Interlinked Modelling of Large Floods by combining one and two-dimensional diffusive wave-approaches...

Interlinked Modelling of Large Floodsby combining one and two-dimensional diffusive wave-approaches

P. Kamrath, N.P. Huber, M. Kufeld, H. Schüttrumpf and J. KöngeterInstitute of Hydraulic Engineering and Water Resources Management, RWTH Aachen University (Germany)

Funding Project Management Coordination

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 1D, 2D nor 3D 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.

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 1D, 2D nor 3D 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?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.


Aspects of floodingAspects 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 2D-flow on the floodplain.

Local detailing

One aspect of local detailing is the flow through a dike breach or polder inlet. Partly 3D-flow.

Macro-scale > 100 kmMacro-scale > 100 km

Meso-scale ~ 15 kmMeso-scale ~ 15 km

Micro-scale ~ 1 kmMicro-scale ~ 1 km


Scales in hydraulic modellingScales in hydraulic modelling

Not all aspects of a flood can be described by a single method

11DD-methods:-methods:

+ + Long time-scalesLong time-scales

+ + Big areasBig areas

+ + High system complexityHigh system complexity

-- Calculation of inundation Calculation of inundation extent.extent.

- - Interaction of floodplain and Interaction of floodplain and river.river.

22DD-methods:-methods:

- - Short time-scales Short time-scales

-- Small Small areasareas

- - Low system complexityLow system complexity

++ Highly detailed, more correct Highly detailed, more correct description of physics.description of physics.

++ Integrated treatment of Integrated treatment of floodplain and river.floodplain and river.

Combining the advantages of 1D and 2D-methods would lead to a tool fulfilling the needs of modern flood forecasting


Hybrid Model:Hybrid Model: Utilizing the advantages of 1D and 2D methods.

Compensating the shortcomings of the single methods

Specialization

High Efficiency


11DD part: 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

f

hS

x

Ability to consider backwater effects

Suitable for stable, large-scale, long-term model runs


Hybrid Model:Hybrid Model:


22DD part: part: 2D diffusive wave equation on a uniform grid “Storage Cell”

Flow between cells is calculated using the Manning-Strickler equation:

where

2, ,

i ii j RB i

j

V hb Q Q

t t

b, 1/ 21/ 2

1 i ji j

j j

h hI

b h h

2/3, , , , , ,i j i j st i j i j i jQ A k R I

,i jA


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

22DD part: part:

Use of a substitute function for small gradients

Use of an implicit equation solver (suitable for ODE problems)


Hybrid Model:Hybrid Model:


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:Coupling:


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:Coupling:

With coupling: Additional boundary conditions are needed


*1 1( , , ... , )t t t t n

dh f h h h

dt

Coupling:Coupling:Explicit prediction of h(t+1)


*1 1( , , ... , )t t t t n

dh f h h h

dt

Coupling:Coupling:Explicit prediction of h(t+1)

** *1 1( , , ... , )t t t t n

dh f h h h

dt

Implicit correction of h(t+1)


Coupling:Coupling: 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.


Coupling:Coupling:

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.


Case Study: Unstrut riverCase Study: Unstrut river

Catchment area of 6340 km²2 reservoirs1 diversion channel (“Flutkanal”)Several bypass flood-control retention basins (“Polder”)

Hydraulic model for 150 km of river reach networkand the adjacent flood plains

31 hydrological loads of different recurrence intervals6 different system states


Simulated hydrological load for the current state:Case Study: Unstrut riverCase Study: Unstrut river


Simulated hydrological load for an improved state:Case Study: Unstrut riverCase Study: Unstrut river


Hydrograph at the outlet of the model area:Case Study: Unstrut riverCase Study: Unstrut river


Conclusion:Conclusion: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.

Interlinked Modeling of Large Floods

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Interlinked Modelling of Large Floods by combining one and two-dimensional diffusive wave-approaches...

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