Post on 26-Oct-2020
1
DYNAS Workshop, 6th-8th December 2004, INRIA
M. M. EstevesEsteves, G. , G. NordNord
PSEM_2D
A process-based soil erosion model at the plot scale
DYNAS Workshop
Rocquencourt 6th-8th December 2004
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DYNAS Workshop, 6th-8th December 2004, INRIA
Introduction
PRIM_2D Plot Runoff and Infiltration Model (1999)PSEM_2D Plot Soil Erosion Model (2003)
These models were designedto dynamically couple hydrological and soil erosion processesto predict the spatial pattern of overland flow hydraulicsto predict the spatial pattern of soil erosionto be used in natural slopes conditionsto consider complex rainfall events
The models work on a rainfall event basisPRIM_2D has been validated (Esteves et al., 2000, J. Hyd.,228)
PSEM_2D model is still under evaluation (Nord and esteves, WRR, submitted)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Objectives
The main goals areto improve our understanding of local overland flow hydraulics
to develop a better understanding of soil erosion processes
to bring a better description of the spatial and temporal variability of soil erosion at the plot scale
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DYNAS Workshop, 6th-8th December 2004, INRIA
Presentation outline
Description of PRIM_2D and PSEM_2D
Applications of PRIM_2DValidation of the model by comparison with observed data
Effect of the micro-topography
Effect of soil surface features pattern (crusted soils)
Applications of PSEM_2D Evaluation of the model by comparison with experimental data
Some numerical examples to show the capabilities of the model
As a conclusion: Future research
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description Model description
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DYNAS Workshop, 6th-8th December 2004, INRIA
The model has three major componentsOverland flow (OF) is generated as infiltration excess
rainfall (hortonian)
OF is routed using the depth averaged two dimensional unsteady flow equations on a finite difference grid
Rainfall and OF hydraulics are used to compute soil erosion
A single representative particle size (D50)
Model description
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : Infiltration
The infiltration algorithm is based on the Green and Amptequation (1911)
( )f
ff hhZ
ZKIc++
=is
Zθθ
If −
=
( )f
ff hhZ
ZKI cc++
=cf ZZ ≤
In the case of crusted soils the profile is divided in two layers
cf ZZ >( )
f
ff hhZ
ZKI ec++
=
( )c
c
s
ce
KZ
KZZZK
+−
=f
f
Zf
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : Overland flow
Fully dynamic two dimensional unsteady flow equations (Barré de Saint-Venant)
Continuity equation:
Momentum equations:
),()()( yxIRth
yvh
xuh
−=∂∂
+∂
∂+
∂∂
0=⎥⎦⎤
⎢⎣⎡ −+∂∂
+∂∂
+∂∂
+∂∂
oxfx SSxhg
yuv
xuu
tu
x direction:
y direction:
g gravitational acceleration (m.s-2)h flow depth (m)R rainfall intensity (m s -1)I rate of infiltration (m s -1)Sox ground slope (x direction)Soy ground slope (y direction)Sfx friction slope (x direction)Sfy friction slope (y direction)u flow velocity (x direction) (m s -1)v flow velocity (y direction) (m s -1)
0=⎥⎦
⎤⎢⎣
⎡−+
∂∂
+∂∂
+∂∂
+∂∂
oyfy SSyhg
yvv
xvu
tv
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : Flow resistance
Friction is approximated using the Darcy-Weisbachequation
The Darcy-Weisbach friction factor is constant
For small depth flows (< 0.1 mm) the velocities are calculated using a kinematic wave approximation
ghvuu
fS fx 8)( 22 +
=
ghvuv
fS fy 8)( 22 +
=
x direction:
y direction:
g gravitational acceleration (m.s-2)h flow depth (m)Sfx friction slope (x direction) Sfy friction slope (y direction)u flow velocity (x direction) (m s -1)v flow velocity (y direction) (m s -1)f Darcy-Weisbach friction factor
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : soil erosion
Transport by runoff
Detachment and re-detachment by raindrop
impactDeposition
Entrainment
Detachment by runoff
Dfd < 0
Dfd > 0
Drd > 0
Tc> qs
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DYNAS Workshop, 6th-8th December 2004, INRIA
A covering Layer of loose sediment (Hairsine and Rose, 1991) ε is conceptualized as the percentage of a grid cell covered by a deposited layer of depth the median particle diameter D50.
