Advances in Environmental Sciences, Development and Chemistry Catastrophic Danube flood scenario between Kienstock and Nagymaros using NLN model V. Bacova Mitkova, P. Pekarova, J. Pekar and rural land use. Wu in [3] investigated potential impact of Abstract—Hydraulic models used in hydrology are demanding climate change on flood risk for the city of Dayton, which lies large amounts of the input data. Therefore, utilization of the at the outlet of the Upper Great Miami River Watershed (Ohio, hydrological models of the wave transformation is one of the USA). He used a statistical model based on regression and alternative solutions for operative real time flood forecasting. This frequency analysis of random variables to simulate annual paper presents application of the simple non-linear river model NLN- Danube for the forecasting of the flood event occurred on the Danube mean and peak streamflow from precipitation input. River in June 2013. The model NLN-Danube is the hydrologic model Hydrological model based on the CSC and kinematic wave aimed on the simulation of discharges in open channels. NLN model functions using gauge-adjusted radar rainfall data was applied simulates flood wave transformation in six river sections: Ybbs– for flash flood prediction in [4]. Simulation of the June 11, Kienstock–Devin/Bratislava–Medvedov–Iza–Sturovo–Nagymaros. 2010, flood along the Little Missouri River, using a hydrologic The second part of this paper presents the simulation of the scenario model coupled to a hydraulic model was investigated in [5]. catastrophic flood for the today river conditions, based on the historical Danube flood from the year 1501. This flood was the Monitoring and evaluation of extreme hydrological highest flood described on the Upper Danube River basin during the phenomena through the different programs, projects and last 600 years. models are also highly actual for the second longest river in Europe – the Danube River – or its tributaries. For example, Keywords — catastrophic flood scenario, Danube River, the floods mapping on the Danube River using radar imaging nonlinear river routing model. SAR (Synthetic Aperture Radar) was reported in [6]. Pekarova et al. in [7] presented the history of floods and extreme flood I. INTRODUCTION frequency analysis of the upper Danube River at Bratislava. A RACTICAL applications of mathematical models and hydrological modeling framework applied within operational Pmathematical methods constantly increase especially in a flood forecasting systems on three Danube tributary basins number of important areas such as hydrology (e.g. flood (Traisen, Salzach and Enns) is presented in [8]. Dankers et al. forecasts in real time, flood protection, planning and design of in [9] dealt with simulation of flood risks for the Upper hydraulic structures, simulation of flood waves). Danube using the hydrologic model LISFLOOD. In [10] Determination of the flood hazard is an important aspect and Bohm & Wetzel analyzed historical floods on the rivers Lech difficult task for hydrologic practice. and Isar. Szolgay [11] used multi-linear discrete cascade This development we can see in the growing number of model for river flow routing and real time forecasting in river publications, projects and mathematical models focused on reaches with variable speed. In [12] the model KLN-MULTI hydrological modeling and forecasting. For example in the last was calibrated and used for modeling of several historical years Smith [1] applied data-based mechanistic (DBM) models flood waves on the Danube River under present hydraulic to forecast flash floods in a small Alpine catchment. Kjeldsen conditions. Blaskovicova et al. in [13] evaluated trends of the [2] tested the effect of urban land cover on catchment flood changes of the average annual and maximum annual response using a lumped rainfall–runoff model, and compared discharges on the Danube River in Bratislava gauging station. flood events from selected UK catchments with mixed urban The Danube River was and still is a symbol of strategic importance and trade. River regime conditions of the Danube River have been continually changing. These changes result This work was supported in part by the Slovak Research and Development Agency under the contract No. APVV-015-10 and by the MVTS „Flood from the natural processes (erosion, sedimentation, vegetation regime of rivers in the Danube river basin“, and it results from the project cover) or anthropogenic activities (modification of the implementation of the “Centre of excellence for integrated flood protection of riverbank, construction of dykes and hydro–power stations). It land” (ITMS 26240120004) supported by the Research & Development has significant impact upon the transformation of flood waves Operational Programme funded by the ERDF. V. Bacova Mitkova is with Institute of Hydrology