Institute of Hydrology Slovak Academy of Sciences
MULTIANNUAL RUNOFF VARIABILITY IN THE UPPER DANUBE REGION
DDDrrrSSSccc... TTThhheeesssiiisss
RRRNNNDDDrrr... PPPaaavvvlllaaa PPPeeekkkááárrrooovvvááá,,, CCCSSSccc...
Bratislava, May 2009
Title: Multiannual runoff variability in the upper Danube region Author: RNDr. Pavla Pekárová, CSc. Publisher: IH SAS Racianska 75, 831 02 Bratislava, Slovakia Year of publication: May 2009 Publication: first Printing: 10 pcs. print version, 50 pcs. CD ROM version WEB link http://147.213.145.2/pekarova
© P. Pekárová
So as the day follows the night because of the Earth’s rotation around its axis, so as the winter follows the summer because of the Earth’s circulation around the Sun, so as the ice ages follow the inter-ice ages because of the Milankovich’s cycles, so also follows the multi-annual dry and wet periods, probably because of the Sun’s deviation from the solar system center of gravity, changes in the solar activity, and thermohaline circulation.
Pavla Pekárová
P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region CONTENTS
PREFACE 10
OBJECTIVES OF THE THESIS 14
1 GAP-FILLING IN DAILY FLOW RECORDS OF THE DANUBE AT BRATISLAVA FOR 1876–1890 15
2 RUNOFF REGIME ANALYSIS 24
2.1 CHANGES IN THE LONG-TERM DAILY REGIME OF THE DANUBE FOR THE PERIODS 1876–1940 AND 1941–2005 24 2.2 CHANGES IN THE LONG-TERM MONTHLY RUNOFF DISTRIBUTION OVER A YEAR 27 2.3 CHANGES IN THE ANNUAL STREAM FLOW CHARACTERISTICS 29 2.4 CONCLUSION 32
3 HURST PHENOMENON, STATIONARITY AND MULTI-ANNUAL VARIABILITY OF RUNOFF 33
3.1 ANALYSIS OF NATURAL FLUCTUATIONS AND LONG-TERM TRENDS OF RUNOFF OF THE MAIN WORLD RIVERS 35 3.1.1 Identification of the long-term runoff trend 39 3.1.1.1 Europe 39 3.1.1.2 North Asia 41 3.1.1.3 North America 41 3.1.1.4 South America 41 3.1.1.5 Africa 42 3.1.1.6 South-eastern Asia and Australia 42 3.1.2 Identification of the long-term variability 43 3.1.2.1 Brief overview of the spectral analysis of random processes 43 3.1.2.2 Combined periodogram method 44 3.1.2.3 Multi-annual periods 45 3.1.3 Identification of the shift of extremes 49 3.1.4 Teleconnection ENSO and NAO phenomena with long-term runoff oscillation 52 3.2 ANALYSIS OF NATURAL FLUCTUATIONS AND LONG-TERM TRENDS IN ANNUAL DISCHARGE ALONG THE DANUBE RIVER 56
4 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.3 ANALYSIS OF NATURAL FLUCTUATIONS AND LONG-TERM TRENDS OF DANUBE DISCHARGE AT BRATISLAVA 62 3.4 CONCLUSION 65
4 LONG-TERM PROGNOSIS OF DANUBE DISCHARGE USING ARMA MODELS AND HARMONIC FUNCTIONS 66
4.1 SCENARIOS BASED ON ANALYSIS OF MONTHLY DISCHARGE SERIES 67 4.2 ARIMA MODELING APPROACH 69 4.2.1 Yearly Danube discharge prediction at Turnu Severin 70 4.2.1.1 Autoregressive model with the harmonic component for Danube: Turnu Severin 71 4.2.1.2 The autoregressive component specification 73 4.2.2 Monthly Danube discharge prediction at Bratislava 76 4.2.2.1 Markov model based on harmonic functions (hidden periods) 76 4.2.2.2 Box-Jenkins SARIMA model involving one regressor – long-term cycle 77 4.3 CONSLUSION 78
5 ASSESSMENT OF T-YEAR MAXIMUM DISCHARGE OF THE DANUBE AT BRATISLAVA 79
5.1 HISTORY OF THE DANUBE FLOODS 80 5.2 ANNUAL MAXIMUM DISCHARGE METHOD 86 5.3 PEAKS OVER THRESHOLD (POT) METHOD 88 5.3.1 Number of peaks 89 5.3.2 Peaks over threshold 90 5.3.3 Annual maximum of POT series 91 5.3.4 Return period 92 5.4 ASSESSMENT OF THE MAXIMUM T-YEAR WATER LEVEL 93 5.5 FLOOD RISK ASSESSMENT 95 5.6 CONCLUSION 95
6 ASSESSMENT OF MAXIMUM RUNOFF VOLUME FOR A GIVEN DURATION OF T-DAY FLOWS (1876–2005) 96
6.1 THEORETICAL EXCEEDANCE CURVES OF MAXIMUM DANUBE RUNOFF WAVE VOLUMES 101 6.2 MAXIMUM RUNOFF VOLUMES ANALYSIS FOR TWO PERIODS: 1876– 1940 AND 1941–2005 102 6.3 CONCLUSION 104
5 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
7 CATASTROPHIC FLOOD SCENARIO FOR THE DANUBE RIVER AT BRATISLAVA 105
7.1 ANALYSIS OF FLOODS REGIME OF THE DANUBE RIVER AT BRATISLAVA 105 7.1.1 Flood occurrence probability for the Danube River at Bratislava 107 7.1.2 Is the runoff extremality of Danube at Bratislava rising? 109 7.2 EXTREME FLOOD WAVE SCENARIOS FOR DANUBE AT BRATISLAVA 110 7.3 CONSLUSION 113
8 CATASTROPHIC FLOOD SCENARIO OF THE DANUBE BETWEEN DEVÍN AND NAGYMAROS 114
8.1 RUNOFF VOLUME BALANCE IN BRATISLAVA–KOMÁRNO RIVER PART 115 8.2 FLOOD TRAVEL TIMES ON DANUBE 116 8.3 DESCRIPTION OF THE NLN-DANUBE MODEL 119 8.3.1.1 NLN-Danube model parameters 121 8.3.2 Results of floods simulation in the reach Devín (Bratislava)–Nagymaros 122 8.3.2.1 NLN-Danube model calibration 124 8.3.2.2 NLN-Danube model verification 130 8.3.2.3 Simulation results - catastrophic flood scenario of the Danube between Devín and Nagymaros 130 8.4 CONCLUSION 131
9 THE THESIS RESULTS AND CONTRIBUTION TO PRACTICE 133
REFERENCES 135
APPENDIXES 143
APP. I. FULL LIST OF STUDIES IN MONOGRAPHS AND JOURNALS CONNECTED TO THIS DRSC. THESIS 143 APP. II. DANUBE 3-HOURLY CATASTROPHIC FLOOD SCENARIO 147
6 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Acknowledgement
This Thesis is an account of my research results accomplished over the period 1996–2009. The hydrological regime of the Slovak and other main world rivers is studied in terms of the catastrophic scenarios and flood simulations for the Danube River. These tasks were accomplished within several scientific project, e.g.: • The joint trilateral Slovak-Hungarian-Austrian project 6/1999 “Improvement of the flood forecasting in the middle Danube basin” coordinated by the Slovak Hydrometeorological Institute(SHMI) in Bratislava. • The joint VEGA SR project 2/6008/99 of the IH SAS and Slovak Technical University (STU) „“Regional hydrologic scenarios for the integrated management of the quantity and quality of surface water resources in Slovakia “, coordinator of the project: RNDr. P. Pekárová, CSc., (1999–2001); • The joint APVT SR project 51-006502 of the IH SAS, SHMI, STU, Faculty of Mathematics, Physics, and Informatics UK, and Faculty of Natural Sciences UK „Assessment of climate change impact on the selected components of the hydrosphere and biosphere in Slovakia“, coordinator of the project: RNDr. P. Pekárová, CSc., (2002–2005); • The joint VEGA SR project 2/5056/25 of the IH SAS and STU “Scenarios of the extreme hydrological events for the integrated management of Slovak rivers “, coordinator of the project: RNDr. P. Pekárová, CSc., (2005–2007); • The joint APVV SR project 51-006502 of the STU and IH SAS „Hybrid flow forecasting models“, (2008–2010); • International project No. 9 within the Regional co-operation of the Danube countries in the framework of the IHP UNESCO 2.4 “Flood Regime of Rivers in the Danube River Basin”, international coordinator: RNDr. Pavla Pekárová, CSc., (2007–2011); www.ih.savba.sk/danubeflood
I would like to express my gratitude to Dr. Aleš Svoboda for valuable reflections and motivation during my scientific work and to Dr. Juraj Pacl and Dr. Peter Škoda for providing historical documents necessary for processing the mean daily flow data of the Danube at Bratislava for 1876–1990. The hydrologic data from Slovakia were obtained from the SHMI in Bratislava. The data were partially obtained also from the official historical publications included in references. The long annual discharge data series of all the continents were obtained from the following data sources: Global Runoff Data Center in Koblenz, Germany; CD ROM of the Hydro-Climatic Data Network (HCDN), U.S. Geological Survey Streamflow Data Set for the United States; CD-ROM World Freshwater Resources prepared by I. A. Shiklomanov in the framework of the International Hydrological Programme (IHP) of UNESCO; URL http://waterdata.usgs.gov. Last, I wish to thank all colleagues from Slovakia and abroad also, for providing me with the above mentioned data.
7 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region Declaration
I declare that for any material submitted in this thesis I did not previously received any scientific degree or diploma. The Thesis includes selected paragraphs from three monographs, from four papers published in prestigious foreign CC journals, from one Slovak journal and from one conference paper. I am the principal author of these publications.
AAA01 PEKÁROVÁ, Pavla - ONDERKA, Milan - PEKÁR, Ján - MIKLÁNEK, Pavol - HALMOVÁ, Dana - ŠKODA, Peter - BAČOVÁ-MITKOVÁ, Veronika. Hydrologic Scenarios for the Danube River at Bratislava. Ostrava: KEY Publishing, 2008. 159 s. ISBN 978-80-87071-51-9. – I. chapter AAB01 SVOBODA, Aleš - PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol. Flood Hydrology of Danube between Devín and Nagymaros. Bratislava: ÚH SAV; SVH, 2000. 96 p. ISBN 80- 967808-9-1. AAB02 PEKÁROVÁ, Pavla. Dynamika kolísania odtoku svetových a slovenských tokov. Bratislava: Veda, 2003. 221 s. ISBN 80-224-07801. ADCA01 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján. Spatial and temporal runoff oscillation analysis of the main rivers of the world during the 19th-20th centuries. In Journal of Hydrology. ISSN 0022-1694, 2003, vol. 274, no. 1, pp. 62-79. (2,16 - IF2007). ADCA02 MITKOVÁ, Veronika - PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján. Analysis of flood propagation changes in the Kienstock-Bratislava reach of the Danube River. In Hydrological Sciences Journal. ISSN 1335-6291, 2005, vol. 50, no. 4, pp. 655- 668. (1,6 - IF2007). ADCA03 PEKÁROVÁ, Pavla - PEKÁR, Ján. Long-term discharge prediction for the Turnu Severin station (the Danube) using a linear autoregressive model. In Hydrological Processes, ISSN 0885-6087, 2006, vol. 20, no. 5, pp. 1217-1228. (1,79 - IF2007). ADCA04 PEKÁROVÁ, Pavla - PEKÁR, Ján. Teleconections of Inter-Annual Streamflow Fluctuation in Slovakia with Arctic Oscillation, North Atlantic Oscillation, Southern Oscillation, and Quasi-Biennial Oscillation Phenomena. In Advances in Atmospheric sciences. ISSN 0256-1530, 2007, vol. 24, no. 4, pp. 655-663. (0,902 - IF2007). ADEA 1 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján. Long-term trends and runoff fluctuations of European rivers. IAHS Series No. 308, ISSN 0144-7815. IAHS, Wallingford, 2006, no. 308, pp. 520-525. ADFB 17 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján. Long-term Danube monthly discharge prognosis for the Bratislava station using stochastic models. In Meteorologický časopis. ISSN 1335-339X, 2007, Vol. 10, No. 2, pp. 211-218. AEC 1 MIKLÁNEK, Pavol - PEKÁROVÁ, Pavla. Flood Regime of the Danube River in Bratislava, Slovakia. In Proceedings International Conference Planning and Management of Water Resources Research Systems. ISBN 978-86-85889-19-6, (ed. Kastori, R.), Novi Sad: Academician Endre Papa, 2008, pp. 99-108.
Pavla Pekárová Bratislava, May 2009
8 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region Co-authors agreement
The co-authors of above mentioned publications agree, that theirs contribution to this work is less than 30%.
Ing. Veronika Bačová Mitková, PhD.
Ing. Dana Halmová, PhD.
RNDr. Pavol Miklánek, CSc.
Mgr. Milan Onderka, PhD.
Doc. RNDr. Ján Pekár, PhD.
Ing. Aleš Svoboda, CSc.
RNDr. Peter Škoda
Bratislava, May 2009
Full list of studies in monographs and journals relevant to this DrSc. Thesis is in Appendix I. Full texts of these publications are in Appendix III.
9 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Preface
With the increase of population – and with the development of civilization in general – an increase of vulnerability of the society is closely connected. It concerns also the threats by high floods as well as by incidents of long periods of droughts. Economic prosperity of each country is closely connected with the availability of sufficient water resources. In general, the economic development and increase of living standard, leads to higher demands of the water consumption (Oki et al., 2006) (even though e.g. the water consumption in Slovakia decreased after 1989 due to economic dampening and increased costs of water). Considering the fact that the water resources are limited, in many regions of the world the social and economic growth will be expressively limited in the future. The amount of water in rivers (the largest utilizable water resources) fluctuates to great extent, due to the Earth rotation around the Sun, and also due to Earth’s axis inclination to the ecliptic plane. In our geographical latitudes, most water in rivers occurs during the spring snowmelt runoff and during the summer atmospheric precipitation maximum, in the months of March (lowland rivers) to July (mountainous rivers). In general, at the end of summer and during the winter months, there is a water deficit in our rivers. On the southern hemisphere, the yearly cycle is opposite, the equatorial and polar regions exhibit their own annual patterns. The expressive seasonal runoff variability during the year, is causing serious problems during periods of the runoff surplus, as well as in water supply during the dry periods. One of the basic objectives of hydrology in the first half of the 20th century, was to propose such measures as to achieve outbalanced and controlled flows in rivers throughout the whole year. Today, water resources requirements are often controversial, depending on various users (water transport, energy production, irrigation, land drainage, protection against floods, industrial and municipal water supply, fish breeding, recreation, water pollution control, biodiversity preservation). These manifold requirements for water in land, inevitably call for an integral water management. With the increasing period of the river discharge observations, it is ever more confirmed, that the water resources utilization is not limited only by their annual evolution, but also by their multi-annual variability. The natural multiannual variability theory is not new (Williams, 1961; Balek, 1968). Already more than 50 years ago – during the Nasser (Asuan) dam design on the Nile – Hurst (1951) expressed the opinion that the whole Earth climatic system is subject to the long-term oscillations. By studying more than 900 time series of various data (Nile water levels of more than 790 years,
10 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region dendrochronological series, sediments of seas and lakes, etc.), he observed a particular behavior of these geophysical time series, which has become known as the „Hurst phenomenon“. Under this name is denoted the tendency of the dry and wet years to cluster together into longer dry and wet years periods. Hurst defined this character of the observed time series by mathematical expression: Rn/Sn = (n/2)h, where Rn is the cumulative sum of deviations from the arithmetic mean, and Sn is the standard deviation of the time series with length n. The h value represents the so called Hurst coefficient. Hurst calculated, that in the average, this coefficient for various geophysical time series, acquires the value h = 0.73. In case of an independent time series of the length n with a normal distribution, the Hurst coefficient should acquire the value of h = 0.5. Tendency of the hydrological time series to exhibit h higher than 0.5 indicates, that in these series the autocorrelation must exist, i.e. that from the statistical point of view, these series must be those with the long-term memory. This controversial discovery of Hurst is in the professional hydrological literature widely discussed, supported and rejected, up to these days. Existence of these regular long term cycles, namely breaks the axiom of independence of the hydrological time series elements. This axiom is a condition for calculation of all hydrological and meteorological characteristics, based on the observed time series. For instance, for determination of the frequency distribution curve of the mean annual discharges Qa, it is assumed that the Qa value does not depend upon its value of the preceding one, e.g. occurring 7-, 14-, 21-, 28-years ago. However, the Hurst coefficient 0.73 proves opposite. It documents, that in the natural time series, a long term fluctuations exist, in more or less regular cycles, with these cycles having a special character, preserved along its whole length. The correct identification (or an eventual clarification of the existence) of such long-term cycles in a particular region, presents an opportunity to predict the runoff development in that region, for 20–30 years in advance. For correct decisions in water resources management in each country, such estimates and predictions would have an immense economical importance (construction of water storage reservoirs, energy production in hydroelectric plants, needs of the water for irrigation, etc.) For instance, in Slovakia after a series of 13 dry years 1982–1995 (Fig.1), a more wet period started after 1996, with incidence of serious floods each year. Floods in recent years, caused heavy damages on private and communal property, even the losses on life in Slovakia. E.g. in catastrophic flood on the Mala Svinka river (eastern Slovakia) in 1998, 47 life’s were lost, during the 2002 summer floods in Slovakia, there were two life’s lost. To mention only few of such events in our region: floods in Moravia (Czech Rep.) in 1997, on the upper Danube in August 2002, in March – April 2006, in the August 2002 in the Czech Rep., or the 2008 summer flood in Ukraine, caused the immense economic damages to property.
11 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
extremly wet 840 wet period period dry period 800 1938-1941 1982-1995
P [mm] 760
720
680 1880 1900 1920 1940 1960 1980 2000
Fig. 1 Moving averages of the mean annual areal precipitation amounts from 203 stations, territory of Slovakia, development within 1881–2008. Extremely dry period 1981–1993, and the wet period 1938–1941.
In this dissertation, I tried to find answers to the following questions: • Do exist regular multi-annual natural cycles in discharge time series? • Is it possible to identify the length of these cycles? • What phenomenon is the cause of the natural multi-annual runoff variability? • What will be the probable runoff development in upper Danube basin in the nearest future years? • Do the hydrological extremes rise? • Will the hydrologic characteristics variability rise? • Do the relationships exist between the dry/wet periods incidence and other (geophysical) factors? It is not easy to answer these questions. In looking for serious answers, it is necessary: • to start from a detailed statistical analysis of as long as possible hydrological data time series (precipitation, discharges), and to eliminate to maximum extent the subjective researcher’s view; • because of the hydrological characteristics regional character, to complete data series by archived material from the respective region, and to try for own analyses – when identifying changes in the data series – to apply many available mathematical tools, to use recent methods of the mathematical statistics, and of the stochastic mathematical modeling; • to compare runoff changes in catchments influenced by the anthropogenic activities to those unchanged; • to take into account several related phenomena: - first of all the anthropogenic activities impact upon the runoff changes in catchments – reservoir constructions, river embankments, areal drainage, etc.,
12 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
- impacts of the temperature increase, - extraterrestrial impacts – e.g. of the Solar activity, Lunar cycles, - impacts of phenomena like ENSO (El Niño Southern Oscillation), NAO (North Atlantic Oscillation). QBO (Quasi biennial Oscillation), AO (Arctic Oscillation), • to analyze these phenomena not only in the regions of Slovakia (or Europe), but also to take into account the mutual teleconnection of climatic, meteorological and hydrologic phenomena over the whole Earth. Only after an objective evaluation of the observed time series, it is possible to express the opinion, whether the hydrologic cycle is subject to permanent irrevocable change, or hydrologic cycle has a temporal, natural, periodical behaviour only. Be it the climate change – change due to the human activities – or a combination of more phenomena, with different weights of their influence upon the runoff? The aim of this Thesis is not the one on climate change impacts upon the runoff changes, but study of the long term natural runoff variability. For studying of the natural runoff variability in any of the river gauging stations, existence of the long term reliable river discharge observations is inevitable. The corresponding catchment should be large enough as to eliminate the local runoff fluctuation impacts, and also for wider regional observations representativeness. As already mentioned, such catchments with the artificial impacts upon runoff (anthropogenic impacts like water transfers to neighboring catchments, reservoirs for multiannual runoff control, etc.) should be disqualified for such analyses. For the above reasons, I have concentrated myself in this Thesis to multiannual variability of the mean annual discharges of the Danube River, gauging station at Bratislava. Since 1876, reliable water level observations are preserved at this station. Discharge measurements here, can be considered representative as to the runoff regime for the upper Danube region/basin. According to Directive 2007/60/EC of the European parliament and of the Council of 23 October 2007 on the assessment and management of flood risks (Directive, 2007), the EU member states shall prepare, inter alia, flood hazard maps and flood risk maps. Flood hazard maps shall cover the geographical areas which could be flooded according to the following scenarios: a) floods with a low probability, or extreme event scenarios; b) floods with a medium probability (likely return period ≥100 years); c) floods with a high probability, where appropriate. When defining partial objectives of this Thesis, I kept close to the above EC Directive (2007). One of such objectives was to elaborate a Danube flood scenario for the Bratislava gauging station, and its routing downstream to the Štúrovo gauge (close to border with Hungary).
13 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region Objectives of the Thesis
The presented Thesis summarizes results of my more than fifteen years research activities in the field of long-term runoff prediction.
Scientific objectives of the Thesis are: 1. To reconstruct the Danube daily discharge series at Bratislava (1876– 1890) based upon daily observations of water levels at the Bratislava gauge; 2. to analyze variability and long term trends of the selected discharge Danube series characteristics for Bratislava gauge; 3. to propose and develop a combined periodogram method for more exact spectral density identification in discharge time series; to analyze trends and periodicity in discharge long term series; to identify occurrence of the wet and dry periods over the world, to identify the influence of the NAO/AO/ENSO/QBO phenomena and the Sun activity on the runoff variability; 4. to present some long-term stochastic prediction methods; to use two of them, the classical harmonic analysis and the Box-Jenkins methodology in order to provide a long-term prediction for Danube discharge time series for the next decade; 5. to analyze the historical Danube floods at Bratislava, in order to determine the N-year floods at that gauge; 6. to analyze the respective flood volumes for the Danube at Bratislava; 7. in sense of the Directive (2007), to elaborate for the Bratislava Danube gauge the catastrophic – 1000-year flood wave scenario; 8. to develop a mathematical model, and to simulate by it the catastrophic flood wave routing through the Slovak Danube reach (Bratislava– Štúrovo).
The Thesis has eight chapters according to the eight scientific objectives mentioned above. It provides a wide survey of the obtained results from the methodological approach to the time series analysis, through stating new hypotheses on the discharge oscillations, up to the application of theoretical results to the practice.
14 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
1 Gap-filling in daily flow records of the Danube at Bratislava for 1876–1890
The Danube is the second greatest river of Europe after the Volga. The Danube River basin (Fig. 1-1) is situated in Central and Eastern Europe. Upstream the Bratislava gauge (1868.8 r km) the river drains an area of 131 338 km2. Long- term mean annual runoff (1876–2005) of the Danube at Bratislava is 64 925 mil. m3 (Pekárová et al., 2008); mean annual discharge is 2058 m3 s-1 and the annual specific yield is 15.68 l.s-1km-2. The Slovak portion of the Danube river spans from 1708.2 river km (mouth of the Ipeľ River) to 1880.2 rkm (mouth of the Morava River), with a total length of 172 km. Upstream Bratislava, the river flows in a concentrated channel with relatively steep riverbed slope. After leaving the Small Carpathians the river looses its slope and flows over an alluvial cone creating a complicated network of river branches downstream to the town of Medveďov. In order to evaluate the hydrological regime of the upper part of the Danube River, the average values of daily discharge readings taken at the Bratislava gauging station were used.
SK Achleiten Nagymaros
Bratislava
a
v a S L
r O o V Bratislava A K Orsova
M I A A D U Hrusov a n S u b T e R The Gabcikovo water I A power station
Danube H U N G A R Y
Fig. 1-1. Location of Danube basin, Bratislava station.
15 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
First water stage measurements on the Danube River at Bratislava were made in 1823. The gauge datum was at 131.08 m J (Adria system). After 1876 the average daily river stages were recorded in Hungarian yearbooks Vízallasok (1890) (Fig. 1-3a,b). In 1942, the Bratislava gauge datum has been lowered by two meters, down to 129.08 m J (Adria system). After 1964, the gauge datum was determined at 128.46 m B.p.v (Baltic system) (Fig. 1-2). First discharge observations at Bratislava, based on measurements of flow velocities, were available as early as 1882 (Škoda and Turbek, 1995; Svoboda et al., 2000). Observations revealed that the river channel at Bratislava was subject to scouring long time before the river was dammed at the town of Čuňovo (due to construction of the Gabčíkovo Hydro Project) in 1992. Deepening of the river’s channel bottom can be assessed from the changes in the rating curve, as shown in Fig. 1-4 (Mitková, 2002; Miklánek et al., 2002).
Water stage during August 2002 flood. 993 cm, 10 370 m3s-1.
Water stage during September 1899 flood. 970 cm, 10 870 m3s-1.
Fig. 1-2 Location of water gauging station in Bratislava. (Foto: Miklánek, February 2008).
16 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Water stage measurements on the Danube River at Bratislava have been routinely processed since 1901. In 2003, the staff of the SHMI (Slovak Hydrometeorological Institute) extended the average daily discharge series by adding data from 1891–1900.
Fig. 1-3a A schematic of the river stage gage at Bratislava, 1895 (from VITUKI’s archives, photo: Miklánek, 2005).
17 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Fig. 1–3b Hungarian historical Danube water- level yearbooks (IH SAS archives, photo Miklánek, 2005).
18 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
1000 2002 1954
900 III. 1899 800 II. 700 I. 600
2002 50 before 1903 100 Q 500 Q WS [cm] 1991 400
300
200 1965 100 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 Q [m 3s -1]
Fig. 1-4 Changes of the Danube rating curve at Bratislava gauge (related to the present gauge zero level).
In 2007, the average daily flow records were extend by adding another 15-years of observations 1876–1890 (Pekárová et al., 2007a). The historical rating curve, valid before 1903 (according to Zatkalík (1965) and Pacl (1955)), was approximated by two third-order polynomials. The average daily water stages for this period were obtained from data sets recorded in archive yearbooks (Vízallasok, 1890). Using discharges (Q) and water stages (WS) for gauge heights below 480 cm, and above 480 cm, the following equations were derived:
Q = -0.0000077 WS3 + 0.02018 WS2 – 3.86 WS + 597.366, for WS ≤ 480 (1.1)
Q = 0.0000016 WS3 + 0.0098 WS2 + 0.0978 WS + 52.69, for WS > 480. (1.2)
The average daily water stages were converted into average daily discharges over the period of fifteen years (1876–1890). Adding these data to the existing records allowed to create a 130-year series (see Fig. 1-5) suitable for a detailed statistical analysis of changes in the runoff regime. Monthly data of the 1876–1890 period are presented in Table 1-1 and Table 1-2.
19 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
12000 2400 1876-1940
10000 2000
8000 1600 ] -1 ] s -1 3 s 3 6000 1200 [m Q [m mov
4000 800 Q
2000 400
0 0 1876 1886 1896 1906 1916 1926 1936
12000 2400 1941-2005
10000 2000 dry period wet period
8000 1600 ] -1 ] s -1 3 s 3 6000 1200 [m Q [m mov
4000 800 Q
2000 400
0 0 1941 1951 1961 1971 1981 1991 2001 Fig. 1-5 Average daily discharges Q of Danube at Bratislava gauge, and their 5-year moving averages Qmov (the bold line), period 1876–2005.
Table 1-1. Average 10 years monthly discharge of Danube at Bratislava 1876-2005
Danube I II III IV V VI VII V IIIIX X XI XII year XI-IV V-X 1876-1885 2300 2254 2251 1975 2336 2629 2485 2244 1830 1596 1524 1724 2095 2004 2187 1886-1895 1577 1670 1966 2301 2563 2740 2547 2387 2130 1580 1400 1244 2010 1693 2324 1896-1905 1391 1542 1974 2531 2835 2869 2431 2517 2132 1521 1304 1291 2030 1672 2384 1906-1915 1498 1487 2163 2402 3191 2947 3170 2317 2267 1642 1356 1566 2172 1745 2589 1916-1925 2097 1712 1709 2168 2917 2642 2574 2325 2224 1624 1415 1495 2077 1766 2384 1926-1935 1436 1442 1660 2095 2458 2835 2530 2332 1713 1497 1543 1235 1900 1569 2228 1936-1945 1398 1801 2408 2866 2790 3270 2632 2380 2075 1906 1798 1601 2244 1979 2509 1946-1955 1572 1635 2071 2343 2406 2425 2955 2096 1480 1219 1328 1362 1910 1718 2097 1956-1965 1314 1585 2117 2368 2837 3182 2667 2291 1679 1436 1385 1457 2028 1704 2349 1966-1975 1582 1825 1853 2384 2671 2872 2978 2442 1756 1495 1431 1682 2083 1793 2369 1976-1985 1706 2038 2127 2391 2609 2686 2464 2305 1799 1566 1431 1649 2064 1890 2238 1986-1995 1763 1639 2221 2593 2563 2720 2397 1976 1715 1295 1477 1860 2020 1925 2111 1996-2005 1690 1916 2569 2474 2705 2407 2436 2123 1934 1842 1771 1642 2127 2010 2241
20 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 1-2. Mean monthly discharge of Danube at Bratislava station
Year I II III IV V VI VII VIII IX X XI XII mean XI-IV V-X 1876 3055 4116 4900 3136 2438 3016 2791 1753 1771 1356 1220 1232 2556 2943 2188 1877 1006 2801 2112 2668 2533 3128 2703 2087 1786 1056 961 1073 1985 1770 2215 1878 1950 1447 3016 2608 3743 2719 2495 2600 2305 1798 1645 1323 2309 1998 2610 1879 1573 1563 1670 1903 2259 2901 3000 2207 1524 1413 1469 2153 1973 1722 2217 1880 5117 4366 2357 1657 2304 2464 2334 3601 2061 2003 2094 2754 2754 3057 2461 1881 2640 2714 2804 1885 2754 2707 2260 1600 2252 1458 1635 1067 2144 2124 2172 1882 889 810 1081 1020 1275 1728 1999 3065 2084 2044 2304 2499 1738 1434 2033 1883 3876 1676 1514 1890 2349 3550 2743 2124 1485 1486 1301 1619 2139 1979 2290 1884 1601 1492 1408 1732 2061 2347 2597 2116 1715 1690 1311 1459 1797 1500 2087 1885 1291 1556 1643 1248 1647 1727 1928 1282 1318 1655 1302 2059 1556 1516 1593 1886 1147 927 1486 2269 1535 2374 2332 2303 1568 1021 906 1209 1591 1324 1855 1887 1542 1446 1280 1700 2270 2285 1600 1686 1294 958 1274 1341 1557 1431 1682 1888 2206 1320 2307 3306 3253 2694 2658 2948 2845 2159 1461 1125 2363 1954 2760 1889 1718 1480 1706 2976 3250 2332 2413 2528 2084 2200 1621 1093 2121 1766 2468 1890 1443 1301 1352 1473 1990 2105 3396 2703 4594 1862 2156 1716 2174 1573 2775 1891 2673 2283 2754 1809 2640 2338 2820 2942 1813 1130 984 1033 2104 1923 2280 1892 1873 2903 1875 2327 2694 5085 3629 2053 2520 1692 1449 1272 2440 1950 2946 1893 1094 2863 2783 2158 2433 2168 2153 1799 1310 1415 1411 1029 1878 1890 1880 1894 1041 1251 1590 1325 2188 2783 2004 2512 1960 2237 1498 1007 1785 1285 2281 1895 1031 930 2531 3673 3377 3235 2462 2398 1309 1127 1241 1618 2084 1837 2318 1896 1602 1022 3271 2696 4216 4319 3093 4098 3064 1953 1294 916 2640 1800 3457 1897 809 2308 2391 2199 3633 3527 2612 5007 3231 1753 1103 1087 2473 1650 3294 1898 887 1605 1948 2130 2499 2654 2662 1879 1140 1129 1108 948 1716 1438 1994 1899 1495 1363 1033 1905 3162 2245 2638 1738 4363 1978 1202 1246 2032 1374 2688 1900 2487 2558 2299 3447 3088 3077 2450 1871 1140 876 1192 1431 2156 2236 2084 1901 905 827 1943 2646 1630 2162 1909 2165 1503 1180 863 1127 1575 1385 1758 1902 1526 1144 1480 2724 2301 3430 2561 2049 1478 1310 910 1322 1856 1517 2188 1903 1944 1454 1466 1854 2187 2065 2860 2886 1768 1576 1756 1836 1976 1718 2224 1904 1088 1671 1654 2583 2377 2559 1549 1349 1828 1650 1708 1517 1791 1704 1885 1905 1161 1464 2257 3127 3254 2649 1975 2128 1801 1806 1908 1477 2086 1899 2269 1906 1425 1074 2833 2210 2578 3797 3599 2402 2477 1802 1294 1305 2240 1690 2776 1907 1472 1204 2177 3363 4660 3438 3244 2146 1632 1031 862 1223 2211 1717 2692 1908 970 1460 1499 1879 3524 2390 1584 1570 2107 1033 812 790 1634 1235 2035 1909 773 1636 1419 2629 2389 2025 3543 2302 1684 1691 1095 1512 1894 1511 2272 1910 2081 1987 1927 2690 4130 3950 3890 2905 3498 1912 2024 2186 2768 2149 3381 1911 1471 1535 2083 2071 2920 3003 1834 1211 1022 1093 872 874 1666 1484 1847 1912 1634 1451 1942 2215 3768 3255 2783 2843 3793 2030 1965 1563 2438 1795 3079 1913 1460 1494 1489 1754 1821 2348 4037 2866 2366 1509 1983 2511 2142 1782 2491 1914 1532 1505 3457 2596 3118 3189 4067 2521 2041 2158 1306 1172 2397 1928 2849 1915 2162 1529 2800 2616 3006 2076 3124 2404 2047 2160 1346 2521 2326 2162 2469 1916 2817 2067 2265 2159 2510 2776 3455 2471 2855 2102 1592 1339 2369 2040 2695 1917 2999 1089 1423 2566 3903 2203 2140 1703 1529 1526 1372 1114 1972 1761 2167 1918 1280 1354 1222 1289 1623 1807 3371 2677 2057 1486 1099 2294 1803 1423 2170 1919 2412 1370 1850 2616 2695 3281 3404 2002 1324 1155 1612 2205 2166 2011 2310 1920 4240 2117 1823 1989 3123 2964 2542 2762 4033 1489 939 877 2409 1997 2819 1921 1574 1576 1172 1411 2327 2554 1937 1430 1267 942 1363 975 1543 1345 1743 1922 1722 1270 2110 2064 2731 2471 2346 2306 2813 2919 1782 2345 2247 1882 2597
21 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
1923 1830 3801 2314 2696 2969 2687 2293 1665 1217 1614 1332 1419 2141 2232 2074 1924 1245 1199 1693 3104 4834 3926 2511 3303 2769 1321 1470 1008 2367 1620 3111 1925 852 1278 1217 1792 2451 1754 1745 2927 2372 1688 1583 1378 1756 1350 2156 1926 2262 2205 2498 2234 2251 5049 5257 3921 1586 1375 1571 1197 2621 1995 3240 1927 1872 1181 1791 3159 3143 2756 2375 2183 2496 1857 1549 1115 2127 1778 2468 1928 1238 2285 1404 1659 2224 2773 1825 1631 1710 1321 1250 1354 1718 1532 1914 1929 1114 745 1620 2036 2240 2497 1798 2081 1268 998 1121 1256 1569 1315 1814 1930 1211 871 1222 1828 2705 2167 1663 2888 1673 2066 2957 1701 1918 1632 2194 1931 1566 1344 2208 2317 2808 2637 2275 2616 2600 2040 1640 1419 2127 1749 2496 1932 2302 1024 998 1668 2306 2474 2993 2138 1289 1250 1385 1159 1753 1423 2075 1933 846 1770 1326 1471 2437 2728 3055 2459 1479 1473 1310 922 1773 1274 2272 1934 1004 989 1596 1617 1400 1493 1852 2010 1792 1202 1035 1013 1420 1209 1625 1935 945 2007 1943 2957 3070 3779 2206 1395 1238 1391 1616 1215 1975 1781 2180 1936 1794 1788 1425 1648 1967 3385 2816 2671 1709 1971 2114 1518 2067 1715 2420 1937 1224 2057 3158 2828 3159 3133 2276 2632 2935 2229 1369 1348 2363 1997 2728 1938 1860 1736 1941 1998 2328 3008 2316 2336 2808 1243 1190 941 1974 1611 2340 1939 1195 1455 1870 2611 2671 3028 2285 2073 1692 2074 2503 3153 2221 2131 2304 1940 1227 1146 3602 2782 2830 4029 3013 2437 2587 1899 1921 1213 2393 1982 2799 1941 1866 2272 3355 3252 2706 2891 2856 3362 3035 2443 2531 1680 2688 2493 2882 1942 1198 1170 3168 2879 3015 2873 2288 2134 1364 1639 1377 1240 2035 1839 2219 1943 978 1293 1255 2284 1964 3267 2674 1477 1246 1084 814 971 1608 1266 1952 1944 1547 1822 1476 4855 3597 3894 3498 2690 1696 1762 2674 2579 2672 2492 2856 1945 1089 3271 2826 3523 3661 3193 2301 1985 1676 2716 1484 1367 2417 2260 2589 1946 1505 2641 2318 2267 1851 2184 3093 1883 1606 1228 1130 1065 1893 1821 1974 1947 1012 900 3359 2326 1728 1594 1925 1090 737 633 1453 1699 1543 1791 1285 1948 3535 3440 2826 2134 2410 2649 4327 2906 1619 1040 900 710 2375 2257 2492 1949 936 867 1229 2413 2610 2488 2008 2827 1727 954 1074 1572 1730 1349 2103 1950 1482 1582 1530 1677 2128 1748 1494 1690 1797 1239 1916 1538 1651 1621 1683 1951 1458 1613 1827 1931 2903 2917 2424 1844 1194 850 976 1152 1759 1493 2022 1952 1089 1055 2847 3719 2623 2740 1659 1393 1491 1607 2326 2031 2048 2178 1919 1953 1259 1518 1655 1923 2187 2369 3146 2214 1144 965 815 664 1657 1306 2004 1954 1081 872 1269 1816 2724 2547 5424 2132 1625 2295 1551 1758 2103 1391 2791 1955 2362 1860 1851 3228 2900 3016 4048 2977 1862 1381 1135 1432 2342 1978 2697 1956 1523 1130 2859 2078 2540 3253 2640 2513 2208 1524 1856 2218 2199 1944 2446 1957 1500 2036 2476 2240 1913 2585 3291 2692 1991 1474 1050 1175 2036 1746 2324 1958 1188 3016 2176 2633 3026 2468 2812 1929 1450 2266 1867 1513 2190 2065 2325 1959 1854 1256 1760 1899 2066 3135 3375 3295 1313 961 953 960 1908 1447 2358 1960 1323 1259 2368 1693 2100 2241 2499 2794 2047 1790 1461 1304 1910 1568 2245 1961 1049 2139 1811 2043 2864 3093 2066 2074 1246 940 975 1826 1841 1640 2047 1962 1523 1885 1655 2684 3497 3296 2372 1771 1193 890 982 1006 1895 1622 2170 1963 927 839 2061 2523 2427 2468 1965 1689 1764 1340 1265 964 1689 1430 1942 1964 770 972 1407 2154 2658 1957 1689 1595 1393 1844 2355 1614 1702 1546 1856 1965 1488 1320 2596 3731 5283 7324 3965 2552 2185 1334 1085 1994 2910 2036 3774 1966 1523 2618 2014 2663 3085 3094 4581 4379 2690 1547 1608 2519 2696 2157 3229 1967 2369 2538 2926 3129 3473 3977 2937 1964 1884 1310 1143 1426 2421 2255 2591 1968 2012 1816 1907 2584 2132 2271 2435 2756 1933 2488 1284 1074 2060 1780 2336 1969 1140 1403 1846 2101 2227 2321 2114 1970 1607 984 955 931 1634 1396 1870 1970 987 2647 2499 3550 3887 4020 3203 3906 2396 2217 2034 1778 2759 2249 3271 1971 1215 1312 1626 2068 1873 2528 1861 1402 1275 1082 964 1250 1538 1406 1670 1972 927 941 937 1723 1859 2152 2418 2042 1120 975 1765 1257 1511 1258 1761 1973 886 1113 1481 2181 3127 2566 1964 1438 1196 1314 1685 1758 1729 1517 1934
22 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
1974 2098 1908 1817 1622 2073 2959 3411 2083 1512 1776 1716 3686 2227 2141 2302 1975 2662 1955 1480 2221 2975 2832 4857 2482 1952 1252 1153 1147 2252 1770 2725 1976 2434 1442 1257 1545 1900 2406 1493 1754 1757 1281 1269 1450 1666 1566 1765 1977 1220 3242 2815 2645 2949 2246 2000 3066 1831 1170 1392 1495 2165 2135 2210 1978 1336 1219 2543 2142 2710 2538 2815 2016 1874 2024 1258 1250 1983 1625 2329 1979 1242 1857 2656 2926 2957 3607 2800 2227 1762 1350 2125 2447 2331 2209 2451 1980 1392 2469 1532 2903 3093 3191 3712 2327 1778 1834 1450 1689 2279 1906 2656 1981 1761 1934 3265 2653 2150 2104 3081 2258 1786 2633 2574 2652 2409 2473 2335 1982 2793 2558 2054 2372 2820 3177 2472 2164 1506 1387 1162 1516 2163 2076 2254 1983 2506 2032 2157 2798 2651 2637 2030 1852 1431 1175 938 1295 1958 1954 1963 1984 1417 1530 1320 2002 2265 2291 2113 1951 2280 1717 1077 1067 1752 1402 2103 1985 962 2094 1668 1923 2598 2667 2128 3433 1989 1094 1064 1627 1936 1556 2318 1986 2308 1401 1759 2517 2827 2861 1847 1708 1338 1118 1109 1125 1828 1703 1950 1987 1893 1938 2732 3191 3354 3809 3370 2790 1804 1358 1388 2308 2499 2242 2748 1988 1619 1653 3479 4160 3023 2696 2118 1959 2147 1287 1322 3171 2388 2567 2205 1989 1987 1728 1862 2083 2143 2187 2588 2150 1913 1670 1460 1444 1937 1760 2109 1990 1114 1898 2148 1718 1897 2276 2533 1333 1456 1276 1692 1313 1719 1647 1795 1991 1770 994 1413 1198 2172 2779 2737 3290 1159 1027 1121 1707 1789 1367 2194 1992 1409 1573 2368 2572 2829 2317 1755 1272 1204 1171 2417 2332 1936 2112 1758 1993 1605 1315 2023 2176 1927 1963 2826 2083 2000 1642 1234 2045 1909 1733 2073 1994 2099 1596 2323 3143 2640 2389 1668 1344 1392 1015 1337 1444 1866 1991 1741 1995 1827 2292 2102 3169 2817 3927 2527 1836 2742 1382 1687 1714 2330 2132 2538 1996 1407 1060 1428 2306 2979 2165 2362 1791 2493 2485 2070 1604 2018 1646 2379 1997 1130 1546 2406 2214 2654 2189 4273 2118 1312 1536 1113 1804 2032 1702 2347 1998 1390 1146 1856 1928 1767 2051 2168 1564 2251 2149 3266 2049 1968 1939 1992 1999 1710 2512 3408 2820 4354 3204 2775 1846 1617 1431 1273 1685 2387 2235 2538 2000 1615 2926 3491 3427 3075 2382 2173 2344 1886 1968 1442 1356 2336 2376 2305 2001 1519 1840 3098 2846 2617 2991 2258 1721 2869 1496 1444 2081 2232 2138 2325 2002 1954 2510 3434 2269 2399 2284 1874 4177 2302 2730 3684 2625 2689 2746 2628 2003 2922 1836 2032 1736 2104 1833 1326 1101 1192 1692 1006 970 1647 1750 1541 2004 1809 1942 1958 2243 2155 2844 2217 1579 1552 1429 1411 1107 1851 1745 1963 2005 1440 1847 2583 2951 2948 2128 2934 2990 1866 1506 1001 1140 2115 1827 2395 2006 1065 1337 2696 4648 3384 3261 1880 2559 1685 1157 1488 1066 2186 2050 2321 Qma 1640 1734 2084 2376 2683 2787 2636 2287 1903 1555 1474 1524 2058 1805 2308 Qmin 770 745 937 1020 1275 1493 1326 1090 737 633 812 664 1420 1209 1285 Qmax 5117 4366 4900 4855 5283 7324 5424 5007 4594 2919 3684 3686 2910 3057 3774 Vm 4.4 4.2 5.6 6.2 7.2 7.2 7.1 6.1 4.9 4.2 3.8 4.1 65 28.2 36.7 Rm 33.5 31.9 42.5 46.9 54.7 55.0 53.8 46.6 37.5 31.7 29.1 31.1 494 215.0 279.4 Vm/Va 6.8 6.5 8.6 9.5 11.1 11.1 10.9 9.4 7.6 6.4 5.9 6.3 100 43 57 cs 1.90 1.29 0.90 0.69 0.93 2.12 1.12 1.05 1.50 0.61 1.54 1.28 0.32 0.74 0.68 cv 0.430 0.399 0.334 0.273 0.257 0.274 0.294 0.305 0.353 0.297 0.344 0.361 0.160 0.198 0.187 Qma – long term average of the mean monthly discharge Qmin – long-term minimum of the mean monthly discharge Qmax – long-term maximum of the mean monthly discharge Vm – monthly runoff volume [103 mil m3] Va – annual runoff volume [103 mil m3] Rm – monthly runoff depth [mm]
23 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
2 Runoff regime analysis
According to the IPCC (2001), consequences of climate change may result in altered density curves of climate elements (air temperature, precipitation, discharge, etc.), thus time series from other periods will likely change also. A hypothetical example of how the density curves of precipitation and runoff series could change is illustrated in Fig. 2-1. The aim of this chapter was to confirm this hypothesis by carrying out an analysis of a discharge time-series of the Danube River at the Bratislava station and subsequent drawing of histograms for old and new period. 2.1 Changes in the long-term daily regime of the Danube for the periods 1876–1940 and 1941–2005
Histograms of average daily flows from two periods: 1876–1940, 1941–2005, are surprisingly similar (see Fig. 2-2). Table 2-1 summarizes some basic statistical characteristics of the average daily flows for the Danube River taking into account both periods. The basic statistical characteristics of the two data sets do not indicate any significant changes; the long-term average discharge differs only by 2 m3s-1, which is negligible.
