Criteria for the choice of flood routing methods for...
Transcript of Criteria for the choice of flood routing methods for...
Criteria for the choice of flood routing methods
for natural channels with overbank flowby
Roger MOUSSA
Laboratoire d'étude des Interactions Sol - Agrosystème - HydrosystèmeUMR LISAH ENSA-INRA-IRD, Montpellier
Context : Flood events
In the world
More than 50 % of the damages caused by natural disasters are due to floods : on average 20 000 deaths/year.
In France
Over a 160 000 km long river network, an area of 22 000 km² is recognised as very prone to flooding: 7 600 villages and 2 000 000 residents are concerned.
Objectives
Develop a spatially distributed hydrological modelling tool to simulate flood events on natural and farmed catchments.
Spatially distributed hydrological modelling of flood events on natural and farmed catchments
I. Process
representation
III.Integration
into adistributed
model
II.Catchment
segmentation
I. Flood routing
Context
Flood routing in natural channels is governed by the Barré de Saint-Venant (1871) equations.
xLateral inflow q(x,t)>0W
B
Longitudinal section Lateral section
ContextI. Flood routing
Saint-Venant system
Equation of mass conservation
0x
yV
x
Vy
t
y=
∂
∂+
∂
∂+
∂
∂
Terms I II III
Equation of energy conservation
( ) 0SSgx
yg
x
VV
t
Vf
=−+∂
∂+
∂
∂+
∂
∂
Terms IV V VI VII VIII
I. Flood routing I.1. Approximation zones
I.1. Approximation zones of the Saint-Venant system(Moussa and Bocquillon, 1996, J. Hydrol.)
Propagation of a sinusoidal function :- Froude number (F²)- a characteristic time of the hydrograph
0,01
0,1
1
10
100
0,01 0,1 1 10 100 1000
Kinematicwave
(IV, V et VI)Diffusivewave
(IV et V)
Gravity wave(VII et VIII)
CompleteSaint-Venant
system
F²=V²/gyDynamic
wave(VI)
(VIII)
(VII)
T+ = TVS/y
W/B = 1
I. Flood routing I.1. Approximation zones
Approximation zones of the Saint-Venant systemwith overbank flow : example W/B = 20
(Moussa and Bocquillon, 2000, Hydrol. Earth System Sc.)F²=V²gy
T+ = TVS/y0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100 1000
KinematicwaveDiffusive
wave
Gravitywave
CompleteSaint-Venant
system
W
B
In some hydrological models, the flood routing model can be usedoutside its application domain.ex : kinematic wave in KINEROS, TOPOG, TOPMODEL, LISEM, QPBRRM.
I. Flood routing I.2. Numerical schemes
I.2. Numerical resolution of the diffusive wave model
In general :
- resolution using finite differences schemes
- problems of numerical stability and convergence
j
j-1
i-1 i
∆ t
∆xt
x
P
i+1O
Case where celerity and diffusivity can be considered constant :
Hayami (1951) analytical solution.
I. Flood routing I.2. Numerical schemes
I.2. Development of new numerical scheme to resolve the diffusive wave equation in flood routing applications over
treelike channels
j+1
j-1
j
i-1 i
∆t
t
x
P uj
uj-1
uj+1
vj-1
vj
vj+1
O
∆xi-1 ∆xi ∆xi+1
- a scheme that enables the use of variable spatial steps (Moussa and Bocquillon, 1996, Hydrol. Pro.).
- a scheme based on the fractional step method that enables to separate convection and diffusion (Moussa and Bocquillon, 2001, J. Hydrol. Eng.).
I. Flood routing I.2. Numerical schemes
Application : flood prevision on the Loire river(between Grangent and Feurs : distance 43 km)
Loire : Event of 20 - 23 September 1980
0
500
1000
1500
2000
2500
3000
3500
4000
0 24 48 72 96 120Time (hours)
Dis
char
ge (m
3 /s)
InputMeasured outputCalculated output
I. Flood routing I.3. Analytical schemes
I.3. Development of a new scheme for the analytic resolution of the diffusive wave equation (Moussa, 1996, Hydrol. Pro.)
- Taking into account uniformly distributed lateral inputs or outputs.
- Identification of the lateral inflow by input/ouput deconvolution.
Input Output
Lateral inflow ? ? ?
L
I. Flood routing I.3. Analytical schemes
Example of application on the Allier river between Prades (1350 km² catchment) and Vieille Brioude (2269 km² catchment) distant of 42 km.
(data source : EPALA)
Allier : Event of april 25 – may 3 1983
0
250
500
750
1000
0 48 96 144Time (hours)
Dis
char
ge (m
3/s) 0
10
20
30
40
Rainfall
Input
Output
Lateralinflow
192
Rai
nfal
l (m
m/2
h)
I. Flood routing I.4. Errors
I.4. Development of a method to estimate numerical errors (Moussa and Bocquillon, 1996, J. Hydrol.)
Three types of error :
eQ = b/aeT = f/eeOsc = d/a
The analysis enables the choice of the spatial increment ∆x and the time step ∆t that minimise the errors.
I. Flood routing Conclusions
Applications
France- Roujan (1 km²)- Gardon d’Anduze (542 km²)- Allier (2269 km²)- Loire (4978 km²)- Moselle (9400 km²)
Canada The diffusive wave equation resolution scheme is integrated in the Hydrotel model and has been used on several Canadian catchments (de 100 à 10000 km²) (Fortin et al., 1995, RSE; 2001a, 2001b, JHE).
