estimate that floods will intensify in the future in terms of increasing the value of the maximum ordinates of hydrographs and also increased flooding. Generally, the trend of increasing maximum flows is expected, as well as the trend of increasing incidences of floods.
Linear trends in the following time series have been analyzed to confirm or disprove this claim in the considered Danube sector:
- maximum annual flows,
- frequency of occurrence of historical floods.
For the needs of the trend analysis in the series of annual maximum flows, the longest possible single series was used compiled from the sub-series of the reconstructed floods in the Kienstock-Bratislava sector from the period 1501-1986 and sub-series of the annual maximum flows of the Danube near Bratislava, taken from the base of the Hydrometeorological Service of Slovakia (Pekarova, 2013). The results of the linear trend calculation in the series of annual maximum flows of the Danube River in the Kienstock-Bratislava sector are shown in Figure 6.
Figure 6: Trend in the maximum flows series of the Danube in the period 1501–2013 on the Kienstock-Bratislava sector.
Based on the results shown, it can be concluded that in the longest possible series of maximum flows at the Danube at the observed sector of Kienstock-Bratislava there is no trend of increasing flows.
The phenomenon of flood frequency along the Danube has been analyzed at all 11 hydrological stations. In accordance with the adopted criterion, defined by Eq. 1, time series of “historical floods” are separated chronologically as well as floods that have the probability of exceedance:
P (Q_{max} ∩ W_{max}) ≤ P {Q_{max} ≥ q_{max,p}) ∩ (W_{max} ≥ w_{max,p})} =p = 2.0 % (2)
On the basis of these data, new time series have been formed of a number of hydrological stations with floods that exceed the following return periods in years:
- number of stations with T ≥ 50 years floods,
- number of stations with T ≥ 100 years floods,
- number of flooded stations with return periods 50 ≤ T ≤ 100 years.
The chronological representation of these time series is shown in Figure 7, with the defined linear trend equations. In the same graph, the field corresponding to the number of hydrological stations in function with the equation of the linear trend line is also marked.
Figure 7: Chronological presentation of the number of hydrological stations along the Danube with the flood occurrence of different return periods and the total number of hydrological stations in function with the trend lines.
The trend lines shown in Figure 7 show a positive trend in all considered time series, which may, at first glance, have negative consequences in assessing and interpreting their statistical significance. Namely, the trend is, in this particularless case, a direct consequence of the considered lengths of the time periods and availability of data, primarily in the periods before 1930 and 1900, when a significantly smaller number of stations were in operation. Therefore, in order to eliminate these deficiencies, a new time series of the number of stations with floods, for different return periods, and the total number of stations in function has been formed, as shown in Figure 8.
Figure 8: Chronological presentation of the ratio of the number of hydrological stations along the Danube with the flood occurrences of different return periods and the total number of hydrological stations in function with trend lines.
The defined trend lines in the series for ratio between the number of hydrological stations with floods for different return periods and the total number of hydrological stations in operation, show that the trends in the series for return periods T ≥ 50 years and 50 ≤ T ≤ 100 years are negative, while the series for the return periods T ≥ 100 years (“historical floods”) showed a positive trend. The positive trend for the series of “historical floods” is insignificant, since the increment of the ratio of 0.05 for the next 100 years, and the assumption that all 11 hydrological stations considered will be operational, indicates that the number of floods will increase for 0.55, which is negligible.
Conclusion
The statistical and stochastic analysis carried out on the time series of maximum flows and the number of stations with the occurrence of floods of various return periods have unambiguously indicated that along the considered Danube sector there is no impact of climate change on increasing maximum flows and frequency of floods, which is in contradiction with most theoretical considerations of the impact of climate change on water resources.
Acknowledgments
The presented results and analyses are the subject of research of the scientific project Assessment of the Impact of Climate Change on Water Resources of Serbia (TR-37005) for the period 2011-2019 financed by the Ministry of Education, Science and Technological Development of the Republic of Serbia. The authors wish to thank the Ministry for providing financial assistance and support.
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