a)
b) Fig. 2-1 Hypothetic change of the density curves of the old (solid line) and new periods; a) changes in mean; b) changes in variance.
24 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3000
2500 1875-1940 1941-2005 2000
f 1500
1000
500
0 0 1000 2000 3000 4000 5000 6000 Q [m 3s -1]
Fig. 2-2 Histograms of the average daily flows of the Danube River at Bratislava for periods 1876–1940, and 1941–2005.
The long-term average annual regime (365 days) of the average daily discharges for the two periods (1876–1940 and 1941–2005) is shown in Fig. 2-3. The arrows point at the most significant differences between the periods in question. In late March, values from the period 1941–2005 exceeded the values from the 1876– 1940 period by 492 m3s-1. In contrast, in the middle of September, the discharges were observed to have dropped by 541 m3s-1 in comparison with those of the previous 65-year period. The time shift in the average daily flows was also analyzed by using cross-correlations. The highest correlation coefficient between the average daily discharges of both periods 1876–1940 and 1941–2005 was found at the shift of +13 days. This may explain the snowmelt in the Danube basin shifted earlier by 13 days due to the increased average daily temperatures. However, this fact can also be attributed to the earlier atmospheric precipitation over the basin.
Table 2-1 Basic statistical characteristics of the average daily flow series of the Danube River at Bratislava, for periods: 1876–1940, 1941–2005 1876–1940 1941–2005 Average 2059.6 2057.6 Standard Error 6.400 6.366 Median 1857.0 1856.0 Standard Deviation 986.1 980.9 Kurtosis 5.254 5.308 Skewness 1.654 1.687 Minimum 580 582 Maximum 10810 10285 Largest(10) 8770 9084 Smallest(90) 725 682
25 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
2900
2500 ] -1 s 3 2100 1876-1940 Q [m 1941-2005 1700
1300 1-Jan 1-Mar 1-May 1-Jul 1-Sep 1-Nov
Fig. 2-3 Histograms of the average daily flows of the Danube River at Bratislava for periods 1876–1940, and 1941–2005.
Fig. 2-4 shows the mean empirical distribution curve of the mean daily discharge at the Bratislava station from the four 30-year periods: 1886–1915, 1916–1945, 1946–1975, and 1976–2005. This information can be used to determine the value of QM, which was reached or exceeded in M-days during the selected period (M-day discharge). On the Fig. 2-4, the interval of 100-year and 1000-year average daily discharge is shown, too.
20000
1886-1915 10000 9000 8000 7000 1946-1975 6000 5000 ]
-1 4000 s 3 3000 100-year discharge Q [m 2000
30-day discharge 1976-2005 1000 1916-1945
330-day discharge 0.40000 0.50000 0.60000 0.70000 0.80000 0.90000 0.95000 0.98000 0.99000 0.99500 0.99800 0.99900 0.99950 0.99990 0.00001 0.00005 0.00010 0.00050 0.00100 0.00200 0.00500 0.01000 0.02000 0.05000 0.10000 0.20000 0.30000 p Fig. 2-4 Average probability of exceedance curves (empirical) of the mean daily discharges of Danube: Bratislava for four periods, logarithmic-probabilistic scale.
26 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The daily discharges were more smoothed and the long-term mean daily discharge was lower in last three decades. Comparing with the reference period 1930–1980, the 30-day discharge is now lower by more than 300 m3s-1, 364-day discharge higher by 160 m3s-1. 2.2 Changes in the long-term monthly runoff distribution over a year
Distribution of runoff over a year is an important river regime characteristic. The annual runoff distribution of the upper Danube reflects the high-mountainous conditions in the headwaters. Some changes in the distribution of the average monthly discharges were identified by a simple determination of the 30-year average values from the 1876–2005 gauging records (Fig. 2-5). The long-term trend in the monthly discharges over the period of observations is near zero. A comparison of the average values from the individual periods is depicted in Fig. 2-6. In 1946–1975, the winter discharges were moderately low, and the July discharges were above the average. This is particularly interesting since the discharge patterns during the period 1976–2005 are similar to the discharge in the period 1876–1905. Over the last period of 30 years, the intra-annual runoff distribution changed considerably. In the winter-spring period (November through April), river discharge remains above the average values, while in the summer (June through September) a decline in the discharge is observed (Fig. 2-6).
8000 Qm,max
] 6000 -1 s 3 4000
Qm [m 2000 Qm, min 0 0.5 0.45 variability decrease
v,m 0.4 c 0.35 0.3 1876 1896 1916 1936 1956 1976 1996
Fig. 2-5 Course of monthly discharges and moving averages of coefficient of variation cv,m of the monthly discharges (for 30 years periods). Danube River at Bratislava station; January, 1976–October, 2006.
27 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
2500 2800 2400 1901- 2300 1930 ] 2200 summer - autumn period, (V. - X.) -1 ] 2300 s
-1 2100 3 s 3 2000
Q [m 1900 Q [m 1800 winter - spring period, (XI. - IV.) 1800 1976-2005 1700 1300 1600 I III V V II IX XI 1850 1870 1890 1910 1930 1950 1970 1990 2010 a)
VI. 2800 2800 VII. V.
2400 IV. 2400 ] ] -1
-1 VIII. s s 3
3 III.
2000 2000 IX. II. Qm [m Qm [m X.
1600 I. 1600
XII. XI. 1200 1200 1876 1896 1916 1936 1956 1976 1996 1876 1896 1916 1936 1956 1976 1996 b) Fig. 2-6 a) Intra-annual distribution changes of the discharge Q in the two 30-year periods: 1901–1930, and 1976–2005 (left); Long-term Danube runoff variability (1876– 2005), increase of winter-spring discharge and declined summer-autumn discharge over the period of 1970–2005 (right); b) Course of 30-year moving averages of monthly discharges (I. – January,... ).
These results are similar to those obtained by Webb and Nobilis (2007). This intraannual redistribution of runoff was probably caused by the change in the basin-wide precipitation patterns (lower summer precipitation), and reservoirs constructed throughout the Danube River basin (increase of the winter minima) (Zsufa, 1999; Andrade-Leal, 2002), also. Another explanation might be the higher air temperature in the upper Danube basin. A warmer climate causes an earlier snowmelt in the winter-spring period, and thus less runoff is observed in the summer when the precipitation totals are high. Therefore, waves resulting from snow-melt and extreme summer rainfall may not occur coincidently. Nonetheless, the phenomenon can be attributed to changes in annual precipitation totals in the upper Danube basin (Fig. 2-7).
28 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
150 650 1901 130 Innsbruck -1930 550 110 1976- 2005 summer-autumn period, (V. - X.) 90 450 P [mm] P [mm] 70 winter-spring period (XI. - IV.) 350 50 30 250 1850 1870 1890 1910 1930 1950 1970 1990 2010 I III V VII IX XI 150 650 1976- 130 2005 550 Muenchen 110 summer-autumn, (V. - X.) 90 450 P [mm ] P [mm ] 70 1901 350 winter-spring period (XI. - IV.) 50 -1930 30 250 I III V V II IX XI 1850 1870 1890 1910 1930 1950 1970 1990 2010
150 450 Wien 130 1901 1976- 400 110 -1930 2005 350 summer-autumn, (V. - X.) 90 300 P [mm ] 70 P [mm ] 250 50 winter-spring period (XI. - IV.) 30 200 I III V V II IX XI 1850 1870 1890 1910 1930 1950 1970 1990 2010
Fig. 2-7 Intra-annual distribution changes of precipitation totals P in the two 30-year periods: 1901–1930, and 1976–2005 (left); Long-term precipitation totals for winter-spring and summer-autumn seasons (1876–2005), stations Innsbruck, Munich (München) and Vienna (Wien), precipitation data series according to www.wetterzentrale.de and Klein et al. (2002).
2.3 Changes in the annual stream flow characteristics
In this part we will evaluate the annual Danube runoff characteristics at Bratislava site. The following 130-years time series were computed (from average daily discharge for each year) Fig. 2-8:
• annual peak flows (Qmaxd);
• 30-day flows (Q30, flows that exceeded 30 days in a year – indicator of higher flows);
• average annual flows (Qa);
• 330-day flows (Q330, flows that exceeded 330 days in a year – indicator of the lower flows);
29 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Danube: Bratislava 10500 y = 1.2419x + 5563.5 ] -1
.s 8500 3
[m 6500
maxd 4500 Q 2500 1870 1890 1910 1930 1950 1970 1990 2010
6400 Danube: Bratislava
] y = -0.8437x + 3402
-1 5300 .s 3 4200 [m 30
Q 3100
2000 1870 1890 1910 1930 1950 1970 1990 2010
2900 Danube: Bratislava
] 2500 -1 .s 3 2100 [m a
Q 1700 y = -0.181x + 2058.7 1300 1870 1890 1910 1930 1950 1970 1990 2010
1800 Danube: Bratislava ]
-1 1500 .s 3 1200 [m
330 900 Q y = 0.6592x + 1059.8 600 1870 1890 1910 1930 1950 1970 1990 2010 1300 Danube: Bratislava ]
-1 1100 .s 3 900 [m
min 700 Q y = 0.6014x + 850.14 500 1870 1890 1910 1930 1950 1970 1990 2010 0.70 Danube: Bratislava 0.60 0.50 v c 0.40 0.30 y = -0.0002x + 0.446 0.20 1870 1890 1910 1930 1950 1970 1990 2010
Fig. 2-8 Variation of the peak annual flows Qmaxd, 30-day flows Q30, mean annual flows Qa, 330-day flows Q330, minimum flows Qmin, and yearly variation coefficients cv series, of the Danube at Bratislava. Deviations from the 5-yearly moving averages, 1876– 2005 period.
30 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
• the annual minimum flows (Qmin);
• the annual variation coefficients (cv). As can be assumed from these graphs, no substantial changes in the mean annual runoff within the last 130 years occurred.
Minimum flows Qmin and 330-day flows Q330, rise moderately, approx. by 0.6 3 -1 m s per year. On the other hand, the 30-day flows Q30 drops moderately, 3 -1 approx. by 0.8 m s per year. The annual series of the variation coefficient cv for the mean daily discharges drop also, b= – 0.0002. The mean daily maxima Qmax series rise slowly (by 1.2 m3s-1 in a year), which compared with the order of the Danube peak flow values is not a substantial figure. The statistical tests did not confirm the increase of daily runoff extremality of the Danube in 1876–2006. Finally, we compared the moving averages of the 15-year periods with 30- and 330-day flows (Fig. 2-9). Trend of the 30-day flows drops; while in the case of the 330-day flows increase. Significance of trends was detected using the CPTA software (Procházka et al., 2001; Pekárová and Pekár, 2007b). From the statistical point of view, no significant trends were confirmed for both of the above discharge characteristics within the used 130-year period. The underlying results reveal that the Danube daily discharge variability at Bratislava in any case did not rise in the 1876–2005 period. It would rather decrease, as document the series of the variation coefficients for the 1876–2005 period. Even in case of a change in the Danube runoff distribution within a year (higher winter-spring runoff), this seems not to influence neither Q30, nor the Q330 values, which do not depend upon the discharge distribution within the year.
3900 1500 ]
-1 Qd30 Qd330
s Linear (Qd330) Linear (Qd30) 3 3700 1400 [m 30
Qd 3500 1300
y = -0.7526x + 3483.9 3300 1200
3100 1100 ] -1 s 3 2900 1000 [m
y = 0.7203x + 985.1 330
2700 900 Qd 1876 1886 1896 1906 1916 1926 1936 1946 1956 1966 1976 1986 1996 2006
Fig. 2-9 Trends of the 15-year moving averages of 30-day and 330-day discharge of Danube in Bratislava.
31 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region 2.4 Conclusion
The reconstructed 130-year series of average daily flows was subject to a statistical analysis in order to reveal possible changes in the characteristics of the discharge series. The comparison between the two 65-year data sets of average daily flows did not reveal any significant changes in the statistical characteristics of the discharge of the Danube River during 1876–2005. This finding is rather surprising, since due to the previous modifications of the channel bed and the tributaries upstream of the Bratislava profile, changes in discharge rates were expected to occur. Mitková (2002) and Pekárová et al. (2004) successfully detected changes in travel times of flood waves for the Danube between Kienstock (Austria) and Bratislava (Slovakia). As the analysis revealed, these changes (shortened travel times of flood waves) did not affect the rate of discharge – the average daily flows. On the other hand, a time change in the long-term average daily flows was identified. At the end of April and March the long-term average flows increased by 492 m3s-1 over the period 1941–2005. This increase can be attributed to the earlier onset of snow-melt in the Danube basin due to the increased atmospheric temperature. In contrast, in mid-September the long-term daily flows dropped by 541 m3s-1 compared to the previous period of 65 years. It seems that the volume of water discharged in March is missing in the river outflow in September. The effect of air temperature on the total annual river discharge has not been confirmed. Long-term annual flows of the Danube River are nearly identical in both of the studied periods. In the long run, however, the annual discharges of the Danube at the Bratislava station do not change. The long-term trend in the monthly discharges over the period of observations is near zero.
32 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3 Hurst phenomenon, stationarity and multi-annual variability of runoff
The development of mankind has depended on availability of water resources. Already the first agricultural civilizations noticed the temporal variability of water resources and oscillation of the dry and wet periods. Some 50 years ago, Hurst (1951) in his studies on the long term storage requirements of the Nile River discovered a special behavior of the hydrological and other geophysical time series. This finding became known as the “Hurst phenomenon”. This behavior is based on the tendency of “wet” years to cluster into wet periods, or of “dry” years to cluster into drought periods (Lin and Lye, 1994). The basic mathematical expression of this phenomenon can be written as:
h Rn/Sn = (n/2) (3.1)
where Rn and Sn are the sample-adjusted range of cumulative departures from the arithmetical sample mean and the sample standard deviation, respectively, for a given time series of length n. Coefficient h denotes the Hurst coefficient. For independent normally distributed events for large n, the Hurst coefficient is h=0.5 (Koutsoyiannis, 2002; Klemeš, 1974). Hurst observed, that, on average, h = 0.73. The tendency for hydrological sequences to yield estimates of h greater than 0.5 has come to be referred to as the Hurst phenomenon – since time series have a “long memory”. Since its discovery, the Hurst phenomenon has been verified in more the 900 geophysical time series: - global mean temperatures (Bloomfield, 1992), flows for river Warta (Radziejewski and Kundzewicz, 1997), annual streamflow records across the continental US (Vogel et al., 1998), annual flow of the Nemunas River, etc. The aim of this paragraph is the analysis of the long-term trends of yearly discharge time series and runoff variability of the River Danube at Bratislava. About 40 years ago, Williams (1961) investigated the nature and causes of cyclical changes in hydrological data of the world. He attempted a correlation between hydrological data and sunspot activity with varying success. The most frequently studied cycles in connection with precipitation, temperature and runoff variability are the 10.5-year (21-year) Hale cycles and the 88-year Gleissberg cycle of solar activity. Another cycle studied in connection with hydrological and climatic data is the 18.6-year cycle lunar–solar tidal period. This period, together
33 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region with solar cycles, is analyzed in detail by Currie (1996). Interesting results were obtained by Charvátová and Střeštík (1995, 2004), who employed the inertial motion of the Sun around the barycentre of the Solar System as the base in searching for the possible influence of the Solar System as a whole on climatic processes, especially on changes in the surface air temperature. Charvátová (2000) explained a solar activity cycle of about 2400 years by solar inertial motion. She described a 178.7-year basic cycle of solar motion. Similarly, Esper et al. (2002), Vasiliev and Dergachev (2002), and Liritzis and Fairbridge (2003) showed that multiannual cycles probably have their origin in motion of the Earth in space. Solanki et al. (2004) report a reconstruction of the sunspot number covering the past 11 400 years. According to their reconstruction, the level of solar activity during the past 70 years is exceptional, and the previous period of equally high activity occurred more than 8000 years ago. These studies underline the theory of the dependence of climate variability of the Earth on solar activity. As the series of measured hydrological and meteorological data become longer and easier to access worldwide it is possible to deal with a large amount of complex historical data. For example, Probst and Tardy (1987) and Labat et al. (2004) studied mean annual discharge fluctuations of major rivers distributed around the world. Probst and Tardy (1987) showed that North American and European runoffs fluctuate in opposition, whereas South American and African runoffs present synchronous fluctuations. Kane (1997) predicted the occurrence of droughts in northeast Brazil. He found that the forecast of droughts based on the appearance of El Niño alone would be wrong half the time. Instead, predictions based on significant periodicities (13 and 26 years) give reasonably good results. Brázdil and Tam (1990), Walanus and Soja (1995), Sosedko (1997), Pekárová et al. (2003) and Rao and Hamed (2003) found several different dry and wet periods (2.6, 3.5, 5, 20–21, 29–30 years) in the precipitation, temperature and discharge time series in the whole world. It is clear that predicting discharge for several years ahead based only on deterministic models does not result in meaningful data. This is why the use of stochastic models proceeding from the stochastic characteristics of the measured discharge time series are required. During the 1990s, rapid progress in long-term time-series modeling was made. This progress was enabled due to the development of several stochastic models of hydrological time series using a random sampling method (the Monte Carlo method), classical time series analysis, spectral analysis, or the Box–Jenkins methodology (van Gelder et al., 2000; Popa and Bosce, 2002; Brockwell and Davis, 2003; Lohre et al., 2003; Rao and Hamed, 2003).
34 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.1 Analysis of natural fluctuations and long-term trends of runoff of the main world rivers
Statistical analysis of the runoff oscillations depends on availability of long time series of data. Systematic measurements of discharge in modern era started relatively late. The longest time series are available in Europe, but they do not exceed 200 years (Probst and Tardy, 1987). Such long series are exceptional and in most of the world only much shorter series exist. The scope of the paragraph is: 1. To demonstrate the existence of the long-term discharge fluctuations (20- 30 years) in rivers of all continents; 2. To verify the hypothesis of the shift in runoff extremes occurrence depending on the longitude and latitude; 3. To discuss the possible relation of SO and NAO to long-term annual runoff variability in different continents. The longest available time series of mean annual discharge of the selected world largest rivers were used to analyze the long-term runoff oscillation. The annual precipitation time series are usually the basis for chapter of the long- term oscillation of dry and wet periods in the basin. We will analyze the annual discharge time series due to following reasons: • The increase of precipitation by one third may increase the runoff by one half. Therefore changes in precipitation series are even more evident in discharge series. • The water balance of the basin depends not only on precipitation, but on temperature as well (evapotranspiration). The discharge series combine both these influences. • The problems of precipitation measurements and evaluation of the areal precipitation in mountain basins are well known. Discharge measurement in the outlet profile of the basin is simpler and more accurate in comparison to areal precipitation. • The analyzes of the long-term runoff oscillations of the large rivers eliminate the local disturbances in precipitation and temperature series due to local orographic peculiarities. The long annual discharge data series of all the continents were obtained from following data sources: i) Global Runoff Data Center in Koblenz, Germany; ii) CD ROM of the Hydro-Climatic Data Network (HCDN), U.S. Geological Survey Streamflow Data Set for the United States; iii) CD-ROM World Freshwater Resources prepared by I. A. Shiklomanov in the framework of the IHP of UNESCO;
35 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region iv) URL http://waterdata.usgs.gov. A set of more than a hundred of annual discharge time series with long periods of observation in all continents was analyzed in the chapter. The river basins were grouped into two regions: I. extra tropics zone of the Northern Hemisphere (between 30°N- 75°N); II. Equatorial zone and mild zone of the Southern Hemisphere (30°N – 40°S). For the final analysis twenty river basins were selected in each region. The selected rivers and stations are in Fig. 3-1. In Table 3-1 there are basic hydrologic characteristics of the series and basins. In Fig. 3-2 there are shown the smoothed yearly discharge series of selected rivers of all the continents by resistant non-linear smoothing technique. The raw data were filtered by two filters in order to attenuate the short-range fluctuations and to extract the long-range climatic variations. In the first step, the 5-years moving medians were computed from the original data. (Medians are not as sensitive on isolated extreme values as the averages are). In the second step, the 5-years weighted moving averages were computed from the medians according to formula:
yi = 1/16 (xi-2 + 4.xi-1 + 6.xi + 4.xi+1 + xi+2) (3.2)
The influence of different methods on data filtration was studied by Currie (1996) and Probst and Trady (1987). Probst and Tardy (1987) compared three complementary filtering methods. They found a difference of one or two years for the localization of maxima and minima discharges in filtered time series.
30° 60°
75° 20 15 16 1 2 19 10 12 14 7 5 13 I. 3 9 11 8 18 4 17 30° 6 14 17 8 15 2 10 1 7 11 16 0° 6 3 4 9 II. 12 18 13 19 40° 5 20
36 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Fig. 3-1 Gauging stations localization of selected rivers (legend in Table 1). Table 3-1 Gauging stations localization and basic hydrologic characteristics: C – country of the station, A – area [103 km2], period of observation (since - to), Qa – mean annual discharge [m3s-1], qa – mean annual yield [l.s-1km2], cs – coefficient of asymmetry, cv – coefficient of variation, min/max – minimal/maximal mean annual discharge [m3s-1]
River station C* A since to Qa qa cs cv min max 1 Yukon River mouth** US 850 1945 1988 6189 7.2 0.46 0.25 2617 10249 2 Mackenzie River mouth CN 1790 1948 1988 10338 5.8 0.75 0.09 8799 13245 3 Fraser River Hope CN 217 1912 1984 2722 12.5 0.29 0.13 1939 3673 4 Columbia mouth US 668 1878 1989 7454 11.2 -0.23 0.18 4510 10375 5 St.Lawrence Ogdensburg, N.Y. US 765 1860 1998 6986 9.1 0.04 0.10 5219 8946 6 Mississippi mouth US 2980 1914 1988 16069 5.4 0.48 0.23 8830 27657 7 Thjorsa Urridafoss IC 7 1947 1993 364 50.6 0.55 0.12 289 477 8 Loire mouth FR 120 1921 1986 838 7.0 0.72 0.33 282 1967 9 Rhine Koeln DE 144 1816 1997 2089 14.5 -0.03 0.19 920 3227 10 Vaenern-Goeta Vaenersborg SE 47 1807 1992 535 11.4 -0.10 0.19 225 768 11 Danube Orsova (1971:Turnu Severin) RO 576 1840 1988 5438 9.4 0.48 0.17 3339 8053 12 Neva Novosaratovka RS 281 1859 1984 2503 8.9 0.18 0.17 1341 3674 13 Dniepr Locmanskaja Kamjanka UA 495 1818 1984 1627 3.3 0.77 0.33 673 3375 14 Ob Salekhard RS 2950 1930 1994 12532 4.2 0.39 0.15 8791 17812 15 Yenisei Igarka RS 2440 1936 1995 18050 7.4 0.20 0.08 15543 20966 16 Lena Kusur RS 2430 1935 1994 16619 6.8 0.48 0.12 12478 22626 17 Songhua Harbin CH 391 1898 1987 1202 3.1 0.53 0.40 386 2671 18 Amur Khabarovsk RS 1630 1896 1985 8569 5.3 1.15 0.25 4281 18593 19 Kolyma Sredne-Kolymsk RS 361 1927 1988 2199 6.1 0.36 0.22 1337 3481 20 Amguema mouth of South Brook RS 27 1944 1984 338 12.7 0.79 0.32 168 637 1 Magdelena mouth CO 260 1904 1990 7139 27.5 0.26 0.08 5361 9587 2 Sao Francisco Juazeiro BZ 511 1929 1994 2692 5.3 1.03 0.30 1603 4798 3 Amazon Obidos BZ 4640 1928 1996 174069 37.5 -0.24 0.10 138555 206941 4 Orinoco Puente Angostura VN 836 1923 1989 30932 37 0.42 0.10 21245 44702 5 La Plata mouth AR 3100 1904 1985 25583 8.3 1.71 0.26 14191 58657 6 Oubangui Bangui CA 500 1911 1994 4116 8.2 -0.03 0.28 782 7360 7 Chari Ndjamena(Fort Lamy) CD 600 1933 1991 1119 2 1.63 0.48 236 3344 8 Niger mouth NG 2090 1920 1985 9275 4 0.44 0.27 3931 15200 9 Congo Kinshasa CG 3475 1903 1983 39536 11.4 0.89 0.10 32253 53908 10 Blue Nile Roseires Dam SU 210 1912 1982 1548 7.4 -0.06 0.18 652 2199 11 White Nile Malakal SU 1080 1912 1982 939 0.9 1.53 0.19 714 1537 12 Zambezi mouth MO 1330 1921 1985 4852 3.6 0.45 0.19 2551 8105 13 Oranje Vioolsdrif SA 851 1964 1986 150 0.2 1.08 0.80 30 449 14 Indus mouth IN 960 1921 1985 7127 7.4 0.42 0.20 3974 11321 15 Ganges *** mouth BA 1730 1921 1985 43704 25.3 3.15 0.03 38222 53170 16 Mekong mouth VI 810 1921 1985 15924 19.7 0.01 0.12 11794 19237 17 Yang-tze Hankou CH 1488 1865 1986 23266 15.6 0.12 0.10 14313 31983 18 Mary River Miva AU 5 1910 1995 38 7.9 1.28 0.90 4 147 19 Darling River Bourke Town AU 386 1943 1994 126 0.3 2.84 1.40 5 856 20 Murray mouth AU 3520 1877 1988 760 0.2 2.59 0.75 38 4091
* AR – Argentina, AU – Australia, BA – Bangladesh, BZ – Brasilia, CA – Central Africa, CD – Chad, CG – Congo (Democratic Republic of), CN – Canada, CO – Colombia, DE – Germany, FR – France, CH – China, IN – India, IC – Iceland, MO – Mozambique, NG – Nigeria, RO – Romania, RS – Russia, SA – South Africa, SE – Sweden, SU – Sudan, UA – Ukraine, US – United States of America, VI – Vietnam, VN – Venezuela ** mouth specifies the data from Shiklomanov CD World Freshwater resources, other data were provided by GRDC Koblenz ***Ganges: delta of Ganges – Brahmaputra – Meghna
37 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3 -1 Q [m s ] Q [m3 s -1 ] 8000 6000 N. America Yukon 4000 Columbia 8000 St. Lawrence 6000 7000 Mississippi 19800 6000 17600
Europe Loire 1200 800 2250 Rhine 2000 Danube 5500 5000 Goeta 600
400 3000 Neva 2000 14000 Ob 20000 Asia 12000 18000 Yenisei 18000 Lena 16000 2400 Kolyma 2000 12000 Amur 8000
S. America Magdalena 7200 6800 30000 25000 La Plata 187000 176000 Amazon 12000 Africa Niger 48000 8000 42000 Congo 5000 Zambezi 4500 4000 45000 Ganges - Brahmaputra - Meghna 42000 Mekong S. Asia Jangzi 16000 25000 14000 22500 1200 Australia Murray 600 1807 1835 1863 1891 1919 1947 1975 2003
Fig. 3-2 Smoothed yearly discharge of selected rivers over the continents using two resistant non-linear smoothing techniques (the 5-years moving medians and the 5-years weighted moving averages).
38 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.1.1 Identification of the long-term runoff trend
3.1.1.1 Europe
In Europe, the longest discharge data series have been available since beginning of the 19th century. Therefore these series are particularly suitable to study the long-term runoff oscillations and trends. In order to identify trends for some European rivers, discharge time series of eleven rivers for West/Central Europe were used (Goeta: Vaenersborg, SE (1807–1992), Rhine: Koeln, DE (1816–1997), Neman: Smalininkai, LT (1912– 1993), Loire: Montjean, FR (1863–1986) Weser: Hann-Muenden, DE (1831– 1994), Danube: Turnu Severin, RO (1840–1988), Elbe: Dečín, CZ, (1851–1998), Oder: Gozdowice, PL (1900–1993), Vistule: Tczew, PL (1900–1994), Rhone: mouth, FR (1921–1986), and Po: Pontelagoscuro, IT (1918–1979)) and six time series for East Europe (Dniepr: Locmanskaja Kamjanka (1818–1984), Neva: Novosaratovka (1859–1984), Northern Dvina: Ust-Pinega (1881–1990), Don: Razdorskaya (1891–1984), Pechora: mouth (1921–1987), and Volga: mouth (1882–1998)). These data series were completed by the multiple regression methods and the standardized average discharge time series was computed. Comparisons of the following pairs of four standardised discharge data filtration methods were made: 1. 3-9-MA - 3 year Moving Average (MA) and 9 year MA. 2. e3s21 - Exponentially Weighted Moving Average (EWMA) - smoothing constant 0.3 and Spencer's 21 MA. 3. r5h11- 5RSSH filter (a nonlinear smoothing technique that includes a median for a value and five points around that value, Resmoothing (R), two Splitting operations to eliminate flat segments in the data (SS), and a Hanning weighted average with weights 0.25, 0.5, and 0.25 (H)), and Henderson's 11 year MA. 4. h5sp21 - Henderson's 5 year moving average and Spencer's 21 MA. The course of the filtered standardized discharge data of the West European time series are given in Fig. 3-3a, of East Europe in Fig. 3-3b, and of Europe in Fig. 3-3c. If we want to identify any trend uninfluenced by the 28-years periodicity of the discharge time series, we must determine the trend during a closed multiple loop both, starting and terminating by either minima (e.g., 1861–1946 in Central Europe) or maxima (e.g., 1847–1930 or 1931–1984 in Central Europe). Trends determined for other periods are influenced by the periodicity of the series and depend on the position of the starting point on the increasing or recession curve. The trend analysis does not show any significant trend change in long-term discharge series (1810–1990) in representative European rivers (Fig. 3-3a). Nevertheless, it is possible to identify multiannual cycles of wet and dry periods.
39 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The dry period occurred in Europe around 1835 and the years 1857–1862 were very dry. In the 20th century the period 1946–1948 was very dry. Another dry period occurred in 1975. If we consider the 28-years cycle, described in next sections, we can expect the next dry period in Central Europe to occur in next years (around 2003).
1.50 3-9-MA e3s21 r5h11 h5sp21w Linear (r5h11) West and Central Europe
1.00
0.50
0.00
-0.50
-1.00 linear trend, y = 9E-05x - 0.0466 -1.50 1807 1835 1863 1891 1919 1947 1975 2003 a)
1.80 3-7-MA e3s21 r5h15 h5sp21 Linear (r5h15) East Europe
1.20
0.60
0.00
-0.60
-1.20 linear trend, y = -0.0008x + 0.087 -1.80 1807 1835 1863 1891 1919 1947 1975 2003 0 b)
1.80 3-7-MA e3s21 r5h15 h5sp21 Linear (h5sp21) Europe
1.20
0.60
0.00
-0.60
-1.20 linear trend, y = 0.0002x - 0.0093 -1.80 1807 1835 1863 1891 1919 1947 1975 2003 c) Fig. 3-3 The course of runoff fluctuation and trends in Europe during 1810–1990. (Smoothed standardized discharge data. a) West/Central Europe, b) East Europe (excluding Volga), c) Europe (excluding Volga).
The largest rivers in the Central Europe are Rhine and Danube. Both rivers are highly influenced by the Alps and their long-term variability of runoff is very similar (
40 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Fig. 3-2). The north-eastern European rivers, e.g. Neman, Neva, Pechora, Northern Dvina, as well as south-eastern European rivers Dnieper, Don, Ural and Volga show very similar occurrence of the dry periods. The Neva river drains the large Finnish and Russian lake basins (Arpe et al., 2000). The big lake rivers are very suitable for the identification of the long-term – multiannual cycles, as the lakes eliminate and smooth the annual variability of the dry and wet years.
