A FIRS ANALYSIS OF HE FLOOD EVENS OF AGS 00 IN LOWER ASRIA BY SING A HYDRODYNAMIC MODEL MICHAEL RIHAR, PEER MILBRAD Institute of Hdraulics, Hdrolog and Water Resources Management Vienna niversit of ecnolog Karlsplatz 3, 040 Vienna, Austria EL 43 5880 30, FAX 43 5880 399 e-mail: trittart@dro.tuwien.ac.at Institute of Computer Science in Civil Engineering niversit of Hannover Am Kleinen Felde 30, 3067 Hannover, German EL 49 5 76 598, FAX 49 5 76 4756 e-mail: milbradt@bauinf.uni-annover.de ABSRAC Getting an overview of te general situation is ver often te first step in an engineering approac towards te analsis of a flood event. If little is known a priori about te terrain, te flow directions and flow conditions, a detailed analsis can onl be performed b investing large amounts of mone and time to gater te required data in a first step. However, for te investigation of a larger area of interest, tis detail is often not necessar and delas te deliver of results to te contracting autorit. e paper sows tat eactness of te digital terrain model and detailed surface rougness information is not alwas required in te drodnamic modelling of a larger area, b analsing te August 00 flooding at te rivers Danube and Kamp in Lower Austria. Simulation is performed wit a two-dimensional finite element model based on te sallow water equations. e results are compared to aerial views tat were made at te peak of te flood event and sow a good conformit wit realit in large parts of te area of interest. Even some of te local effects of te combined flooding of two rivers are precisel predicted b te coarse analsis model. KEYWORDS Danube, flooding, drodnamic model, sallow water equations, parameter sensitivit INRODCION In August 00, a catastropic flood event following several das of eav rainfall struck large parts of Central and Eastern Europe. Among te most affected places were villages and towns at te Black Sea, as well as alongside te rivers of Vltava in te Czec Republic, te Elbe in German, but also te Danube and man of its tributaries trougout te nortern regions of Austria. e cit of Vienna, Austria s capital, is protected b a flood protection sstem tat was mainl built during te ears of 975 troug 985, featuring a second river bed
wic is normall used for recreational purposes but fulfils te purpose of increasing te cross section of te river in case of a passing flood wave (Freisitzer and Maurer, 985). Vienna s flood protection is dimensioned for a discarge of 4,000 m³/s, owever due to inundation and retention effects upstream of te cit, te peak of te wave in August 00 was estimated to ave reaced rougl 0,000 m³/s, terefore te event did not cause damage to te capital cit. Figure : Broken road embankment and pipes for district eating, near Stratzdorf But man regions upstream of Vienna were igl affected b te flooding, especiall te ver flat region were te river Kamp meets te Danube in Lower Austria (see figure 3 for an overview); figure gives an impression of te damage tat occurred in vast parts of tat area. Just a week after te flood wave ad passed Vienna, it was decided to do a first drodnamic analsis of te event in te region of interest. e main goals were to compare te results of te numerical computation to information gatered from te inundation area, and if tese results were satisfactor perform several case studies to find out wic part of te area was flooded b eac of te two rivers. Furtermore, suc an investigation would sow wic of te effects tat occurred in real world are represented b te coarse drodnamic model, enabling te user to decide weter an in-dept investigation would be needed in certain parts of te region. In order to perform tis analsis, te following information ad to be gatered: Aerial views of te flood event taken at te point of time wen te peak of te flood wave passed te area of interest in te afternoon of August 4, 00 were gatered and evaluated to draw inundation lines for comparison wit tose from te model to be constructed later. For te drodnamic simulation itself, it was necessar to use a digital terrain model. It was decided to use a terrain model wit a squared grid size of 50 meters, for two reasons: first, te computation area is larger tan 00km², and a
larger grid size greatl reduces cost; secondl, from an engineering point of view it is important to know weter a ver detailed model is needed at all to reproduce te effects seen in realit. Cross sections and information about bed elevations of Kamp and Danube were used to augment te digital terrain model wit river information. Finall, te eact flow and stage drograps measured during te flood event were collected and used as boundar conditions to te drodnamic model. HE FLOOD EVEN During te first das of August 00, several low-pressure sstems moved from te Britis Isles to Central Europe, causing umid air to be transferred to Austria. Especiall in te Kamp catcment, eav rainfalls over a period of several das caused an etraordinar catastropic event tat was estimated wit an annualit of,000 to 0,000 ears (Gutknect et al., 00). As a consequence in Stiefern, just nort of te investigation area, te water level of te river Kamp reaced almost seven meters, tat s about five meters above te mean water level, in te earl morning ours of August 8, 00 (see figure a). But just si das later, a second flood wave caused b anoter series of severe rainfalls again it te Kamp valle wit a maimum water level of almost si meters. At te same time, te river Danube was also at ig watermarks following te propagation of two flood waves. In te cit of Krems, te western boundar of te computational domain, te water level rose to almost 0 meters on August 4, 00 (figure b) a mere five meters above mean level. Here, te second flood wave was b far te dominant one, causing severe inundations east of Krems. Stiefern / Kamp Stein-Krems / Donau 700 000 650 950 600 900 550 850 500 800 W (cm) 450 W (cm) 750 400 700 350 650 300 600 50 550 00 