Therefore ε is calculated as:
Model description: Soil erosion
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
Sediment mass conservation equation (Bennet,1974)
)(1)()()(fdrd
s
yx DDycq
xcq
thc
+=∂
∂+
∂∂
+∂
∂ρ
h water depth (m)c sediment concentration (m3 m-3)ρs sediment particle density (kg m-3) qx unit runoff discharge (x direction) (m2 s-1 )qy unit runoff discharge (y direction) (m2 s-1 )Drd soil detachment rate by rainfall (kg m-2 s-1 )Dfd soil detachment/deposition rate by runoff (kg m-2 s-1 )
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
Soil detachment by rainfall is a function of the rainfall intensity (Li, 1979)
Before sediment movement
(kg m-2 s -1)
α soil detachability coefficient by rainfall (kg m-2 mm-1)p an exponent set to 1.0 according to the results of Sharma et al. [1993]h water depth (m)ld loose sediment depth (m)zm the maximum penetration depth of raindrop splash (m)R rainfall intensity (m s-1)
⎟⎟⎠
⎞⎜⎜⎝
⎛−
mzh1 Damping effect of the water film at
the soil surface 182.069.6 Rzm ×=
where
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
Soil detachment by rainfall
Detachment
Re-detachment
After sediment movement
(kg m-2 s -1)
(kg m-2 s -1)
ε function of the area of the covering layer (0-1)α soil detachability coefficient by rainfall (kg m-2 mm-1)αd soil re-detachability coefficient by rainfall (kg m-2 mm-1)p an exponent (1.0) h water depth (m)zm the maximum penetration depth of raindrop splash (m)R rainfall intensity (mm h-1)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
Soil detachment or deposition by runoff : a model proposed by Foster and Meyer [1972]
When • qs<Tc, additional sediment detachment • qs>Tc, excessive sediment deposition
)( scfd qTD −∝ (kg m-2 s-1)
Tc sediment transport capacity of the flow (kg m-1 s-1)qs sediment discharge per unit flow width in theflow direction (kg m-1 s-1)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
When Tc>qs (Dfd>0) net erosion occurs and the detachment and entrainment rates are given by:
Detachment (kg m-2 s -1)
Entrainment (kg m-2 s -1)
τf is the flow shear stress in the flow direction (Pa)τc is the critical shear stress of a spherical sediment particle [Yang, 1996] (Pa)τsoil the critical shear stress of the soil (Pa)Kr is the rill erodibility parameter (s m–1)Tc sediment transport capacity of the flow (kg m-1 s-1)qs sediment discharge per unit flow width in the flow direction (kg m-1 s-1)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
When Tc<qs (Dfd<0) net deposition occurs and the deposition rates is given by [Foster et al., 1995]:
(kg m-2 s -1)
ϕ is a raindrop induced turbulence coefficient assigned to 0.5.Vf is the particle settling velocity (m s–1)q is the water dicharge per unit flow width in the flow direction (m 3 s-1 m-1)Tc sediment transport capacity of the flow (kg m-1 s-1)qs sediment discharge per unit flow width in the flow direction (kg m-1 s-1)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
Flow sediment transport capacity is based on the flow shear stress τf (Foster, 1982)
kcfcT )( ττη −= (kg m-1 s-1)
η coefficient of efficiency of sediment transport (m0.5 s2 kg –0.5 ) τf flow shear stress acting on the soil particles (Pa)τc critical shear stress of sediment (Pa)k an exponent taken as 1.5 (Finkner et al.,1989)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Numerical methods
Hydrological model and erosion model are treated independently since it is assumed that the flow dynamics are not affected by the suspended sediment
The Saint Venant equations are solved using the MacCormack scheme
The mass balance equation for sediment is solved using a second-order centered explicit finite difference scheme
For numerical stability of the scheme and computational efficiency the time step is optimised
Topographic elevations are re-estimated at each time step if there is runoff
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description
Flow chart of PSEM_2D
Model description: Numerical methods
To avoid directional bias of the Mac Cormack scheme the order is reversed every time step(predictor-forward, corrector-backward then
predictor-backward, corrector-forward).