3.1.1.2 North Asia
The regular decrease and increase of discharge is observed in the large rivers of Russia - Siberia (Ob, Yenisei, Lena, Kolyma). Systematic observation of discharge of these rivers started only after 1930. The length of these series is sufficient for identification of the 14-years cycle (Lukjanetz and Sossedko, 1998), only. However, the 28-years cycle can be found in the Amur river. In these rivers the maximum and minimum values do not occur in the same years (see Fig. 3-2), e.g. a local maximum occurred in 1972 on Ob, in 1975 on Yenisei, and in 1980 on Kolyma. The time shift (delay) of the extremes in eastward direction will be analyzed by cross-correlation in the next paragraph.
3.1.1.3 North America
The annual discharge data series of the largest rivers were used for the identification of the cycles (Mississippi, St. Lawrence, Mackenzie, Yukon, and Columbia, see Fig. 3-2). The St. Lawrence River, similar to Neva in Russia, drains a large lake district. Unlike Europe, where it was very dry, the years 1945-1949 were wet in North America. The runoff extremes in Europe and in the North America do not occur in the same years. A prevailing wet period in Europe corresponds to a dry period in the North America. This hypothesis will be analyzed by cross-correlation in next sections.
3.1.1.4 South America
Discharge series of three large rivers of the South America are in Fig. 3-2 (Amazon, Magdalena, La Plata). It is interesting that the series of Magdalena (Northern Hemisphere) create a mirror image of the La Plata series (Southern Hemisphere). The discharge measurements of the world’s largest river Amazon were unsound in the past. The available data series are ambiguous before 1950 and different values are published in different databases (e.g. GRDC). If we compare Amazon's data to those of another large Equatorial river, Congo in Africa, we can observe a shift of several years in the extremes occurrence.
41 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.1.1.5 Africa
The alternating of the dry and wet periods is much stronger in African rivers compared to European ones. Whereas the time series of rivers in the Northern Hemisphere require smoothing by moving averages in order to identify the long- term discharge oscillations, the African rivers show the oscillations without smoothing. The African rivers with relatively long discharge series are Niger, Congo ( Fig. 3-2), White and Blue Nile (about 90 years). The length of the series is sufficient to prove the 14-years cycles only, but not longer ones. Unfortunately, no long discharge series are available in the South Africa. The African rivers north of the Equator (Niger, Chari, Ubangi) have dry periods in the same years as the central European rivers, while the rivers southern of the Equator (Zambezi, Shire) have a reverse occurrence of the extremes. The Congo River is influenced by its tributaries from the Northern Hemisphere (Ubangi) as well as from the Southern Hemisphere (Kasai, Lualaba). From the long-term point of view the runoff of Congo is similar to the runoff of the White Nile, which drains the Victoria Lake situated exactly on the Equator.
3.1.1.6 South-eastern Asia and Australia
Cluis (1998) analyzed trends of the Pacific and Asia rivers. According to his analysis the runoff decreased or remained stable between the Equator and 40°N at the end of the last century. In Australia the runoff did not change after elimination of the cyclic component. The longest discharge data series in south-eastern Asia are those of Yangzi. The data show a regular 14-years cycle. The Ganges (Ganges – Brahmaputra – Meghna) river is characterised by the steadiest runoff, and the coefficient of variation of the annual discharge is only 0.03. The mean annual discharge varies between 41 000 and 45 000 m3s-1 except 1957 (38 221 m3s-1) and 1974 (51 169 m3s-1). The long-term runoff is relatively constant. Unlike Ganges the Australian rivers exhibit a clear periodicity and variability. The coefficient of variability of Darling discharge series is up to 1.36 (the minimum and maximum annual discharge was 5 m3s-1, and 856 m3s-1, respectively). Cluis (1998) related the variability of runoff to El Niño and La Niña episodes (see discussion in next sections). Similar to South America and Africa, the occurrence of wet periods northern of the Equator in south-eastern Asia seems to go along with dry periods southern of the Equator (see Yangzi in Fig. 3-2).
42 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.1.2 Identification of the long-term variability
It is possible to identify the cyclicity or randomness in the time series by auto- correlation and spectral analysis. Both methods were used to look for the long- term cycles of runoff decrease and increase in the analyzed runoff time series.
3.1.2.1 Brief overview of the spectral analysis of random processes
Estimation of both, the auto-covariance and the auto-correlation functions of n given empirical series {}xi i=1 , is the base tool of time series analysis. The auto-covariance function R (τ ) can be estimated by the formula
n−τ ∑()xi − x .()xi+τ − xi+τ R ()τ = i=1 , (3.3) n −τ where: x – mean of {}xi .
The normalized auto-covariance function (with respect to the standard deviation s x ) provides an estimation of the auto-correlation function r (τ ) of the form
R(τ ) r(τ ) = 2 , (3.4) sx where: τ = 012, , ,...m; m = n/2.
Function r ()τ reaches its values within the interval <-1, 1>. The spectral analysis is used to examine the periodical properties of random n processes {}xi i=1 . The spectral analysis generalizes a classical harmonic analysis by introducing the mean value in time, of the periodogram obtained from the individual realizations. The fundamental statistical characteristic of a spectral analysis is its spectral density. The basic tool in estimating the spectral density is the periodogram. A periodogram (a line spectrum) is a plot of frequency and ordinate pairs for a specific time period. This graph breaks a time series into a set of sine waves of various frequencies. It is used to construct a frequency spectrum. A periodogram can be helpful in identifying randomness and seasonality in time series data, and in recognizing the predominance of negative or positive autocorrelation – a help you often need to identify an appropriate model for forecasting a given time series. If the periodogram contains one spike, the data may not be random. The spectral density is defined as a mean value of the set of periodogram for n→∞.
43 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The periodogram is calculated according to:
2 2 n 2 ⎧ n n ⎫ 1 −iτλ 1 ⎪⎛ ⎞ ⎛ ⎞ ⎪ = x e j I(λj) ∑ τ = ⎨⎜∑∑xxτ .sin(τλ .j )⎟ + ⎜ τ .cos( τλ .j )⎟ ⎬ . 2πn τ =1 2πn ⎝ ⎠ ⎝ ⎠ ⎩⎪ τ ==1 τ 1 ⎭⎪ (3.5)
We compute the squared correlation between the series and the sine/cosine waves of frequency λj. By the symmetry I(λj) = I(-λj) we need only to consider I(λj) on 0 ≤ λj ≤ π.
For real centred series the periodogram I(λj) can be estimated by auto-covariance function as 1 ⎛ n−1 ⎞ I(λ jj) =+..cos(.)⎜ RR0 2∑ τ τλ ⎟ , (3.6) 2π ⎝ τ =1 ⎠ for Fourier frequencies:
2π. j n λ = , where j = 1, (3.7) j′ n 2
3.1.2.2 Combined periodogram method
It is clear that from the relationship (3.6) it follows that for low frequencies, i.e. for long periods, we compute the periodogram with a sparse step. For example, if a time series is 100 years long, the periodogram is only computed for periods of 100/2 = 50 years, 100/3 = 33.3 years, 100/4 = 25 years, etc. If the real period is of 29 years, then we don't get the correct period. This is why it is necessary to pay the maximum attention to the analysis and not to rely only on results provided by mathematical tests without the appropriate analysis. One way how to reveal the real period is decreasing the length of the measured series, i.e. computing the periodogram for different "random" selections of the series followed by computing the average value of the periodogram. The result of this process we will name as combined periodogram. In order to obtain such a combined periodogram a code PERIOD was written. This program computes periodogram for series successively shortened by two years (Pekárová, 2003).
44 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.1.2.3 Multi-annual periods
Neva and St. Lawrence rivers are very suitable for study of the long-term runoff oscillations, because the variability is smoothed by the great water accumulation in the lakes they drain. As an example, there are the auto-correlations and periodograms of St. Lawrence (North America), Neva (Europe), Amur, Yangzi (both Asia), and Congo (Africa) in Fig. 3-4. There were used raw data. The auto-correlation and periodogram of St. Lawrence River show very marked 30-years periodicity of runoff increase and decrease. In Amur time series there is the 28-years period combined with the 14-years period. In Rhine, Yenisei, Lena, Yangzi, Congo, and Amazon time series the 14- and 7-years periods are more evident. We must realize that the 28-years period could not be identified due to short time series. Hydrological time series are of maximum length of 200 years. Using periodograms in order to identify the significant periods can lead to important errors. This is why a new, above described, method of combined periodogram was used. To illustrate the proposed method we analyzed an artificial series of the length of 1999 members (years) that was created as a cosine combination of three periods - 29, 11, and 6.4 years. If we analyze this series in the ordinary way (1999 members), we get a periodogram as it is shown in Fig. 3-5a. Here, all three periods are clearly identified. The length of the series of 1999 members is sufficient for exact identification of long-term 30-50 year periods. If we draw a periodogram on the basis of a 79 year time series (in the case we have only a 79 year series of observations), among the long periods we get a significant period of 26.3 years (see Fig. 3-5b.). On the other hand, if we draw a periodogram on the basis of a 99 year time series (in the case we have a 99 year series of observations), among the long periods we get a significant period of 33 years (see Fig. 3-5c.). Hence, the difference in the long period identification is significant. The combined periodogram method sufficiently thickens the spectrum. In the spectrum a 28-30 years spike, which at best corresponds to the reality, gets distinct (Fig. 3-5d). In Fig. 3-7 you can see combined periodograms of sixteen rivers from different continents that have the longest discharge time series. For these rivers the cycles of about 3.6–4; 6–7; 11; 14; 20–22; and 26–30 years were identified. The longest cycle of about 26–30 years was found for Neva, Goeta, Danube, Amur, La Plata rivers. In the data of Yangzi, Rhine, Vltava, Ural, Mississippi, Congo, and Amazon an about 14 years cycle dominates. For these river another 7 years cycle can be identified. Another significant cycle of 20–22-years can be found for Murray, Zambezi, Vltava, Danube, Dniepr, and St. Lawrence.
45 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
0. 6 10.E+6 28 St. Law rence 8.E+6 0. 3 6.E+6 k 0. 0 4.E+6 14 8 2.E+6 -0. 3 000.E+0 0 7 14 21 28 35 42 49 56 9.3 6.6 5.1 4.1 3.5 3.0 2.7 2.4 2.2 56.0 16.0 lag Period [year] St. Law rence
0. 6 5.E+6 Ne va 28 0. 3 4.E+6 3.E+6 0. 0 6.2 k 2.E+6 11 -0. 3 1.E+6 -0. 6 000.E+0
0 7 14 21 28 35 42 49 56 7.0 5.3 4.3 3.6 3.1 2.7 2.4 2.2 2.0 18.7 10.2 lag Neva 112.0 Period [y ear]
0. 6 50.E+6 28 Am ur 40.E+6 0. 3 30.E+6 k 20.E+6 0. 0 10.E+6 -0. 3 000.E+0 0 7 14 21 28 35 42 49 56 7.6 5.3 4.0 3.2 2.7 2.3 2.0 2.4 2.2 84.0 14.0 lag Amur Period [y ear ]
0.3 150.E+6 Yangzi 13.5 7.1 0.2 0.1 100.E+6 k 0.0 50.E+6 -0.1 -0.2 000.E+0
0 7 14 21 28 35 42 49 56 7.6 5.8 4.7 3.9 3.4 3.0 2.6 2.4 2.2 20.2 11.0 121.0 lag Yangzi Period [year]
0. 6 2.5E+08 Congo 2.0E+08 0. 3 1.5E+08 k 14 7 1.0E+08 0. 0 5.0E+07 -0. 3 0.0E+00 0 7 14 21 28 35 42 49 56 6.5 4.5 3.4 2.8 2.3 2.0 72.0 12.0 lag Congo Period [year] a) b) Fig. 3-4 a) Auto-correlation and b) periodograms of St. Lawrence, Neva, Amur, Yangzi and Congo (raw annual discharge).
46 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
1.2E+05 5.0E+03 29 1.0E+05 4.0E+03 26.3 8.0E+04 6.4 3.0E+03 6.58 6.0E+04 2.0E+03 11.3 4.0E+04 11 2.0E+04 1.0E+03 0.0E+00 0.0E+00 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 a) b)
5.0E+03 5.0E+03 6.4 29 4.0E+03 4.0E+03 33 3.0E+03 6.6 3.0E+03 11 2.0E+03 2.0E+03 1.0E+03 1.0E+03 0.0E+00 0.0E+00 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 c) d) Fig. 3-5 a) Periodogram on the basis of a 1999 year time series; b) Periodogram on the basis of a 79 year time series; c) Periodogram on the basis of a 99 year time series; d) Combined periodogram on the basis of a 99 year time series.
The auto-correlation analysis leads to similar results; see the auto-correlation of Rhine River raw discharge series in Fig. 3-6a. Here, it is difficult to identify the 14-years period. But if we plot the 3-years moving averages of the auto- correlation coefficients (Fig. 3-6b), the 14-years period becomes visible. Seven wet years alternate seven dry years. Due to sufficient length of the Rhine time series (181 years), the length of the cycles is faithful.
0. 2 0. 1 Rhine km Rhine 0. 1 k 0. 0 0. 0 -0. 1
-0. 2 -0. 1 0 7 14 21 28 35 42 49 56 0 7 14 21 28 35 42 49 56 lag lag a) b) Fig. 3-6 a) Auto-correlation coefficients and b) 3-years moving averages of the auto- correlation coefficients of the Rhine river.
47 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
2.0E+8 7.0E+6 Yangzi 14 Neva 28 7
1.0E+8 20 3.5E+6
0.0E+0 0.0E+0 2 3 456789 2 3 456789 2 3 456789 2 3 456789 10 100 10 100 2.8E+6 2.0E+5 Rhine Cologne Goeta
1.4E+6 1.0E+5
0.0E+0 0.0E+0 2 3 456789 2 3 456789 2 3 456789 2 3 456789 10 100 10 100 3.0E+4 1.2E+7 Vltava Danube
1.5E+4 6.0E+6
0.0E+0 0.0E+0 2 3 456789 2 3 456789 2 3 456789 2 3 456789 10 100 10 100 4.0E+6 6.0E+7 Dniepr Amur
2.0E+6 3.0E+7
0.0E+0 0.0E+0 2 3 456789 2 3 456789 2 3 456789 2 3 456789 10 100 10 100 2.0E+7 1.1E+7 Yenisei St. Lawrence
1.0E+7 5.6E+6
0.0E+0 0.0E+0 2 3 456789 2 3 456789 2 3 456789 2 3 456789 10 100 10 100 4.0E+7 1.6E+8 Lena Mississippi
2.0E+7 8.0E+7
0.0E+0 0.0E+0 2 3 456789 2 3 456789 2 3 456789 2 3 456789 10 100 10 100 3.0E+8 3.0E+9 Congo Amazon
1.5E+8 1.5E+9
0.0E+0 0.0E+0 2 3 456789 2 3 456789 2 3 456789 2 3 456789 10 100 10 100 6.0E+6 Murray 4.0E+8 LaPlata
3.0E+6 2.0E+8
0.0E+0 0.0E+0 2 3 456789 2 3 456789 2 3 456789 2 3 456789 10 100 10 100
Fig. 3-7 Combined periodograms of sixteen rivers.
48 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.1.3 Identification of the shift of extremes
Cross-correlation analysis was used to find the discharge relation between two rivers. The correlation coefficients, r, between two discharge series were repeatedly computed for time shifts of 0, 1, 2, 3, … years. The cross-correlation coefficients between Danube and Rhine discharge series are plotted in Fig. 3-8a. The figure shows an existence of a direct relation (without time shift) between raw annual discharge series of Danube and Rhine. The coefficient of correlation for the zero shift is equal to 0.617.
0.6
0.4
r 0.2
0
-0.2 -42 -28 -14 0 14 28 42 Danube - Rhine l a)
0.3
0.2
0.1
r 0
-0.1
-0.2 -42 -28 -14 0 14 28 42 Goeta - Nev a l b) Fig. 3-8 a) Cross-correlation of the mean annual runoff series (1860-1995) of Danube and Rhine (r- coefficient of correlation, l –shift in years). b) Cross-correlation of the mean annual runoff series (1860-1990) of Goeta and Neva (r- coefficient of correlation, l –shift in years).
A similarly evident relation is between Goeta and Neva raw discharge series (Fig. 3-8b). In the plot of cross-correlation coefficients we can also see the 28- years cycle of wet and dry periods. In case of these lake rivers we can also observe the dependence of runoff on previous years. The cross-correlation analysis of rivers in different longitudinal zones indicates the shift in extremes occurrence. It can be demonstrated by comparison of large European and Asian rivers in Russia (Fig. 3-9). The same results were obtained by Probst and Tardy (1987).
49 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
0.6 0. 45 0. 45 0.3 0.3 0. 15 0. 15 0 r 0 r -0. 15 -0. 15 -0 .3 -0 .3 -0. 45 -0. 45 -28 -14 0 14 28 -28 -14 0 14 28 Neva - Ob l Ob - L ena l
0. 45 0. 45
0.3 0.3 0. 15 0. 15 0 r 0 r -0. 15 -0. 15 -0 .3 -0 .3 -0. 45 -28 -14 0 14 28 -28 -14 0 14 28 Lena - Koly ma Ob - Amur l l
Fig. 3-9 Cross-correlation of the mean annual runoff series of Neva – Ob, Ob – Lena, Lena – Kolyma and Ob – Amur (r- coefficient of correlation, l –shift in years).
The shift of the discharge extremes between Neva and Ob is about 3 years, between Ob and Lena 3 years, and between Lena and Kolyma 7 years. The total shift between Neva and Kolyma is about 13 years. If we take into account that the basin of Neva is situated at the 20°E meridian and Kolyma basin at 160°E meridian, the mean delay of the extremes occurrence is about 1 year per 10° longitude eastwards. The cross-correlation analysis of St. Lawrence and Neva raw discharge series (Fig. 3-10) shows the shift in extremes occurrence as well. The lag is 19 years eastward, i.e., 9 years westward. The regular cyclicity of the correlogram follows from the 28-years periodicity of Neva and St. Lawrence discharge series. Keeping the eastward orientation of the shift demonstrated at the Siberian rivers, we will allege Neva – St. Lawrence shift of about 18 years. Cross-correlation between Thjorsa (Iceland) and Goeta (Sweden) is in Fig. 3-11a. The coefficient of correlation between two series is r = –0.55. The relatively high negative correlation means, that during dry period in Scandinavia there is a wet period in Iceland. The shift of extremes occurrence is about 7 years. Cross-correlation of Congo and Amazon, two of the world largest rivers, gives also interesting results. The wet and dry periods do not occur in the same years and the shift of the extreme occurrence is about 7 years (Fig. 3-11b).
50 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
0.3
0.15
0
r -0.15
-0.3 -9 19 -0.45 -42 -28 -14 0 14 28 42 St. Lawrence - Nev a l
0.3
0.15
0
r -0.15
-0.3
-0.45 -42 -28 -14 0 14 28 42 Neva - Amur l
0.3
0.15
0
r -0.15
-0.3
-0.45 -42 -28 -14 0 14 28 42 Amur - St. Lawrence l Fig. 3-10 Cross-correlation of the mean annual runoff series of Amur and St. Lawrence (about 16 years), St. Lawrence and Neva (about 9 years), Neva and Amur (about 4 years), (r- coefficient of correlation, l –shift in years).
0.4 0.3
0.2 0.15 0 0 r -0.2 r -0.15 -0.4
-0.6 -0.3 -21 -14 -7 0 7 14 21 -21 -14 -7 0 7 14 21 Thjorsa - Goeta l Congo - Amazon l
a) b) Fig. 3-11 a) Cross-correlation of the mean annual runoff series (1947-1993) of Thjorsa and Goeta (r- coefficient of correlation, l –shift in years b) Cross-correlation of the mean annual runoff series of Congo and Amazon (r- coefficient of correlation, l –shift in years)
51 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.1.4 Teleconnection ENSO and NAO phenomena with long-term runoff oscillation
The variability of runoff results from the global system of oceanic streams, the global circulation of the atmosphere, and the transport of moisture (precipitation). The motive power of all such processes is the solar energy. Solar activity impacts (expressed in sun spot numbers) are also studied in this respect. The relationship between runoff and Southern Oscillation Index (SOI) and similarly between runoff and North Atlantic Oscillation Index (NAOI) will be discussed in this section. In Fig. 3-12a there are the 3-years moving averages of the Southern Oscillation Index (SOI), which represent the alternation of El Niño and La Niña periods between 1876 and 1999. The circles indicate the about 28-years periods of El Niño occurrence. In Fig. 3-12b there are the 3-years moving averages of the North Atlantic Oscillation Index (NAOI). Annual index of the NAO in this chapter is based on the difference of normalized sea level pressures (SLP) between Ponta Delgada, Azores and Stykkisholmur/Reykjavik, Iceland (Stephenson, 1999). The NAO cycles are of about 20–-30 years according to Cílek (1998). The cycle depends on the deep oceanic circulation originating in the Southern Hemisphere. It takes 20–30 years until the water mass moves from the south to the north. The air pressure gradient between Azores and Iceland decreases when the warm water mass appears in the top layers of the North Atlantic and therefore the weather in Europe is influenced by east winds.
a) 10 SOI La Nina
0
El Nino -10 1856 1884 1912 1940 1968 1996
3 NAOI 1.5 0 -1.5 -3 1856 1884 1912 1940 1968 1996 b) Fig. 3-12 a) Three years moving averages of Southern Oscillation Index (SOI) and identification of El Niño periods (1876–2000). b) Three years moving averages of North Atlantic Oscillation Index (NAOI) (1864– 2000).
52 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
0. 2 0. 1 0. 1 SOI km SOI 0. 0 k 0. 0 -0. 1 -0. 2 -0. 3 -0. 1 0 7 14 21 28 35 42 49 56 0 7 14 21 2 8 35 42 49 56 lag lag
0.3 0.1 NAOI 0.2 km NAOI 0.1 k 0.0 0.0 -0.1 -0.2 -0.3 -0.1 0 7 14 21 28 35 42 49 56 0 7 14 21 28 35 42 49 56 lag lag a) b) Fig. 3-13 a) Auto-correlation coefficients and b) 3-years moving averages of the auto- correlation coefficients of the SOI and NAOI.
Huang et al. (1998) applied a multiresolution cross-spectral analysis technique to resolve the temporal relationship between the NAO and ENSO. According to our cross-correlation analysis the shift between SOI and NAOI is about 4 years. Periods of ENSO and NAO phenomena were identified by auto-correlograms and periodograms. The auto-correlograms of SOI and NAOI are in Fig. 3-13a. The cyclicity of both indexes is more evident if we plot the 3-years moving averages of the auto-correlation coefficients (Fig. 3-13b). SOI shows the 28-years cycle. As follows from combined periodograms (Fig. 3-14), SOI has a significant period of 13–14 years; other 6.5-; 4.2-year and 3,6-year periods were found, as well. NAOI has a unique significant period of 7.7-year. In Fig. 3-15, there are the cross-correlations of the Southern Oscillation Index (SOI) and mean annual discharge of the Mary river (Australia), as well as of the North Atlantic Oscillation Index (NAOI) and mean annual discharge of the Danube river (Europe). There is a direct relationship between Mary discharge and SOI, and an indirect relationship between Danube discharge and NAOI. This means that the Mary River discharge is higher during higher SOI values (La Niña phase). The Danube River discharge is lower during higher NAOI periods. We are aware of the fact that the relationships are weak and the annual means of the indexes can not be used for prediction of the runoff development. The analysis of shorter periods (monthly means) may improve the relation.
53 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
6.0E+02 3.59 SOI 5.0E+02 6.5 4.0E+02 13.5 5.6 4.14 3.0E+02 43 2.0E+02 24 1.0E+02 0.0E+00 9.73 8.70 7.90 7.19 6.61 6.09 5.69 5.32 5.00 4.72 4.46 4.24 4.04 3.84 3.67 3.51 3.37 3.23 3.11 3.00 2.89 2.79 2.70 2.62 2.54 2.46 2.39 2.32 2.26 2.20 2.14 2.09 2.03 57.50 34.33 23.80 18.50 15.13 12.78 11.10 125.00
6.0E+01 7.7 NAOI 5.0E+01 4.0E+01 3.0E+01 2.0E+01 1.0E+01 0.0E+00 9.21 8.38 7.72 7.13 6.65 6.21 5.84 5.50 5.21 4.94 4.70 4.48 4.28 4.10 3.92 3.77 3.63 3.50 3.38 3.26 3.15 3.05 2.96 2.87 2.79 2.71 2.63 2.56 2.50 2.43 2.37 2.32 2.26 2.21 2.16 2.11 2.07 2.02 65.50 40.33 27.80 21.75 17.57 14.88 12.88 11.38 10.11 141.00 Fig. 3-14 Combined periodograms of SOI and NAOI.
0.45 0. 3 0. 3 0.15 0.15 0 r 0 r -0.15 -0.15 -0.3
-0.3 -0.45 -28 -14 0 14 28 -28 -14 0 14 28 Mary - SOI l Danube - NAOI l
a) b) Fig. 3-15 Cross-correlation of a) the Southern Oscillation Index (SOI) and mean annual runoff of Mary river (Australia), b) the North Atlantic Oscillation Index (NAOI) and mean annual runoff of Danube river (Europe).
The aim of the chapter was to look for the cycles of the alternating dry and wet periods in the available discharge time series of the selected large rivers of the world. We identified the 14-years cycle (about 7 dry years alternated by seven wet years), amplified by the 28-years cycle, and 20-22- years cycle in some regions. Of course, the cycles are not regular, but in the long-term mean (about 180 years) they are near the mentioned values. The statistical analysis of the available long discharge series of the selected large rivers of the world show the main 3.6-, 7-, 13–14-, 20–22-, and 28–32-year cycles of extreme river discharge. Also the time shift of the periods exists in
54 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region dependence on longitude and position relative to the Equator (Equatorial Zone, Northern or Southern Hemisphere). There is a direct relationship between the length of series and the length of the cycles, which can be identified by statistical analysis. To identify 28-years cycle we need at least 90-100 years data series. Trends have not been detected for the large European river discharges. However the cyclic behavior between dry and wet periods are very clear. Neither the trends of runoff decrease nor increase were found in long runoff series of the large European rivers. The cyclic occurrence of dry and wet periods was proved, however. The temporal shift of the runoff extremes occurrence was identified by cross- correlation analysis. The dry and wet periods do not occur in the same years over the world, but their appearance is not random only. The influence of SO and NAO on the runoff cycles was also analyzed. The 13- 14-years period of SOI was identified by periodogram. Such a 14-years period was found also in most of the analyzed discharge series. It is dubious to assign the runoff variability all over the world to El Niño phenomenon, but they both are probably a manifestation of the same natural system. The runoff of most Australian and Pacific rivers is higher during El Niño episode. The trend analysis and the analysis of periodicity of the available long discharge series show the following: The trend analysis of the long discharge time series (more than 180 years) of the large West/Central European rivers (Goeta, Rhine, Neman, Loire, Weser, Danube, Elbe, Oder, Vistule, Rhone, and Po) shows no significant trend of the annual mean river discharge. In south-eastern European Rivers (Dniepr, Don, and Volga) decrease of runoff was found during 1881–1990. If we want to identify any trend uninfluenced by the 28-years periodicity of the discharge time series, we must determine the trend during a closed multiple loop both, starting and terminating by either minima (e.g., 1861– 1946 in Central Europe) or maxima (e.g., 1847–1930 or 1931–1984 in Central Europe). Trends determined for other periods are influenced by the periodicity of the series and depend on the position of the starting point on the increasing or recession curve. If we want to compare the regime characteristics of the shorter periods (e.g. 10 years), we must select for the comparison such a period in the past that corresponds to the same phase of the cycle (with time shift of about 28 years). Significant change in discharge characteristics found by such analysis can be related to climate change. Nevertheless, we must take into account the existence of longer cycles that were not found yet because of the length of the available discharge series (Klige et al., 1989).
55 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region 3.2 Analysis of natural fluctuations and long-term trends in annual discharge along the Danube River
We assembled the mean annual runoff series of seven stations along the River Danube (Fig. 3-16) from the Global Runoff Data Center, Koblenz, database with the aim to analyze the long-term variability of the mean annual runoff along the River Danube: (1) Hofkirchen; (2) Achleiten; (3) Kienstock (Krems–Stein till 1970); (4) Bratislava; (5) Nagymaros; (6) Turnu Severin (Orsova till 1970); (7) Ceatal Izmail. The basic statistical characteristics of annual discharge time series for the period 1901–2000 are presented in Table 3-2. Details on monitoring of Danube runoff are given in Svoboda et al. (2000). To detect the non- homogeneities in discharge series we used the AnClim software developed by Štepánek (2003). The homogeneity of discharge series was tested by the Alexandersson standard normal homogeneity test (Alexandersson, 1986).
3
1 5 2 47.78°N 18.95°E 4 7
6 1. Hofkirchen 44.7°N 22.42°E 2. Achleiten D a n u 3. Kienstock b e 4. Bratislava 5. Nagymaros 6. Turnu Severin 250 km 7. Ceatal Izmail
Fig. 3-16 Scheme of River Danube basin; location of water gauging stations considered.
Table 3-2 Basic hydrological characteristics of discharge time series, Danube River: Qa – 3 -1 -1 2 average annual discharge [m s ], qa – mean annual specific yield [l.s km ], cs – coefficient of asymmetry, cv – coefficient of variation Station HofkirchenAchleiten Kienstock Bratislava NagymarosTurnu Severin Ceatal Izmail 1901–20001901–2000 1901–20001901–20001901–2000 1901–2000 1921–2000 Area 47496 76650 95970 131329 183533 576232 807000
Qa 639 1423 1821 2033 2341 5609 6419 Median 629 1407 1817 1999 2335 5498 6355 qa 13.46 18.56 18.97 15.48 12.75 9.73 7.95 cs 0.14 0.11 0.23 0.24 0.34 0.61 0.41 cv 0.20 0.16 0.16 0.16 0.17 0.17 0.18
Qamin 343 983 1285 1420 1630 3782 4024
Qamax 925 1869 2525 2856 3331 8265 9370
56 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The data from the Turnu Severin station are very important for the trend analysis, as they have been collected from a rocky profile since 1840 and we can trust them. The absolute minimum annual discharge in Orsova (today Turnu Severin) 3 -1 was observed in 1863, Qamin = 3471 m s , while the absolute maximum one was 3 -1 in 1915, Qamax = 8265 m s (Fig. 3-17a). The analysis of the Orsova data shows that the wettest decade was in 1910–1919, while the driest one was in 1857– 1866, when the absolute maximum and minimum annual discharge was observed, respectively. The wet and dry periods, as well as the long-term trends, are easy to show on the plots of the filtered values. We used several (low-pass, band-pass, high-pass) filters for visual identification of the cyclic component. In Fig. 3-17b, the course of filtered discharge values using a Hodrick–Prescott filter with parameter α=10, 50, 500, and 5000 are presented (Maravall and Del Rio, 2001; Pekárová and Miklánek, 2004b). The wet and dry periods are easy to identify in the graph. To analyze the possible existence of a long-term trend in the discharge data (at the Bratislava and Turnu Severin stations) we used the CTPA (Change and Trend Problem Analysis) software (Procházka et al., 2001), which is aimed at detecting point changes in time series. We applied two tests: (1) a test of trend existence and (2) a test of trend appearance. The tests did not reject the null hypotheses (the series fluctuates along its constant mean) at a significance level 0.05 in the Bratislava and Turnu Severin discharge series. The course of the individual dry and wet periods is similar along the whole river stretch. Fig. 3-17c shows the plot of double 5-year moving averages of the Danube discharge at seven stations. These results indicate that the period around the year 1860 was the driest period in central and eastern Europe since 1840. It is interesting to note that in the pe- riod around the year 1860 the mean annual air temperature in the upper Danube basin was lower by about 1 °C compared with the 1990s. Fig. 3-18a plots the yearly temperature series from Budapest, Bratislava, Prague, Vienna and Hohenpeissenberg stations smoothed by a Hodrick–Pressott filter. The relative homogeneity of the temperature series for the period 1780–2004 was tested by the procedure suggested by Alexandersson and Moberg (1997) and by a CUSUM test of change in linear regression (with Vienna as the stated reference station). The two driest periods of the instrumental era occurred in different temperature conditions. For the local cold periods in 1874–84 and 1935–45 the annual Danube discharges at Turnu station were above the normal level, whereas during the local warm periods in 1860–70 and 1945–55 the discharges were below the normal level. A weak negative correlation was found between the annual Danube runoff and the annual surface temperature at the Vienna station for the period 1840–2000. According to the CUSUM test, the linear regression between the annual Danube discharge Q and that of surface temperature T in Vienna station in the year 1953 changed form from Q = 10345 – 512.T in 1841–1953 to Q = 10800 – 525.T in 1954–2000 (Fig. 3-18b). A one-degree temperature growth should have led to the annual discharge decrease by about 500 m3s-1, i.e. by about 10 percent. From the
57 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region long-term point of view, this hasn’t happened yet and we haven’t calculated any significant decrease of Danube River’s discharge at Turnu station for whole period 1840–2000.
8000 Danube: Turnu Severin Qm ax
] 7000 -1 .s
3 6000 5000 Q [m 4000 Qm in 3000 1840 1860 1880 1900 1920 1940 1960 1980 2000 a)
HP-10 Danube: Turnu Severin 6500 HP-50 HP-500 HP-5000 6000 ] -1 s 3 5500 Q[m
5000 extreme dry periods 4500 1840 1860 1880 1900 1920 1940 1960 1980 2000 b)
4500 7600 7. Ceatal 4000 Iz mail 6900
3500 6200
3000 5500 6. Turnu Severin 2500 4800 ] 6, 7 ] 1, 2, 3, 4, 5 -1
-1 5. Nagymaros s 3 s 3 2000 4100 4. Bratislava Q [m Q [m 3. Stein-Krems - Kienstock 1500 3400 2. Achleiten 1000 2700
1. Hofkirchen 500 2000 1840 1860 1880 1900 1920 1940 1960 1980 2000 c) Fig. 3-17 a) Course of average annual discharge, Danube: Turnu Severin, 1841–2000. b) Course of filtered average annual discharge, Danube: Turnu Severin, 1841– 2000, HP filter for α = 10, 50, 500, 5000. c) The double 5-year moving averages of discharge at seven Danube stations along the river.
58 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
12.3 9.5 11.3 Budapest
8.5 10.3 Bratislava T[°C] 7.5 9.3 Wien Prague 8.3 6.5 Hohenpeissenber T[°C]
7.3 5.5 1770 1790 1810 1830 1850 1870 1890 1910 1930 1950 1970 1990 2010 a)
7500 Q = 10800-525.x 1954-2000 6500 ] -1 s 3 5500 Q [m
4500 Q = 10345 -512.T 1841-1953 3500 7.5 8.5 9.5 10.5 11.5 T [°C] b) Fig. 3-18 a) Courses of the filtered annual air temperature, HP-filter α=50. Budapest, Bratislava, Prague: Klementinum, Vienna, and Hohenpeissenberg stations, 1780– 2004 period. b) Relation between the annual Danube runoff for and annual air temperature in Vienna station. Change in linear regression (Q = 10345 –512.T for period 1841– 1953, and Q = 9366 – 384.T for period 1953–2000).
The variability of streamflow results from the global system of oceanic streams, the global circulation of the atmosphere, and the transport of moisture (precipitation). In recent years, many scientists have studied relationships between atmospheric phenomena (e.g. Arctic oscillation (AO), Southern oscillation (SO), Pacific decadal oscillation (PDO) and North Atlantic oscillation (NAO)) and some hydrological and climatic characteristics (e.g. total precipitation, air temperature, discharge, snow and ice cover, flood risk, sea-level series, or coral oxygen isotope records, dendrochronological series). For example, Jevrejeva and Moore (2001), Jevrejeva et al. (2003) studied variability in time series of ice conditions in the Baltic Sea within the context of NAO and AO winter indices using a singular spectrum analysis and wavelet approach. According to these authors, the cross-wavelet power for the time series indicates that the times of largest variance in ice conditions are in excellent agreement with significant power in the AO at 2.2–3.5, 5.7–7.8, and 12–20 year periods; similar
59 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region patterns are also seen with the SO index (SOI) and Niño-3 sea-surface temperature series. Compagnucci et al. (2000), in order to analyze other wavelength phenomena and to examine the influence of the El Niño–SO (ENSO) events, employed a wavelet filter for removing the strong annual wave in the Atuel river streamflow data. Anctil and Coulibaly (2003) described the local interannual variability in southern Quebec streamflow based on wavelet analysis, and identified plausible climatic teleconnections that could explain these local variations. The span of available observations, 1938–2000, allows the depiction of the variance for periods up to about 12 years. The most striking feature in the 2–3- and 3–6-year bands (the 6–12-year band was dominated by white noise and was not considered further) is a net distinction between the timing of the interannual variability in local western and eastern streamflows that may be linked to the local climatology. Tardif et al. (2003) studied variations in periodicities of the radial growth response of black ash exposed to yearly spring flooding in relation to hydrological fluctuations at Lake Duparquet in northwestern Quebec. They detected periodicities of about 3.5, 3.75, and 7.5 years in all the dendrochro-nological series, with the 3.75- and 7.5-year components being harmonics of a 15-year periodicity. The NAO refers to swings in the atmospheric sea-level pressure difference between the Artic and subtropical Atlantic that are associated with changes in the mean wind speed and direction (Hurrell et al., 2003). Whereas runoff in western and northern Europe increases with positive values of the NAO and AO indices during the period 1901–2000 (Arpe et al., 2000; Turkes and Erlat, 2003; Lapin, 2004; Lindström and Bergström, 2004; Pekárová and Miklánek, 2004a,b; Pekárová and Pekár, 2004), in the middle and lower parts of the Danube basin the annual precipitation totals and runoff decrease with positive NAO values. The 28–29-year runoff variability can be clearly identified in the Neva River series (Pekárová et al., 2003). The Neva River drains the territory of the Finnish and Russian lakes, which accumulate large volumes of water and, thus, multiannually regulate and smooth the runoff. The driest year on Neva was the year 1940 with the mean discharge of 1340 m3s-1, while the wettest one was 1924 with the mean discharge of 3670 m3s-1. The driest 5-yrs period on Neva occurred in 1938–1942, by about 7 years earlier than in the Danube basin. We should notice that the period 1938–1942 was quite wet in the Danube basin. Such analysis supports the hypothesis, that the dry periods do not occur in European rivers simultaneously, but they are a few years shifted depending on location of the basins. The time lag of the dry periods between Danube and Neva runoff is about 11-12 years (Fig. 3-19). From Fig. 3-17 it is clear that the annual Danube runoff fluctuates around the long-term average. To predict the annual discharge for several years ahead, the identification of the cyclical component of the runoff as accurate as possible is necessary (Shmagin and Trizna, 1992).