07.Aug 08.Aug 09.Aug 0.Aug.Aug.Aug 3.Aug 4.Aug 5.Aug 6.Aug 7.Aug 500 07.Aug 08.Aug 09.Aug 0.Aug.Aug.Aug 3.Aug 4.Aug 5.Aug 6.Aug 7.Aug Figure a: Stage drograp at Stiefern/Kamp Figure b: Stage drograp at Krems/Danube HYDRODYNAMIC MODEL Digital terrain and river model In terms of information concerning a river course, ordinar digital terrain models normall just reflect its water surface; information about bed levels and cross sections is not contained terein. erefore, in a first step, known cross section data of bot rivers were used to create an approimated river model in te computer. A sufficient number of geograpic coordinates of te river courses were taken out of a map, and interpolated cross sections were computed for tese coordinates. Because a linear interpolation of te river courses between tose coordinates would ave led to discontinuities wit intersecting cross sections, te approimated river bed was computed b using natural cubic splines to connect te geograpic points b preserving te first and second derivatives of te resulting curve. Natural cubic splines ave te disadvantage tat te are not locall controlled, tus a cange in one point s coordinates in turn canges all curve segments, not onl te curve
segment to te net point. However, as long as all points are cosen in a decent distance to eac oter, suc a curve gives a good representation of te river course. e cross section data being used was augmented wit eigt information of te embankment crest. However, all oter dams and man-made structures in te flooded areas are not represented specificall in te digital terrain model. ere are two main reasons for tis: first te analsis of te aerial views as sown tat most dams in te region of interest were useless because eiter te water was overflowing or te structures simpl broke. Second, te eact eigts of tese structures are unknown and it would ave taken a lot of field measurements to gater te required data. e computational result confirms tat suc a procedure still gives acceptable results in te area of interest. e combined digital terrain and river model is accompanied b a digital rougness model. wo different cases ave been investigated, in a first variant for bot terrain and rivers a Strickler coefficient of 40 is used, in a second variant tis parameter is modified to 0 for all terrain elements ecept te rivers wic gives a more realistic modelling of te situation. Furter detailing of te rougness model did not ield an visible improvement of te results. Hdrodnamic Model e instantaneous water levels and flows are obtained from te solution of te verticall integrated equations of continuit and conservation of momentum in two orizontal dimensions: ( ) ( ) ( ) ( ) ( ) ( ) t g t g t W B W B = Ω = Ω = ϕ ϕ sin sin () is te instantaneous water surface above datum, and representing te velocities in - and -direction, is te mean water dept, Ω te angular velocit of te eart s rotation, and ϕ te latitude of te area of interest. e wind sear parameter W is set to zero in tis investigation, but te parameters for turbulent ecange and friction B ave to be taken into account. urbulence is modelled b te edd-viscosit approac named b Smagorinsk: ( ) ( ) = = () e coefficient i is computed b ( ) : i s c = (3)
were c s is a constant and is te caracteristic lengt of te grid. Bottom friction enters te computation b using Strickler s law: ( ) ( ) B B = = g g ( ) ( ) 4 3 4 3 k k Str Str B B (4) k Str is te abbreviation for te Strickler friction coefficient described in te previous section and B describes te bottom slope in bot coordinate directions. e sallow water equations are solved wit stabilized finite elements on a triangular mes (Milbradt, 995). Discretisation in time is performed b an eplicit Euler tecnique, tus te maimum time step is limited b te Courant condition. For te computation of te time step onl tose elements are being used wic are not completel dr. e numerical treatment of wetting and dring is implemented in te following wa: A minimal limit of te water dept is set fort for all elements in te computational domain. As soon as te water dept is less tan tis limit at one node, te element is considered partiall dr, resulting in onl a standard Galerkin approimation being performed. Witin te element, a orizontal water surface is assumed and its level is approimated b te water levels of te surrounding elements (Milbradt, 00). Boundar conditions e numerical model emplos two areas of inflow and one were outflow takes place. Inflow is modelled b appling known water levels and discarge data at te two gauge stations of Krems (western domain boundar) for te river Danube and Stiefern (just nort of te computational domain) for te river Kamp. e outflow region is muc larger, consisting of te river Danube wit known discarge at te droelectric station of Altenwört plus te flooded area nort of it were little is known about discarges or water levels. At te location of te droelectric station, te known discarge condition is applied. Due to te slope in te Danube valle, a gradient of te water surface is all tat is known about te oter parts of te outflow region. Due to te fact tat te computational model does not contain an option to set te surface gradient to a known value, tis was vicariousl modelled b setting all boundar nodes to a dept sligtl less tan teir neigbour nodes. Wit tis modelling approac, water can onl leave but not enter te computational domain at te flooded region. Simulation A full unstead simulation of te computational domain was performed using stage and discarge data of ten das between August 7 and August 7 (see figure ). e unknown Strickler coefficient for te flooded areas was varied to find te best fitting results. Furtermore, tree variants of te flood event were considered to find te influence of ever river to te complete event: Alternating flood stages at bot Danube and Kamp wit te oter river at mean water levels and bot rivers at flood level in a tird variant.