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DYNAS Workshop, 6th-8th December 2004, INRIA
Boundary conditionsIn the plot version the boundaries are 3 non porous walls and an open boundary (outlet)
Dummy cells are added to model wall boundary
At the outlet no condition is required because the flow is supercritical
Initial conditionAt the beginning of the simulation
h(x,y,0) = 0 u(x,y,0) = 0 v(x,y,0) = 0
c(x,y,0) = 0
Model description: Initial and boundary conditions
u = 0 u = 0
v = 0
inwardboundaries
upslope
downslope
y
dummy cellsu=0 v=0h=h_inwardc=c_inward
We consider that rainsplash transportation outside the plot isbalanced by sediment coming from the area surrounding the plot.
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : Calibrated parameters
Transport by runoff
Detachment and re-detachment by raindrop
impactDeposition
Entrainment
Detachment by runoff
Dfd < 0
Dfd > 0
Drd > 0
Tc> qs
τsoil
Kr
α
αd
η
hf,f
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Data
The model needs information on
Slopes and elevations (Digital Elevation Model)
Map of soil surface features distribution
Infiltration parameters (hf, initial WC,Kc,Ks)
Map of DW friction factor
Soil erosion parameters (η,Kr, τsoil, D50)
Map of α and αd, (αd=10 α)
Rainfall (time, intensities)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Parameter identfication
The parameter identification is carried out in three stages
We started with parameters estimation based on physical characteristics and published data
Some of soil erosion parameters are defined using data available in the literature (δs=0.047, τsoil is estimated using the WEPP soil database)
Calibration is undertaken for hf (crusted soils) and/or f on one rainfall event
Calibration is undertaken for η,Kr, τsoil using the ranges of values found in the literatureWEPP: Water Erosion Prediction Project (US Dept. Agr.)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Applications of Applications of PRIM_2DPRIM_2D
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DYNAS Workshop, 6th-8th December 2004, INRIA
Examples of application PRIM_2D
Two runoff plots located on the same hillslopeHomogeneous soil surface feature (ERO)
one type of crust: erosion
Heterogeneous surface feature (JAC)
erosion crust and sandy aeolian micro mounds
• Grid resolution 0.25 by 0.25 m• Both plots have the same subsoil• Initial soil water content were obtained from
neutron probe measurements• Verification runs
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DYNAS Workshop, 6th-8th December 2004, INRIA
Examples of application PRIM_2D
Homogeneous soil surface feature (ERO)
Heterogeneous surface feature (JAC)
Runoff plots in Niger(West Africa)
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DYNAS Workshop, 6th-8th December 2004, INRIA0 2 40
2
4
6
8
10
12
14
ERO
0 2 40
2
4
6
8
10
12
14
16
18
20
0.95
Sandy mounds
Erosion crusts
JAC EROSoil properties Soil texture Loamy sand Loamy sand θs sat. W C (-) 0.296 0.296
hf (m) 1.3795 1.3795 Ks (m/s) 2.15 E-05 2.15 E-05Surface properties
ErosionZc (m) 0.005 0.005
hf (m) 1.3795 1.3795 Ks (m/s) 1.70 E-08 1.70 E-08 f 0.25 0.25
Sandy moundsZc (m) 0.05
hf (m) 0.18 Ks (m/s) 1.90 E-06 f 0.70
JAC EROLength (m) 20.0 14.25Width (m) 5.0 5.0Max slope (x) 0.19 0.12Max slope (y) 0.17 0.21
Examples of application PRIM_2DJAC
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DYNAS Workshop, 6th-8th December 2004, INRIA
PRIM_2D Validation
04 september 94
0
20
40
60
80
100
120
140
160
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000Time (s)
Disch
arge
and
rainf
all i
nten
sity
(mm/h
)
Rainfall Observed Calculated
An exemple of validation run