Significant frequencies λj (periods Tj = 2π/λj) of discharge time series for all Danube stations were identified using the combined periodogram method; see
60 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Pekárová (2003) or Pekárová et al. (2003). The combined periodograms obtained of the Danube runoff at Achleiten, Bratislava, and Turnu Severin stations are drawn in Fig. 3-20. In the Danube discharge time series the following significant periods were found: about 29–31, 20–21, 14, 5, 4.2, 3.64, and 2.4 years. The significance of the appropriate periods was tested by the Fisher–Whittle test (Pekárová et al., 2003). The periods of 2.1–2.4, 3.6, 5–6, 7, 10–11, 14, 20–22, and 28–30 years were found in almost all world discharge series (as well as in precipitation and temperature series) analyzed within different geographical zones, and they can be considered as the general regularity. The regularity is related to general oceanic and atmospheric circulation, part of which are also the quasi-biennial oscillation, ENSO, AO, PDO and NAO phenomena. The long-term runoff variability has its own (today unknown), possibly extraterrestrial, origin (Currie, 1996; Charvátová and Střeštík, 2004).
2900 6100
2700 5800 ] Neva -1 2500 5500 ] Danube s -1 3 s 3 2300 Nev a 5200 Q [m
Danube: Turnu Q [m 2100 4900 1840 1860 1880 1900 1920 1940 1960 1980 2000
Fig. 3-19 Course of filtered annual discharge [m3s-1], Danube: Turnu Severin and Neva. HP-filter for α=400.
200 Danube: Hofkirchen 500 Danube: Achleiten 160 400 120 300 80 200 40 100 0 0 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 30 40 50 70 80 30 40 50 70 80 20 60 90 20 60 90 10 100 200 10 100 200 100 Danube: Bratislava 400 Danube: Turnu 80 300 60 200 40 20 100 0 0 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 30 40 50 70 80 20 60 90 20 30 40 50 60 70 80 90 200 10 100 10 100 200 Fig. 3-20 Combined periodograms of the raw mean annual discharge of Danube River at Achleiten (1901–1999), Bratislava (1901-2000) and Turnu Severin stations (1841- 2000). Significant periods are in years.
61 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3.3 Analysis of natural fluctuations and long-term trends of Danube discharge at Bratislava
This paragraph is focused on dry and wet multi-annual cycles identification in the monthly and annual runoff characteristics for the Danube River at Bratislava. The Hurst coefficient h of the average annual discharge (1876–2005) is 0.59. The multi-annual cyclic component of the average annual discharge at Bratislava was identified through the Hodrick-Prescott filter (Fig. 3-21) (Maravall and Del Rio, 2001), and by spectral analysis. Analyzing of time series can be useful in identifying periodicity in time series, e.g. Autocorrelation Analysis (AC), Power Spectrum Analysis (PSA), Singular Spectrum Analysis (SSA), Maximum Entropy Spectrum Analysis (MESA), Empirical Orthogonal Functions Method (EOFs) / Fourier Analysis (FA), Method of Main Components (MMC), etc. (Jevrejeva and Moore, 2001; Rao and Hamed, 2003; Liritzis and Fairbridge, 2003; Van Gelder et al., 2000; Procházka et al., 2001). In this part, we used the AC method, SSA method, MESA method, and the combined periodogram method (described by Pekárová et al., 2003) to identify inter-annual dynamics patterns of the monthly and annual Danube discharge time series. Fig. 3-22 depicts an autocorrelogram and a combined periodogram (Pekárová, 2003; Pekárová et al., 2006, 2007a) of the average monthly discharges (12- months seasonality was removed from the time series). The spectral analysis confirmed that the occurrence of multi-annual cycles within dry and wet periods exhibits the following durations: 2.35; 3.65; 5.6; 7; 10.5; 12-14; 21; and 28-30 years. In the Fig. 3-23 the results of spectral analysis are shown. The most significant period in the Danube’s annual discharge at the Bratislava station that was identified in the periodogram and by the maximum entropy.
2410 HP-10 HP-50 HP-400 HP-6400 HP50000 ] -1 s 3 2055 [m a Q
? dry periods 1700 1870 1885 1900 1915 1930 1945 1960 1975 1990 2005
Fig. 3-21 Identification of the multi-annual dry and wet periods, and of the long-term trend, by the Hodrick-Prescott filter, for lambda = 10, 50, 400, 6400, and 50000. Period 1870–2005, average annual flows of Danube in Bratislava.
62 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
247 0.2 264 302 43.8 160 20.6 204 22 345 13.3 25.2 362 412m 15 3.65 121 17 28.7 0.1 1.2 10.1 30 34y Rk 0
-0.1 136 278 438 29/2.4 68/5.6 11.3 23 -0.2 36.5 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 lag [month]
1.4E+07 Danube River 1.2E+07 ENSO NAO Sun - QBO Bratislava Sun - 1.0E+07 ENSO Wolf 8.0E+06 Wolf AO 6.0E+06 4.0E+06 2.0E+06 0.0E+00 2.3 2.4 2.6 2.7 2.9 3.1 3.2 3.4 3.6 3.8 4.1 4.3 4.5 4.8 5.1 5.4 5.7 6.1 6.5 6.9 7.3 7.8 8.3 8.8 9.4 10.1 10.8 11.5 12.4 13.3 14.3 15.5 16.8 18.3 20.0 22.0 24.8 28.0 32.0 38.5 47.0 60.0 90.0
period [year] 130.0
Fig. 3-22 An autocorrelogram (top) and a combined periodogram (down) of the average monthly discharges at Bratislava without 12-months seasonality, cycles in months/years
a b
c d Fig. 3-23 Spectral analysis of the mean annual discharge of the Danube River for the period 1876–2006: a) periodogram; b) PS Tukey; c) PS Blackman and Tukey d) PS MESA (software AnClim, Štepánek, 2003); Values were normalized. (RN - red noise; WN – white noise, 95%, the 95% confidence level)
63 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
1.E+06 160000 4.2 14 21 Danube: 140000 Wolf 10.5 8.E+05 Bratislava 120000 1876-2005 6.E+05 10.5 100000 3.6 7 5.2 80000 4.E+05 2.35 27 60000 40000 2.E+05 60 Power spectrum Power spectrum 20000 5.2 21 36 42 0.E+00 0 110100110100 Period (yr) Period (yr)
1000 400 2.35 6.4 (log) QBOIm 350 SOIw 3.6 300 5.3 42 100 250 26 6.4 200 2.4 13 10 150 100 Power spectrum Power spectrum 50 1 0 110100110100 Period (yr) Period (yr)
30 25 AOIw NAOIw 60 36 60 25 20 21 7.8 20 21 36 15 7.8 13.1 15 2.35 2.35 10 10 13.1 5
5 Power spectrum Power spectrum 0 0 110100110100 Period (yr) Period (yr)
Fig. 3-24 Combined periodogram of (a) the annual discharge time series of the Danube River (1876–2005); (b) the annual Wolf Numbers (1876–2005); (c) the Quasi- Biennial Oscillation Index (QBOIm) – monthly time series for the period 1953– 2001 according to Marquardt and Naujokat (1997); (d) the Winter Southern Oscillation Index (SOIw), 1866–2004 (Ropelewski and Jones, 1987; Allan et al., 1991); (e) the Winter NAO Index (NAOIw) from Li and Wang (2003a,b) – long- term trend removed; and (f) the Winter AO Index (AOIw) Index from Li and Wang (2003a,b)– long-term trend removed. spectrum analysis (MESA) – was of 4.2 years; whereas applying an power spectrum analysis (Tukey) – the period lasts 3.6 years. Moreover, periods of 2.35, 5.2, 7, 10.5 and 21 years were also identified to be significant. Next, multi-annual cycles of annual time series of Sun activity (Wolf numbers), Arctic Oscillation (AO), North Atlantic Oscillation (NAO), Southern Oscillation (SO), and Quasi-Biennial Oscillation (QBO) phenomena were analyzed (Fig. 3-24).
64 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region 3.4 Conclusion
The Hurst coefficient and spectral analysis confirmed the occurrence of multi- annual cycles within dry and wet periods. By auto-correlogram and periodogram, the following cycles were found in discharge series: 2.35; 3.6; 4.3; 7; 10.5; 12- 14; 21; and 28-30 years. As Pekárová and Pekár (2007b) have shown, the 2.35 cycle in discharge series is connected to QBO (Quasi-Biennial Oscillation) phenomenon. The 5.2, 10.5, and 21 year cycles are connected to the Sun’s activity. The cycles of about 3.6, 13 and 26 years in the discharge time series could depend on the SO. The cycles of about 7, 28 and 60 years are connected with the NAO and AO phenomena, and with the thermohaline circulation of the oceans. There exist the teleconnection between multiannual discharge variability, Sun activity and thermohaline circulation. Transport of temperature by thermohaline circulation is probably the cause of time lag occurrence of the multiannual dry and wet periods in discharge series in different Earth regions. This results imply, that the annual runoff series are non-stationary, a natural deterministic multi-annual cycle has been discovered. In making a long-term prediction, the deterministic component in the time series – trends, seasonality and multi-annual cycles – are extrapolated into the future. Various mathematical stochastic-deterministic models are used, being more or less successfully in predicting the behavior of the respective time-series.
65 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
4 Long-term prognosis of Danube discharge using ARMA models and harmonic functions
Here it should be noted that it is considerably difficult to create scenarios for changes in river discharge. The following factors need to be included in simulating the runoff regime of rivers: • Anthropogenic activities in the watershed (deforestation, construction of water reservoirs, urbanization, water diversions, irrigation etc.); • Long-term natural fluctuation of runoff (natural fluctuations in precipitation and air temperature); • Long-term increase in air temperature (climate change). Szolgay et al. (2007) studied and projected changes in river runoff for 20 selected watersheds in Slovakia, but the Danube river was not involved in their monograph. In the following analysis the results of several global and regional rainfall-runoff models were used published over the past eight years (e.g. Nijssen et al., 2001 – VIC model; Arnell, 2003 – Macro-scale model; Lehner et al., 2006 – Water GAP; Nohara, 2006 – GRiveT model, Dankers et al., 2007 – LISFLOOD model). These models are based on a host of global and regional climate models. The authors themselves claim that it is particularly difficult to simulate the flow regime for the Danube River by means of global models. Nevertheless, two scenarios were considered in simulating the changes in monthly average flows. The first scenario – Qscen I. – is based on the work of Arnell (2003) and Nohara (2006) (Fig. 4-1a). This model suggests that a reduction in runoff can be expected (approx. 20 %) for the Danube at station Turnu-Severin.
3000 3500
2500 3000 ] ] -1
-1 2500 s s
3 2000 3 2000 1500
Qm [m 1500 Qm [m 1000 Qob1876-2005 1000 Qob1876-2005 Qscen I. Arnell+Nohara Qscen II. Dankers 500 500 I III V V II IX XI I III V V II IX XI a) b) Fig. 4-1 Comparison between historical records of river flow and two scenario of river runoff for the Danube at Bratislava: a) Arnell and Nohara, b) Dankers.
66 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The second scenario – termed as Qscen II., incorporating the temperature scenario H12A2 – based on work of Dankers et al. (2007) assumes that there will be no change as to the annual average flow; however, a significant change in the intra-annual flow regime can be expected (Fig. 4-1b). 4.1 Scenarios based on analysis of monthly discharge series
The analysis of time series of monthly discharge of the Danube reveal that the increase in air temperature over the past 30 years was not accompanied with increasing runoff variability of the Danube. Conversely, as stated above, variability in the monthly flows decreased considerably after 1975. Based on this it can be assumed that the variability in monthly discharge of the Danube at Bratislava will decrease due to the expected warming of air in the future. Annual patterns of the runoff will flatten due to the earlier onset of snow-melt in the Alps and anthropogenic activity – construction of additional water reservoirs on the Danube and its tributaries. Linear trends in monthly time-series of discharge are depicted in Fig. 4-2.
3500 Qm [m 3 s -1 ]
3000
VI V 2500 IV III
2000
II
1500 I
1000 1876 1926 1976 2026 3500 Qm [m 3 s -1 ]
3000
VII 2500
V III 2000 IX
XII XI 1500 X
1000 1876 1926 1976 2026
Fig. 4-2 Filtered values and linear trends in monthly discharge of the Danube at Bratislava by 2025.
67 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3000
2500 ] -1 s 3 2000 Qm [m 1500 Qob 1876-2005 Qob 1976-2005 1000 I II III IV V V I V II V III IX X XI XII a)
3000
2500 ] -1 s 3 2000 Qm [m 1500 Qob 1876-2005 Qscen,trend 2025 1000 I II III IV V V I V II V III IX X XI XII b) Fig. 4-3 a) Comparison of long-term observed Danube monthly discharges for two periods: 1876–2005 and 1976–2005; b) Scenario of monthly discharges for 2025 based on the linear trend functions.
Fig. 4-3 and Table 4-1 shows the expected discharge of the Danube in the time horizon 2025.
Table 4-1 Scenario of the Danube monthly discharges for 2025 based on the linear trend functions Discharge I II III IV V VI VII VIII IX X XI XII year 3 -1 Qscen,trend [m s ] 1700 1900 2300 2550 2600 2550 2300 2050 1800 1650 1700 1800 2075 Qscen,trend [%] 3.7 9.6 10.4 7.3 -3.1 -8.5 -12.7 -10.4 -5.4 6.1 15.3 18.1 0.8
68 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
4.2 ARIMA modeling approach
To model the Danube discharge (yearly, monthly) time series, several linear autoregressive models were tested (Shmagin and Trizna, 1992; Pekárová and Pekár, 2006; Komorník et al., 2006; Mares et al., 2007). Box-Jenkins (B-J) models represent a reasonable method to describe the periodical time series with essential stochastic behavior. These models are highly flexible and capable of modeling (stochastically) the seasonality and the trends in a more precise way than other conventional analysis techniques. The basic component of these models is an independent and normally distributed random variable Et (Pekárová and Pekár, 2006). The ARMA(p,q) model of order p and q can be defined as a combination of the AR (auto-regressive) and MA (moving average) processes and can be described in the following form
Yt = ϕ1Yt-1 +...+ ϕpYt-p + Et + Θ1Et-1 +...+ ΘqEt-q , (4.1) where: Et - independent and normally distributed random variable with 2 zero mean value m=0 and variance σE ,
Θi - parameters of MA polynomial of order q,
ϕi - parameters of AR polynomial of order p. In an operator-based form, the model can be written as:
ϕ(B) Yt = Θ(B) Et , (4.2)
where: B - reversion shift operator defined as BYt = Yt-1 Θ - regular MA operator of order q, ϕ - regular AR operator of order p. In designing the ARIMA(p,d,q) model, stationarity of the analyzed series (Y) is not required. Instead of the original series, this model operates with series (Z) of differences of the first order or any higher order. For the differences of the first order, the following applies:
Zt = Yt –Yt-1, Zt-1 = Yt-1 –Yt-2 , ..., . (4.3)
The generalized operator form is:
1 Zt = ∇ Yt = (1-B)Yt , (4.4)
69 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
where: ∇1 - the backwards difference operator. The final form of the ARIMA model can be written as:
d ϕ (B) ∇ Yt = Θ(B) Et. (4.5)
In the B-J methodology, the seasonality as well as the trend are modeled stochastically. The general form of the SARIMA(p,d,q)x(P,D,Q)L model takes the following form:
12 d D 12 ϕ (B) ϕ(B )∇ ∇ 12 Yt = Θ(B)Θ(B )Et, (4.6)
D where ∇ 12 - the seasonal backwards difference operator, ϕ - the regular SAR (seasonal auto-regressive) operator of the order p, Θ - the regular SMA (seasonal moving average) operator of the order q.
In order to identify this model it is necessary to analyze the particular components of the time series in the following sequence: • Identification of a trend (differentiating of order d) and seasonality (seasonal differentiating of order D); • Selection of a model type (AR, MA, ARMA) and determination of the model’s order; • Estimation of model parameters; • Verification of the model.
4.2.1 Yearly Danube discharge prediction at Turnu Severin
When modeled the annual Danube discharge several linear autoregressive models were used. These models can be described in the following general form:
m X t = A0 + ∑()Aj cos(λ j t) + B j sin(λ j t) + ARIMA + CR + ε t t = 1, .., N. (4.7) j=1 a harmonic a B-J impact white component component of R noise
70 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region where:
Xt - the mean annual discharge;
λj - the significant frequencies given by the periodogram;
Aj , B j , j = 1,2, … m - parameters of the harmonic component (A0 – the mean of the time series); ARIMA - the autoregressive component (Box-Jenkins model); C - the regressive coefficient of an exogenous impact R on the discharge (e.g., North-Atlantic Oscillation – NAO);
εt - the stochastic component (white noise).
Successively the following model types were tested (Pekárová, 2003): 1. a model based on harmonic functions (hidden periods); 2. linear Box-Jenkins autoregressive models AR, MA, ARMA, and SARIMA (Box and Jenkins, 1976); 3. a model involving a harmonic (deterministic) component and a B-J autoregressive component; 4. a model involving a harmonic (deterministic) component, a B-J autoregressive component, and a regressive component modeling the impact of the winter NAO phenomena. Model 4 can predict one year only. Therefore we focus on Model 3.
4.2.1.1 Autoregressive model with the harmonic component for Danube: Turnu Severin
In order to obtain the long-term annual discharge prediction we proceed according to the following steps: • to take the time series of logarithms of annual discharge and center it; • to remove the harmonic (deterministic, wavelet) component from the time series using model PYTHIA (the sum on the right-hand side of the equation (2)); the obtained time series is called residuals; • to remove the autoregressive component from the residuals (we found the appropriate Box-Jenkins autoregressive model); the obtained time series is called innovations (shocks); • to test the correctness of the model specification (the autoregressive part of the B.-J. model must be stationary, the moving average part must be invertible, and innovations must be Gaussian white noise); • to predict dynamically the annual discharge, to specify the appropriate confidence intervals.
71 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The harmonic component specification The deterministic (harmonic) component of the model is identified in the form:
m X t = A0 + ∑()Aj cos(λ j t) + B j sin(λ j t) + ε t t = 1, ..., N (4.8) j=1
Here, the parameters Aj , B j , j = 1,2, … m in (4.8) are estimated by
2 N A j = ∑ xttj.cos(λ .) , (4.9) N t =1
2 N B jt= xt.sin()λ j . . N ∑ t =1 (4.10)
Then, a simple prediction of the stochastic process at time z can be given as
m ⎡ ⎛ 2π ⎞ ⎛ 2π ⎞⎤ x = A + ⎢A .cos⎜ ()N + z ⎟ + B .sin⎜ ()N + z ⎟⎥. (4.11) N +z 0 ∑ j ⎜ T ⎟ j ⎜ T ⎟ j=1 ⎣⎢ ⎝ j ⎠ ⎝ j ⎠⎦⎥
On the basis of (4.9)–(4.11) a model for predicting the harmonic component of the discharge time series (model PYTHIA) was developed (Pekárová, 2003). Parameters of the model are given in Table 4-2. By the verification of the model PYTHIA we calibrated model on the period 1840–1980 and simulated values for period 1981–2000 were compared to the measured discharge. The results obtained by the model depend on the proper cycle length’s estimation.
Table 4-2 Parameters of the model (4.8) for m=18, T(j) – periods in years j T(j) A(j) B(j) J T(j) A(j) B(j) 1 140 -0.00966 -0.02017 10 12.5 0.01911 0.02576 2 105 0.01722 -0.01637 11 10.7 0.02496 -0.02411 3 75 0.01364 -0.00828 12 8 -0.01261 -0.03019 4 57 0.00404 0.02246 13 4.99 -0.02647 0.04409 5 47 0.02174 -0.02835 14 3.64 0.05156 -0.02939 6 42 0.04426 0.02443 15 4.3 -0.04078 -0.00556 7 31.4 -0.00653 0.0695 16 2.4 -0.05727 -0.00443 8 21.3 -0.04212 -0.05034 17 1.6 -0.00202 0.00533 9 14 0.01168 0.04632 18 1.2 -0.01942 -0.01105
72 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
For example, when the period length of 3.64 was estimated with the error of 0.2 year, the error of the prediction at year 10 can be up to two years. After removing the cyclical component from the residuals, we look for the autoregressive component.
4.2.1.2 The autoregressive component specification
The autoregressive component in residuals is identified by the Box–Jenkins methodology. Before doing this, it is necessary to verify whether the residuals are (at least weakly) stationary, i.e. whether the methodology is applicable. In order to do this, we use the augmented Dickey–Fuller test. Since the test statistic (-5.2760) is less than the 5% critical value of the test (-1.9419), the hypothesis that the time series considered is non-stationary is rejected at a significance level of 0.05. The Box–Jenkins model consists of two parts, i.e. that of autoregression and that of moving averages. The partial autocorrelation function (PACF) tells us that for residuals the autoregressive part is at most of the order 30, whereas the autocorrelation function (ACF) gives us that the moving average part is at most of the order 26. Here, the limit of the significance of the coefficients at the 5% level is ±0.158. The values of the autocorrelation function and the partial autocorrelation function are shown in Fig. 4-4. In order to choose the appropriate model, the following statistics and criteria were taken into account: adjusted R2, sum of squared residuals, Akaike information criterion, stationarity and invertibility of the model. Statistical properties of all possible ARMA models within a given range show that the most appropriate model among them is ARMA(30, 26) with non-zero parameters as given in Table 4-3. The table also contains the statistical characteristics of the model and its parameters.
0.3 0.3
0.15 0.15
0 0 r r -0.15 -0.15
-0.3 -0.3 1 6 11 16 21 26 31 36 1 6 11 16 21 26 31 36 ACF Danube l PACF Danube l
Fig. 4-4 Autocorrelation function (ACF) and Partial autocorrelation function (PACF) of the residuals (the annual discharge time series after removing the deterministic part of the discharge).
73 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 4-3 Statistical properties of the ARMA model and its parameters for Danube: Turnu Severin discharge Variable Coefficient Std. Error t-Statistic Prob. AR(15) -0.206551 0.073183 -2.822376 0.0056 AR(18) 0.242639 0.069500 3.491226 0.0007 AR(30) -0.172386 0.064778 -2.661200 0.0088 MA(4) 0.135307 0.050743 2.666549 0.0087 MA(5) -0.149948 0.060415 -2.481961 0.0144 MA(7) 0.381937 0.077993 4.897084 0.0000 MA(10) 0.186058 0.052844 3.520883 0.0006 MA(21) -0.401109 0.053639 -7.477894 0.0000 MA(26) -0.156082 0.053861 -2.897875 0.0045 R-squared 0.374663 Mean dependent var 0.006263 Adjusted R-squared 0.333658 S.D. dependent var 0.119508 S.E. of regression 0.097554 Akaike info criterion -1.750585 Sum squared resid 1.161057 Schwarz criterion -1.553053 Log likelihood 123.6633 Durbin-Watson stat 1.968596
Now we verify whether the ARMA component of the model is specified correctly. The moduli of all inverted roots of the characteristic equation of the autoregressive part are less than unity (i.e. all roots lie outside the unit circle); hence, the specified autoregressive process is stationary. Similarly, the module of all inverted roots of the characteristic equation of the moving average part are less than unity; hence, the specified moving average process is invertible. Finally, we verified that innovations are Gaussian white noise; namely, we show that innovations satisfy the following two properties: 1. they are independent (there is no correlation between any two terms); 2. they are identically distributed from N(0, σ2). All statistical tests resulted in the conclusion that the model was built correctly. The model was used in order to predict the annual Danube discharge at Turnu Severin station. The predicted data for 20 years ahead are presented in Fig. 4-5. The dry period around 1990 should be followed by a wet period peaking at around year 2005. At Turnu Severin, the year 2006 should be the wettest.
74 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
3 -1 Q [m s ] Danube 9000
measured values
7000
5000
3000 1840 1860 1880 1900 1920 1940
3 -1 Q [m s ] Danube 9000
7000
predicted values 5000
3000 1940 1960 1980 2000 2020 2040
Fig. 4-5 Prediction of the annual discharge of Danube River at Turnu Severin by autoregressive model with harmonic component, period 2001–2020. Confidence intervals, 0.05 significance level. Gray bold line – predicted values, black line with triangles – measured values.
The long-term Danube discharge time series and the stochastic prediction analysis at Turnu Severin led to the following results:
• The minimum annual discharge in Orsova was in 1863, Qamin = 3471 3 -1 3 -1 m s , while the maximum one was in 1915, Qamax = 8265 m s . The analysis of the Orsova data shows that the wettest decade was in 1910– 1919, and the driest decade was 1857–1866, when the maximum and minimum runoffs were observed respectively. • The results of the statistical analysis of discharge time series indicate that the period around the year 1860 was the driest period in central and eastern Europe since 1840. It is interesting to note that in the period around the year 1860 the mean annual air temperature in the upper and middle Danube basin was lower by about 1 °C compared with the 1990s.
75 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
It is important to note that the two driest periods of the instrumental era occurred under different temperature conditions. • Discharge fluctuations of 28–31, 20–21, 14, 4.2 and 3.6 years were found in the series. • In order to provide long-term predictions, four different models were developed: harmonic models, linear autoregressive Box–Jenkins models, autoregressive models with a harmonic component, combined autoregressive models with a harmonic component and a regressive component expressing the impact of the NAO. • According to the model results, the dry period around 1990 in the Danube basin should be followed by a wet period peaking at around year 2005 and 2010. For the Danube at Turnu Severin, the year 2006 should be the wettest. Finally, we should comment on the occurrence of the uncertainty in the results obtained by stochastic models. These results cannot be considered as definitive. The time series has to be completed by new data; it is necessary to analyze not only annual discharge time series, but also those of extremes. It should be profitable to analyze time series observed over shorter time steps (monthly) than those of the annual time step.
4.2.2 Monthly Danube discharge prediction at Bratislava
The following two model types were used for Danube monthly discharge prediction: • a model based on harmonic functions (hidden periods – long-term cycles); • the SARIMA model involving B-J seasonal autoregressive moving average components, and one regressor – long-term cycles.
4.2.2.1 Markov model based on harmonic functions (hidden periods)
In simulating monthly flows by applying harmonic functions, the following procedure was followed: • A logarithm of the series of average monthly discharge was calculated in order to remove the seasonal element (annual cycle). The resulting series of residua was further tested on “normality”; • The PYTHIA model (Pekárová, 2003) was used to predict the series of residua over a period of 8 years ahead based on the assessed significant periods; • The seasonal element was added to the predicted residua, upon which the series was de-logarithmed.
76 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 4-4 shows the significant periods T, being identified by the autocorrelogram and combined periodogram. Fig. 4-6a illustrates the prediction of mean values of monthly discharges for the Danube River for 2006–2013.
Table 4-4 Significant periods in months, Fourier coefficients A(j), B(j), model PYTHIA j T(j) A(j) B(j) month year 1 20.4 1.70 0.00772 -0.02795 2 29 2.42 0.00033 -0.00845 3 41 3.42 -0.0062 -0.02493 4 44 3.67 0.01675 -0.00283 5 52 4.33 0.01769 0.02168 6 60 5.00 0.02258 0.00073 7 84 7.00 -0.02093 0.00674 8 102 8.50 -0.01085 -0.00911 9 122 10.17 -0.02046 -0.00562 10 148 12.33 -0.00382 0.01598 11 169 14.08 0.01175 -0.02079 12 248 20.67 0.01468 -0.02021 13 266 22.17 -0.0116 -0.0215 14 346 28.83 -0.01634 0.00375
4.2.2.2 Box-Jenkins SARIMA model involving one regressor – long-term cycle
Box-Jenkins (1976) autoregression models (ARMA, ARIMA, SARIMA, etc.) have found a wide range of applications, especially in business and marketing. However, these models proved unsuccessful for predicting hydrological time series. Introducing another regressor – a long-term variability of the cycle – we managed to achieve better characteristics of the autoregressive models. In this case, the classical model SARIMA was used; however, one additional regressor was added to the model. The test results are summarized in Table 4-5, resulting predictions are drawn in Fig. 4-6b.
Table 4-5 SARIMA Model Summary Forecast model selected: SARIMA(1,0,0)x(0,1,1)60 + 1 regressor Cyklus Sampling interval = 1.0 month(s); Length of seasonality = 60 Math adjustment: Log base 10; Seasonal differencing of order: 1 Parameter Estimate Stnd. Error t P-value AR(1) 0.501605 0.0249486 20.1055 0.000000 SMA(1) 0.917566 0.00770562 119.078 0.000000 Cyklus 0.0489896 0.0286753 1.70842 0.087557 Estimated white noise variance = 0.013656 with 1198 degrees of freedom Estimated white noise standard deviation = 0.116859
77 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
5500 observed 4500
] simulated
-1 3500 s 3 2500 Q [m 1500
500 Jan-80 Jan-85 Jan-90 Jan-95 Jan-00 Jan-05 Jan-10 a)
5500
4500 ]
-1 3500 s 3 2500 Q [m 1500
500 Jan-80 Jan-85 Jan-90 Jan-95 Jan-00 Jan-05 Jan-10 b) Fig. 4-6 Prediction of the mean monthly discharge of the Danube River at Bratislava, period 1901–2005 calibration, period 2006–2013 prediction: a) model PYTHIA, b) model SARIMA, Upper and lover 95% confidence interval.
4.3 Conslusion
This chapter presents some results of the long-term prediction of average annual and monthly discharges of the Danube River for eight years ahead by applying two stochastic models. The results of this part suggest that the water year 2008 is likely to be dry, while in 2009–2010 elevated discharge is likely to be observed. Beyond 2011 a very dry period is expected to come. We are fully aware of the high uncertainty that arises from the use of such stochastic predictive models. Efficiency of predictions decreases considerably with the extent of prediction. Further analysis of several more European rivers will, however, enable to explain the long-term discharge variability, which nowadays remains unknown, and thus it is considered a random variable in stochastic models. Efficiency of predictions is likely to improve in the future, thus models such as these presented in this monograph will be widely used in hydrological practice.
78 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
5 Assessment of T-year maximum discharge of the Danube at Bratislava
Considering climate change, the scientific community is interested in studying the occurrence of extreme hydrological events. Higher frequency of extreme flows and increase in runoff in many regions in the second half of the 20th century have been published by many authors (Foster et al., 1997; Milly et al., 2002; Peterson et al., 2002; Walter et al., 2004; Micevski et al., 2006). Zhang et al. (2001) shows that higher occurrence frequency of annual maximum water level over time is not influenced by a single factor (climate change), but there exist other multiple factors resulting from human activities. But there are cases when measured data indicate a decrease or no change in the magnitude and flood frequency (Aizen et al., 1997; Zhang et al., 2001; Holko and Kostka, 2005; Bača and Mitková, 2007). Estimation of T-year maximum discharge belongs to the most important tasks for engineering hydrology. For estimating design flows at a gauging station, statistical methods are usually deployed. Selection of an appropriate distribution function, method of parameter estimation, as well as selection of an period to be analyzed - often depends on the tradition in the country where they are used. Probability distributions and methods for parameter estimation were subject of many studies (Kohnová et al., 2005a,b, 2006; Szolgay et al., 2007). Analyzes of computing methods for QT discharges are presented in the work of Szolgay et al. (1996), Hlavčová et al. (2005) or Szolgay and Kohnová (2003c). The method of annual maximum series is the most frequently used method for probabilistic assessments in hydrology, but values obtained from this method cannot provide adequate information about a river’s flow regime. The annual maximum discharge series consider only one value per year. However, the use of annual maximum series may involve some information loss. For example, some peaks within a year may be higher than the maximum flow in others years, and hence they remain ignored (Kite, 1997; Chow et al., 1988). This situation can be avoided by using the peaks over threshold (POT) method. Data series of the POT method consider all values exceeding certain threshold (Bayliss, 1999; Rao and Hamed, 2000). When POT data series is determined, it is necessary to consider the independence of the flood waves.
79 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
In this chapter the annual maximum discharge method and the POT method were applied on discharge series of the Danube at Bratislava. The record covers a period of 131 years (1876–2006). 5.1 History of the Danube floods
According to Kresser (1957) and Horváthová (2003), the oldest evidence of floods on the Danube goes back 1012. Other floods with severe consequences, as documented in historical annals, occurred in 1210, 1344, 1402, 1466, 1490, 1499, 1501, 1526, 1572, 1594, 1598, 1670, 1682, 1721, 1787, 1809, 1876, 1897, 1899, 1954, 1965, 2002. There are indirect pieces of evidence that these floods were of a size comparable to the 1899 and 1954 floods (Photo 5–1). The flood of August 1501 can be taken as the highest flood that was ever observed in the upper Danube reach (and also in Bratislava) according to reliable historical records of the Austrian Hydrographic Service. The peak discharge at Vienna was estimated at up to 14 000 m3.s-1. There is also some evidence of floods in the 16th-17th century (1594, 1598, 1670, and 1682). The most severe flood occurred in the 18th century (1787) – which became to be known as the “All Saints’ Flood” – at the end of October and beginning of November. The peak discharge at Vienna reached 11 800 m3 s-1 according to the historical annals at the Austrian Hydrographic Service. The first flood records in the Slovak portion of the Danube trace back to 1526 and are documented in the municipal archives of the city of Bratislava. However, the morphology of the watercourse was different at that time. In the medieval ages there were either no or only very low flood-preventing dikes alongside the river. The stream channel had low capacity and the water often flooded the lower parts of the city (including a part of the city’s downtown - Main Square). The 1526 flood occurred unexpectedly over night, with an aftermath of 53 fatalities. Other series of severe floods damaged Bratislava in the period from 1721 and 1809. In the winter of 1809, the flood and ice sheets destroyed several houses in the vicinity of the river. The most damaged parts of the city were: Zuckermadl, Vydrica, Gorkého St., Jesenského St., and Laurinská St., as well as Grösslingova St.. The entire residential area in the suburbs of Petržalka (Engerau) was destroyed. After 28 years, on January 27, 1837, flood waters returned once again. The water overflowed two ice barriers and flooded the surrounding area. Only thanks to a few brave fellows, who destroyed the barriers, the water could flow freely away. During the flood of 1850 (February 5) the streets of Bratislava were under water again. Flood marks on old building in the downtown are still showing the height to which water reached during the medieval (Photo 5–2). The water stage was by nearly 200 cm higher than that of 1954. The far largest flood on the Danube in the nineteenth century occurred in September of 1899 (Fig. 5-1). This flood was a consequence of a flush-flood on the Inn River, a tributary emptying into the Danube (Kresser, 1957). The flood culminated on September 17, 1899, at 0600 hrs., and reached 11 200 m3 s-1
80 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
(stage: 972 cm) at the Krems station; and 10 500 m3 s-1 at the Vienna station. According to Angelini (1955), the peak water level at Bratislava was observed on September 19, with a stage of 970 cm (10 870 m3 s-1).
Photo 5–1 Building with the Danube flood marks in Schönbühel, Austria (photo P. Pekárová).
81 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Photo 5–2 Flood 1850 marks on Laurinská street in center of Bratislava, and the mark in detail (photo P. Pekárová).
82 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The largest flood on the Danube in the previous century occurred in July, 1954 (Photo 5–3). The flood peaked at Bratislava on 15 July with a stage of 984 cm (10 400 m3 s-1). According to Szolgay and Kohnová (2003), this was an 80-year flood. The other high floods (in order of peak discharge) in the second half of the 20th century were floods in 1991 (Photo 5–5, Photo 5–6), 1965 (Photo 5–4), and in 1975. During the flood of August 15-16, 2002, two waves with discharges of about - 6800 and 10 370 m3 s-1, respectively, (corresponding water stage of 993 cm) were recorded at the Bratislava station.
12000 Kienstock Qm 10000 ]
-1 Bratislava Qm
s 8000 3 6000
Q [m 4000 2000 13.IX.99 18.IX.99 23.IX.99 28.IX.99 a)
12000 10000 Kienstock Qm ]
-1 Bratislava Qm s 8000 3 6000
Q [m 4000 2000 8.VII.54 13.VII.54 18.VII.54 23.VII.54 b)
13000 11000 Bratislava Qm ] Kienstock Qm -1 9000 s 3 7000 5000 Q [m 3000 1000 5.VIII.02 10.VIII.02 15.VIII.02 20.VIII.02 c)
Fig. 5-1 Observed discharge at Kienstock (data from the period prior to 1975 were recalculated from the Krems station) and Bratislava: a) 1899, b) 1954, and c) 2002.
83 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Photo 5–3 Discharge measurement during flood 1954 on Danube in Štúrovo (photo from (HMÚ, 1954)).
Photo 5–4 Breakthrough of the Danube dike near Patince in 1965 (photo Makeľ).
84 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Photo 5–5 Flood 1991 on Danube in Bratislava (photo P. Miklánek).
Photo 5–6 Flood 1991 mark on Hullám čárda on Danube bank near Gabčíkovo, and the mark in detail (photo V. Bezák).
85 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
5.2 Annual maximum discharge method
In general, the severity of a flood, with respect to its peak flow, is expressed as the probability of its occurrence or exceedance. The series of the annual maximum discharges (AMS) are shown in Fig. 5-2. Theoretical log-normal and log-Pearson type-III distribution curves were used to calculate the probability of exceedance of the Danube AMS for the period 1876–2006. In Fig. 5-3 empirical and theoretical (log-Pearson type III) distribution curve of the maximum discharge and 5% and 95% confidence limits are shown. The calculated T-year maximum discharges of the Danube at Bratislava for the period 1876–2005 are listed in Table 5-1. The frequency curve (see Fig. 5-3) is only an estimate of the population curve; and in fact, it is not an exact representative feature of the flood being studied. A streamflow record is only a data sample. How well this sample will predict the total flood experience depends upon the size of the sample, its accuracy, and whether the underlying distribution is known or not. Confidence limits provide either a measure of the uncertainty of the estimated exceedance probability of a selected discharge or a measure of the uncertainty of the discharge at a chosen level of exceedance probability. Application of confidence limits to water resources planning and decision-making policies depends upon the needs of the user (Bulletin 17b, 1982). The relationship between the probability of exceedance p of a certain annual discharge Qmax and the return period T is generally given as p=1/T. In Slovakia historically is used the following formula (Szolgay et al., 2007): p = 1 – e-1/T . (5.1) which is based on peak over threshold (POT) method. Then return period is given by formula (see Fig. 5-4): T = –1/(ln(1-p)). (5.2)
11000 y = 3.3894x + 5555.7 Danube: Bratislava 10000
] 9000 -1
.s 8000 3 7000 [m 6000 max
Q 5000 4000 3000 1870 1890 1910 1930 1950 1970 1990 2010
Fig. 5-2 Annual maximum discharge Qmax series during period 1876–2006, Danube: Bratislava.
86 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
16000 1501 flood 14000 1787 flood
] 12000 -1 s 3 10000
8000
Qmax [m Qmax 6000
4000
2000 0.400 0.500 0.900 0.050 0.100 0.200 0.600 0.700 0.800 0.950 0.980 0.001 0.002 0.005 0.010 0.020 0.300 0.990 %
Fig. 5-3 Empirical and theoretical – log-Pearson type III (mean log =3.7471; σ=0.1186; skew=0.1869) distribution curve of the maximum discharge, period 1876–2006, 5% and 95% confidence limits. Historical floods in the year 1501 and 1787, Danube: Bratislava.
16000 1501 flood 14000
] 12000 -1 s
3 1787 flood 10000
8000
Qmax [m Qmax 6000
4000
2000 0.1 1.0 10.0 100.0 1000.0 returnpriod [years]
Fig. 5-4 Return period of floods on Danube at Bratislava gage according to theoretical – log-Pearson type III exceedance curve.
