1. Interlinked Modelling of Large Floods by combining one and two-dimensional diffusive wave-approaches P. Kamrath, N.P. Huber, M. Kufeld, H. Schüttrumpf and J. Köngeter Institute of Hydraulic Engineering and Water Resources Management, RWTH Aachen University (Germany) Funding Project Management Coordination

2. Hypothesis: Hypothesis: The „future“ is to take risks and possible scenarios (dike breaks, inundation, polder systems) into account. Essential is the analysis of a flood in its complete scale in time and in space. At the moment this can neither be done with 1 D, 2 D nor 3 D methods. A solution could be the use of hybrid methods, that combine approaches of different dimensionality and therefore allow a wider spectrum of possible applications than conventional methods. Interlinked Modelling of Large Floods 1D or 2D modelling is „state of the art“ for the numerical evaluation of floods. What will happen in the future? Coupled Models – Why? Prospect: Prospect: The future belongs to 3D-approaches – Someday we will be able to model rivers and lakes in 3D and high spatial resolution.

3. Interlinked Modelling of Large Floods Aspects of flooding Complexity of modelling is proportional to the time and space considered: Large areas and long periods lead to high costs.  Problem of scales Complexity of system Branches, unions, merging of hydrographs from sub-catchments. Interactions Exchange and reciprocal influence of flooded areas and the river. Partly 2 D -flow on the floodplain. Local detailing One aspect of local detailing is the flow through a dike breach or polder inlet. Partly 3 D -flow. Macro-scale > 100 km Meso-scale ~ 15 km Micro-scale ~ 1 km

4. Interlinked Modelling of Large Floods Scales in hydraulic modelling Not all aspects of a flood can be described by a single method 1 D -methods: + Long time-scales + Big areas + High system complexity -Calculation of inundation extent. - Interaction of floodplain and river. 2 D -methods: - Short time-scales -Small areas - Low system complexity +Highly detailed, more correct description of physics. +Integrated treatment of floodplain and river.  Combining the advantages of 1 D and 2 D -methods would lead to a tool fulfilling the needs of modern flood forecasting

5. Interlinked Modelling of Large Floods Hybrid Model: Utilizing the advantages of 1 D and 2 D methods. Compensating the shortcomings of the single methods Specialization High Efficiency

6. Interlinked Modelling of Large Floods 1 D part: Diffusive wave approximation of the St. Venant equations: Friction slope equals change in water surface (non-inertia) Energy-gradient expressed through Manning-Strickler equation  Ability to consider backwater effects  Suitable for stable, large-scale, long-term model runs

7. Interlinked Modelling of Large Floods Hybrid Model:

8. Interlinked Modelling of Large Floods 2 D part: 2D diffusive wave equation on a uniform grid  “Storage Cell” Flow between cells is calculated using the Manning-Strickler equation: where b

9. Interlinked Modelling of Large Floods Resulting equations are stiff ordinary differential equations (ODE)  The smaller the gradient of water level between cells, the harder it is to obtain a solution 2 D part:  Use of a substitute function for small gradients  Use of an implicit equation solver (suitable for ODE problems)

10. Interlinked Modelling of Large Floods Hybrid Model:

11. Interlinked Modelling of Large Floods The modules exchange information through boundary conditions. All modules (1D or 2D) have to be in synch (exchange information for the same point in time). Information flows in two directions (bi-directional). Principle: Without coupling: Q and h in point B result from St. Venant equations + boundary conditions in A und C Coupling:

12. Interlinked Modelling of Large Floods The modules exchange information through boundary conditions. All modules (1D or 2D) have to be in synch (exchange information for the same point in time). Information flows in two directions (bi-directional). Principle: Coupling: With coupling: Additional boundary conditions are needed

13. Interlinked Modelling of Large FloodsCoupling: Explicit prediction of h(t +1 )

14. Interlinked Modelling of Large FloodsCoupling: Explicit prediction of h(t +1 ) Implicit correction of h(t +1 )

15. Interlinked Modelling of Large FloodsCoupling: Boundary condition for Q in section 2 is obtained through simulation of section 1. By simulating section 2 the actual height of the water surface at the end of section 1 is obtained. This value is kept in memory for the prediction. Additionally the consistency of corrected prediction and computed value is checked.

16. Interlinked Modelling of Large FloodsCoupling: For the coupling between 1D and 2D modules an additional function Q(h) is needed. Dike overtopping and flow through flood gates is modelled by using the Poleni equation.

17. Interlinked Modelling of Large Floods Case Study: Unstrut river Catchment area of 6340 km² 2 reservoirs 1 diversion channel (“Flutkanal”) Several bypass flood-control retention basins (“Polder”) Hydraulic model for 150 km of river reach network and the adjacent flood plains 31 hydrological loads of different recurrence intervals 6 different system states

18. Interlinked Modelling of Large Floods Simulated hydrological load for the current state: Case Study: Unstrut river

19. Interlinked Modelling of Large Floods Simulated hydrological load for an improved state: Case Study: Unstrut river

20. Interlinked Modelling of Large Floods Hydrograph at the outlet of the model area: Case Study: Unstrut river

21. Interlinked Modelling of Large FloodsConclusion: Multi-dimensional methods are capable of compensating shortcomings of mono-dimensional methods by coupling. The presented coupling of 1D and 2D methods enables flood analyses of larger scales in time and space, of finer resolution or based on more scenarios, respectively. The presented method focuses on the combination of different specialised approaches to calculate hydraulics. Additional modules allow the treatment of specific aspects, i.e. dike break, flow through conducts, groundwater infiltration etc. Evaluation „Future-Hypothesis“: A Risk Assessment requires large sets of reliable hydrodynamic input data which may be provided by hybrid models due to their increased efficiency.

22. Interlinked Modeling of Large Floods Thank you for your attention kufeld@iww.rwth-aachen.de – pk@paul-kamrath.de