application of the random walk theory for simulation of flood hazzards jeddah flood 25 november 2009
TRANSCRIPT
APPLICATION OF THE RANDOM WALK THEORY FOR SIMULATION OF FLOOD
HAZZARDS: JEDDAH FLOOD 25 NOVEMBER 2009
Amro Elfeki, and Jarbou Bahrawi
Dept. of Hydrology and Water Resources Management, Faculty of Meteorology, Environment & Arid Land Agriculture, King Abdulaziz University
Images of The 25th Nov. 2009 Storm Event. Objectives. Brief Review of Hydrodynamic Models for
Urban Flood Simulations. The Proposed Urban Flooding Model Concept. Simulation of Urban Flooding (Model
Results). Conclusions.
Elfeki, and Bahrawi
Outline
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Images of Flood on the 25th Nov. 2009 at KAU Campus and Surrounding
Streets
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Developing an urban flooding modelling technique that has the following features:
- Conceptually simple.- Numerically stable.- Efficient in terms of computer cost (Time and Storage).
Using the developed model to simulate the flood event on the 25th of Nov. 2009 in Jeddah city.
Elfeki, and Bahrawi
Objectives
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Hydrodynamic Models for Flood Propagation
0
0
( )f
Q Ax tu u hu g g S St x x
- Q = discharge
u = velocity of flowh = water depthg = acceleration due to gravitySo= bed slopeSf = friction slopeA = channel cross section
Elfeki, and Bahrawi
Saint Venant Equations in 2D
2 2 22
13
2 2 22
13
( ) ( ) 0 .
( ) ( ) ( )
( ) ( ) ( )
b
b
h hu hv continuity eqt x y
zhu hu huv h u vgh gh gn u x momentum eqt x y x x h
zhv huv hv h u vgh gh gn v y momentum eqt x y y y h
- -
- -
u = x-component of the flow velocity v = y-component of the flow velocity x, y = coordinatesn = Manning roughness coefficientzb = bed elevation
Elfeki, and Bahrawi
Analogy with 1-D Advection Diffusion Model
1
.
o fu u u h S S
g t g x xdynamic dyn quasi diffusive kinematicwave steady wave wave wave
-
2
2
1
2 o
Q Q QD ct x x
Qc andB hQDBS
-
B= channel widthc =flood wave celerityD= dispersion coefficient
The proposed hydrodynamic model is based on a simplified form of St. Venant equations (eliminate local acceleration and inertial terms) and combining the simplified equations with continuity to form a diffusion type partial differential equation (Diffusive wave model).
The solution of the model is performed based on the analogy with “Random Walk Theory” used to solve transport equation in groundwater.
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The Proposed Model Concept
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Analogy with 2-D Advection Diffusion Model
xx xy
yx yy
h h h h hu v D Dt x y x x y
h hD Dy x y
- -
2
2 22
13
2
2 22
13
( ) ( ) 0 .
( ) ( ) ( )
( ) ( ) ( )
b
b
h hu hv continuity eqt x y
zhu hu huv hgh ght x y x x
u vgn u x momentum eqh
zhv huv hv hgh ght x y y y
u vgn v y momentum eqh
-
-
-
-
Dxx= is the dispersion coefficient in x-direction due to flow in x-directionDyy= is the dispersion coefficient in y-direction due to flow in y-directionDXy= is the dispersion coefficient in x-direction due to flow in y-directionDyX= is the dispersion coefficient in x-direction due to flow in x-direction
0.5
0.5
1003.281
1003.281
k zux
k zvy
∆z = the difference in bed elevation between two cells
∆x and ∆y = are the cell size in x and y directions
k is roughness coefficient given by McCuen (1989) and SCS (1972) provide values of k for several flow situations .