87 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
5.3 Peaks over threshold (POT) method
The POT series includes all maximum discharges over the defined threshold. The number of peaks (n) in the statistical series must be higher than N, where N is number of years of the complete record. The first threshold can be chosen near the Qa value (long-term mean discharge per year). But this value is rather low, thus the POT series may exhibit high diffusion and may also include some insignificant maximum values. Therefore, a threshold value is chosen accordingly to the POT series with inclusion of the average 5 maximum values per year. In order to guarantee independence of the POT data, the following criteria were used (Bayliss, 1999): • Time period between two peaks that occurred consecutively must be at least three times the time of the rising limb. • Minimum discharge between two peaks must be less than 2/3 of the peak discharge of the first wave. An example of how the chosen data were used for the POT method is shown in Fig. 5-5. The maximum discharge was obtained on the fourth day, therefore the peak E can be automatically included into the POT series. The time of rising limb E is about 15 hours. The D peak lagged less than 15 hours behind the E peak. Wave D is a dependent variable, hence it cannot be included into the POT data series (the same situation is for the peak wave - F). The C peak is time- independent of E and minimum discharge between E and C is less than 2/3 of the E value, and therefore the C peak can be included into the POT series. The peak of the wave A is less than the threshold and cannot be included into the POT data series. The occurrence of maximum flows is a random process defined with:
χ()t = sup Ζν ; Ζν = Χ -x B . (5.3) ν ≥1
50 E C F 40 B D 30
20 A discharge 10
0 0123456 day
Fig. 5-5 Application of the data selection of the POT method.
88 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Distribution function of annual maximum is
F()x = P {}χ()t ≤ x (5.4)
To obtain this distribution function one must combine the following two main variables: 1. number of peaks in each year ν ;
2. flow exceedance over threshold Z = X − xB
5.3.1 Number of peaks
The number of peaks in an interval (0, t) – one year in this analysis – is a random variable ηt which can take values 0, 1, 2, …. with probabilities
pν ()t = P {ηt =ν }. The occurrence of peaks during the time interval can then be described by a Markov process with the following intensity function:
P{}η()t + Δt −η(t) λ()t,ν = lim Δt→0 Δt . (5.5)
The probability of occurrence of peak exceedance is given as:
p' t = λ t,ν −1 p t − λ t,ν p t ν () ( )ν −1 () ( ) ν ( ), p' t = −λ t,0 p t ο () ( )()ο . (5.6)
The solution to this equations (5.6) represents the probability law of occurrence of peaks and depends on the form of intensity function λ (Vukmirovič and Petrovič, 1995): λ()t Poisson λ()t,ν = λ()t (1−ν a) Bernoulli (binomial) (5.7) λ()t (1+ν b) negative binomial The record of daily discharge (131 years, 1876–2006) from the Bratislava gauging station was chosen as an example of how the POT method can be employed. As threshold value was chosen a discharge of 3000 m3s-1, and according to criteria presented by Bayliss (1999), the POT data were selected (362 peaks). Number of peaks has a Poison distribution, the average number of peaks per year is 2.76 (Fig. 5-6).
89 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
0.30 0.25
y 0.20 0.15
Probabilit 0.10 0.05 0.00 012345678 number
Fig. 5-6 Poisson distribution of the number of the discharge peaks, Danube: Bratislava.
5.3.2 Peaks over threshold
Distribution function for peak exceedance flow is defined as:
H ()z = P {Z ≤ z } (5.8)
Distribution can be generalized as three-parameter Gamma distribution with the following density function:
⎧ a ⎫ k k +1 ⎡ ⎛ k +1⎞⎤ aΓ k−1 ⎪⎢Γ⎜ ⎟⎥ a ⎪ a ⎛ z ⎞ ⎪ ⎝ a ⎠ ⎛ z ⎞ ⎪ (5.9) h()z = ⎜ ⎟ exp⎨⎢ ⎥ ⎜ ⎟ ⎬ k+1⎛ k ⎞ μ ⎢ ⎛ k ⎞ ⎥ μ μΓ ⎜ ⎟ ⎝ ⎠ ⎪ Γ⎜ ⎟ ⎝ ⎠ ⎪ ⎪⎢ ⎥ ⎪ ⎝ a ⎠ ⎩⎣ ⎝ a ⎠ ⎦ ⎭
Such distribution functions as two-parameter Gamma, Weibull’s (Fig. 5-7, Fig. 5-8, Fig. 5-9), Erlang’s or exponential distributions are special cases of this general distribution. For purposes of rough estimation it is recommended to pick either one-parameter distribution (exponential, Rayleigh’s) or two-parameters distribution (Weibull or Gamma). Distribution of the maximum does not have more than four parameters.
Exponential H(z)=1-exp(-z/μ) Weibull H(z)=1-exp(z/β)α (5.10)
90 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
12000
10000
] 8000 -1 s 3 6000
Qpot [m 4000
2000 0.500 0.001 0.005 0.010 0.050 0.100 0.200 1.000 p Fig. 5-7 Exceedance curve of the maximum discharge over the threshold (threshold is 3000 3 -1 m s ). QPOT series for the Danube at Bratislava, period 1876–2006 (empirical ant theoretical (Weibull) distribution curve).
10000
8000 Weibull ]
-1 6000 s 3
Q[m 4000
2000
0 1 10 100 1000 Return period
Fig. 5-8 Return period curve of discharge Qpot for the Danube at Bratislava, period 1876– 2006 (Weibull), threshold is 3000 m3s-1.
5.3.3 Annual maximum of POT series
Distribution of the annual maximum is obtained by combing the distributions of the number of peaks and distributions of peak exceedance over a threshold value (Todorovič, 1970):
∞ ν F()x = po + ∑[]H ()x pν ()t . ν =1 (5.11)
91 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Fig. 5-9 Histogram of discharges Qpot for the Danube at Bratislava, period 1876–2006 and Weibull density function.
If the number of peaks follows the Poisson distribution, then F(x) takes the form
F()x = exp{}− Λ[]1+ H (x) . (5.12)
Should the number of peaks exhibit a binomial distribution (Bernoulli’s) or even a negative binomial distribution (Pascal’s), the distribution of annual maximum is Binomial distribution for the number of peaks
a Λ F x = e−Λ ⎡1+ ⎛e a −1⎞H x ⎤ () ⎢ ⎜ ⎟ ()⎥ ⎣ ⎝ ⎠ ⎦ (5.13)
Negative binomial distribution for the number of peaks −b −Λ F x = e−Λ ⎡1− ⎛1− e b ⎞H x ⎤ () ⎢ ⎜ ⎟ ()⎥ ⎣ ⎝ ⎠ ⎦ . (5.14)
5.3.4 Return period
Return period T of maximum discharge at POT method is traditionally defined as
1 T ()x = . (5.15) 1− F()x
92 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The return period T is expressed in years, taking values equal or greater than 1, because its distribution exhibits values between 0 and 1. Since F(x) only asymptotically converges to 0 or 1, in practice it is seldom justified to consider a return period outside the interval 2 ≤ T (x) ≤ 5N . Theoretical definition of the return period implies that the value x can be expected at least once every T-th year. Return period can be determined as:
1 T1 ()x = , (5.16) 1− H1 ()x
where H1(x) is the distribution function of POT series set for n/N=1 (average number of peaks (n) in a year equal to 1, N – number of years). Definition (25) remains valid if the distribution of the number of peaks is Poissonian. The relationship between the two return periods is given as:
1 T = . (5.17) 1 lnT − ln()T −1
Comparison of the series of annual maximum discharges Qmax and the T-year discharge computed from POT data series QmaxPOTw is listed in Table 5-1. The values, computed according to log-Pearson type III distribution from Qmax are the higher. 5.4 Assessment of the maximum T-year water level
To estimate the T-year water stages (H) a.s.l. we used the T-year peak discharge values determined from the log-Pearson type-III distribution and the actual rating curve (relation between stages a.s.l. and discharges). This rating curve for Danube at Bratislava station (VUVH, 2003) is shown on Fig. 5-10. Computed T-year absolute water levels are indicated in Table 5-2. The 1000-year water stage of the Danube at the Bratislava station was estimated to be between 139.65–140.91 m a.s.l (see Fig. 5-11).
3 -1 Table 5-1 T-year peak flow Qmax [m s ] i) log-Pearson type III distribution; ii) log-normal distribution; and iii) the QmaxPOTw of the Danube at Bratislava within 1876–2005 T 1000 500 200 100 50 20 10 5 [m3s-1] i) 13975 13044 11837 10943 10054 8877 7966 7009 ii) 12920 12195 11231 10494 9743 8740 7959 7147 iii) 13000 12300 11300 10600 9800 8700 7800 7000
93 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 5-2 T-year water level H [m a.s.l.] according to log-Pearson type III distribution of Qmax, CL- confidence limits; the Danube at Bratislava within 1876–2005 T in years 1000 500 200 100 50 20 10 5 P=p.100 % 0.1 0.2 0.5 1 2 4.9 9.5 18 [m a.s.l.] i) 140.23 139.80 139.18 138.67 138.14 137.38 136.74 136.04 i) 95% CL 139.65 139.24 138.67 138.22 137.73 137.04 136.46 135.81 i) 5% CL 140.91 140.45 139.78 139.23 138.64 137.78 137.08 136.30
142 H = -2.2548E-08Q2 + 1.0751E-03Q + 1.2961E+02 141 H1000 140 H 139 100 138 H50 137 136 100 50
135 1000 H (m a.s.l) Q Q 134 Q 133 132 131 130 0 2000 4000 6000 8000 10000 12000 14000 Q (m 3s-1)
Fig. 5-10 Relation between absolute water level H [m a.s.l.] and discharges Q [m3s-1], Danube: Bratislava station.
142 H = -2.2548E-08Q2 + 1.0751E-03Q + 1.2961E+02
141 5% CL
H1000
140 H (m a.s.l) 95% CL 139 1000 Q
138 10000 11000 12000 13000 14000 15000 16000 Q (m 3s-1)
Fig. 5-11 1000-year absolute water level H [m a.s.l.] according to log-Pearson type III distribution of Qmax, CL- confidence limits; the Danube at Bratislava within 1876–2005.
94 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region 5.5 Flood risk assessment
Flood risk R is defined as the probability that one or more events will exceed a given flood magnitude within a specified period of N years. Accepting the flow frequency curve to be accurately representing the flood exceedance probability, an estimate of the risk may be computed for any chosen time period (Bulletin 17b, 1982). Two basic approaches may be used to compute the risk: nonparametric and parametric methods. Parametric methods which use the binomial distribution require that the annual exceedance frequency be exactly known. The binomial expression for risk estimation is:
N! R = .p I (1− p) N −I (5.18) I I!(N − I)!
where: RI is the estimate of the risk in N years with the exact I number of flood events exceeding a flood magnitude with annual exceedance probability p. When I equals 0, equation (5.18) reduces to:
R = (1− p) N 0 (5.19)
where R0 is the estimated probability of non-exceedance of the chosen flood magnitude in N years. From this, the risk R of one or more exceedance becomes:
N R (1 or more) = 1− (1− p) . (5.20)
For a 1-year period the probability p of exceedance (which is the reciprocal of the recurrence interval (return period) T for T>10), expresses the risk. There is a 1 percent chance that the 100-year flood will be exceeded in a given year. This statement, however, ignores the considerable risk that a rare event will occur during the lifetime of a structure. 5.6 Conclusion
The frequency curve on Fig. 5-3 can be used to estimate the probability of a Danube flood exceedance during a specified time period N. For instance, there is a 45.3% chance that the flood with annual exceedance probability of P=1 percent (e.g. p=0.01 discharge 10 900 m3s-1, and water level 138.67 m a.s.l.) will be exceeded one or more times in the next 60 years at Bratislava gage.
95 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
6 Assessment of maximum runoff volume for a given duration of t-day flows (1876–2005)
Apart from the peak runoff the most important flood characteristic is the flood volume. In order to find solutions to some water management and hydrotechnical problems, it is necessary to know not only values of the peak discharge Qmax, but also the shape of the flood wave or the peak runoff volume Vmax. In applied hydrology it is difficult to assign values of flood wave volume to a particular probability of exceedance and corresponding values of T-year discharges. Their dependence is irregular to a considerable extent, so a flood wave hydrograph of a given exceedance probability must be known, too. The significance of flood wave volume – as an important hydrological characteristic – was evident during the 1965 flood. During this flood event, the river dikes broke under the pressure exerted by the long duration of high water stages, but not because of the extremely high water stages themselves. Slovak and Czech hydrologists Bratránek (1937), Čermák (1956), Dzubák (1969), Zatkalík (1970), Hladný et al. (1970) dealt with this issue also. In assessing the climate change impacts on the river runoff regime (extremes, flood hydrographs and drought periods), it is expected – as it was mentioned – that the increase in air temperature may cause (or already has caused) an increase in the extreme flows and flood volumes. Since a 130-year series of the mean daily discharge of the Danube at Bratislava gauging station (Pekárová et al., 2007a-d) is available, we could calculate the 130-year series of the highest (annually) 2-, 5-, 10-, 15-, 20-, 25-, 30- and 60- consecutive days wave volumes. These series were subsequently divided into two 65-year sub-series and changes in their cumulative probability distribution functions were analyzed. For calculation of annual maximum runoff volumes of particular durations, a reconstructed 130-year mean daily discharge series (1876–2005) of the Danube at the Bratislava gauging station was used (Fig. 6-1), Pekárová at al. (2007a). The runoff volume series are shown in Fig. 6-2 and Table 6-1.
96 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 6-1 The maximum yearly discharge Qmax [m3.s-1] and maximum yearly flood volume V [mil m3] for various runoff wave duration t (2, 5, 10, 15, 20, 25, 30 and 60 days), Danube River, Bratislava Year Qmax V2 V5 V10 V15 V20 V25 V30 V60 1876 8166 1401 3285 6476 9203 12147 14500 16335 24877 1877 5047 859 2050 3708 5077 6177 7020 8108 15136 1878 4698 798 1936 3738 5374 6978 8412 9806 17436 1879 4109 702 1562 4314 6767 9120 11292 13185 24433 1880 8722 1471 3101 5512 7850 10021 11915 13697 24644 1881 7419 1042 2296 4033 5215 6573 8099 9455 16078 1882 6024 1089 3024 6436 8290 9449 10405 11216 17652 1883 8722 1489 3577 6318 7686 8681 9516 10239 16328 1884 3692 635 1426 2715 3833 4798 5828 6802 13358 1885 3487 595 1384 2542 3468 4195 4858 5413 9708 1886 3824 639 1500 2873 4035 5198 6247 7308 12820 1887 3436 564 1284 2421 3893 4714 5335 6534 11918 1888 4985 815 1863 3608 5097 6537 7870 9076 17323 1889 3692 637 1574 3058 4491 5852 7261 8615 16378 1890 8227 1415 3412 6211 8277 9992 11416 12483 19762 1891 4471 745 1799 3389 4600 5649 6710 7946 15018 1892 8380 1428 3255 5577 7881 9748 11620 13346 22769 1893 4127 696 1650 3236 4624 6029 7481 8721 14925 1894 3483 587 1393 2710 3918 5049 6127 7246 12960 1895 6979 1205 2954 5325 7079 8605 10042 11239 19095 1896 6295 1063 2510 4615 6302 8017 9627 11391 22244 1897 10140 1745 4037 6664 8597 10169 11671 13319 21993 1898 3526 598 1414 2757 3969 5163 6445 7762 13968 1899 10870 1852 4336 7124 8886 10212 11289 12299 16496 1900 4912 832 1961 3657 5175 6615 8009 9590 17190 1901 4316 684 1668 3237 4508 5491 6307 7065 12376 1902 4805 754 1744 3340 4704 6061 7471 8891 16111 1903 6485 1031 2189 3460 4555 5686 7103 8439 15097 1904 3653 572 1370 2620 3844 4982 6060 7085 13646 1905 3968 658 1623 3135 4532 5892 7289 8499 16652 1906 6110 1007 2221 4023 5470 6963 8263 9875 19130 1907 6077 1028 2539 4856 6851 8543 10714 12398 21826 1908 4943 832 2018 3891 5514 6891 8199 9275 15481 1909 6061 984 2229 3808 5389 6981 8211 9380 15386 1910 6110 1009 2283 3987 5657 7450 9258 10997 21252 1911 4984 823 1811 3456 4911 6295 7519 8608 15471 1912 6698 1131 2611 4684 6335 8258 9773 10988 19331 1913 4846 806 1939 3779 5388 7211 8705 10508 18175 1914 6029 1005 2291 4203 6026 7894 9378 10688 18966 1915 5851 943 1996 3296 4592 5879 7056 8162 14818 1916 4510 746 1798 4092 5576 6565 7790 8979 16309 1917 6698 1122 2566 4370 5713 7414 8896 10218 17123 1918 6175 1029 2413 4152 5532 6713 7878 9035 16193 1919 5168 846 1989 3685 5034 7550 9837 11366 17595
97 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
1920 8616 1433 3279 5333 7122 8855 9991 11135 17930 1921 4192 690 1423 2420 3500 4583 5600 6660 12869 1922 4616 790 1740 3206 4710 5951 7299 8520 14986 1923 8685 1488 3445 5468 6759 7800 8692 9754 15743 1924 6583 1090 2602 4963 7045 8880 10727 12603 22969 1925 7005 1067 2425 3880 5114 6189 7297 8311 13960 1926 7810 1203 2893 5732 8312 10899 13387 16024 28549 1927 4297 710 1713 3300 4748 6141 7535 9055 16774 1928 6208 996 2149 3492 4359 5530 6735 7774 13217 1929 3430 577 1374 2566 3610 4707 5711 6886 12474 1930 4787 805 1863 3486 4848 5953 6809 7670 13361 1931 4444 728 1638 3111 4250 5382 6376 7566 14161 1932 5210 849 1824 3155 4469 5825 6948 8302 14157 1933 4516 753 1721 3059 4337 5648 7003 8312 15507 1934 3000 477 1156 2265 3160 3882 4798 5609 10593 1935 5042 849 2035 3845 5471 6984 8409 9941 17830 1936 5084 845 2051 3760 5211 6508 7786 9037 16647 1937 4891 810 1826 3262 4850 6267 7645 9120 16739 1938 5350 854 1858 3521 5289 6676 7787 8747 14489 1939 5084 1041 2403 4130 5636 6958 8303 9440 15651 1940 7260 1232 2896 5034 6750 8306 9755 10984 18457 1941 5611 867 1929 3539 4971 6206 7701 9033 17501 1942 5467 915 2191 4055 5610 7016 8337 9646 16326 1943 5103 839 1963 3665 5009 6153 7378 8596 15777 1944 6926 1157 2796 5503 8016 10099 11722 13270 22804 1945 5611 916 2110 3864 5514 6959 8261 9705 18771 1946 5828 959 2245 3698 4880 6097 7161 8141 14009 1947 4958 925 2251 4344 6251 7709 8970 10133 18765 1948 6674 1089 2492 4557 6551 8437 10016 11332 19596 1949 7160 1184 2747 4424 5413 6393 7460 8609 13810 1950 3153 501 1093 2030 2924 3854 4759 5587 10511 1951 5511 881 1807 3017 4134 5389 6620 7826 15145 1952 5376 919 2165 4027 5839 7250 8920 10633 17945 1953 4594 774 1764 3244 4646 6005 7307 8516 15317 1954 10400 1728 4152 7410 9640 11524 13078 14330 20999 1955 6797 1128 2626 4565 6119 7874 9346 10951 19688 1956 7080 1168 2540 4007 4893 5819 7111 8438 15428 1957 6714 1132 2642 4733 6004 7273 8481 9360 16000 1958 6500 1068 2279 4018 5767 7155 8238 9219 15483 1959 7315 1209 2682 4281 5463 6994 8707 9923 17904 1960 4431 690 1539 2916 4144 5186 6325 7697 14024 1961 5068 917 1884 3253 4411 5559 6868 8374 15766 1962 5690 806 1853 3670 5394 7081 8674 10151 17739 1963 4042 666 1568 2830 3885 4822 5751 6722 13075 1964 4180 890 1977 3234 4176 5113 6065 6951 12602 1965 9224 1577 3902 7457 10696 13799 16509 19179 33998 1966 7302 1196 2811 4902 6501 8347 9948 12468 23454 1967 5101 862 2031 3680 5514 7111 8661 10309 19645 1968 5250 825 1860 3107 4123 5182 6529 7849 13602
98 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
1969 4080 683 1474 2494 3445 4381 5367 6268 12013 1970 6865 1163 2756 4513 6247 7890 9100 10950 21342 1971 4124 627 1395 2514 3777 4851 6011 6956 11885 1972 4520 703 1630 2761 3703 4836 6095 7081 12223 1973 4946 815 1917 3529 4849 5989 7146 8242 14784 1974 5441 1122 2518 4121 5561 6997 8396 9978 16631 1975 8715 1445 3359 5733 7631 9377 11191 12818 20110 1976 4497 735 1677 2819 3856 4858 5777 6674 11244 1977 6370 1030 2106 3567 4848 6202 7709 9326 15746 1978 4426 676 1547 2998 4203 5460 6462 7449 14255 1979 6568 1115 2561 4299 5789 7085 8211 9695 17349 1980 5432 876 1933 3394 5054 6618 8228 9714 18044 1981 7686 1256 2869 4834 6186 7256 8860 10224 16000 1982 5808 878 1896 3389 4649 6055 7369 8703 16304 1983 4463 671 1493 2860 4226 5436 6573 7744 14304 1984 3693 591 1307 2588 3660 4783 5693 6554 12152 1985 7650 1241 2558 4049 5324 6417 8021 9083 14784 1986 4552 708 1541 2926 4186 5453 6691 7924 14877 1987 5414 943 2198 3502 5210 6965 8564 10272 19098 1988 6872 1178 2805 5216 7207 9190 11220 13021 21810 1989 5128 580 1363 2588 3798 4789 5892 7020 13082 1990 5347 856 1818 3208 4331 5290 6262 7433 12818 1991 9430 1555 3331 5160 6833 8077 9111 10356 17839 1992 6095 983 2033 3691 5063 6203 7288 8213 15084 1993 6097 838 1822 3255 4817 6037 7056 7966 13446 1994 5990 919 2184 3908 5253 6473 7645 8657 15640 1995 5832 910 2071 3668 5252 6716 8497 10195 17675 1996 6393 989 1987 3178 4472 5918 6994 7998 14152 1997 7432 1193 2673 4538 6440 8594 10214 11619 17725 1998 4646 927 1977 3516 5291 6759 7918 8856 14313 1999 5846 986 2447 4591 6496 8414 10156 11747 19785 2000 5268 819 1891 3641 5203 6768 8573 10199 18646 2001 5603 933 2184 3770 5217 6596 7762 8991 16479 2002 10370 1737 3844 6084 7837 9166 10233 11294 17240 2003 4435 739 1795 3338 4437 5416 6329 7559 12476 2004 4864 717 1622 2940 4087 5251 6379 7440 13150 2005 6741 1091 2385 3854 5544 6825 7995 9044 16882
A method described in detail by Mitková et al. (2002) was used to calculate the maximum runoff volume series for various runoff wave duration t (2, 5, 10, 15, 20, 25, 30 and 60 days). The maximum annual flood volume was determined for the chosen runoff wave of t-duration.
99 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
10000 1934
8000 ] -1 s
3 6000 4000 Q [m
2000
0 01-Jan 01-Feb 01-Mar 01-Apr 01-May 01-Jun 01-Jul 01-Aug 01-Sep 01-Oct 01-Nov 01-Dec
10000 1965
8000 ] -1 s
3 6000
4000 Q [m
2000
0 01-Jan 01-Feb 01-Mar 01-Apr 01-May 01-Jun 01-Jul 01-Aug 01-Sep 01-Oct 01-Nov 01-Dec Fig. 6-1 Example of the Danube daily mean discharges Q in two years (in year 1934 was calculated the lowest 60-days runoff volume V60; and year 1965 was calculated the highest 60-days runoff volume V60).
2000 15000 ] ] 3 3 1500 10000 1000 500 5000 V2 [mil m 0 V20 [mil m 0 1875 1900 1925 1950 1975 2000 2025 1875 1900 1925 1950 1975 2000 2025
20000 5000 ] 3 ] 3 4000 15000 3000 10000 2000 1000 5000 V5 [mil m 0 V25 [mil m 0 1875 1900 1925 1950 1975 2000 2025 1875 1900 1925 1950 1975 2000 2025
8000 25000 ] ] 3 3 6000 20000 15000 4000 10000 2000 5000 V10 [mil m 0 V30 [mil m 0 1875 1900 1925 1950 1975 2000 2025 1875 1900 1925 1950 1975 2000 2025
15000 40000 ] ] 3 3 10000 30000 20000 5000 10000 V15 [mil m 0 V60 [mil m 0 1875 1900 1925 1950 1975 2000 2025 1875 1900 1925 1950 1975 2000 2025
Fig. 6-2 Flood wave volume series of the Danube for various flood durations (e.g. V15 means runoff volume in 15 days).
100 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Considering the 2-day and 5-day maximum runoff volumes, the flood of 1899 was the highest one within the period 1875–2005. But considering the 10- to 60- day runoff volumes, the highest flood was that of 1965. 6.1 Theoretical exceedance curves of maximum Danube runoff wave volumes
First, a theoretical probability distribution function was chosen for the given duration of runoff t and than T-year extreme runoff wave volumes were calculated (Mitková et al., 2002). A log-normal distribution function was selected for calculation of the T-year maximum runoff volume with the given runoff time duration t. Theoretical exceedance probability curves of the runoff volumes of the Danube at Bratislava, for the runoff duration t = 2-, 5-, 10-, 15-, 20-, 25-, 30-, and 60- days, in logarithmic-probability scale are demonstrated in Fig. 6-3. Return periods were calculated according to (5.2). The results suggest (Table 6-2), that 100-year maximum of 2-day runoff volume (V2) is 1766 mil. m3, 5-day (V5) one is 4079 mil. m3 and 10-day (V10) one is 7004 mil. m3.
100000 V2 V5 V10 V15 V20 V25 V30 V60
10000 ] 3 Vmax [mil. m 1000
100 -year volume 1 -year volume 100 0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 95.0 98.0 99.0 99.5 99.8 99.9 P [%]
Fig. 6-3 Theoretical (log-normal) exceedance function of the runoff volumes of the Danube at Bratislava, for runoff duration t equal to t = 2-, 5-, 10-, 15-, 20-, 25-, 30-, and 60- days, in logarithmic-probability scale.
101 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 6-2 The T-year runoff volumes Vt [million m3] of the Danube at Bratislava within 1876–2005. P=p.100% T 1000 500 200 100 50 20 10 5 2 1 P % 0.1 0.2 0.5 1 2 4.9 9.5 18 39 63 V2 2189 2062 1894 1766 1636 1462 1327 1188 993 836 V5 5070 4773 4379 4079 3775 3370 3055 2730 2278 1915 V10 8566 8100 7480 7004 6519 5868 5359 4829 4084 3477 V15 11281 10706 9936 9343 8735 7916 7271 6596 5638 4848 V20 13874 13189 12271 11562 10834 9849 9073 8256 7093 6130 V25 16172 15402 14368 13567 12742 11625 10741 9807 8473 7362 V30 18350 17504 16364 15479 14567 13328 12345 11305 9811 8563 V60 30658 29352 27586 26209 24782 22833 21276 19618 17217 15187
6.2 Maximum runoff volumes analysis for two periods: 1876–1940 and 1941–2005
The long-term observation series of the Danube flow at Bratislava, and of the evaluated flood volume series is also suitable for tests of significance of the climate change impacts. We divided the original 130-year series into two sub- series, each with a duration of 65 years. The basic statistical characteristics of both sub-series are shown in Table 6-3. We attempted to test whether the both series (with the differences as shown in Fig. 2-1) can be considered statistically belonging to the same population. For the two main statistical parameters of the series – mean and variance – the null hypothesis H0: means (variances) are statistically equal against alternative hypothesis H1: means (variances) are statistically different were stated. In both cases, the null hypotheses were not rejected on a 0.05 significance level, even for all flood durations. The relevant density curves are demonstrated in Fig. 6-4, some of the tests results are given Table 6-4. In Fig. 6-5 it is illustrated how the density curves of the flood volumes of the Danube at Bratislava changed. It can be seen that curves changed in both directions. From the results (Table 6-3 and Table 6-4) it follows, that the hypothesis of both series belonging to the same distribution was not rejected at the 0.05 significance level, and the changes in mean and variance are neither driven to one direction nor significant (Fig. 6-5a,b). These results are confirmed by values of the test H0 (test of mean equality of all old and new runoff volume series V2–V60).
102 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
(X 0.0001) (X 0.0001) 15 6 Variables Variables 5 12 V2a V5a V2b V5b 4 9 3 6 density density 2 3 1 0 0 0 0.4 0.8 1.2 1.6 2 012345 (X 1000) (X 1000)
(X 0.0001) (X 0.0001) 4 3 Variables Variables V10a 2.5 V15a 3 V10b V15b 2 2 1.5 density density 1 1 0.5 0 0 12345678 1357911 (X 1000 (X 1000
(X 0.00001) (X 0.00001) 24 16 Variables Variables 20 V20a V25a V20b 12 V25b 16 12 8 density 8 density 4 4 0 0 2 4 6 8 10 12 14 0 3 6 9 12 15 18 (X 1000) (X 100
(X 0.00001) 16 (X 0.00001) 10 Variables Variables V30a 12 8 V60a V30b V60b 6 8 4 density 4 density 2
0 0 0.2 0.5 0.8 1.1 1.4 1.7 2 0.2 0.7 1.2 1.7 2.2 2.7 3.2 3.7 (X 1000 (X 1000
Fig. 6-4 The probability density curves of the different flood volumes of the Danube in Bratislava, for two periods: Vta – old period 1876–1940; Vtb – new period 1941– 2005; t – runoff duration.
103 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 6-3 Statistical characteristics of the flood volumes Vt [million m3] time sub-series of the Danube at Bratislava : Vta = 1876–1940 and Vtb = 1941–2005 V2a V2b V5a V5b V10a V10b V15a V15b Sum 61201 63014 142199 142866 260081 251060 359266 346474 Aver 942 969 2188 2198 4001 3862 5527 5330 Stdev 299 262 702 619 1166 1044 1467 1383 Min 477 501 1156 1093 2265 2030 3160 2924 Max 1852 1737 4336 4152 7124 7457 9203 10696 V20a V20b V25a V25b V30a V30b V60a V60b Sum 452333 435796 539295 521892 623038 606208 1092510 1067070 Aver 6959 6705 8297 8029 9585 9326 16808 16416 Stdev 1761 1699 2030 1947 2257 2205 3641 3653 Min 3882 3854 4798 4759 5413 5587 9708 10511 Max 12147 13799 14500 16509 16335 19179 28549 33998
Table 6-4 Results of the tests (variable F and P-value) F P-value F P-value F P-value V2 0.319 0.5727 V15 0.619 0.4328 V30 0.437 0.5095 V5 0.008 0.9297 V20 0.702 0.4035 V60 0.374 0.5418 V10 0.511 0.4759 V25 0.589 0.4443 Qmax 0.897 0.3452
Box-and-Whisker Plot Box-and-Whisker Plot
V2a V25a
V2b V25b
0 0.4 0.8 1.2 1.6 2 0 3 6 9 12 15 18 a) (X 1000) b) (X 1000) Fig. 6-5 Change of the statistical characteristics of the old and new series for flood durations: a) 2 days, and b) 25 days. 6.3 Conclusion
The conclusion of this chapter is that the runoff volume regime during the floods (in term of mean values, variances and consequently of probability distribution function) has not changed substantially during the last 130 years, which is of importance to water management and water managers. This conclusion pertains not only the short-term flood runoff episodes (V2), but also the long-term ones (V60). There is a possibility to assess the potential flood extent in the case when the flood bank of the Danube River would break, like in 1965.
104 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
7 Catastrophic flood scenario for the Danube River at Bratislava
According to Directive 2007/60/EC of the European Parliament of 23 October 2007 on the assessment and management of flood risks (Directive, 2007), the Member States shall among others to prepare description of the floods which have occurred in the past and which had significant adverse impacts on human. It is also needed to elaborate for each river basin district flood hazard maps according to the following scenarios: (a) floods with a low probability, or extreme (catastrophic) event scenarios; (b) floods with a medium probability (likely return period ≥ 100 years); (c) floods with a high probability. In large international river basins – such as the Danube – it is necessary to synchronize the methodologies and to prepare common procedures. In the framework of the International Hydrological Programme of UNESCO the programme of the Regional co-operation of the Danube countries is running for more than 40 years. Several projects were finalized within the collaboration. The topic of floods was touched by several of them in last years: • Project 4: Coincidence of flood flow of the Danube river and its tributaries (Prohaska et al., 1999); • Project 5.2: Flow regime of river Danube and its catchment (Belz et al., 2004). • Project 7: Regional analysis of the annual peak discharges in the Danube catchment (Stănescu et al., 2004). 7.1 Analysis of floods regime of the Danube River at Bratislava
From the whole 130-years series (1876–2005) of mean daily discharge of the Danube at Bratislava (Fig. 7-1) we counted all floods over 4000, 5000, 6000, 7000, 8000, 9000, and 10000 m3s-1. Totally we analyzed 322 flood waves in the 130-years period. In Table 7-1 there are listed the numbers of floods in individual classes in the whole 130-years period, and in two 65-years subsets, respectively. Columns in Fig. 7-2 show number of floods in selected classes and in individual months of the year. The Danube floods at Bratislava occur in May – June most frequently. Four floods with peak discharge exceeding 10 000 m3s-1 occurred
105 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region during the 130-years period (see Fig. 7-3). Extreme flood occurred once in July (1954) and September (1899), and twice in August (1897, 2002).
10810 10000
8000 ] -1 s
3 6000
Qd [m 4000
2000
580 0 1876 1896 1916 1936 1956 1976 1996 Fig. 7-1 Average daily Qd discharge period 1876-2006, Danube: Bratislava.
Table 7-1 Number of floods in selected classes (over 4000 m3s-1) Period 4000-4999 5000-5999 6000-6999 7000-7999 8000-8999 9000-9999 above 10000 total 1876–2005 181 73 42 11 9 2 4 322 1876–1940 86 24 21 5 7 0 2 145 1941–2005 95 49 21 6 2 2 2 177
50 10000 m3s-1 45 9000
40 8000 7000 35 6000 5000 30
N 4000 25
20
15
10
5
0 I II III IV V V I V II V III IX X X I X II
Fig. 7-2 Number of floods in selected classes and in individual months.
106 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
12000 12000 1897 peak 4.08.1897 1899 peak 19.09.1899 10000 10000 ] stage 940 cm ] stage 970 cm -1 8000 -1 8000
s 3 -1 3 -1 s 3
Qd 10 140 m s 3 Qmax 10 870 m s 6000 6000 4000 4000 Qd [m Qd [m 2000 2000 0 0 24.VII 03.VIII 13.VIII 23.VIII 08.IX 18.IX 28.IX 08.X
12000 12000 1954 peak 15.07. 1954 2002 peak 15-16. 08. 2002 10000 10000 stage 984 cm ] ] stage 993 cm -1 8000 Qmax -1 8000
s s 3 -1 3 3 Qmax 10 370 m s 6000 10 400 m3 s -1 6000 4000 4000 Qd [m Qd [m 2000 2000 0 0 01.VII 11.VII 21.VII 31.VII 04.V III 14.V III 24.V III 03.IX
12000 1965 peak 16.06.1965 10000 stage 918 cm 3 -1
] Qmax 9 225 m s -1 8000 s 3 6000 4000 Qd [m 2000 0 01.V 11.V 21.V 31.V 10.VI 20.VI 30.VI 10.VII
Fig. 7-3 Flood waves with peak discharge above 10 000 m3s-1, and 1965 flood; Danube at Bratislava.
7.1.1 Flood occurrence probability for the Danube River at Bratislava
In general, the severity of a flood, with respect to its peak flow, is expressed as the probability of its occurrence or exceedance. Here we used the series of the annual maximum discharges (Qmax) (Fig. 7-4) and theoretical log-Pearson type- III distribution curves to calculate the probability of exceedance of the Danube for the period 1876–2005 (paragraph 5.2).
11000 10 870
] 3rd flood activity level
-1 9000 .s 3 7000 [m
max 5000 Q y = 3.3894x + 5576 3000 1876 1886 1896 1906 1916 1926 1936 1946 1956 1966 1976 1986 1996 2006
Fig. 7-4 Annual maximum discharges (Qmax) series of Danube at Bratislava, period 1876– 2006, long-term trend.
107 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
On Fig. 5-3 and 5-4 empirical and theoretical (log-Pearson type III) frequency curve of the maximum discharge and 5% and 95% confidence limits are shown. The calculated T-year maximum discharges of the Danube at Bratislava for the period 1876–2005 are listed in Table 7.2a.
Table 7.2a T-year peak flow Q [m3s-1] log-Pearson type III distribution; CL- confidence limits; the Danube at Bratislava, 1876–2005 T in years 1000 500 200 100 50 20 10 5 Q 13975 13044 11837 10943 10054 8877 7966 7009 95% CL 12736 11957 10940 10176 9411 8384 7577 6711 5% CL 15632 14485 13017 11936 10875 9490 8438 7356
Table 7-2 Number of days with discharge above 4000, 5000, …, 10 000 m3s-1 during the historical floods of the Danube with peak flow above 8000 m3s-1, in the second column is the month of the flood occurrence year month 4000 5000 6000 7000 8000 9000 10000 1954 7 20 14 10 9 7 4 1 1899 9 13 9 8 7 5 4 3 1897 8 15 9 7 6 4 4 2 2002 8 11 9 6 4 4 3 1 1965 6 30 30 27 18 9 3 1991 8 7 5 5 3 2 1 1883* 1 10 9 9 7 4 1876* 2 10 10 10 9 3 1923* 2 8 7 6 4 3 1880* 2 12 5 3 2 2 1890 9 18 11 9 6 2 1892 6 28 14 5 4 2 1920 9 11 8 6 4 2 1975 7 21 9 6 5 2 2002 3 7 5 4 3 2 *- winter – ice floods
108 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
7.1.2 Is the runoff extremality of Danube at Bratislava rising?
In general, an opinion prevails that with the atmospheric temperature increase, the runoff extremality is also rising – the peaks rise and the minimum flows drop down It is possible to confirm or to question this opinion only through a detailed statistical analysis of the various runoff characteristics. Impact of the anthropogenic activity upon the flood number occurrence can be assessed by analysis of the annual maximum discharge series Qmax. The analysis of number of floods in individual classes and in two sub-periods in Table 7-1 does not show any increase of number of extreme floods over 3 -1 10 000 m s at Bratislava.