Slovak Academy of in the river channel. Sciences, Bratislava, Slovakia, (e-mail: [email protected]). On the basis of the development mentioned above the short- P. Pekarova is with Institute of Hydrology Slovak Academy of Sciences, term forecasting of the flows becomes more demanded. From Racianska 75, 831 02 Bratislava, Slovakia, (phone: +4212 44259311, Fax: +4212 44259311, e-mail: [email protected]). this reason it is necessary to use and to deal with new methods J. Pekar is with the Faculty of Mathematics, Physics and Informatics, and procedures that better reflect changes in hydrological river Comenius University, Bratislava, Slovakia (e-mail: [email protected]). ISBN: 978-1-61804-239-2 393 Advances in Environmental Sciences, Development and Chemistry conditions. This process cannot be considered closed. (PQTVV− ). ∆ = − i+1 i + 1 i+1 i , (2) Forecasting models and methods have to be constantly updated to the latest conditions and current situation in the basin. For where: this purpose simple river model NLN-Danube [14], [15] was Pi+1,Qi+1 - the average i/o of the interval i+1; constructed. Development of conceptual non-linear reservoir Vi+1,Vi - storage at the interval i+1 and i. cascade models was one of several approaches to incorporate nonlinearity into hydrological routing models (see [16]-[20]). From equations (1) and (2) we receive: The objective of this paper is to present (on the example of extreme flood situation on the Danube River) results needed /1 EX 1/ EX for flood protection obtained using a relatively simple tool of Qi+1 − Qi (PQTi+1− i+ 1 ). ∆ = engineering hydrology. Firstly, short description of the non- B /1 EX (3) linear river model NLN-Danube is presented. Secondly, the model NLN-Danube was used for forecasting of the flood The equation (3) defines the non-linear function f of one event occurred in June 2013, calibrated on the flood event on unknown Qi+1, the Danube River in August 2002. Forecasting of the June 2013 flood discharges by model NLN-Danube was done on the Q /1 EX − Q1/ EX Danube River reach Kienstock–Sturovo. Finally the simulation f( Q )= ( P − Q ). ∆ T − i+1 i i+1 i+1 i+ 1 B /1 EX of transformation of the potentially catastrophic flood by the , (4) model NLN-Danube for present river regime conditions was which is searched by linearisation (Newton) method done. f (Q ()k ) II. NONLINEAR ROUTING MODEL NLN–DANUBE QQ(k+ 1) = ()k − i+1 i+1 i+1 f′ Q ()k ()i+1 , (5) A. Model description Model NLN-Danube [15] goes out from model NONLIN by what gives in our case the iteration formula: Svoboda (1993, 2000). Model of each section of the simulated system is based upon the concept of a series of equal non- (PQTQ−()k ). ∆ − ((k ) ) 1/ EX − (QB )1/EX . − 1/ EX linear reservoirs, thus belonging to the category of (k+ 1) ()k i+1 i+ 1 [ i+1 i ] QQi+1 =i+1 + (k ) (1− EX )/EX − 1/ EX −1 hydrological conceptual non-linear models. Model input (P) ∆TQ + ()..i+1 B EX represents the input into the first reservoir of the cascade . (6) (Figure 1), its output is the input into the second one in series, The parameters of the transformation curve shape are etc., and the output from the last reservoir is the output (Q) expressed by ratio parameter B, from the model of the section. EX N.∆T P Q B = BK , (7) V1 V2 VN where: N - number of storages in one section of the model; BK - ''time constant'' of an equivalent linear system. Fig. 1 Scheme of the NLN-Danube model The iteration process (6) is performed with accuracy of 0.001. Parameters of the model calibration are: Movement of the wave through reservoir is defined by BK - time constant of the equivalent linear system [hrs]; discharge (Q) and by volume of reservoir (V) as: ∆T - length of the time step [hrs]; QC - corresponds to the maximum capacity of the main EX 3 -1 QBV= . (1) river channel (flow, when water enters the inundation) [m s ]; where: EX - the nonlinearity parameter, dimensionless; Q - reservoir output; N - number of reservoirs in series, dimensionless; V - volume of reservoir [m3]; NU, NL - tributaries in section (yes=1, no=0). EX - the nonlinearity parameter; B. Model calibration B - the proportionality parameter. Model NLN–Danube was calibrated on set of the summer The flood wave propagation is modeled in equidistant floods occurred during 1991– March 2002 for river reach discrete time steps 0, 1, 2, … m. The difference between two Kienstock–Nagymaros (Figure 2). The up stream water steps is given by parameter ∆T. In time steps i and i+1, for gauging station Kienstock was chosen because it is located at a known input Pi+1 and output Qi, the unknown output Qi+1 is sufficient distance from Bratislava and gives a fair forecast determined from the continuity equation within the time lead time. interval i+1 of the length ∆T as: ISBN: 978-1-61804-239-2 394 Advances in Environmental Sciences, Development and Chemistry 11500 Devin/Bratisl.