RESLS e limits of te flooded regions are plotted alongside wit te water dept (coloured in magenta tones in figure 3) and compared to te actual boundaries of te flooded area (green line in figure 3) at te point of time te aerial views were made. Figure 3 sows te computation of bot rivers at flood level wit Strickler s friction coefficient of 40 for te rivers and 0 for all oter areas. Figure 3: Comparison between real and computed boundar of te flooded area (August 4, 4 pm.) It is visible tat te flooded area is almost correctl predicted in te east of te river Kamp s confluence wit te Danube. An error near te town of Grafenwört is eplicable due to te national road (visible in red) acting as dam in te real flood event. e river Kamp splits into two streams near te town of Hadersdorf; onl te main river was modelled but te second stream is reflected b surface eigts in te digital terrain model, tus an overland flow can be seen at tis area. Apparentl, te information about te embankment crest of te river Kamp was not precise enoug in all regions. Furtermore, te cit of Krems was saved from flooding due to te cit s mobile flood protection sstem wic could not be included in te computations. at s te reason for te incorrect result in and near Krems. Finall, te village of eiß apparentl emploed anoter means of flood protection wit success, most probabl sandbags were used. e fact tat no inundations occurred sout of te Danube is correctl represented b te numerical model. In realit, flooding occurred also in tat region, but not due to te river Danube but some tributaries tat enter te river at a later point of time. Even toug te computational results do not fit te information from te aerial views in ever detail, a good conformit can be seen. A more detailed digital terrain model along wit including dams and man-made structures ma give better results but at te same time at a muc iger project cost. However, for an engineer s
consideration of a flood event, a less cost-intensive stud like te one presented ere, ma be enoug for man situations. As a main result of te stud, it is found tat te friction coefficient in te land region does not significantl influence te overall size and sape of te flooded area. A significance can of course be seen wen flow velocities and directions are eamined. For an investigation of tat kind, te application of eact rougness data is crucial, but for drawing te inundation line of te flooded regions it need not necessaril be modelled in detail, as te eample sows. In figure 4, a detailed plot of te flow situation in a bend of te river Kamp, not far from te location were figure was taken, is depicted. e picture features a colour filled contour plot of te flow velocities and vectors, indicating te flow direction. In addition, isolines are being used to indicate te terrain eigt and make te river bed more clearl visible. e main flow direction is from left to rigt, resulting from te Danube inundation. In te vicinit of te river Kamp, te water is drawn-in and tus canges its main direction. After te bend, te water escapes from te river bed again and reaces maimum velocities of around 3 m/s wen crossing te embankment in a weir-like wa. Even toug te penomenon in realit contains turbulent and igl treedimensional effects, its two-dimensional representation is correctl predicted in te model s computational results. Figure 4: Flow situation in a bend of river Kamp, superimposed b water from te Danube
CONCLSIONS A stud of te August 00 flood event in Lower Austria using a tecnique of abstraction to reduce modelling costs as been presented. e resulting flood map is in good agreement wit te information gatered from aerial views, even toug te data is not correct in some places, mostl due to te result of uman actions. Detailed information about terrain rougness is not required as long as te engineer is mainl interested in water levels of te flooded terrain. Also, te contribution of eac river to te entire flood event can be studied ver well on te presented model. Finall, some important local effects are reproduced b te drodnamic model, wic overall leads to a qualitative good result at a comparativel low modelling cost. For future researc, a more detailed investigation will be required if te focus lies on te analsis of morpodnamic processes in te flooded terrain, flood forecasts for evacuation and rescue plans or te dispersion of pollutants b etension of te onedimensional case (rittart, 00). A surve of tat kind would ave to be based on a digital terrain model wit a iger resolution, containing most of te visible structures tat were abstracted for te sake of savings in time and costs in te stud presented ere. ACKNOWLEDGEMENS e autors would like to tank te Austrian Federal Office for Calibration and Measurement and te Austrian Arm Aviation for providing aerial views of te flooded regions at no cost. Also, we would like to epress our gratitude to te drolog department of te state of Lower Austria and te Federal Waterwas Division for making flow and stage drograps of te rivers Kamp and Danube available to us. REFERENCES [] Freisitzer, K., Maurer, J. (ed.): Das Wiener Modell; Compress GmbH, Wien, 985 [] Gutknect, D., Reszler, C., Blöscl, G.: Jartausend-Hocwasser am Kamp?; Report, Institute of Hdraulics, Hdrolog and Water Resources Management, Vienna niversit of ecnolog, 00 [3] Milbradt, P.: Zur matematiscen Modellierung großräumiger Wellen- und Strömungsvorgänge; Dissertation, Institute of Computer Science in Civil Engineering, niversit of Hannover, 995 [4] Milbradt, P.: Holistic modeling of morpodnamic processes wit stabilized finite elements, Hdroinformatics, 00 [5] rittart, M.: Lösung der otzonengleicungen mit der Software analt ; Report, Institute of Hdraulics, Hdrolog and Water Resources Management, Vienna niversit of ecnolog, 00