Table 7-3 Summary statistics of Qmax_1 and Qmax_2 Qmax_1 1876–1940 Qmax_2 1941–2005 Count 65 65 Average 5646.62 5918.54 Median 5084.0 5611.0 Variance 3.08538E6 2.26893E6 Standard deviation 1756.52 1506.3 Minimum 3000.0 3153.0 Maximum 10870.0 10400.0 Skewness 0.884688 1.03705 Coefficient of variation 31.1076% 25.4505%
Table 7-4 Testing results of change of mean value in the winter-spring and the summer- autumn seasons. 95.0% confidence interval t-tests to compare means F-tests to compare standard deviations Qmax 1: 5646.62 +/- 435.246 Std. deviation of Qmax_1: Qmax 2: 5918.54 +/- 373.242 [1497.93;2123.86] Std. deviation of Qmax_2: [1284.54;1821.3] Null hypothesis: mean1 = mean2 Null hypothesis: sigma1 = sigma2 (1) Alt. hypothesis: mean1 NE mean2 (1) Alt. hypothesis: sigma1 NE sigma2 assuming eq. var.: t = -0.947 P = 0.345 F = 1.35984 P-value = 0.221598 not assuming eq. var.: t = -0.947 P = 0.345
(2) Alt. hypothesis: mean1 > mean2 (2) Alt. hypothesis: sigma1 > sigma2 assuming eq. var.: t = -0.947 P = 0.827 F = 1.35984 P-value = 0.110799 not assuming eq. var.: t = -0.947 P = 0.827
(3) Alt. hypothesis: mean1 < mean2 (3) Alt. hypothesis: sigma1 < sigma2 assuming eq. var.: t = -0.947 P = 0.172 F = 1.35984 P-value = 0.889201 not assuming eq. var.: t = -0.947 P = 0.172
109 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Our intention is to confirm or reject the hypothesis about the change of statistical characteristics of Qmax series in period 1876–2005. The Qmax series was split into two 65-years sub-series Qmax_1 and Qmax_2. Basic statistical characteristics of both sub-sets are in Table 7-3. We tested the hypotheses whether subsets (1876–1940 and 1941–2005) are from the same distribution. We tested changes in mean value and in standard deviation. Testing results are in Table 7-4. The P-value is in all cases bigger than 0.05, and we cannot reject the null hypothesis on 0.05 confidence level that both periods have the same mean value, as well as standard deviation. 7.2 Extreme flood wave scenarios for Danube at Bratislava
As mentioned before, the flood hazard maps are to be created for all inundation areas according to Directive (2007) on flood risk for the following scenarios: (a) floods with a low probability, or extreme event scenarios (likely return period ≥ 1000 years); (b) floods with a medium probability (likely return period ≥ 100 years); (c) floods with a high probability, where appropriate.
To run the hydraulic model for simulation of flood extent on the territory we need not only peak flow Qmax, but the shape of the flood wave as well. It is obvious, that the short wave flattens earlier and floods less territory. An important element in construction of the catastrophic 1000-year flood scenario is a correct determination of the flood peak discharge, as well as of the flood hydrograph shape. We created the scenario waves based on observed historical waves at Bratislava. In Fig. 7-5 are shown flood hydrographs constructed from mean daily flows of the Danube floods in years 1899, 1924, 1926, 1965, and 1975. Besides the analysis of floods from the „discharge observation period“ we tried also to reconstruct the hydrograph of the probably most destructive Danube flood of the last millennium which occurred in August 1501. Marks of peak levels of this flood exist along the Austrian section of Danube, which are highest ever recorded there, in some river sections exceeding those reached in 1954 by almost 2 (two) meters (Kresser, 1957). In the same source its peak discharge is estimated close to 14000 m3s-1at Vienna. It originated probably by coincidence of peaks of the upper Danube together with the largest tributary from Austrian territory – Inn. As the flood peak moved downstream and the cyclonal disturbance eastwards, the flood peaks from the Austrian right hand tributaries gradually coincided with the main river peak reaching its maximum somewhere close to Vienna. It probably attenuated then after passing the Devín gate at Bratislava and entering the Great Danubian Plain downstream.
110 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Analysis of the 1954 flood formation indicates a similar meteosynoptical situation with the exception that the cyclonal disturbance over Austria in 1954 did not penetrate that far to the east. Consequently, the lowest right hand tributaries of Danube from Lower Austria did not contribute significantly to the flood peak. As a result of the above considerations, we decided to take for further analysis as a catastrophic flood scenario a hydrograph at Bratislava with peak flow 14000 m3s-1 and shape similar to that of the 1954 flood. Three-hourly discharge values of that hydrograph are in Table 7-5. In Fig. 7-6 there are the scenario floods with recurrence period T = 1000, 100, and 50, years. The 100-year flood occurs on the Danube at Bratislava most probably in August, less probably in July or September.
7000 10000 Bratislava Bratislava 6500 9000
8000 ] 6000 ] -1 s -1
7000 3 5500 s 3 6000 5000
5000 Q [m
Q [m 4500 4000 3000 4000 2000 3500 1.5.1924 3.5.1924 5.5.1924 7.5.1924 9.5.1924 29.4.1924 11.5.1924 13.5.1924 15.5.1924 17.5.1924 14.9.1899 16.9.1899 18.9.1899 20.9.1899 22.9.1899 24.9.1899 26.9.1899 28.9.1899 30.9.1899 2.10.1899 4.10.1899 6.10.1899 7500 Bratislava 10000 7000 9000
] 8000 -1 ]
s 6500 -1
3 7000 s 6000 3 6000
Q [m 5000 5500 Q [m 4000 Bratislava 5000 3000 Komárno 2000 2.7.1926 5.7.1926 8.7.1926 3.6.65 8.6.65 3.7.65 8.7.65 17.6.1926 20.6.1926 23.6.1926 26.6.1926 29.6.1926 11.7.1926 14.7.1926 29.5.65 13.6.65 18.6.65 23.6.65 28.6.65
10000 Bratislava 9000 8000 Komarno ]
-1 7000 s 3 6000 5000 Q [m 4000 3000 2000 2.7.75 4.7.75 6.7.75 8.7.75 30.6.75 10.7.75 12.7.75 14.7.75 16.7.75 18.7.75 20.7.75 22.7.75
Fig. 7-5 Mean daily flows of Danube in stations Bratislava and Komárno, during significant floods, in period 1899-1975.
111 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 7-5 Catastrophic scenario hydrograph at Bratislava (or Devín gauge) assumed to be the historical flood of 1501 (estimated).
Q Q Q. Q. Q. 1.8. 3:00 3760 7.8. 6:00 5414 13.8. 9:00 11745 19.8. 12:00 10395 25.8. 15:00 5258 1.8. 6:00 3645 7.8. 9:00 5393 13.8. 12:00 11948 19.8. 15:00 10247 25.8. 18:00 5184 1.8. 9:00 3578 7.8. 12:00 5360 13.8. 15:00 12285 19.8. 18:00 10058 25.8. 21:00 5123 1.8. 12:00 3564 7.8. 15:00 5333 13.8. 18:00 12488 19.8. 21:00 9821 26.8. 0:00 5063 1.8. 15:00 3551 7.8. 18:00 5319 13.8. 21:00 12656 20.8. 0:00 9653 26.8. 3:00 4995 1.8. 18:00 3537 7.8. 21:00 5299 14.8. 0:00 12758 20.8. 3:00 9450 26.8. 6:00 4914 1.8. 21:00 3510 8.8. 0:00 5265 14.8. 3:00 12893 20.8. 6:00 9248 26.8. 9:00 4820 2.8. 0:00 3483 8.8. 3:00 5225 14.8. 6:00 13095 20.8. 9:00 9052 26.8. 12:00 4752 2.8. 3:00 3362 8.8. 6:00 5198 14.8. 9:00 13298 20.8. 12:00 8910 26.8. 15:00 4718 2.8. 6:00 3321 8.8. 9:00 5164 14.8. 12:00 13365 20.8. 15:00 8775 26.8. 18:00 4617 2.8. 9:00 3274 8.8. 12:00 5103 14.8. 15:00 13608 20.8. 18:00 8573 26.8. 21:00 4556 2.8. 12:00 3254 8.8. 15:00 5042 14.8. 18:00 13743 20.8. 21:00 8370 27.8. 0:00 4509 2.8. 15:00 3240 8.8. 18:00 5063 14.8. 21:00 13770 21.8. 0:00 8168 27.8. 3:00 4455 2.8. 18:00 3237 8.8. 21:00 5096 15.8. 0:00 13885 21.8. 3:00 7979 27.8. 6:00 4388 2.8. 21:00 3237 9.8. 0:00 5171 15.8. 3:00 14013 21.8. 6:00 7830 27.8. 9:00 4334 3.8. 0:00 3233 9.8. 3:00 5265 15.8. 6:00 14020 21.8. 9:00 7695 27.8. 12:00 4293 3.8. 3:00 3227 9.8. 6:00 5670 15.8. 9:00 14033 21.8. 12:00 7614 27.8. 15:00 4266 3.8. 6:00 3267 9.8. 9:00 5994 15.8. 12:00 13973 21.8. 15:00 7520 27.8. 18:00 4226 3.8. 9:00 3308 9.8. 12:00 6413 15.8. 15:00 13905 21.8. 18:00 7412 27.8. 21:00 4172 3.8. 12:00 3341 9.8. 15:00 6784 15.8. 18:00 13838 21.8. 21:00 7277 28.8. 0:00 4151 3.8. 15:00 4050 9.8. 18:00 6885 15.8. 21:00 13770 22.8. 0:00 7155 28.8. 3:00 4131 3.8. 18:00 4658 9.8. 21:00 7135 16.8. 0:00 13635 22.8. 3:00 7034 28.8. 6:00 4111 3.8. 21:00 5265 10.8. 0:00 7223 16.8. 3:00 13568 22.8. 6:00 6912 28.8. 9:00 4091 4.8. 0:00 5535 10.8. 3:00 7553 16.8. 6:00 13473 22.8. 9:00 6818 28.8. 12:00 4077 4.8. 3:00 5805 10.8. 6:00 7763 16.8. 9:00 13412 22.8. 12:00 6750 28.8. 15:00 4064 4.8. 6:00 5940 10.8. 9:00 7965 16.8. 12:00 13311 22.8. 15:00 6683 28.8. 18:00 4059 4.8. 9:00 6136 10.8. 12:00 8168 16.8. 15:00 13230 22.8. 18:00 6575 28.8. 21:00 4057 4.8. 12:00 6143 10.8. 15:00 8289 16.8. 18:00 13095 22.8. 21:00 6480 29.8. 0:00 4057 4.8. 15:00 6318 10.8. 18:00 8438 16.8. 21:00 12960 23.8. 0:00 6413 29.8. 3:00 4057 4.8. 18:00 6413 10.8. 21:00 8573 17.8. 0:00 13028 23.8. 3:00 6332 29.8. 6:00 4054 4.8. 21:00 6480 11.8. 0:00 8694 17.8. 3:00 12893 23.8. 6:00 6210 29.8. 9:00 4050 5.8. 0:00 6548 11.8. 3:00 8782 17.8. 6:00 12758 23.8. 9:00 6055 29.8. 12:00 4043 5.8. 3:00 6757 11.8. 6:00 8910 17.8. 9:00 12663 23.8. 12:00 5940 29.8. 15:00 4037 5.8. 6:00 6804 11.8. 9:00 9045 17.8. 12:00 12528 23.8. 15:00 5832 29.8. 18:00 4030 5.8. 9:00 6858 11.8. 12:00 9180 17.8. 15:00 12413 23.8. 18:00 5738 29.8. 21:00 4016 5.8. 12:00 6818 11.8. 15:00 9329 17.8. 18:00 12285 23.8. 21:00 5663 30.8. 0:00 4010 5.8. 15:00 6784 11.8. 18:00 9518 17.8. 21:00 12083 24.8. 0:00 5603 30.8. 3:00 3996 5.8. 18:00 6683 11.8. 21:00 9700 18.8. 0:00 11948 24.8. 3:00 5569 30.8. 6:00 3999 5.8. 21:00 6608 12.8. 0:00 9788 18.8. 3:00 11853 24.8. 6:00 5535 30.8. 9:00 4003 6.8. 0:00 6413 12.8. 3:00 9923 18.8. 6:00 11718 24.8. 9:00 5515 30.8. 12:00 4016 6.8. 3:00 6440 12.8. 6:00 10044 18.8. 9:00 11583 24.8. 12:00 5481 30.8. 15:00 4023 6.8. 6:00 6305 12.8. 9:00 10145 18.8. 12:00 11475 24.8. 15:00 5441 30.8. 18:00 4037 6.8. 9:00 6095 12.8. 12:00 10274 18.8. 15:00 11360 24.8. 18:00 5420 30.8. 21:00 4043 6.8. 12:00 5873 12.8. 15:00 10476 18.8. 18:00 11219 24.8. 21:00 5407 31.8. 0:00 4023 6.8. 15:00 5792 12.8. 18:00 10665 18.8. 21:00 11084 25.8. 0:00 5393 31.8. 3:00 4000 6.8. 18:00 5657 12.8. 21:00 10935 19.8. 0:00 10976 25.8. 3:00 5387 31.8. 6:00 3983 6.8. 21:00 5528 13.8. 0:00 11070 19.8. 3:00 10908 25.8. 6:00 5360 31.8. 9:00 3962 7.8. 0:00 5468 13.8. 3:00 11205 19.8. 6:00 10692 25.8. 9:00 5346 31.8. 12:00 3956 7.8. 3:00 5434 13.8. 6:00 11475 19.8. 9:00 10530 25.8. 12:00 5306 31.8. 15:00 3956
112 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
15000
13000 T=1000 11000 T=100 T=50 ]
-1 9000 s 3
7000 Q [m
5000
3000
1000 1-VIII 6-VIII 11-VIII 16-VIII 21-VIII 26-VIII 31-VIII
Fig. 7-6 Scenario floods for high, medium and low probability (recurrence period T = 1000, 100, 50 years), Danube, Bratislava.
7.3 Conslusion
The Danube is an international river flowing through 13 countries and its basin interferes with even 18 countries. To meet the requirements of the new Directive (2007) of the European Parliament on the assessment and management of flood risks, the close collaboration of these countries is needed. The aim of the chapter was to analyze the floods regime and to create flood scenarios of different exceedance probability. The analysis of 130 years series of mean daily discharge and maximum annual discharge Qmax shows zero trends of the series. The series of extreme discharges has constant statistical characteristics. We tested the hypotheses whether subsets (1876–1940 and 1941–2005) have the same distribution. We tested changes in mean value and in standard deviation. We cannot reject the null hypothesis on 0.05 confidence level that both periods have the same mean value, as well as standard deviation. The scenario flood waves were created from measured historical flood waves of the Danube at Bratislava. The mean daily discharge series in this station is available since 1876. This 130-years series is long enough to use observed historical flood waves and it is not necessary to construct the required flood scenarios indirectly by simulations using e.g. rainfall-runoff models (Pekárová et al., 2005), or by indirect methods of estimation (Pekárová et al., 2007b).
113 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
8 Catastrophic flood scenario of the Danube between Devín and Nagymaros
The goal of this chapter is simulation of the catastrophic flood wave transformation between Devín and Nagymaros under recent river reach conditions by means of the nonlinear reservoir river model NLN-Danube. To compare flood hydrographs and their travel times in Danube River section Krems: Stein – Nagymaros, data from following discharge stations along the Danube River were analyzed Fig. 8-1: • Krems: Stein, (Kienstock since 1970), Austria; • Bratislava, Slovakia; • Medveďov, Slovakia; • Komárno, Slovakia; • Štúrovo, Slovakia; • Nagymaros, Hungary. Basic data of these stations are in table Table 8-1. In connection with construction of water structures on the Danube, in recent years several stations have been relocated. In 1970 the station Stein Krems was relocated to Kienstock, in 1992 the station Medveďov, and in 1995 the station Komárno were relocated as well. The last one was moved to a close location upstream of the mouth of Váh tributary, and thus also of rivers Nitra, Žitava and Small Danube (the left hand Danube arm).
K
a Morava KREMS m 2003 rkm p C 2. KIENSTOCK B DEVIN S L O V A K I A VIENNA 1879 rkm 2015 rkm 3. BRATISLAVA 1868 rkm Ipel
D Hron n Váh A e s i P Danube o 1. YBBS a a r w h e 2060 rkm s T c r b s C b i a Y F n a l 7. NAGYMAROS E 1696 rkm ube Power station A U S T R I A Dan A - Melk B - Altenworth 6. STUROVO C - Greifenstein 4. MEDVEDOV a b 1718.6 rkm D - Freudenau 1805 rkm a 5. KOMARNO E - Gabcikovo R 1766 rkm H U N G A R Y Fig. 8-1 Scheme of the gauging stations of the selected section of the Danube River (rkm: river kilometer from the mouth of the Danube River).
114 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 8-1 Basic characteristics of the used Danube discharge stations Station Station charge H Q area Gauge zero slope r.kilometer year year km2 m a.s.l. m/km km Stein-(Kienstock) Since 1975 95970.0 Krems: Stein 1829 - 1970 1829 1829 96045.0 2003.54 Devín 1926 1931 131244.0 132.87 1879.78 Bratislava 1876 1901 131331.1 128.43 0.4 1868.75 Medveďov 1925 - 1992 1925 1979 132170.0 108.42 1805.40 Medveďov Since 1992 1993 1993 132168.0 108.42 0.35 1806.30 Komárno 1931 - 1995 1917 1931 171622.6 103.69 1766.20 Komárno Reloc.upstream of Váh 1996 1996 151961.6 103.40 1767.10 Iža (Komárno) Subst. for Komárno 1930 1985 171627.5 103.56 1763.96 Štúrovo 1934 - 172438.0 100.96 0.06 1718.60 Nagymaros 183533.0 1696.25
Significant changes in the transport and transformation capacities of the Danube River channel have resulted from anthropogenic activities in the last century. An extensive system of hydropower projects has been constructed on the upper Danube (Germany, Austria and Slovakia). Furthermore, in the river reach Kienstock–Bratislava (2015.2 rkm, Austria; 1868.75 rkm, Slovakia), three water works were put into operation: Altenwörth (1973–1976), Greifenstein (1982– 1985) and Freudenau (1992–1997). This may have had a significant impact upon the flood wave transformation regime of the river as well as on other hydrological phenomena (Bardossy and Molnar, 2004). Čížová (1992), Hajtášová et al. (1995a,b) and Svoboda et al. (2000) indicated that the travel times (mainly of smaller flood waves) on the upper part of Danube decreased by 25–30% in the 1990s in comparison to the 1970s. Zsuffa (1999) analyzed the daily water stages before and after 1976. He found a higher incidence of small and medium floods in the later years. It may be that the regulation of the upper Danube changed the coincidence of flood peaks in the main stream and tributaries. 8.1 Runoff volume balance in Bratislava–Komárno river part
Instead of the original station Komárno serves now the newly established station Iža. Since 1992 the discharge in Bratislava is under the influence of the water levels in Čuňovo reservoir – a part of the Gabčíkovo water structure. In Fig. 8-2 are shown the mean annual flows along the Slovak Danube river part in three hydrological years 1995/96–1997/98. ´ In the three years there is the average flow in Medveďov by 66 m3s-1 lower (3.4 per cent) than in Bratislava gauge. According to Dulovič (1992) there was in years 1981–1990 a drop of discharge between Bratislava and Komárno by 98 m3s-1, thus by almost 5 per cent. This drop is fairly higher in periods of high flows.
115 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
2200 Bratislava 2100 Medveďov
] 2000 -1 Komárno s 3 1900
Q [m 1800 1700 1600 1995/96 1996/97 1997/98 a)
1.01 Bratislava Medveďov Komárno 1 0.99
% 0.98 0.97 0.96 0.95 1995/96 1996/97 1997/98 b) Fig. 8-2 Mean annual flows of Danube in hydrological years 1995/96 –1997/98 in three stations; a) mean annual flows; b) relative values as to the flow in station Bratislava.
The reason of this is, first, the intake downstream of Bratislava into the Danube arms Malý Danube (left hand, Slovakia) and Mosonyi Duna (right hand, Hungary), second, the outflow from the Danube natural river bed into the huge groundwater gravel deposits forming the Danube river valley on both sides of the river (Škoda and Turbek, 1995). In hydrological year 1996/97 in spite of left hand tributaries Rába (mean annual flow 130 m3s-1) and Lajta (inclusive Mosonyi Duna) upstream of Komárno, the mean annual flow in Komárno station was lower than in Bratislava. This demonstrates a significant contribution of the Danube flows to the groundwater storage in the Bratislava – Komárno river reach. This is to be accounted for when using mathematical river models based on the continuity equation. It is then obvious that the model simulated hydrographs for station Medveďov will show higher runoff volumes than the observed (measured) ones. This problem can be overcome by subtracting the corresponding runoff volume in the river part Bratislava – Medveďov. 8.2 Flood travel times on Danube
Travel times of extreme floods are of particular importance for hydrological forecasts and flood warnings. Čížová (1992) indicates these travel times for Danube sections Linz–Bratislava and Vienna–Bratislava for two periods: 1923– 1966 and 1975–1991. According to her results, the travel times between Linz and Bratislava decreased significantly from 20–40 hours to 5–20 hrs in the water stage range at Linz 300–500 cm.
116 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
rkm 2050
Stein 2000 Altenworth
Greifenstein 1950 Wien
1900
Bratislava 1954 1850
1897
Medveďov 1800
Komárno 1899 1750
Štúrovo 1997
Nagym ar os 1700 0 24 48 72 96 120 144 hod. Fig. 8-3 Travel times of floods on Danube in years 1897, 1899, 1954 and 1997.
Similarly, according to Hajtášová et al. (1995), the travel times (mainly of smaller flood waves) on the Austrian Danube decreased by 25 to 30 per cent. In Fig. 8-3 the travel times between Krems: Stein–Nagymaros are demonstrated of five flood waves. Between Bratislava and Nagymaros, the travel time of flood waves in 1996–1998 was 43 to 67 hours which corresponds to speed from 1.07 m.s-1 to 0.68 m.s-1. Lower floods (up to 5000 m3s-1) travel faster (43 hrs.), higher floods (over 6500 m3s-1) travel slower (50 hrs.). Slowest travel floods following another significant flood (67 hrs.). Travel time from Bratislava to Štúrovo during 1897 flood was 72 hours (mean peak velocity v=0.57 m.s-1), in 1899 it was 55 hours (v=0.75 m.s-1) and in 1954 it traveled 66 hours (v=0.63 m.s-1). Travel time of the first and second wave in 1997 in the 250 km Danube section between Jochenstein and Greifenstein (Fig. 8-4) was 9 hours (v=7.72 m.s-1). Travel time in the same year between Devín and Nagymaros of the first flood was 57 hours (v=0.89 m.s-1), and of the second flood it was 48 hours (v=1.06 m.s-1). It seems, that due to the construction of the water structures on the Danube in Austria and Germany, the flood waves velocities increased even more than indicated in the above cited sources.
117 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
8000 Jochenstein-m Greifenstein-m 7000 Devín-m Nagymaros-m 6000
5000
4000
3000
2000
1000 3.7.97 0:00 3.7.97 0:00 4.7.97 0:00 5.7.97 0:00 6.7.97 0:00 7.7.97 0:00 8.7.97 0:00 9.7.97 0:00 1.8.97 0:00 2.8.97 10.7.97 0:00 10.7.97 0:00 11.7.97 0:00 12.7.97 0:00 13.7.97 0:00 14.7.97 0:00 15.7.97 0:00 16.7.97 0:00 17.7.97 0:00 18.7.97 0:00 19.7.97 0:00 20.7.97 0:00 21.7.97 0:00 22.7.97 0:00 23.7.97 0:00 24.7.97 0:00 25.7.97 0:00 26.7.97 0:00 27.7.97 0:00 28.7.97 0:00 29.7.97 0:00 30.7.97 0:00 31.7.97 a)
8000 4500 8000 5000
4500 7000 4000 7000 4000 6000 6000 3500 3500
5000 3000 5000 3000 Greifenstein + 9h 2500 4000 Greifenstein + 9h 2500 4000 Devín + 30h Devín + 30h 2000 Nagymaros + 90h 3000 Nagymaros + 81h 2000 3000 Jochenstein + 0h Jochenstein + 0h 1500 2000 1500 2000 1000 6.7.97 0:00 7.7.97 0:00 8.7.97 0:00 9.7.97 0:00 18.7.97 0:00 19.7.97 0:00 20.7.97 0:00 21.7.97 0:00 22.7.97 0:00 23.7.97 0:00 6.7.97 12:00 7.7.97 12:00 8.7.97 12:00 9.7.97 12:00 10.7.97 0:00 18.7.97 12:00 19.7.97 12:00 20.7.97 12:00 21.7.97 12:00 22.7.97 12:00 23.7.97 12:00 b) 10.7.97 12:00 c) Fig. 8-4 a) Travel of flood in July 1997 in the Danube section Jochenstein – Nagymaros. b) Peaks of the flood I. in four stations with the time shift. c) Peaks of the flood II. (with the time shift).
Flow regime conditions of the Danube River have been continually subject to change. These changes result from natural processes (erosion, sedimentation, vegetation cover) or anthropogenic activities (modification of the river bank, construction of hydropower stations). It is evident that the routine hydrological forecasting methodologies due to changed Danube runoff conditions in Austria need to be changed. The station Vienna, so far the base for downstream forecasts, because of changes related to construction of Freudenau water structure and due to a short forecast lead time is becoming unsatisfactory for longer forecasts. Should a forecasting method be based on a hydrological mathematical model, a suitable starting points of forecasts for Bratislava would be Kienstock upstream of the water structure Altenwörth, or release from water structures Altenwörth (or Greifenstein). Because of water flow changes in the Kienstock–Bratislava reach (Fischer-Antze and Gutknecht, 2004), such a meteorological situation as occurred in 1899 or 1954 would—under present channel condition—result in a diametrically different hydrograph shape of the flood wave at Bratislava station. The estimation of the
118 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region hypothetical transformation of historical waves under present conditions is possible only by model simulations. For this purpose the river model NLN- Danube was developed and calibrated for present channel conditions. Development of conceptual nonlinear reservoir cascade models was one of several approaches to incorporate nonlinearity into hydrological routing models (see e.g. Laurenson, 1964, 1986; Malone and Cordery, 1989; Corbus, 2002). Recently Sriwongsitanon et al. (1998) and Bentura and Michel (1997) investigated the relationship between parameters of the storage–discharge relationship, channel and flow motion properties and the travel time of flood waves. 8.3 Description of the NLN-Danube model
The NLN-Danube model (Pekár et al., 2001) is derived from the NONLIN model (Svoboda, 1993). The NLN-Danube model simulates flood wave transformation in the six river sections: Ybbs–Kienstock–Devín–Medveďov–Komárno– Štúrovo–Nagymaros (Fig. 8-5). The model of each section of the simulated system is based upon the concept of a series of equal nonlinear reservoirs; thus, it belongs to the category of hydrological conceptual nonlinear models. Model input (P) represents the input into the first reservoir of the first section, its output is the input into the second reservoir in the series, etc., and the output (Q) from the last reservoir is the output from the first model section.
reser 1. 2. N P Q
Fig. 8-5 Scheme of the river part – model NONLIN, (Svoboda, 2003).
Movement of the wave through the reservoir is defined by discharge (Q) and volume of reservoir (V) (Fig. 8-6 ) as:
Q = B ⋅V EX (8.1) where: Q - the reservoir output (m3 s-1); V is the volume of reservoir storage (m3); EX - the nonlinearity parameter; and B - the proportionality parameter.
119 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Q EX>1 EX=1
EX<1 QC F BK=ΔV/ΔQ
ΔQ
ΔV
V Fig. 8-6 Transformation function in NONLIN model (Svoboda, 2003).
The flood wave propagation is modeled in equidistant discrete time steps 0, 1, 2, …, M. The difference between two steps is given by the parameter ΔT. In time steps i and i + 1, for known input Pi+1 and output Qi, the unknown output Qi+1 is determined from the continuity equation within the time interval i+1 of the length ΔT as:
(Pi+1 − Qi+1 ) ⋅ ΔT = Vi+1 −Vi (8.2) where:
Pi+1, Qi+1 - the average input and output signals in the interval i+1; and
Vi+1, Vi - storages at the intervals i+1 and i.
From equations (8.1) and (8.2) one obtains:
Q1/ EX − Q1/ EX (P − Q ) ⋅ ΔT = i+1 i (8.3) i+1 i+1 B1/ EX
Equation (8.3) defines the nonlinear function f of one unknown, Qi+1:
Q1/ EX − Q1/ EX f (Q ) = (P − Q ) ⋅ ΔT − i+1 i (8.4) i+1 i+1 i+1 B1/ EX
120 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
which is solved by the linearization method (Newton method):
(k ) (k +1) (k ) f (Qi+1 ) Qi+1 = Qi+1 − (k ) (8.5) f ′()Qi+1
This leads to the iteration formula:
(k ) (k ) 1/ EX 1/ EX −1/ EX (k+1) (k ) (Pi+1 − Qi+1 )⋅ ΔT − [(Qi+1 ) − (Qi ) ]⋅ B Qi+1 = Qi+1 + (k ) (1−EX ) / EX −1/ EX −1 (8.6) ΔT + (Qi+1 ) ⋅ B ⋅ EX
The parameters of the transformation curve shape are expressed by ratio parameter B,
EX ⎛ N ⋅ ΔT ⎞ B = ⎜ ⎟ (8.7) ⎝ BK ⎠ where: N - the number of storages in one section of the model; and BK is the “time constant” of an equivalent linear system.
8.3.1.1 NLN-Danube model parameters
BK - time constant of the equivalent linear system [hrs.]; DT - length of the time step [hrs.]; QC - corresponds to the maximum capacity of the main river channel (flow, when water enters the inundation) [m3 /sec]; EX - system nonlinearity, dimensionless; N - number of reservoirs in series, dimensionless; IT - linear translation, dimensionless value defining the number of the time steps DT by which the output has to be displaced in time direction. As it can be seen from Fig. 8-6 besides the parameter EX, the shape of the routing curve (and thus the routing effect) depends substantially upon the parameter BK which, together with parameter QC, defines the position of the point F and consequently the attenuation effect below and above this point. This should be kept in mind when determining the optimal model parameters.
121 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
8.3.2 Results of floods simulation in the reach Devín (Bratislava)–Nagymaros
The Danube reach between Devín (Bratislava) and Nagymaros was divided into four sections (Fig. 8-7): 1. Devín (Bratislava)–Medveďov (DEME); 2. Medveďov–Komárno (Iža) (MEIZ); 3. Komárno (Iža)–Štúrovo (IZST); 4. Štúrovo–Nagymaros (STNA). The NLN-Danube model run under the WINDOWS OS as EXCEL worksheet (Fig. 8-8, Fig. 8-9).
Morava
1. DEVÍN BRATISLAVA Ipe Danube ľ Hron Váh
P o w e r C a n The Gabčíkovo water a 2. l power station ČUŇOVO e Danub
3. MEDVEĎOV 5. ŠTÚROVO 4. KOMÁRNO a 6. NAGYMAROS b á a) R
WITHDRAWAL HRON LOSSES VÁH IPEĽ 3 200 m3/s 3 100 m /s 150 m /s
1 2 3 4
OV OV
Ď
KOMÁRNO 1766 rkm ŠTÚROVO 1718 rkm 1805 rkm NAGYMAROS 1696 rkm MEDVE
DEVÍN 1879.8 rkm b) Fig. 8-7 a) Danube River section Devín – Nagymaros. b) Model scheme after 1996.
122 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Fig. 8-8 NLN-model main menu.
Fig. 8-9 NLN-Danube model parameters for Danube River sections.
123 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
The NLN-Danube model was used for the simulation of the scenario catastrophic flood on the Danube River between Devín and Nagymaros. To simulate passing of a hypothetical catastrophic flood through this Danube River reach up to Nagymaros we used the input flood scenario for Bratislava station described in chapter 7. For our purposes, only the NLN-Danube model results for the four section, Devín (Bratislava before 1992)–Medveďov–Komárno–Štúrovo– Nagymaros river reach were used. A large set of the historical discharge data series was collected from the Danube (Devín (Bratislava)–Nagymaros stations) and from the Danube tributaries. The dataset includes discharge of the largest floods from the period 1899–2002 (1899, 1924, 1926, 1954, 1965, 1975, 1977, 1991, 1997, 1998, 2002). The hourly, or 3- hourly discharge data of floods were prepared based on the archive data of SHMI (Slovak Hydrometeorogical Institute); and of Angelini (1955), Kresser, (1957, 1970), and Zatkalík (1970); from Beiträge zur Hydrographie Österreichs No. 9 and No. 29; and from the Slovak year book of surface waters (1955–2006) (Mitkova, 2006).
8.3.2.1 NLN-Danube model calibration
Flood hydrographs from the years 1954, 1991, and 2002 are rather extreme, but their shape is fairly simple. Such events (Fig. 8-10) are suitable for calibration of models. According to SHMÚ (1955) the flood discharges of the 1954 event were evaluated (3-hourly time step) for stations Bratislava and Komárno, only water levels for station Štúrovo. In this last station, however, three discharge observations were taken at times close to the flood peak. These we used for an estimate of the Štúrovo 1954 rating curve, and using the water level data, also reconstructed the Štúrovo 1954 hydrograph. So it was possible to calibrate the hydrological river model (NLN-Danube in our case) not only for the river section Bratislava–Komárno, but also for Komárno–Štúrovo Danube section, based on the 1954 flood data. The basic source of data was the 1954 flood report of SHMÚ (1955). These 3-hourly values we supplemented by the Komárno hydrograph reconstruction taking into account the estimated outflow through the breach of the right hand Danube dike (bund) on the Hungarian side upstream of Komárno. These data, together with the above described reconstruction of the Štúrovo hydrograph, are in Table 8-2. Peaks of flood hydrograph in years 1977, 1981 and 1996 did not exceed 8000 m3s-1 and were of a relatively short duration (Fig. 8-11). Flood hydrographs of years 1992, 1996, 1997 and 1998 represent the period after completion of the water structure Gabčíkovo. The peak operation of the hydro- power plant can be clearly seen, particularly at lower discharges (Fig. 8-12). At higher discharges the influence of water structure operation gradually disappears. However, in case of 1998 flood, it is clearly seen on Medveďov hydrograph and can be detected even at the one at Komárno. Hydrograph is smoothed out eventually at Nagymaros.
124 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
10000 Čuňovo-c Medveďov-c 9000 Komárno-c. 8000 Štúrovo-c Nagymaros-c 7000
6000
5000
4000
3000
2000
1000 1.8.91 0:00 2.8.91 0:00 3.8.91 0:00 4.8.91 0:00 5.8.91 0:00 6.8.91 0:00 7.8.91 0:00 8.8.91 0:00 9.8.91 0:00 a) 22.7.91 0:00 23.7.91 0:00 24.7.91 0:00 25.7.91 0:00 26.7.91 0:00 27.7.91 0:00 28.7.91 0:00 29.7.91 0:00 30.7.91 0:00 31.7.91 0:00 10.8.91 0:00 11.8.91 0:00 12.8.91 0:00 13.8.91 0:00 14.8.91 0:00 15.8.91 0:00 16.8.91 0:00 17.8.91 0:00 18.8.91 0:00 19.8.91 0:00 20.8.91 0:00 21.8.91 0:00
10000 Bratislava-m 9000 Medveďov-m 8000 Medveďov-c
7000
6000
5000
4000
3000
2000
1000 1.8.91 0:00 2.8.91 0:00 3.8.91 0:00 4.8.91 0:00 5.8.91 0:00 6.8.91 0:00 7.8.91 0:00 8.8.91 0:00 9.8.91 0:00 b) 22.7.91 0:00 23.7.91 0:00 24.7.91 0:00 25.7.91 0:00 26.7.91 0:00 27.7.91 0:00 28.7.91 0:00 29.7.91 0:00 30.7.91 0:00 31.7.91 0:00 10.8.91 0:00 11.8.91 0:00 12.8.91 0:00 13.8.91 0:00 14.8.91 0:00 15.8.91 0:00 16.8.91 0:00 17.8.91 0:00 18.8.91 0:00 19.8.91 0:00 20.8.91 0:00 21.8.91 0:00
10000 Bratislava-m 9000 Komárno-m 8000 Komárno-c.
7000
6000
5000
4000
3000
2000
1000 1.8.91 0:00 2.8.91 0:00 3.8.91 0:00 4.8.91 0:00 5.8.91 0:00 6.8.91 0:00 7.8.91 0:00 8.8.91 0:00 9.8.91 0:00 c) 22.7.91 0:00 23.7.91 0:00 24.7.91 0:00 25.7.91 0:00 26.7.91 0:00 27.7.91 0:00 28.7.91 0:00 29.7.91 0:00 30.7.91 0:00 31.7.91 0:00 10.8.91 0:00 11.8.91 0:00 12.8.91 0:00 13.8.91 0:00 14.8.91 0:00 15.8.91 0:00 16.8.91 0:00 17.8.91 0:00 18.8.91 0:00 19.8.91 0:00 20.8.91 0:00 21.8.91 0:00 Fig. 8-10 Danube 3-hourly flood hydrographs, NLN-Danube calibration wave, 1991 a) modeled (c); b) compared observed (m) and modeled (c) at Medveďov; c) compared observed and modeled at Komárno.