-L L Tij ijuvD VV
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Random Walk Theory for Solving DWM
2 2xyxx
p p L T
DD u vX t t X t u t t Z V t Z V t
x y V V
-
2 2yx yyp p L T
D D u vY t t Y t v t t Z V t Z V t
x y V V
xx xy yx yyh h h h h h hu v D D D Dt x y x x y y x y
- -
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Inundation Depth
( ) ( ) pnVh t h t t
x y -
h(t) = the water depth at time th(t-∆t) = the water depth at time tn = number of particle in the cellVp= the volume of water per particle (volume from the hydrograph divided by the number of particles chosen in the model
Procedure:
Extraction of Wadi Qows Catchment using WMS based on DEM (30 m) form NASA.
Identifying Land Use and Land Cover (from Satellite Images) and Estimation of CN.
Formulating data in a GIS Format (Arc-View). Rainfall Frequency Analysis (SMADA). Rainfall-Runoff Modeling (HEC-HMS). The Proposed Hydrodynamic Model for Urban Flood Modeling. Superimposing the Inundated Area (model output) on Satellite
Images (SURFER).Elfeki, and Bahrawi
The General Framework for Urban Flood Modelling
Wadi Qows Catchment
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#
0 3 Kilometers
N
21°2
9'36
" 21°29'36"
21°3
2'04
" 21°32'04"
39°22'12"
39°22'12"
39°24'40"
39°24'40"
39°27'08"
39°27'08"
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Wadi Qows Land Use and Land Cover Maps
Wadi Area(km2)
Length (km)
Slope (m/m)
Mean basin
elevation (m)
CN
Wadi Qows
63.4 17 0.0518 143.5 70
Main parameters of Wadi Qows
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Spatial Distribution of the 25th of Nov 2009 Storm
25th of Nov 2009 Storm Recorded by Radar from Global Precipitation Mission (UNESCO, G-WADI and California University)
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Rainfall Statistical Analysis
Fitting probability distribution functions to the rainfall data at King Abdulaziz Airport Station (Data from General Presidency of Meteorology, KSA)
Standard Error
Best Probability Distribution King Abdulaziz Airport Station
2 Parameter Log-normal 53.723 Parameter Log-normal 23.09
Pearson Type III 17.85Log-Pearson Type III 20.96
Gumbel Type I 20.96
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Synthetic Flood Hydrograph of Wadi Qows for the 25th Nov. 2009 Storm
SCS Method has been used to generate synthetic flood hydrograph of Wadi Qows for the 25th Nov. 2009 storm (HEC-HMS)
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Urban Flooding: Modeled Area
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Regions and Buildings Representation in the Study
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
• The area is divided into cells 20 by 20 ms.
• Buildings and streets are assumed to have the same sizes.
• The Buildings are of infinite tall.
• The flow is only allowed to move in the streets and around the buildings.
• The flow is driven from East to West under ground surface gradients.
• Not all buildings are represented in the model.
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Simulation of the Flooded Area
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
0 0.1 0.5 1
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
W ater D epth (m )
Time = .5 Hr
Time = 1.5 Hr
Tim e = 4.5 Hr
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
0 0.1 0.5 1
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
W ater D epth (m )
Time = .5 Hr
Time = 1.5 Hr
Tim e = 4.5 Hr
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
0 0.1 0.5 1
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
W ater D epth (m )
Tim e = .5 Hr
Time = 1.5 Hr
Time = 4.5 Hr
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Visual Comparison
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
0 0.1 0.5 1
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
526000 527000 528000 529000 530000 531000 532000
2376000
2377000
2378000
2379000
W ater D epth (m )
Time = .5 Hr
Time = 1.5 Hr
Time = 4.5 Hr
A model has been proposed for flood simulation in urban areas. The model is based on a simplified version of St. Venant equations )diffusive wave model( in two dimensions and solved by the random walk method.
The model is suitable to show the flooding of initially dry areas.
The model is in its early stage it cannot reproduce the details of the flow structure.
Compared to other numerical schemes it has the advantage that it is efficient in terms of computational costs.
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Conclusions
Future research will address issues that are not yet resolved to further improve the quality and the reliability of the results for flood hazard assessment.
Elfeki, and Bahrawi
Outlook