ArgentinaSalado (1500 km²) (MSc. Del Valle Morresi, 2001).
Spatially distributed hydrological modelling of flood events on natural and farmed catchments
I. Process
Representation
III.Integration
into adistributed
model
II.Catchment
segmentation
The study site : Tech, Têt, Agly, Aude, Orb, Héraultand Vidourle catchments (738 to 5346 km²)
II. Catchment segmentation II.1. GIUH
II.1. Identification of a Geomorphological Unit Hydrograph(Moussa, 2003, Hydrol. Pro.)
0 12 24 36 48 60 720
1
2x 10-5
Time (hours)
Dis
char
ge (m
3 /s) Agly
Vidourle
OrbHérault
Têt
Aude
Tech
Comparison of the Unit hydrograph transfer function of seven Mediterranean basins.
This transfer function takes into account : - the channel network structure.- the spatial variability of rainfall.
II. Catchment segmentation II.2. Contribution of hydrological units
0
35
70
P1 (m
m/h
)
RuissellementInfiltration
0
35
70
P2 (m
m/h
)
0
35
70
P3 (m
m/h
)
0
35
70
P4 (m
m/h
)
0
35
70
P5 (m
m/h
)
0
35
70
P6 (m
m/h
)
0
35
70
P7 (m
m/h
)
0
250
500
750
1000
00:00 12:00 00:00 12:00 00:00 12:00
Evénement du 22-24 octobre 1977 (heures:minutes)
Déb
it (m
3 /s)
Sbv1Sbv2Sbv3Sbv4Sbv5Sbv6Sbv7Débit caculé (bassin)Débit mesuré (bassin)
II.2. Identification of the contribution of each sub-catchment.Example : The Gardon d’Anduze(545 km²)(Moussa, 1997, Hydrol. Pro.)
II. Catchment segmentation II.2. Contribution of hydrological units
0
250
500
750
1000
00:00 12:00 00:00 12:00 00:00 12:00
Event of 22-24 october 1977 (hours:minutes)
Dis
char
ge (m
3 /s)
Sbv1Sbv2Sbv3Sbv4Sbv5Sbv6Sbv7Débit caculé (bassin)Débit mesuré (bassin)
Spatially distributed hydrological modelling of flood events on natural and farmed basins
I. Process
representation
III.Integration
into adistributed
model
II.Catchment
segmentation
The MHYDAS spatially distributed hydrological model(Modelling HYDrological AgroSystems)
(Moussa et al., 2002, Hydrol. Pro.)
Groundwater level
Channel routingDiffusive wave
Stream-aquifer interactionEmpirical equation based on Darcy’s law
Hydrological unitHydrological unit
Overland flowKinematic wave equation Rainfall
Infiltration(Green and Ampt)
III. Distributed modelling III.3. Test of scenarios
Testing the channel network management impact
0
250
500
750
00:00 04:00 08:0030 April 1993 (hour : minute)
Dis
char
ge (l
/s)
ReferenceScenario
0
250
500
750
3:00 7:00 11:0031 August 1994 (hour : minute)
Dis
char
ge (l
/s)
Actual ditch network Hypothetical scenario
Conclusions
Development of a spatially distributed hydrological modelling approach (MHYDAS) that is well adapted to natural and farmed catchments based on :
- The analysis of the Saint-Venant equations for flood routing with overbank flow, and the choice of the numerical method that minimises errors.
- Catchment segmentation into hydrological units and calculation of a transfer function based on catchmentgeomorphology.
- Multiscale calibration and validation.
- Human management impact analysis.
ReferencesMoussa R, Bocquillon C. 1994. TraPhyC-BV : A hydrologic information system. Environmental Software 9(4) :
217-226.Moussa R, Bocquillon C. 1996. Algorithms for solving the diffusive wave flood routing equation. Hydrological
Processes 10(1) : 105-124.Moussa R. 1996. Analytical Hayami solution for the diffusive wave flood routing problem with lateral inflow.
Hydrological Processes 10(9) : 1209-1227.Moussa R, Bocquillon C. 1996. Criteria for the choice of flood-routing methods in natural channels. Journal of
Hydrology 186(1-4) : 1-30.Moussa R, Bocquillon C. 1996. Fractal analyses of tree-like channel networks from digital elevation model data.
Journal of Hydrology 187(1-2) : 157-172.Moussa R. 1997. Geomorphological transfer function calculated from digital elevation models for distributed
hydrological modelling. Hydrological Processes 11(5) : 429-449.Moussa R. 1997. Is the drainage network a fractal Sierpinski space? Water Resources Research 33 (10) : 2399-2408.Moussa R, Bocquillon C. 2000. Approximation zones of the Saint-Venant equations for flood routing with overbank
flow. Hydrology and Earth System Sciences 4(2) : 251-261.Moussa R, Bocquillon C. 2001. Fractional-step method solution of diffusive wave equation. Journal of Hydrologic
Engineering 6(1) : 11-19.Moussa R, Voltz M, Andrieux P. 2002. Effects of the spatial organization of agricultural management on the
hydrological behaviour of a farmed catchment during flood events. Hydrological Processes 16 : 393-412.Moussa R. 2003. On morphometric properties of basins, scale effects and hydrologic response.Hydrological Processes 17(1) : 33-58.