125 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Table 8-2 Flood discharges of the 1954 event (3-hourly time step) for stations Bratislava, Komárno, and Štúrovo (according to Svoboda et al,. 2000) Day Bratisl. Komárno Štúrovo Day Bratisl. Komárno Štúrovo Day Bratisl. Komárno Štúrovo 01.07.54 03 2785 3000 3000 07.07.54 06 4010 4690 4470 13.07.54 09 8700 5880 5500 01.07.54 06 2700 3025 2970 07.07.54 09 3995 4685 4500 13.07.54 12 8850 5940 5550 01.07.54 09 2650 3050 2950 07.07.54 12 3970 4650 4490 13.07.54 15 9100 6000 5600 01.07.54 12 2640 3060 2930 07.07.54 15 3950 4635 4480 13.07.54 18 9250 6070 5650 01.07.54 15 2630 3085 2900 07.07.54 18 3940 4610 4470 13.07.54 21 9375 6150 5700 01.07.54 18 2620 3060 2870 07.07.54 21 3925 4590 4470 14.07.54 00 9450 6220 5750 01.07.54 21 2600 3040 2850 08.07.54 00 3900 4580 4450 14.07.54 03 9550 6300 5800 02.07.54 00 2580 3055 2830 08.07.54 03 3870 4560 4420 14.07.54 06 9700 6400 5850 02.07.54 03 2490 3050 2800 08.07.54 06 3850 4500 4370 14.07.54 09 9850 6490 5900 02.07.54 06 2460 3020 2790 08.07.54 09 3825 4450 4350 14.07.54 12 9900 6550 6000 02.07.54 09 2425 3000 2780 08.07.54 12 3780 4430 4250 14.07.54 15 10080 6650 6100 02.07.54 12 2410 2990 2770 08.07.54 15 3735 4400 4150 14.07.54 18 10180 6740 6200 02.07.54 15 2400 2980 2760 08.07.54 18 3750 4370 4120 14.07.54 21 10200 6950 6300 02.07.54 18 2398 2970 2750 08.07.54 21 3775 4350 4100 15.07.54 00 10285 6830 6400 02.07.54 21 2398 2950 2750 09.07.54 00 3830 4310 4100 15.07.54 03 10380 7050 6500 03.07.54 00 2395 2920 2740 09.07.54 03 3900 4280 4100 15.07.54 06 10385 7200 6600 03.07.54 03 2390 2900 2740 09.07.54 06 4200 4240 4050 15.07.54 09 10395 7300 6700 03.07.54 06 2420 2870 2730 09.07.54 09 4440 4190 4000 15.07.54 12 10350 7450 6770 03.07.54 09 2450 2850 2720 09.07.54 12 4750 4180 3970 15.07.54 15 10300 7600 6850 03.07.54 12 2475 2835 2710 09.07.54 15 5025 4180 3950 15.07.54 18 10250 7750 6920 03.07.54 15 3000 2825 2710 09.07.54 18 5100 4190 3920 15.07.54 21 10200 7900 7000 03.07.54 18 3450 2870 2700 09.07.54 21 5285 4200 3900 16.07.54 00 10100 7980 7120 03.07.54 21 3900 2900 2700 10.07.54 00 5350 4220 3920 16.07.54 03 10050 8060 7250 04.07.54 00 4100 3000 2800 10.07.54 03 5595 4225 3950 16.07.54 06 9980 8120 7370 04.07.54 03 4300 3100 2900 10.07.54 06 5750 4270 4000 16.07.54 09 9935 8190 7500 04.07.54 06 4400 3250 2950 10.07.54 09 5900 4350 4050 16.07.54 12 9860 8300 7650 04.07.54 09 4545 3400 3000 10.07.54 12 6050 4410 4100 16.07.54 15 9800 8400 7800 04.07.54 12 4550 3500 3070 10.07.54 15 6140 4480 4150 16.07.54 18 9700 8450 7950 04.07.54 15 4680 3610 3150 10.07.54 18 6250 4570 4200 16.07.54 21 9600 8500 8100 04.07.54 18 4750 3700 3220 10.07.54 21 6350 4650 4250 17.07.54 00 9650 8540 8170 04.07.54 21 4800 3790 3300 11.07.54 00 6440 4740 4350 17.07.54 03 9550 8580 8250 05.07.54 00 4850 3840 3400 11.07.54 03 6505 4800 4450 17.07.54 06 9450 8630 8320 05.07.54 03 5005 3890 3500 11.07.54 06 6600 4890 4500 17.07.54 09 9380 8650 8400 05.07.54 06 5040 4000 3570 11.07.54 09 6700 4980 4580 17.07.54 12 9280 8670 8450 05.07.54 09 5080 4110 3650 11.07.54 12 6800 5040 4610 17.07.54 15 9195 8700 8500 05.07.54 12 5050 4160 3720 11.07.54 15 6910 5070 4640 17.07.54 18 9100 8750 8550 05.07.54 15 5025 4220 3800 11.07.54 18 7050 5090 4700 17.07.54 21 8950 8800 8600 05.07.54 18 4950 4300 3850 11.07.54 21 7185 5140 4750 18.07.54 00 8850 8800 8650 05.07.54 21 4895 4380 3900 12.07.54 00 7250 5200 4820 18.07.54 03 8780 8800 8700 06.07.54 00 4750 4420 4000 12.07.54 03 7350 5280 4900 18.07.54 06 8680 8750 8750 06.07.54 03 4770 4460 4100 12.07.54 06 7440 5340 5000 18.07.54 09 8580 8700 8800 06.07.54 06 4670 4500 4170 12.07.54 09 7515 5400 5100 18.07.54 12 8500 8670 8800 06.07.54 09 4515 4590 4250 12.07.54 12 7610 5460 5150 18.07.54 15 8415 8650 8800 06.07.54 12 4350 4620 4300 12.07.54 15 7760 5520 5200 18.07.54 18 8310 8630 8770 06.07.54 15 4290 4650 4350 12.07.54 18 7900 5580 5250 18.07.54 21 8210 8600 8750 06.07.54 18 4190 4680 4370 12.07.54 21 8100 5650 5300 19.07.54 00 8130 8590 8720 06.07.54 21 4095 4710 4400 13.07.54 00 8200 5690 5370 19.07.54 03 8080 8570 8700 07.07.54 00 4050 4705 4420 13.07.54 03 8300 5760 5450 19.07.54 06 7920 8510 8650 07.07.54 03 4025 4705 4450 13.07.54 06 8500 5820 5470 19.07.54 09 7800 8450 8600
126 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region continuation of the table Day. Bratislava Komárno Štúrovo Day Bratislava Komárno Štúrovo Day Bratislava Komárno Štúrovo 19.07.54 12 7700 8350 8550 25.07.54 06 3970 5130 5350 31.07.54 00 2980 3330 3390 19.07.54 15 7590 8250 8500 25.07.54 09 3960 5080 5300 31.07.54 03 2963 3300 3380 19.07.54 18 7450 8130 8450 25.07.54 12 3930 5040 5250 31.07.54 06 2950 3280 3370 19.07.54 21 7275 8000 8400 25.07.54 15 3895 4995 5200 31.07.54 09 2935 3265 3360 20.07.54 00 7150 7920 8300 25.07.54 18 3840 4920 5150 31.07.54 12 2930 3260 3350 20.07.54 03 7000 7870 8200 25.07.54 21 3795 4850 5100 31.07.54 15 2930 3250 3340 20.07.54 06 6850 7780 8120 26.07.54 00 3750 4820 5000 31.07.54 18 2929 3230 3320 20.07.54 09 6705 7700 8050 26.07.54 03 3700 4780 4900 31.07.54 21 2927 3220 3300 20.07.54 12 6600 7600 7970 26.07.54 06 3640 4730 4820 01.08.54 00 2926 3220 3300 20.07.54 15 6500 7520 7900 26.07.54 09 3570 4675 4750 20.07.54 18 6350 7460 7850 26.07.54 12 3520 4620 4670 20.07.54 21 6200 7400 7800 26.07.54 15 3495 4560 4600 21.07.54 00 6050 7320 7720 26.07.54 18 3420 4490 4550 21.07.54 03 5910 7250 7650 26.07.54 21 3375 4420 4500 21.07.54 06 5800 7200 7570 27.07.54 00 3340 4480 4400 21.07.54 09 5700 7150 7500 27.07.54 03 3300 4340 4300 21.07.54 12 5640 7100 7450 27.07.54 06 3250 4270 4200 21.07.54 15 5570 7050 7400 27.07.54 09 3210 4200 4100 21.07.54 18 5490 6970 7350 27.07.54 12 3180 4150 4050 21.07.54 21 5390 6900 7300 27.07.54 15 3160 4100 4000 22.07.54 00 5300 6850 7200 27.07.54 18 3130 4050 3950 22.07.54 03 5210 6800 7100 27.07.54 21 3090 4000 3900 22.07.54 06 5120 6720 7000 28.07.54 00 3075 3950 3850 22.07.54 09 5050 6650 6900 28.07.54 03 3060 3900 3800 22.07.54 12 5000 6580 6850 28.07.54 06 3045 3840 3770 22.07.54 15 4950 6510 6800 28.07.54 09 3030 3780 3750 22.07.54 18 4870 6450 6750 28.07.54 12 3020 3730 3720 22.07.54 21 4800 6400 6700 28.07.54 15 3010 3680 3700 23.07.54 00 4750 6300 6620 28.07.54 18 3007 3640 3650 23.07.54 03 4690 6200 6550 28.07.54 21 3005 3600 3600 23.07.54 06 4600 6100 6470 29.07.54 00 3005 3560 3590 23.07.54 09 4485 6000 6400 29.07.54 03 3005 3515 3580 23.07.54 12 4400 5950 6360 29.07.54 06 3003 3490 3570 23.07.54 15 4320 5900 6320 29.07.54 09 3000 3460 3560 23.07.54 18 4250 5850 6270 29.07.54 12 2995 3430 3550 23.07.54 21 4195 5805 6250 29.07.54 15 2990 3415 3540 24.07.54 00 4150 5750 6150 29.07.54 18 2985 3400 3520 24.07.54 03 4125 5700 6050 29.07.54 21 2975 3380 3500 24.07.54 06 4100 5640 5950 30.07.54 00 2970 3375 3490 24.07.54 09 4085 5580 5850 30.07.54 03 2960 3370 3480 24.07.54 12 4060 5500 5770 30.07.54 06 2962 3365 3470 24.07.54 15 4030 5410 5700 30.07.54 09 2965 3365 3460 24.07.54 18 4015 5330 5650 30.07.54 12 2975 3350 3450 24.07.54 21 4005 5260 5600 30.07.54 15 2980 3350 3440 25.07.54 00 3995 5220 5500 30.07.54 18 2990 3355 3420 25.07.54 03 3990 5180 5400 30.07.54 21 2995 3355 3400
127 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
7000 Bratislava-mer. Medveďov-mer. 6000 Komár no- mer .
5000
4000
3000
2000
1000 1.8.77 0:00 1.8.77 0:00 2.8.77 0:00 3.8.77 0:00 4.8.77 0:00 5.8.77 0:00 6.8.77 0:00 7.8.77 0:00 8.8.77 0:00 9.8.77 30.7.77 0:00 30.7.77 0:00 31.7.77 0:00 10.8.77 9000 Bratislava-mer. 8000 Medveďov-mer.
7000 Komár no- mer .
6000
5000
4000
3000
2000
1000 3.8.81 0:00 4.8.81 0:00 5.8.81 0:00 6.8.81 0:00 7.8.81 0:00 8.8.81 0:00 9.8.81 0:00 1.9.81 0:00 2.9.81 0:00 10.8.81 0:00 11.8.81 0:00 12.8.81 0:00 13.8.81 0:00 14.8.81 0:00 15.8.81 0:00 16.8.81 0:00 17.8.81 0:00 18.8.81 0:00 19.8.81 0:00 20.8.81 0:00 21.8.81 0:00 22.8.81 0:00 23.8.81 0:00 24.8.81 0:00 25.8.81 0:00 26.8.81 0:00 27.8.81 0:00 28.8.81 0:00 29.8.81 0:00 30.8.81 0:00 31.8.81 0:00
7000 Devín-mer. Medveďov-mer. 6000 Komárno-mer. Nagymaros-mer. 5000
4000
3000
2000
1000 1.11.96 0:00 1.11.96 17.10.96 0:00 18.10.96 0:00 19.10.96 0:00 20.10.96 0:00 21.10.96 0:00 22.10.96 0:00 23.10.96 0:00 24.10.96 0:00 25.10.96 0:00 26.10.96 0:00 27.10.96 0:00 28.10.96 0:00 29.10.96 0:00 30.10.96 0:00 31.10.96 0:00 Fig. 8-11 Observed (mer.) flood hydrographs (3-hourly step) 1977, 1981 and 1996, of the Danube at stations Bratislava, Medveďov, Komárno and Nagymaros.
128 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
7000 Bratislava-mer.
6000 Medv eďov-mer. Komár no- mer . 5000
4000
3000
2000
1000 1.12.92 0:00 2.12.92 0:00 3.12.92 0:00 4.12.92 0:00 5.12.92 0:00 6.12.92 0:00 7.12.92 0:00 8.12.92 0:00 9.12.92 0:00 14.11.92 0:00 15.11.92 0:00 16.11.92 0:00 17.11.92 0:00 18.11.92 0:00 19.11.92 0:00 20.11.92 0:00 21.11.92 0:00 22.11.92 0:00 23.11.92 0:00 24.11.92 0:00 25.11.92 0:00 26.11.92 0:00 27.11.92 0:00 28.11.92 0:00 29.11.92 0:00 30.11.92 0:00 10.12.92 0:00 11.12.92 0:00 12.12.92 0:00 13.12.92 0:00 14.12.92 0:00
8000 Devín-mer. Medveďov-mer. 7000 Komárno-mer. Nagymaros-mer. 6000
5000
4000
3000
2000
1000 3.7.97 0:00 3.7.97 0:00 4.7.97 0:00 5.7.97 0:00 6.7.97 0:00 7.7.97 0:00 8.7.97 0:00 9.7.97 0:00 1.8.97 0:00 2.8.97 10.7.97 0:00 10.7.97 0:00 11.7.97 0:00 12.7.97 0:00 13.7.97 0:00 14.7.97 0:00 15.7.97 0:00 16.7.97 0:00 17.7.97 0:00 18.7.97 0:00 19.7.97 0:00 20.7.97 0:00 21.7.97 0:00 22.7.97 0:00 23.7.97 0:00 24.7.97 0:00 25.7.97 0:00 26.7.97 0:00 27.7.97 0:00 28.7.97 0:00 29.7.97 0:00 30.7.97 0:00 31.7.97
5000 Devín-mer. Medveďov-mer. 4500 Komárno-mer. 4000 Nagymaros-mer.
3500
3000
2500
2000
1500
1000 4.3.98 0:00 5.3.98 0:00 6.3.98 0:00 7.3.98 0:00 8.3.98 0:00 9.3.98 0:00 10.3.98 0:00 10.3.98 0:00 11.3.98 0:00 12.3.98 0:00 13.3.98 0:00 14.3.98 0:00 15.3.98 0:00 16.3.98 0:00 17.3.98 0:00 18.3.98 0:00 19.3.98 0:00 20.3.98 0:00 21.3.98 0:00 22.3.98 0:00 23.3.98 0:00 24.3.98 0:00 25.3.98 0:00 26.3.98 0:00 27.3.98 0:00 28.3.98 Fig. 8-12 Observed (mer.) flood hydrographs (3-hourly step) 1992, 1997 and 1998, of the Danube at stations Bratislava-Devín, Medveďov, Komárno and Nagymaros.
129 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
In 2003 the NLN-Danube model was recalibrated using hourly discharge of a flood measured in August 2002 (Mitková, 2006). During this flood, two waves with discharges of about 6800 and 10 300 m3 s-1, respectively, were recorded at Bratislava (Devín) station. The result of simulation is shown in Fig. 8-13.
12000 Devin Medveďov 10000 Komárno Štúrovo Nagymaros 8000 ] -1 s 3 6000 Q [m
4000
2000
0 06.08.02 08.08.02 10.08.02 12.08.02 14.08.02 16.08.02 18.08.02 20.08.02 22.08.02 24.08.02 00:00 00:00 00:00 00:00 00:00 00:00 00:00 00:00 00:00 00:00
Fig. 8-13 Danube 1-hourly simulated flood hydrographs, NLN-Danube model, calibration wave , 2002.
8.3.2.2 NLN-Danube model verification
The NLN-Danube model was verified on major flood waves that occurred in March 2002, March 1998, and July 1997. The results of the verification of the NLN-Danube model showed that the model adequately simulates the present hydraulic conditions in the given river reach.
8.3.2.3 Simulation results - catastrophic flood scenario of the Danube between Devín and Nagymaros
Graphical interpretation of results is in Fig. 8-14 (values are in Table in Appendix III). In these figures is first shown the simulated wave in Čuňovo, Medveďov, Komárno and Štúrovo. Then follows besides the input hydrograph in Bratislava (Devín since 1996), the observed and simulated graphs in Medveďov, and the same in Komárno. We choose this arrangement for better comparison of the simulated and observed hydrographs during the whole course of flood, not only of the peak values.
130 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
15000
Čuňovo-c 14000 Medveďov-c Komárno-c. 13000 Štúrovo-c Nagymaros-c 12000
11000
10000
9000
8000
7000
6000
5000
4000
3000 1.8. 0:00 1.8. 0:00 2.8. 0:00 3.8. 0:00 4.8. 0:00 5.8. 0:00 6.8. 0:00 7.8. 0:00 8.8. 0:00 9.8. 0:00 1.9. 0:00 2.9. 0:00 3.9. 30.7. 0:00 31.7. 0:00 10.8. 0:00 11.8. 0:00 12.8. 0:00 13.8. 0:00 14.8. 0:00 15.8. 0:00 16.8. 0:00 17.8. 0:00 18.8. 0:00 19.8. 0:00 20.8. 0:00 21.8. 0:00 22.8. 0:00 23.8. 0:00 24.8. 0:00 25.8. 0:00 26.8. 0:00 27.8. 0:00 28.8. 0:00 29.8. 0:00 30.8. 0:00 31.8. 0:00 Fig. 8-14 Danube 3-hourly catastrophic flood scenario at Čuňovo, Medveďov, Komárno, Štúrovo and Nagymaros, NLN-Danube model output.
8.4 Conclusion
The above presented results lead to following conclusions: • Model parameters derived from the highest observed flood wave of 1954 were not optimal for simulation of floods from recent years. Therefore for NLN-Danube model calibration also the 1991 and 2002 floods were used. After this parameters correction the results of the simulation runs appear satisfactory. • Comparison of the observed and modeled flood hydrographs in stations Medveďov and Komárno are satisfactory. The analysis indicates that the results can be influenced to quite a significant degree, by the external inflows (tributaries) of rivers Váh, Hron and Ipeľ and also by the operation of the Gabčíkovo water structure. For smaller flood event the partial use of the Čuňovo reservoir storage can be significant. As long as a reliable forecast of the Gabčíkovo structure operation will not be available for the hydrological forecast lead time, a substantial improvement of the downstream forecast accuracy cannot be expected, even after introduction of the most progressive and modern data collection and transmission
131 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
system, neither the installation of the most sophisticated forecasting methods. In general, in such large basins as the Danube up to Bratislava (close to 131×103 km2), each particular high flood formation has its own history. This was documented excellently almost 50 years ago by Kresser (1957, 1970), who also analyzed the disastrous Danube flood of August 1501 (!), most probably the highest flood on the Danube in the last millennium. This flood apparently originated by coincidence of the discharge peaks at the rivers Inn and the upper Danube, at Passau in Germany, and, during its propagation through the Austrian Danube, the resultant peak gradually coincided with those of the important tributaries downstream. This was apparently the result of the meteosynoptical evolution over the catchment with intensive cyclonic activity moving slowly eastward. Such evolution of the flood event is extremely rare, but still physically feasible today, and maybe not so highly improbable under conditions of predicted global warming. However, in forecasting such disastrous floods with a reasonable lead time, the travel times in all relevant sections of the Danube would play a vital role in any of the forecasting methodologies. The water management authorities along the whole Slovak and Hungarian Danube reach are aware for sure to what extent is the adjacent territory protected against floods. The above analysis results in Fig. 8-14 show in concrete figures what an extraordinary, catastrophic flood would mean. Its occurrence probability is extremely low but it cannot be excluded. And about the „extremely low“ probability of occurrence of such catastrophes we are justified to doubt in the light of floods which occurred during the last decades on the rivers Mississippi and Missouri, Rhein, Morava and Oder, Zambezi and Limpopo, Tisa and its tributaries from Eastern Slovakia. When the Danube will have its turn? With respect to the fact that hydrological regime of the Danube River at Bratislava has to a great extent a character of the Central-European mountain river, it is possible to extrapolate these results (particularly those claiming no climate change impact) also for other rivers in Slovakia originating in its Carpathian mountain region. In future, however, it will be desirable to confirm this hypothesis on other Slovak river(s) with long runoff data series, possibly on the base of reconstructed discharge values by indirect methods (analogy, mathematical runoff modeling, etc.).
132 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
9 THE THESIS RESULTS AND CONTRIBUTION TO PRACTICE
To quote Klemeš (1998): the things rotate, pulse and oscillate, wherever in put your eye. In some instances, the signal is evident – as e.g. the seasonal changes within the year, sometimes it is difficult to identify – as e.g. the lunar-solar signal in the temperature time series (Currie, 1996; Bucha and Charvátová, 1996; Charvátová, 2000). Sometimes we can see clearly the series behavior and character, but we do not understand its mechanism. Sometimes, the series behavior and its character are clearly visible but its mechanism remains unknown – this is the case of the Sun’s 11-years cycle. On the other side, sometimes we understand the phenomenon’s mechanism but its character remains hidden – as it was in case of the climatic signals and of the orbital Earth’s motion. More regions of the world suffer with the multiannual dry periods. Also occurrence of the flood phenomena in the world is high. It is documented by flood catastrophes during the last two decades on the rivers Mississippi, Missouri, Rhein, Elbe and Oder, Zambezi, Limpopo, and also in Slovakia on the Danube, Morava or Tisza rivers. The main results and new knowledge of the presented Thesis can be summarized as follows: - The daily mean discharge time series of the river Danube at Bratislava has been supplemented with data from years 1876–1890. So it has been extended into the full-uninterrupted daily data series for the length of 130 years. Such series of the daily mean discharges is suitable for statistical analyses of the hydrological characteristics changes, and also for identification of the multiannual (up to 30- years) cycles. - Using the combined periodogram method and the series filtration, in the discharge time series, the variegation cycles of dry and wet time periods were searched. For such objective, the time series were used, of more than 100 rivers of the world. From the longer cycles in the series the approximately 28–30 and 20–22 yrs. cycles of the dry and wet periods occurrence were identified. However, the cycle lengths is not exactly 28 and 21 years, but in the long term average, they come close to these values. From the shorter cycles, those with 7.8-, 6.5-, 5.2-; 4.14-, 3.65, and 2.4- years were identified. - These periods were documented for the discharge series of the analyzed rivers in various physiographic latitudes of the world. It is then possible to consider this piece of knowledge as generally valid for the whole Earth. These periods are connected with the Solar activity and with the
133 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
thermohaline circulation (ocean conveyor belt). Their parts are also the El Niňo, AO, NAO, and QBO phenomena. - Through the cross-correlations (two variables), time shift of the dry and wet periods was identified depending upon the geographical longitude and latitude of the river basins location. From these results it follows, that the dry and wet periods do not occur at the same time on various locations. This time shift depends upon the basins location, and it follows upon the shift in the precipitations occurrence. - The trend analysis did not indicate any significant trends in runoff series on the territory of Europe as a whole (neither of the Danube basin), for the last 150 years. - There were analyzed also time series of the extreme flood discharges of Danube at Bratislava, as well as those of flood volumes of these floods. Here also the statistical tests did not confirm any statistically significant trends. - A scenario was elaborated of the catastrophic 1000-year flood of Danube for the Bratislava gauging profile. Using a simple (one-dimensional) hydrological model, this catastrophic flood wave was routed down the Danube from Bratislava to Štúrovo through the almost whole Danube section on the territory of Slovakia. Of course, the whole hydrological system of the Earth is subject to random geophysical and also (anthropogenic) shocks. Therefore, it is necessary always to take into account also random behavior of the hydrological time series.
The Thesis contribution to practice From results of the Thesis it follows, that in the mean yearly discharge time series, significant multi-annual natural river runoff variability exist. If the cycle lengths are correctly identified, it is then possible, for a given region, to forecast occurrence of the dry periods. Such information are extremely valuable as to correct decisions in water resources management, for the next time horizon of approximately 20 years. Therefore, it is necessary to best understand the multi- annual runoff variability, and to take it into account in the water management planning.
Pavla Pekárová
134 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
References
Aizen, V. B., Aizen, E. M., Melack, J. M., Dozier, J., 1997. Climatic and hydrologic changes in the Tien Shan, Central Asia. J. Clim., 10, 1393–1404. Alexandersson H, Moberg A., 1997. Homogenization of Swedish temperature data. Part I: Homogeneity test for linear trends. J. Climatol., 17: 25–34. Alexandersson H., 1986. A homogeneity test applied to precipitation data. J. Climatol., 6: 661– 675. Anctil F, Coulibaly P., 2003. Wavelet Analysis of the Interannual Variability in Southern Québec Streamflow. J. Climate, 17: 163–173. Andrade-Leal, R. N., Bachhiesl, M., Drabek, U., Gutknecht, D., Haiden, T., Holzmann, K., Hebenstreit, K., Kirnbauer, R., Nachtnebel, H. P., 2002. Hydrological prediction models in operational use in the hydro-power industry. Österreichische Wasser- und Abfallwirtschaft 54, 9–10, 129–134. Angelini, H., 1955. Danube flood in July 1954, Bratislava. Hydrological Study. HMI Department of Hydrology, Bratislava, Slovak Republic (in Slovak). Arnell, N., W., 2003. Effects of IPCC SRES* emissions scenarios on river runoff: a global perspective. Hydrology and Earth System Sciences, 5, 619–641. Arpe K. Bengtsson L. Golitsyn GS. Efimova LK, Mokhov II, Semenov VA, Khon VCh., 2000. Analysis of variation in a hydrological cycle at the Ladoga catchment and in the Neva runoff in the 20th and 21st centuries with a global climate model. Meteorologia i Gidrologia 12: 5–13. Bača, P., Mitková, V., 2007. Analysis of seasonal extreme flows using Peaks Over Threshold method. J. Hydrol. Hydromech., 55, 1, 16–22. Balek, J., 1968 Linear Extrapolation of the Average Annual Runoff of Selected Rivers of Four Continents. (In Czech.) J. Hydrol. Hydromech., 16, 3, 402–428. Bardossy, A. and Molnar, Z., 2004. Statistical and geostatistical investigations into the effects of the Gabcikovo hydropower plant on the groundwater resources of northwest Hungary. Hydrol. Sci. J. 49(4) 611–623. Bayliss, A. C., 1999. Deriving flood peak data. Flood estimation Hanbook. 3, 273–283. Belz, J. U., Goda, L., Buzás, Z., Domokos, M., Engel, H., and Weber, J., 2004. Flow regime of river Danube and its catchment. The Danube and its catchment – A hydrological monograph, follow-up volume VIII/2, Koblenz & Baja, 152 pp. Benický, J., 1992. Increase of Flood Risk by Means of Runoff Acceleration – Is It a Paradox of Flood Protection? Proc. XVIth Conference of the Danubian Countries on Hydrological Forecasting. Koblenz, 135-140. Bentura, P. L. F. and Michel, C. 1997. Flood routing in a wide channel with a quadratic lag-and- route method. Hydrol. Sci. J. 42(2), 169–185. Bloomfield, P., 1992. Trends in global temperature. Climatic change, 21, 1–16.
135 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Bonacci, O., Trninić, D., 2006. Analysis of discharges along the Danube River watercourse. 23nd conference of the Danube countries on the hydrological forecasting and hydrological bases of water management. Belgrad, CD ROM, 9 pp. Bors, W., 1998. Hochwasserereignis im Juli 1997 an Donau, March und Thaya – ein vorläufiger hydrologischer Bericht der Wasserstraßendirektion. Mitteilungsblatt Hydrographischer Dienst in Österreich, 76, BMLF, Wien, 51-60. Box GEP, Jenkins GM., 1976. Time Series Analysis, Forecasting and Control. Revised Edition. Holden Day, San Francisco. Bradley, R., S., 1994. Reconstruction of Climate from A.D. 1000 to the Present. Proc. “Contemporary climatology” (Ed. by Brázdil and Kolář). Brno, 12–21. Bratránek, A., 1937. Determination of the flood protection storage in reservoirs (in Czech). Publication No.20, State hydrological and hydrotechnical institute, Prague . Brázdil R, Tran N Tam., 1990. Climatic changes in the instrumental period in Central Europe. In Climatic change in the historical and the instrumental periods. Brázdil R (ed). Masaryk University, Brno, 223–230. Brázdil, R., Kolář, M. (Eds.), 1994. Contemporary Climatology, Brno, 620pp. Brockwell PJ, Davis RA., 2003. Introduction to Time Series and Forecasting. Springer-Verlag: New York; 434. Bulletin 17b, 1982. Flood flow frequency. US Geological Survey, Virginia, 194 pp. Čermák, M., 1956. Flood wave volumes. J. Hydrol. Hydromech., 4. Charvátová I, Střeštík J., 1995. Long-term changes of the surface air temperature in relation to Solar inertial motion. Climatic Change 29: 333–352. Charvátová I, Střeštík J., 2004. Periodicities between 6 and 16 years in the surface air temperature in possible relation to solar inertial motion. J of Atmospheric and Solar- Terrestrial Physics 66: 219–227. Charvátová I., 2000. Can origin of the 2400-year cycle of solar activity be caused by solar inertial motion? Ann Geophys.-Atmosph. Hydrosph. and Space Scienc. 18: 399–405. Chow, V. T., Maidment, D. R., Mays, L. W., 1988: Applied hydrology. McGraw-Hill, New York, NY. Čížová, M., 1992. Influence of hydrological forecast by anthropogenic activity. In: Proc. XVIth Conf. of the Danube Countries on Hydrological Forecasting (Kelheim, Germany), 301– 305. German International Hydrological Programme / Operational Hydrological Programme National Committee, Koblenz, Germany. Compagnucci RH, Blanco SA, Figliola MA, Jacovkis PM., 2000. Variability in subtropical Andean Argentinean Atuel river; a wavelet approach. Environmetrics 11: 251–269. Corbus, C., 2002. Contributions to approaching the floods propagation with the help of the theory of the systems. In: CD Proc. XXIst Conf. of the Danube Countries on Hydrological Forecasting (Bucharest, Romania). National Institute of Meteorology and Hydrology, Bucharest. ISBN 973-0-02759-5. Currie RG., 1996. Variance contribution of luni-solar (Mn) and solar cycle (Sc) signals to climate data. Int. J. of Climatology 16: 1343–1364. Dankers, R., Christensen, B.O., Feyen, L., Kalas, M., De Roo, 2007. Evaluation of very high- resolution climate model data for simulating flood hazards in the Upper Danube Basin. J. of Hydrol., 347, 319–331.
136 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Directive (2007). Directive 2007/60/EC of the European Parliament and of the Council of 23 October 2007 on the assessment and management of flood risks. Dulovič, L., 1992. Discharge Balance of the Danube River Downstream from Bratislava. Proc. XVIth Conference of the Danubian Countries on Hydrological Forecasting. Kelheim, 174–178. Dzubák, M., 1969. Determination of the peak daily precipitation law by means of the global exceedance curves (in Slovak). J. Hydrol. Hydromech., 17, 3, 209–225. Esper J, Cook ER, Schweingruber FH., 2002. Low-frequency signals in long tree-ring chronologies for reconstructing past temperature variability. Science 295: 2250–2253. Fischer-Antze, T. and Gutknecht, D., 2004. Morphological changes of the Danube River east of Vienna over the last nine years. In: CD Proc. XXIInd Conf. of the Danube Countries on the Hydrological Forecasting and Hydrological Bases of Water Management (Brno, Czech Republic). Czech Hydrometeorological Institute, Prague. ISBN 80-86690-19-9. Foster, M. J., Werritty, A., Smith K., 1997. The nature, causes and impacts of recent hydroclimatic variability in Scotland and Northern Ireland. Proceedings, Sixth National Hydology Symposium. Wallingford: British Hydrological Society. Füry, J., 1998. History of Floods and Flood Protection of Danube Plains. (In Slovak.) Proc. Conf. “Floods and flood protection”. Dom techniky ZSVTS, Banská Bystrica, 9–15. Hajtášová, K., Kunsch, I., Svoboda, A., 1995. Hydrological Forecasting on the Slovak Danube Reach: History and Contemporaneity. (In Slovak.) Proc. Int. Conf. ”Danube – the artery of Europe”. ZSVTS, Bratislava, 183–193. Hajtášová, K., Martinka, K., Minárik, B., Panenka, I., 1985. Methods of Operational Hydrological Forecasts. (In Slovak.) Final report, Res. task II-5-2/4. SHMÚ Bratislava. Hladný, J. (Ed.), 1997. Impacts of a Potential Climate Change on Hydrology and Water Resources in the Czech Republic. Praha, 134 pp. Hladný, J., Doležal, F., Makeľ, M., Sacherová, D., 1970. Peak runoff volumes of a given duration (in Czech). Hydrologigal conditions of the CSSR, Vol. III. HMÚ (1956). Water Levels and Runoff 1954. (In Slovak.) HMÚ, Praha. HMÚ (1968) Hydrological Yearbook 1965. (In Slovak.) HMÚ, Praha. Holko, L., Kostka, Z., 2005. Analýza maximálneho denného prietoku v horských povodiach stredného Slovenska. In Hydrologie malého povodí 2005, ISBN 80-02-01754, Ústav pro hydrodynamiku, 119–124. Horváthová, B., 2003. Flood is not only high water. (In Slovak.) VEDA, Bratislava, 232 pp. Hurrell JW, Kushnir Y, Ottersen G, Visbeck M, (Eds), 2003. The North Atlantic Oscillation – Climatic Significance and Environmental Impact. Geoph. Mon. 134, American Geophysical Union, Washington; 280. Hurst, H. E., 1951. Long term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng., 116, 770–808. IPCC 2001, Climate Change 2001. The scientific basis. Contribution of Working Group 1 to the Third Assessment Monograph of the IPCC. Cambridge University Press, UK, 944 pp. Jevrejeva S, Moore JC, Grinsted A., 2003. Influence of the arctic oscillation and El Nino- Southern Oscillation (ENSO) on ice conditions in the Baltic Sea: The wavelet approach. J Geoph. Res.-Atmosph, 108, D21, art. no. 4677. Jevrejeva S, Moore JC. 2001. Singular Spectrum Analysis of Baltic Sea ice conditions and large-scale atmospheric patterns since 1708. Geoph. Res. Letters 28: 4503-4506.
137 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Jones, P. D., Jónsson, T. and Wheeler, D. (1997) Extension to the North Atlantic Oscillation using early instrumental pressure observations from Gibraltar and South-West Iceland. Int. J. Climatol. 17, 1433–1450. Kane RP. 1997. Prediction of droughts in north-east Brazil: Role of ENSO and use of periodicities. International Journal of Climatology, 17: 655–665. Kite, G. W., 1977: Frequency and risk analysis in hydrology. Water Res. Publications, Fort Collins, CO. Klein Tank, A.M.G., Wijngaard, J.B., Konnen, G.P., Bohm, R., Demar´e, G., Gocheva, A., Mileta, M., Pashiardis, S., Hejkrlik, L., Kern-Hansen, C., Heino, R., Bessemoulin, P., Muller-Westermeier, G., Tzanakou, M., Szalai, S., Palsdottir, T., Fitzgerald, D., Rubin, S., Capaldo, M., Maugeri, M., Leitass, A., Bukantis, A., Aberfeld, R., van Engelen, A.F.V., Forland, E., Mietus, M., Coelho, F., Mares, C., Razuvaev, V., Nieplova, E., Cegnar, T., Antonio Lopez, J., Dahlstrom, B., Moberg, A., Kirchhofer, W., Ceylan, A., Pachaliuk, O., Alexander, L.V., Petrovic, P., 2002: Daily dataset of 20th-century surface air temperature and precipitation series for the European Climate Assessment. International Journal of Climatology 22, 1441–1453. Klemeš, V., 1974: The Hurst phenomenon: A puzzle? Water Resourc. Res., 10, 4, 675–688. Klige, R. K, Selivanov, A. O., Voronov, A. M., 1989. Water Regime Changes in the Soviet Union Territory during the Last Thousand Years. (In Russian.) Vodnye resursy, 5, 28–40. Kohnová, S., Kriegerová, I., Podolinská,J., Szolgay, J., Hlavčová, K., 2005b. Regional methods for design flood computation in Slovakia (Review and Comparison): In: Nachtnebel, H.P., Jugovic, C.J., eds.: Ninth International Symposium on Water Management and Hydraulic Engineering. Ottenstein, Austria, 369–376. Kohnová, S., Lapin, M., Szolgay, J., Gaál, L., 2005a. Methodology for the selection of 10-day maximum precipitation totals and their statistical analysis in the upper Hron region. Contributions to Geophysics and Geodesy, 35/3, 299–318. Komorník, J., Komorníková, M., Mesiar, R., Szokeová, D., Szolgay, J., 2006. Comparison of forecasting performance of nonlinear models of hydrological time series. Physics and Chemistry of the Earth, 31, 18, 1127–1145. Koutsoyiannis, D., 2002. The Hurst phenomenon and fractional Gaussian noise made easy. Hydrological Sciences Journal, 47, 4, 573–595. Kresser, W., 1957. Die Hochwässer der Donau. Springer Velag, Wien, 95 pp. Kresser, W., 1970. The change in the flood discharge in the Danube at Vienna resulting from hydraulic structures along the river and its drainage area. In: Proc. XVIth Conf. of the Danube Countries on Hydrological Forecasting (Kelheim, Germany), 183–189. German International Hydrological Programme / Operational Hydrological Programme National Committee, Koblenz, Germany. Kundzewicz, Z. W. and Robson, A. J., 2004. Change detection in hydrological records – a review of the methodology. Hydrol. Sci. J. 49(1), 7–19. Labat D., Goddéris Y., Probst J. L., Guzot J. L., 2004. Evidence for global runoff increase related to climate warming. Adv. Water Resour., 27, 631–642. Lapin M., 2004. Detection of changes in the regime of selected climatological elements at Hurbanovo. Contribution to Geophysics and Geodesy 34: 169–193. Laurenson, E. M. (1964) A catchment storage model for runoff routing. J. Hydrol. 2, 141–163.
138 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Lehner, B., Döll, P., Alcamo, J., Henrichs, T., Kaspar, F., 2006: Estimating the impact of global change on flood and drought risks in Europe: A continental, integrated analysis. Climate Change. doi:10.1007/s10584-006-6338-4, 273–299. Li, J., Wang, J., 2003a. A new North Atlantic Oscillation index and its variability. Adv. Atmos. Sci., 20(5), 661–676. Li, J., Wang, J., 2003b. A modified zonal index and its physical sense. Geophys. Res. Lett., 30(12), 1632, doi:10.1029/2003GL017441. Lindström G, Bergström S., 2004. Runoff trends in Sweden 1807–2002. Hydrological Sciences Journal 49: 69–83. Liritzis I, Fairbridge R., 2003. Remarks on astrochronology and time series analysis of Lake Sake varved sediments. J. Balkan Geoph. Soc. 6: 165–172. Lohre M, Sibbertsen P, Konnig T., 2003. Modeling water flow of the Rhine River using seasonal long memory. Watre Resour. Res. 39: 1132. Malone, T. A. and Cordery, I., 1989. An assessment of network models in flood forecasting. In: New Directions for Surface Water Modeling (Proc. Baltimore Symp.) (ed. by M. L. Kavvas), 115–124. IAHS Publ. 181, IAHS Press, Wallingford, UK. Maravall A, Del Rio A., 2001. Time aggregation and the Hodrick-Prescott filter. Documento de Trabajo No. 0108, Banco de Espana, 43. Mares, I., Mares, C., Stanciu, A., 2007: A hidden Markov model for the discharges in Danube lower basin associated with SLP over Atlantic European region. ICESM Abstracts, 1, ICESM2007-A-00172, Marquardt, C., Naujokat, B., 1997. An update of the equatorial QBO and its variability. 1st SPARC Gen. Assemb, Melbourne Australia, WMO/TD-No. 814(1), 87–90. Micevski, T., Franks, S. W., Kuczera, G., 2006: Multidecadal variability in coastal eastern Australian flood data. J. of Hydrol., 327, 219–225. Miklánek, P., Mikuličková, M., Mitková, V., Pekárová, P., 2002. Changes of floods travel times on upper Danube. CD ROM Proceedings, XXI. Conference of the Danube countries, Bucharest, Romania, 12 pp. Milly, P. C. D., Wetherald, R. T., Dunne, K. A., Delworth, T. L., 2002. Increasing risk of great floods in a changing climate. Nature 415, 514–517. Misik, M. and Capekova, Z., 2001. The relation of flood regime and anthropogenic activities in Danube section near Bratislava. In: Proc. Influence of Anthropogenic Activities on the Water Regime of Lowland Territory. Institute of Hydrology Slovak Academy of Sciences, Michalovce, Slovakia, 98–101 (in Slovak). Mitkova, V., 2002. Travel time changes of the flood on Danube River. Acta Hydrol. Slovaca 3(1), 20–27. Institute of Hydrology Slovak Academy of Sciences, Bratislava (in Slovak with English summary). Mitková, V., 2002. Changes in travel times of flood waves on the Danube (In Slovak). Acta Hydrologica Slovaca, 3, 1, 20–27. Mitková, V., 2006. Analýza zmien transformácie povodňových vĺn Dunaja v úseku Kienstock- Nagymaros. Dizertačná práca, ÚH SAV, Bratislava, 122 s. Mosný, V., 1995. Consequence of Changes in Air Temperature and Precipitation upon Changes of Runoff Variability in the Modelled Basin of River Hron. (In Slovak.) National climate programme of the Slovak Republic, Bratislava, Vol. 3, 79–96.
139 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Nacházel, K. (1984) On Some Problems Concerning the Deviation of Statistical Characteristics of Average Monthly Flow Series and Their Mathematical Models. (In Czech.) J. Hydrol. Hydromech., 32, 1, 3-31. Nijssen, B., O’Donnell, G. M., Lettenmaier, D., Lohmann, D., Wood, E. F., 2001. Predicting the discharge of global rivers. J. Climate, 14, 3307-3323. Nohara, D., Kitoh, A., Hosaka, M., Oki, T., 2006. Impact of climate change on river discharge projected by multimodel ensemble. Journal of Hydrometeorology, 7, 1076–1089. Oki, T., Valeo, C., Heal, K.(eds), 2006. Hydrology 2020: an integrating science to meet world water challenges. IAHS Publication; no. 300. Wallingford, UK, IAHS Press, 190 p. Pacl, J., 1955. Danube floods in July 1954. (In Slovak). Hydrological study HMI, Praha, 26 p. Pekárová P, Miklánek P, Pekar J., 2003. Spatial and temporal runoff oscillation analysis of the main rivers of the world during the 19th–20th centuries. J. Hydrol. 274: 62–79. Pekárová P, Miklánek P., 2004a. Abflusstrends slowakischer Flüsse und mögliche Zusammenhänge mit ENSO/NAO - Erscheinungen. Österreichische Wasser- und Abfalllwirtschaft, Springer, 1-2: 17–25. Pekárová P, Miklánek P., 2004b. Occurrence of the dry periods in European runoff series. In CD ROM - XXII. Conference of the Danubian Countries. Brno, 12p. Pekárová P, Pekar J., 2004. Teleconnections AO, NAO, SO, AND QBO with interannual streamflow fluctuation in the Hron Basin. J. Hydrol. Hydromech. 52: 279–294. Pekárová, Kohnová, S., Miklánek, P. and Szolgay, J., 2007b. Uncertainties in estimation of design peak flow with 100-year return period. Ed. Mari Heinonen, Proc. Third Int. Conf. on Climate and Water, Helsinki, Finnish Environment Institute SYKE, 372–378. Pekárová, P., 2003. Dynamika kolisania odtoku svetovych a slovenskych riek (Dynamics of Runoff Fluctuation of the World and Slovak rivers). VEDA Publishing House, Bratislava, Slovak Republic. 222. Pekárová, P., Halmová, D. and Mitková, V., 2005. Simulation of the catastrophic floods caused by extreme rainfall events - Uh River basin case study. J. Hydrol. Hydromech., 53, 4, 219–230. Pekárová, P., Halmová, D., Miklánek, P., Onderka, M., Pekár, J., Škoda, P., 2008. Is the water temperature of the Danube river at Bratislava (Slovakia) rising? Journal of Hydrometeorology. (in press). Pekárová, P., Miklánek, P., 1996. The Balance of Pollutant Loads by Slovak Rivers into the Danube River. Proc. XVIIIth Conference of the Danube countries on hydrological forecasting and hydrological bases and water management data. TU, Graz, Vol.E, E85– E90. Pekárová, P., Miklánek, P. and Pekár, J., 2007b. Long-term Danube monthly discharge prognosis for the Bratislava station using stochastic models. Meteorol. Čas., 10, 211–218. Pekárová, P., Miklánek, P., Pekár, J., 2006. Long-term trends and runoff fluctuations of European rivers. IAHS-AISH Publication, 308, Wallingford, 520–525. Pekárová, P., Miklánek, P., Pekár, J., 2007. Long-term Danube monthly discharge prognosis for the Bratislava station using stochastic models. Meteorologický časopis, 10, 211–218. Pekárová, P., Onderka, M., Pekár, J., Miklánek, P., Halmová, D., Škoda, P. and Bačová Mitková, V., 2008. Hydrologic scenarios for the Danube River at Bratislava. Key Publishing, Ostrava, 160 pp. http://www.ih.savba.sk/danubeflood
140 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Pekárová, P., Pacl, J., Škoda, P., Miklánek, P., 2007a. Supplementation of average daily discharge data of the Danube River in Bratislava with the historical period 1876–1890. Acta Hydrologica Slovaca, ISSN 1335-6291, 8, 1, 3–12. Pekárová, P., Pekár, J., 2006. Long-term discharge prediction for the Turnu Severin station (the Danube) using a linear autoregressive model. In Hydrological Processes. ISSN: 0885- 6087, 20, 5, 1217–1228. Pekárová, P., Škoda, P., Onderka, M., Pacl, J., Pekár, J., 2007c. Analysis of discharge variability of the Danube river in Bratislava for 1876–1940 and 1941–2005. Ed. Josip Petraš, 10 th International Symposium on Water Management and Hydraulic Engineering, 04- 09.09.2007 Šibenik, Croatia, Zagreb, Faculty of Civil Engineering, 2007, ISBN 978-953- 6272-21-1, 10 pp. Peterson, B. J., Holmes, R. M., McClelland, J. W., Vorosmarty, C. J., Lammers, R. B., Shiklomanov, A. I., Shiklomanov, I. A., Rahmstorf, S., 2002. Increasing river discharge to the Artic Ocean. Science 298, 2171–2173. Popa R, Bosce C., 2002. Fuzzy nearest neighbour method for monthly inflows forecasting into “Iron Gates I” reservoir. In CD ROM - XXI Conference of the Danubian Countries. Bucharest, ISBN 973-0-02759-5, 7p. Probst J, Tardy Y., 1987. Long range streamflow and world continental runoff fluctuation since the beginning of this century. J. Hydrol. 94: 289–311. Prochazka M, Deyl M, Novicky O., 2001. Technology for Detecting Trends and Changes in Time Series of Hydrological and Meteorological Variables - Change and Trend Problem Analysis (CTPA). User’s Guide. CHMI, Prague; 25p. Prohaska, S., Isailović, D., Srna, P. and Marčetić, I., 1999. Coincidence of flood flow of the Danube river and its tributaries. The Danube and its catchment – A hydrological monograph, follow-up volume IV, Bratislava, 187 pp. Radziejewski, M., Kundzewicz, Y., W., 1997. Fractal analysis of flow of the river Warta. Journal of Hydrology, 200, 280–294. Rao AR, Hamed K., 2003. Multi-taper method of analysis of periodicities in hydrologic data. J. Hydrol., 279: 125–143. Rao, A. R., Hamed, K. H., 2000. Flood frequency analysis. CRC Press LLC, N. W. Corporate Blvd., Boca Raton, Florida. Shmagin, B.,A., Trizna, M., 1992. A long-term prognosis of average annual flows of Danube River in Orsova station. Acta Facultatis Rerum Naturalium Universitatis Comeniane, Geographica 33, 233–243. Škoda, P., Turbek, J., 1995. Monitoring of the Danube River hydrologic regime (In Slovak). Proc. Int. Conf. “Danube – the artery of Europe”. ZSVTS, Bratislava, 194–206. Solanki SK, Usoskin IG, Kromer B, Schüssler M, Beer J., 2004. Unusual activity of the Sun during recent decades compared to the previous 11,000 years. Nature 431: 1084–1087. Sosedko M., 1997. Regular alternation of high and low streamflow periods in the river basin of the Carpathians. Annales Geophysicae, Part II, Supplement II to Vol. 15, C 310. Sriwongsitanon, N., Ball, J. E. and Cordery, I., 1998. An investigation of the relationship between the flood wave speed and parameters in runoff routing models. Hydrol. Sci. J. 43(2), 197–212. Stănescu, V. A., Ungureanu, V., and Mătreaţă, M., 2004. Regional analysis of the annual peak discharges in the Danube catchment. The Danube and its catchment – A hydrological monograph, follow-up volume VII, Bucharest, 64 pp.
141 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Štepánek, P., 2003. AnClim - software for time series analysis. Dept. of Geography, Fac. of Natural Sciences, MU, Brno; http://www.sci.muni.cz/~pest/AnClim.html. Svoboda, A., Pekárová, P., Miklánek, P., 2000. Flood hydrology of Danube between Devín and Nagymaros. SVH – ÚH SAV, 96 pp. Szolgay, J., Kohnová, S., 2003. Possibilities of standardizing the methods of maximum runoff computations for flood protection. In: Proc. Ekotechnika. Slovak University of Technology, Bratislava, 78–85 (in Slovak). Szolgay, J., Kohnová, S., Hlavčová, K., Minárik, M., 2007c. K používaniu Langbeinovho vzorca pre dobu opakovania v hodnotení povodňového rizika. In: (Čejp, Julínek, Říha, eds.) Rizika ve vodním hospodářství, Práce a studie FAST VUT, Brno, 494–499. Takáč, I., 1989. The Average Annual Discharge Oscillation Regularities at Selected Stations in the SSR. (In Slovak.) Proc. “CPZV 04: Origin, protection and usability of the drinking water resources” (Ed. Balco, M.). ÚH SAV, Stará Lesná, 36–41. Tardif, J, Dutilleul P, Bergeron Y. 2003. Variations in Periodicities of the Ring Width of Black Ash (Fraxinus nigra Marsh.) in Relation to Flooding and Ecological Site Factors at Lake Duparquet in Northwestern Québec. Biologic. Rhythm Res. 29: 1–29. Turkes M, Erlat E. 2003. Precipitation changes and variability in Turkey linked to the North Atlantic oscillation during the period 1930–2000. Intern. J. Climat. 23: 1771–1796. Van Gelder PHAJM, Kuzmin VA, Visser PJ., 2000. Analysis and statistical forecasting of trends in river discharges under uncertain climate changes. In: River Flood Defence. Booklet 9. Tönsmann, F, Koch M. (eds). ISBN-Nr.: 3-930150-20-4. 10 p. Vasiliev SS, Dergachev VA., 2002. The approximate to 2400-year cycle in atmospheric radiocarbon concentration: bispectrum of C-14 data over the last 8000 years. Annales Geoph. 20: 115–120. Vízallasok, 1890. River stages of the Danube River (In Hungarian). Hornyanszky Viktor Könyvnyomdaja, Budapest. Vogel, R., M., Tsai, Y., Limbrunner, J., F., 1998. The regional persistence and variability of annual streamflow in the United States, Wat. Resour. Res., 34, 12, 3445–3459. VÚVH, 2003: 1D model koryta Dunaja od profilu Devín po profil Čuňovo a konzumpčná krivka merného profilu Bratislava rkm 1 868.750. 3 pp. Walanus A, Soja R., 1995. The 3.5 yr period in river runoff – is it random fluctuation? In Proccced. Hydrological Processes in the Catchment, Wiezik B. (ed). Cracow; 141–148. Walter, M. T., Wilks, D. S., Parlange, J. –Y., Schneider, R. L., 2004. Increasing evapotranspiration from the conterminous United States. J. of Hydrometeorol., 5, 405– 408. Williams GR., 1961. Cyclical variations in the world-wide hydrological data. J. of Hydraulic division, 6: 71–88. Zatkalík, G., 1965. The 1965 Danube Flood. (In Slovak.) Vodní hospodářství, 12, 1965, 519– 526. Zatkalík, G., 1970. Calculation of the Basic Parameters of Discharge Waves. (In Slovak.) PhD thesis, Sf SVŠT, Bratislava, 70 pp. Zhang, X., Harvey, K. D., Hogg, W. D., Yuzyk, T. R., 2001. Trends in Canadian stream flow. Wat. Resour. Res., 37, 987–998. Zsufa, I., 1999. Impact of Austrian hydropower plants on the flood control safety of the Hungarian Danube. Hydrological Sciences Journal, 44, 3, 363–371.
142 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
Appendixes
App. I. Full list of studies in monographs and journals connected to this DrSc. thesis
AAA Monographs AAA01 PEKÁROVÁ, Pavla - ONDERKA, Milan - PEKÁR, Ján - MIKLÁNEK, Pavol - HALMOVÁ, Dana - ŠKODA, Peter - BAČOVÁ-MITKOVÁ, Veronika. Hydrologic Scenarios for the Danube River at Bratislava. Ostrava: KEY Publishing, 2008. 159 s. ISBN 978-80-87071-51-9. AAB01 SVOBODA, Aleš - PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol. Flood Hydrology of Danube between Devín and Nagymaros. Bratislava: ÚH SAV; SVH, 2000. 96 p. ISBN 80-967808-9-1. AAB02 PEKÁROVÁ, Pavla. Dynamika kolísania odtoku svetových a slovenských tokov. Bratislava: Veda, 2003. 221 s. ISBN 80-224-07801.
ABD Chapters in monographs ABD01 PEKÁROVÁ, Pavla. Zákonitosti kolísania priemerných ročných prietokov. In Národný klimatický program. - Bratislava: SHMÚ: MŽP SR, 2000, no.9, pp. 39- 57. ABD02 PEKÁROVÁ, Pavla. Telekonekcia ročných prietokov s SO, NAO, AO a QBO javmi. In Scenáre zmien vybraných zložiek hydrosféry a biosféry v povodí Hrona a Váhu v dôsledku klimatickej zmeny. - Bratislava: Veda, 2005. pp. 81-104.
ADCA CC journals ADCA01 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján. Spatial and temporal runoff oscillation analysis of the main rivers of the world during the 19th-20th centuries. In Journal of Hydrology. ISSN 0022-1694, 2003, vol. 274, no. 1, pp. 62-79. (2,16 - IF2007). ADCA02 MITKOVÁ, Veronika - PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján. Analysis of flood propagation changes in the Kienstock-Bratislava reach of the Danube River. In Hydrological Sciences Journal. ISSN 1335-6291, 2005, vol. 50, no. 4, pp. 655-668. (1,6 - IF2007). ADCA03 PEKÁROVÁ, Pavla - PEKÁR, Ján. Long-term discharge prediction for the Turnu Severin station (the Danube) using a linear autoregressive model. In Hydrological Processes, ISSN 0885-6087, 2006, vol. 20, no. 5, pp. 1217-1228. (1,79 - IF2007).
143 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
ADCA04 PEKÁROVÁ, Pavla - PEKÁR, Ján. Teleconections of Inter-Annual Streamflow Fluctuation in Slovakia with Arctic Oscillation, North Atlantic Oscillation, Southern Oscillation, and Quasi-Biennial Oscillation Phenomena. In Advances in Atmospheric sciences. ISSN 0256-1530, 2007, vol. 24, no. 4, pp. 655-663. (0,902 - IF2007). ADCA5 PEKÁROVÁ, Pavla - HALMOVÁ, Dana - MIKLÁNEK, Pavol - ONDERKA, Milan - PEKÁR, Ján - ŠKODA, Peter. Is the Water Temperature of the Danube River at Bratislava, Slovakia, Rising? In Journal of Hydrometeorology. ISSN 1525-755X, 2008, vol. 9, issue 5, pp. 1115-1122. (2.195 - IF2007).
ADEA 2 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján. Long-term trends and runoff fluctuations of European rivers. IAHS Series No. 308, ISSN 0144-7815. IAHS, Wallingford, 2006, no. 308, pp. 520-525. ADEA 3 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol. Abflusstrends slowakischer Flüsse und mögliche Zusammenhänge mit ENSO/NAO - Erscheinungen. In Österreichische Wasser- und Abfalllwirtschaft. ISSN 0945-358X, 2004, vol. 56, no. 1-2, pp. 17-25.
Other journals ADEB 1 HALMOVÁ, Dana - PEKÁROVÁ, Pavla - PEKÁR, Ján - ONDERKA, Milan. Analyzing temporal changes in maximum runoff volume series of the Danube River. In IOP Conference Series: Earth and Environmental Science: IOP Electronic Journal. ISSN 1755-1315, 2008, vol. 4, pp. 12007. http://www.iop.org/EJ/toc/1755-1315/4/1. ADEB 2 PEKÁROVÁ, Pavla - ŠKODA, Peter - MIKLÁNEK, Pavol - HALMOVÁ, Dana - PEKÁR, Ján. Detection of changes in flow variability of the upper Danube between 1876-2006. In IOP Conference Series: Earth and Environmental Science: IOP Electronic Journal. ISSN 1755-1315, 2008, vol. 4, pp. 012028. http://www.iop.org/EJ/toc/1755-1315/4/1. ADFA 1 PEKÁROVÁ, Pavla - ONDERKA, Milan – PEKÁR, Ján – RONČÁK, Peter – MIKLÁNEK, Pavol. Prediction of water quality in the Danube River under extreme hydrological and temperature conditions. In Journal of Hydrology and Hydromechanics. ISSN 0042-790X, 2009, vol. 57, no. 2, pp. 3–15. ADFA 2 PEKÁROVÁ, Pavla - HALMOVÁ, Dana - MIKLÁNEK, Pavol. Simulácia režimu odtoku za zmenených klimatických podmienok v povodí Ondavy. In Journal of Hydrology and Hydromechanics. ISSN 0042-790X, 1996, vol. 44, no. 5, pp. 291-311. ADFA 3 SVOBODA, Aleš - PEKÁROVÁ, Pavla. Katastrofálna povodeň z júla 1998 v povodí Malej Svinky - simulácia jej priebehu. In Journal of Hydrology and Hydromechanics. ISSN 0042-790X, 1998, vol. 46, no. 6, pp. 356-372. ADFB 1 PEKÁROVÁ, Pavla - PEKÁR, Ján. Identifikácia dlhodobých trendov a fluktuácií hydrologických radov: Časť I. Hodrickov-Prescottov filter a metóda kombinovaného periodogramu. In Journal of Hydrology and Hydromechanics. ISSN 0042-790X, 2003, vol. 51, no. 1, pp. 27-38.
144 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
ADFB 2 PEKÁROVÁ, Pavla. Identifikácia dlhodobých trendov a fluktuácií hydrologických radov (Časť II. Výsledky). In Journal of Hydrology and Hydromechanics. ISSN 0042-790X, 2003, vol. 51, no. 2, pp. 97-108. ADFB 3 PEKÁROVÁ, Pavla - PEKÁR, Ján. Teleconnections of AO, NAI, SO and QBO with interannual streamflow fluctuation in the Hron basin. In Journal of Hydrology and Hydromechanics. ISSN 0042-790X, 2004, vol. 52, no. 4, pp. 279- 290. ADFB 4 PEKÁROVÁ, Pavla - HALMOVÁ, Dana - MITKOVÁ, Veronika. Simulation of the catastrophic floods caused by extreme rainfall events - Uh River basin case study. In Journal of Hydrology and Hydromechanics. ISSN 0042-790X, 2005, vol. 53, no. 4, s. 219-230. ADFB 5 PEKÁROVÁ, Pavla. Metódy dlhodobej predpovede priemerných ročných prietokov. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2000, roč. 1, č. 1, s. 67-78. ADFB 6 PEKÁROVÁ, Pavla - PEKÁR, Ján - MIKLÁNEK, Pavol. Riečny model nelineárnej kaskády NLN - Danube pre Dunaj v úseku Ybbs - Nagymaros v softvérovom prostredí MS Excel 97. In Acta Hydrologica Slovaca. ISSN 1335- 6291, 2001, roč. 2, č. 2, s. 241-246. ADFB 7 MITKOVÁ, Veronika - PEKÁROVÁ, Pavla - MIKULIČKOVÁ, Michaela. Predpoveď vodných stavov na Dunaji v stanici Bratislava. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2002, roč. 3, č. 1, s. 46-53. ADFB 8 PEKÁROVÁ, Pavla - PEKÁR, Ján. Použitie Hodrickovho-Prescottovho filtra na určenie dlhodobého trendu hydrologických radov. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2002, roč. 3, č. 2, s. 203-212. ADFB 9 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol. Dlhodobé kolísanie teploty vzduchu a jeho telekonekcia so severoatlantickou osciláciou (NAO). In Acta Hydrologica Slovaca. ISSN 1335-6291, 2003, roč. 4, č. 1, s. 154-164. ADFB 10 PEKÁROVÁ, Pavla - SZOLGAY, Ján - MITKOVÁ, Veronika - KUBEŠ, Richard. Kalibrácia dvoch hydrologických riečnych modelov transformácie povodňových vĺn Dunaja v úseku Kienstock - Bratislava. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2004, roč. 5, č. 1, s. 24-33. ADFB 11 MITKOVÁ, Veronika - KUBEŠ, Richard - SZOLGAY, Ján - PEKÁROVÁ, Pavla. Simulácia transformácie historických povodňových vĺn Dunaja z roku 1899 a 1954 v úseku Kienstock - Bratislava za súčasných odtokových pomerov. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2004, roč. 5, č. 1, s. 52-62. ADFB 12 MITKOVÁ, Veronika - KOHNOVÁ, Silvia - PEKÁROVÁ, Pavla. Porovnanie odhadov maximálnych sezónnych prietokov v profile Dunaj - Bratislava. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2004, roč. 5, č. 1, s. 34-41. ADFB 13 PEKÁROVÁ, Pavla. Klimatická zmena, kolísanie klímy a neistoty stanovenia hydrologických charakteristík tokov v meniacom sa prírodnom prostredí. In Acta Hydrologica Slovaca. - Bratislava: Ústav hydrológie SAV. ISSN 1335-6291, 2004, roč. 5, č. 2, s. 308-318. ADFB 14 PEKÁROVÁ, Pavla - PACL, Juraj - ŠKODA, Peter - MIKLÁNEK, Pavol. Doplnenie priemerných denných prietokov Dunaja v Bratislave za historické obdobie 1876-1890. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2007, roč. 8, no. 1, s. 3-11.
145 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
ADFB 15 PEKÁROVÁ, Pavla - PEKÁR, Ján. Viacročná variabilita charakteristík odtoku Dunaja v Bratislave. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2007, roč. 8, no. 1, s. 12-21. ADFB 16 PEKÁROVÁ, Pavla - HALMOVÁ, Dana - MIKLÁNEK, Pavol - PEKÁR, Ján. Analýza zmien maximálnych objemov odtoku Dunaja za dve obdobia 1876-1940 a 1941-2005. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2007, roč. 8, no. 2, s. 164-172. ADFB 17 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján. Long-term Danube monthly discharge prognosis for the Bratislava station using stochastic models. In Meteorologický časopis. ISSN 1335-339X, 2007, roč. 10, č. 2, s. 211-218. ADFB 18 PEKÁROVÁ, Pavla - MIKLÁNEK, Pavol - PEKÁR, Ján - OLBŘÍMEK, Juraj. Analýza zmien štatistických charakteristík denných úhrnov zrážok na stanici Hurbanovo v rôznych obdobiach Časť I. Viacročná variabilita a spektrálna analýza. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2008, roč. 9, č.1, s. 64- 75. ADFB 19 PEKÁR, Ján - PEKÁROVÁ, Pavla - OLBŘÍMEK, Juraj - MIKLÁNEK, Pavol. Analýza zmien štatistických charakteristík denných úhrnov zrážok na stanici Hurbanovo v rôznych obdobiach Časť II. Frekvenčná analýza. In Acta Hydrologica Slovaca. ISSN 1335-6291, 2008, roč. 9, č.1, s. 77-88. ADFB 20 PEKÁROVÁ, Pavla - HALMOVÁ, Dana - MIKLÁNEK, Pavol - PEKÁR, Ján. Analýza zmien N-ročných minimálnych prietokov rieky Dunaj v stanici Bratislava za obdobie rokov 1876/77–2005/06. In Acta Hydrologica Slovaca. ISSN 1335- 6291, 2008, roč. 9, č. 2, s. 252-261.
AEC 2 MIKLÁNEK, Pavol - PEKÁROVÁ, Pavla. Flood Regime of the Danube River in Bratislava, Slovakia. In Proceedings International Conference Planning and Management of Water Resources Research Systems. ISBN 978-86-85889-19-6, (ed. Kastori, R.), Novi Sad: Academician Endre Papa, 2008, pp. 99-108.
146 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region
App. II. Danube 3-hourly catastrophic flood scenario
Danube Bratislava Medveďov Komárno Štúrovo Nagymaros 1.8. 3:00 3760 3760 3760 3760 3760 1.8. 6:00 3702 3751 3758 3759 3760 1.8. 9:00 3640 3733 3754 3758 3759 1.8. 12:00 3602 3712 3748 3756 3758 1.8. 15:00 3576 3690 3738 3752 3756 1.8. 18:00 3557 3669 3727 3745 3752 1.8. 21:00 3533 3647 3715 3737 3746 2.8. 0:00 3508 3625 3700 3727 3739 2.8. 3:00 3435 3594 3683 3715 3730 2.8. 6:00 3378 3559 3663 3701 3718 2.8. 9:00 3326 3520 3640 3684 3705 2.8. 12:00 3290 3482 3614 3665 3689 2.8. 15:00 3265 3446 3587 3643 3671 2.8. 18:00 3251 3414 3559 3619 3650 2.8. 21:00 3244 3385 3530 3593 3627 3.8. 0:00 3239 3361 3502 3567 3603 3.8. 3:00 3233 3339 3475 3539 3577 3.8. 6:00 3250 3324 3450 3513 3550 3.8. 9:00 3279 3316 3428 3487 3524 3.8. 12:00 3310 3315 3409 3462 3498 3.8. 15:00 3680 3377 3404 3443 3475 3.8. 18:00 4169 3509 3421 3432 3456 3.8. 21:00 4717 3706 3469 3437 3446 4.8. 0:00 5126 3930 3546 3462 3450 4.8. 3:00 5465 4164 3647 3509 3471 4.8. 6:00 5703 4392 3767 3577 3512 4.8. 9:00 5919 4611 3899 3664 3571 4.8. 12:00 6031 4810 4040 3767 3648 4.8. 15:00 6174 4996 4184 3881 3740 4.8. 18:00 6293 5170 4331 4004 3844 4.8. 21:00 6387 5330 4476 4132 3957 5.8. 0:00 6467 5477 4619 4263 4076 5.8. 3:00 6612 5621 4760 4396 4199 5.8. 6:00 6708 5758 4897 4528 4325 5.8. 9:00 6783 5885 5031 4660 4452 5.8. 12:00 6800 5997 5161 4790 4578 5.8. 15:00 6792 6094 5284 4916 4704 5.8. 18:00 6737 6172 5400 5039 4827 5.8. 21:00 6673 6231 5507 5158 4948 6.8. 0:00 6543 6268 5605 5271 5065 6.8. 3:00 6491 6295 5692 5377 5177 6.8. 6:00 6398 6307 5769 5475 5283 6.8. 9:00 6247 6300 5835 5566 5384 6.8. 12:00 6060 6271 5889 5648 5477 6.8. 15:00 5926 6230 5931 5720 5563 6.8. 18:00 5791 6178 5961 5783 5641 6.8. 21:00 5660 6116 5980 5835 5709 7.8. 0:00 5564 6050 5989 5877 5769
147 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region continuation of the Table A 7.8. 3:00 5499 5983 5988 5909 5819 7.8. 6:00 5456 5919 5980 5932 5860 7.8. 9:00 5425 5858 5965 5945 5892 7.8. 12:00 5392 5801 5945 5950 5914 7.8. 15:00 5362 5746 5921 5948 5928 7.8. 18:00 5341 5696 5893 5939 5935 7.8. 21:00 5320 5649 5863 5925 5934 8.8. 0:00 5292 5604 5831 5906 5927 8.8. 3:00 5258 5560 5797 5883 5914 8.8. 6:00 5228 5518 5763 5857 5897 8.8. 9:00 5196 5477 5727 5828 5875 8.8. 12:00 5149 5435 5691 5797 5850 8.8. 15:00 5096 5391 5653 5765 5822 8.8. 18:00 5079 5351 5615 5730 5792 8.8. 21:00 5088 5316 5577 5694 5760 9.8. 0:00 5129 5292 5541 5658 5726 9.8. 3:00 5197 5280 5508 5622 5691 9.8. 6:00 5434 5300 5481 5588 5656 9.8. 9:00 5714 5354 5465 5556 5621 9.8. 12:00 6063 5446 5462 5530 5589 9.8. 15:00 6423 5571 5476 5512 5561 9.8. 18:00 6654 5708 5506 5505 5540 9.8. 21:00 6894 5855 5551 5509 5527 10.8. 0:00 7058 6003 5608 5525 5523 10.8. 3:00 7306 6160 5678 5554 5531 10.8. 6:00 7534 6323 5759 5596 5549 10.8. 9:00 7750 6490 5850 5649 5580 10.8. 12:00 7959 6659 5950 5714 5622 10.8. 15:00 8124 6826 6057 5788 5675 10.8. 18:00 8281 6988 6170 5871 5739 10.8. 21:00 8427 7147 6287 5962 5811 11.8. 0:00 8560 7301 6407 6060 5892 11.8. 3:00 8671 7449 6529 6162 5980 11.8. 6:00 8791 7592 6652 6269 6074 11.8. 9:00 8918 7731 6775 6380 6173 11.8. 12:00 9049 7868 6899 6492 6276 11.8. 15:00 9189 8004 7023 6607 6382 11.8. 18:00 9353 8142 7147 6723 6490 11.8. 21:00 9526 8282 7271 6839 6601 12.8. 0:00 9657 8419 7396 6957 6713 12.8. 3:00 9790 8555 7521 7075 6826 12.8. 6:00 9917 8689 7645 7194 6940 12.8. 9:00 10031 8819 7769 7312 7055 12.8. 12:00 10152 8948 7892 7431 7170 12.8. 15:00 10314 9078 8015 7550 7286 12.8. 18:00 10490 9212 8137 7668 7401 12.8. 21:00 10712 9353 8261 7786 7517 13.8. 0:00 10891 9496 8385 7905 7632 13.8. 3:00 11048 9639 8510 8024 7748 13.8. 6:00 11262 9787 8636 8143 7864
148 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region continuation of the Table A 13.8. 9:00 11503 9942 8764 8263 7980 13.8. 12:00 11725 10102 8894 8383 8097 13.8. 15:00 12005 10270 9026 8505 8214 13.8. 18:00 12246 10444 9161 8628 8332 13.8. 21:00 12451 10618 9298 8752 8450 14.8. 0:00 12604 10789 9437 8878 8570 14.8. 3:00 12748 10956 9577 9006 8692 14.8. 6:00 12922 11122 9719 9135 8814 14.8. 9:00 13110 11288 9861 9266 8938 14.8. 12:00 13237 11450 10005 9398 9064 14.8. 15:00 13423 11612 10148 9531 9190 14.8. 18:00 13583 11773 10292 9665 9318 14.8. 21:00 13676 11927 10435 9800 9447 15.8. 0:00 13781 12075 10578 9935 9577 15.8. 3:00 13897 12220 10720 10071 9707 15.8. 6:00 13958 12358 10860 10207 9839 15.8. 9:00 13996 12487 10998 10342 9970 15.8. 12:00 13984 12604 11134 10477 10102 15.8. 15:00 13945 12708 11266 10611 10234 15.8. 18:00 13891 12800 11394 10744 10365 15.8. 21:00 13831 12880 11517 10874 10495 16.8. 0:00 13733 12945 11634 11002 10624 16.8. 3:00 13650 12999 11746 11127 10752 16.8. 6:00 13562 13042 11851 11249 10877 16.8. 9:00 13487 13076 11950 11367 11001 16.8. 12:00 13399 13101 12043 11481 11121 16.8. 15:00 13314 13117 12129 11590 11238 16.8. 18:00 13205 13123 12208 11694 11352 16.8. 21:00 13082 13120 12280 11793 11462 17.8. 0:00 13055 13115 12347 11886 11567 17.8. 3:00 12974 13105 12406 11975 11668 17.8. 6:00 12866 13086 12460 12057 11765 17.8. 9:00 12764 13062 12507 12134 11856 17.8. 12:00 12646 13030 12548 12205 11943 17.8. 15:00 12530 12992 12583 12271 12024 17.8. 18:00 12407 12947 12611 12330 12100 17.8. 21:00 12245 12894 12633 12384 12170 18.8. 0:00 12096 12832 12648 12432 12236 18.8. 3:00 11975 12766 12658 12473 12295 18.8. 6:00 11846 12695 12661 12509 12349 18.8. 9:00 11715 12619 12657 12539 12397 18.8. 12:00 11595 12540 12648 12563 12439 18.8. 15:00 11478 12457 12633 12581 12476 18.8. 18:00 11348 12370 12613 12593 12507 18.8. 21:00 11216 12279 12587 12598 12532 19.8. 0:00 11096 12185 12556 12599 12551 19.8. 3:00 11002 12091 12519 12593 12565 19.8. 6:00 10847 11992 12478 12582 12572 19.8. 9:00 10688 11887 12432 12565 12574 19.8. 12:00 10542 11779 12381 12543 12570
149 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region continuation of the Table A 19.8. 15:00 10394 11666 12324 12515 12561 19.8. 18:00 10226 11549 12263 12482 12546 19.8. 21:00 10024 11423 12197 12443 12525 20.8. 0:00 9838 11292 12125 12400 12499 20.8. 3:00 9644 11155 12047 12351 12468 20.8. 6:00 9446 11011 11965 12296 12431 20.8. 9:00 9249 10861 11876 12236 12389 20.8. 12:00 9079 10708 11782 12170 12340 20.8. 15:00 8927 10555 11682 12099 12287 20.8. 18:00 8750 10397 11577 12022 12228 20.8. 21:00 8560 10236 11467 11939 12163 21.8. 0:00 8364 10069 11352 11851 12092 21.8. 3:00 8171 9899 11231 11757 12015 21.8. 6:00 8001 9727 11106 11657 11933 21.8. 9:00 7848 9554 10975 11552 11845 21.8. 12:00 7731 9385 10840 11441 11751 21.8. 15:00 7625 9221 10702 11325 11650 21.8. 18:00 7518 9059 10560 11203 11545 21.8. 21:00 7397 8900 10415 11076 11433 22.8. 0:00 7276 8743 10268 10944 11316 22.8. 3:00 7155 8588 10119 10809 11193 22.8. 6:00 7033 8434 9969 10669 11065 22.8. 9:00 6925 8284 9817 10525 10932 22.8. 12:00 6838 8138 9664 10378 10795 22.8. 15:00 6760 7997 9510 10229 10653 22.8. 18:00 6667 7860 9357 10077 10508 22.8. 21:00 6574 7726 9204 9923 10359 23.8. 0:00 6493 7596 9052 9767 10206 23.8. 3:00 6412 7471 8900 9611 10052 23.8. 6:00 6311 7347 8750 9453 9895 23.8. 9:00 6183 7221 8601 9296 9736 23.8. 12:00 6061 7094 8452 9138 9577 23.8. 15:00 5947 6967 8304 8981 9416 23.8. 18:00 5842 6841 8156 8823 9255 23.8. 21:00 5753 6719 8010 8667 9093 24.8. 0:00 5678 6600 7864 8510 8931 24.8. 3:00 5623 6488 7721 8355 8770 24.8. 6:00 5579 6382 7580 8201 8609 24.8. 9:00 5547 6284 7442 8048 8449 24.8. 12:00 5514 6193 7307 7897 8290 24.8. 15:00 5477 6108 7177 7748 8132 24.8. 18:00 5449 6028 7051 7602 7976 24.8. 21:00 5428 5955 6930 7460 7822 25.8. 0:00 5410 5889 6814 7321 7672 25.8. 3:00 5398 5829 6703 7187 7524 25.8. 6:00 5379 5773 6597 7057 7381 25.8. 9:00 5362 5722 6496 6932 7242 25.8. 12:00 5334 5673 6401 6812 7107 25.8. 15:00 5296 5626 6310 6698 6978 25.8. 18:00 5240 5577 6223 6589 6854
150 P. Pekárová, DrSc. Thesis Multiannual runoff variability in the upper Danube region continuation of the Table A 25.8. 21:00 5182 5527 6140 6485 6735 26.8. 0:00 5122 5475 6061 6387 6622 26.8. 3:00 5059 5422 5983 6292 6514 26.8. 6:00 4986 5366 5908 6202 6411 26.8. 9:00 4903 5306 5834 6115 6313 26.8. 12:00 4827 5243 5761 6031 6219 26.8. 15:00 4773 5181 5689 5950 6129 26.8. 18:00 4695 5117 5617 5871 6042 26.8. 21:00 4626 5051 5546 5793 5958 27.8. 0:00 4567 4986 5474 5716 5876 27.8. 3:00 4511 4922 5404 5641 5796 27.8. 6:00 4449 4857 5333 5566 5717 27.8. 9:00 4391 4793 5263 5492 5640 27.8. 12:00 4342 4731 5193 5419 5564 27.8. 15:00 4304 4671 5124 5346 5488 27.8. 18:00 4265 4614 5056 5274 5413 27.8. 21:00 4218 4558 4989 5202 5339 28.8. 0:00 4185 4505 4923 5132 5266 28.8. 3:00 4158 4455 4860 5063 5194 28.8. 6:00 4134 4409 4798 4995 5122 28.8. 9:00 4112 4366 4738 4928 5052 28.8. 12:00 4095 4326 4680 4863 4984 28.8. 15:00 4079 4290 4625 4801 4917 28.8. 18:00 4069 4257 4573 4740 4852 28.8. 21:00 4063 4228 4524 4682 4789 29.8. 0:00 4060 4203 4478 4627 4729 29.8. 3:00 4058 4182 4436 4575 4671 29.8. 6:00 4056 4163 4396 4526 4616 29.8. 9:00 4053 4146 4360 4480 4564 29.8. 12:00 4048 4132 4326 4437 4515 29.8. 15:00 4042 4118 4296 4397 4470 29.8. 18:00 4036 4106 4268 4360 4428 29.8. 21:00 4026 4094 4242 4327 4388 30.8. 0:00 4018 4082 4218 4296 4352 30.8. 3:00 4007 4071 4196 4267 4319 30.8. 6:00 4003 4060 4176 4241 4288 30.8. 9:00 4003 4052 4157 4217 4260 30.8. 12:00 4010 4045 4141 4195 4235 30.8. 15:00 4016 4041 4125 4175 4211 30.8. 18:00 4026 4039 4112 4157 4189 30.8. 21:00 4035 4038 4101 4140 4170 31.8. 0:00 4029 4037 4091 4126 4152 31.8. 3:00 4014 4033 4083 4113 4136 31.8. 6:00 3998 4028 4074 4102 4122 31.8. 9:00 3980 4021 4066 4091 4110 31.8. 12:00 3968 4013 4058 4082 4098 31.8. 15:00 3962 4005 4050 4072 4088 31.8. 18:00 3958 3998 4042 4064 4078 31.8. 21:00 3955 3991 4034 4055 4069 1.9. 0:00 3952 3985 4027 4047 4060
151