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DYNAS Workshop, 6th-8th December 2004, INRIA
PRIM_2D Validation
0
10
20
30
40
0 5 10 15 20 25 30 35 40
Observed (mm)
Calc
ulat
ed (m
m)
calibrationvalidation1:1
Runoff depth
05
101520
25303540
0 5 10 15 20 25 30 35 40
Observed (mm)
Calc
ulat
ed (m
m)
calibrationvalidation1:1
Infiltration depth
0
1000
2000
3000
4000
0 1000 2000 3000 4000
Observed (s)
Calc
ulat
ed (s
)
calibrationvalidation1:1
Time to peak
Calc
ulat
ed (m
m/h
)
0
25
50
75
100
125
150
175
200
0 25 50 75 100 125 150 175 200
Observed (mm/h)
calibrationvalidation1:1
Maximum discharge
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DYNAS Workshop, 6th-8th December 2004, INRIA
PRIM_2D Validation
0
100
200
300
400
500
600
700
0 100 200 300 400 500 600 700
Observed (s)
Calc
ulat
ed (s
)
calibrationvalidation1:1
Time to begin runoff
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DYNAS Workshop, 6th-8th December 2004, INRIA
Plot scale results
ERO 25 august 94 20:31:00
020406080
100120140160
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
Time (s)
Run
off a
nd R
ainf
all
inte
nsity
(mm
/h)
Rainfall Observed Computed
JAC 25 august 94 20:31:00
020406080
100120140160
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
Time (s)
Run
off a
nd R
ainf
all
inte
nsity
(mm
/h)
Rainfall Observed Computed
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DYNAS Workshop, 6th-8th December 2004, INRIA
Plot scale results
Plot Rain(mm)
Ov. flow(mm)
Peak disch.(mm/h)
Infiltration(mm)
ERO obs. 23.9 14.3 91.6 9.6
ERO cal. 23.9 14.5 95.2 9.4
Rel. error - -1.9 % + 3.9 % + 1.3 %
JAC Obs. 23.9 11.9 68.7 12.0
JAC cal. 23.9 11.3 69.2 12.6
Rel. error - - 5.0 % + 0.7 % + 5.0 %
Efficiency ERO : 0.879 Efficiency JAC : 0.913
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DYNAS Workshop, 6th-8th December 2004, INRIA0 1 2 3 4 50
2
4
6
8
10
12
14
0 1 2 3 4 50
2
4
6
8
10
12
14
0 1 2 3 4 50
2
4
6
8
10
12
14
16
18
20
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Velocities (m/s)
0.5
0 1 2 3 4 50
2
4
6
8
10
12
14
16
18
20
JACJAC
ERO
EROWater
depth (m)
Time 789 s(max discharge)
Distributed results
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DYNAS Workshop, 6th-8th December 2004, INRIA0 1 2 3 4 50
2
4
6
8
10
12
14
16
18
20
0.043
0.048
0.053
0.058
0.063
0.068
0.073
0.078
0.083
0.088
0.093
0.098
0 1 2 3 4 50
2
4
6
8
10
12
14
0.043
0.0435
0.044
0.0445
0.045
0 1 2 3 4 50
2
4
6
8
10
12
14
16
18
20
0
0.01
0.02
0.03
0.04
0.05
0.06
0 1 2 3 4 50
2
4
6
8
10
12
14
JACJAC
ERO
EROInfiltration depth (m)
Shear velocities(m/s)
Time 789 s
Distributed results
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DYNAS Workshop, 6th-8th December 2004, INRIA0 2 4
0
2
4
6
8
10
12
14
16
18
20
0
50
100
150
0 500 1000 1500 2000 2500
mm
/h
A small pond
B rill
D top
C rill
0
0.1
0.2
0.3
0 500 1000 1500 2000 2500
(m/s
)
0
0.0025
0.005
0.0075
0.01
0 500 1000 1500 2000 2500
(m)
0
0.02
0.04
0.06
0 500 1000 1500 2000 2500
(m/s
)
0
500
1000
1500
0 500 1000 1500 2000 2500Time (s)
Velocities
Water depth
Shear velocities
ReynoldsRainfall
Point results
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DYNAS Workshop, 6th-8th December 2004, INRIA
Effect of the microtopography
The microtopography is represented by
the topographic map of the plot (JAC)
a plane surface with the same mean slope
All other parameters are the same
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DYNAS Workshop, 6th-8th December 2004, INRIA
Effect of the microtopography
25 august 94 20:31:00
0102030405060708090
100
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400Time (s)
Run
off a
nd R
ainf
all
inte
nsity
(mm
/h) Observed
Computed Plan. Computed Topo.
Simulation Rain(mm)
Ov. flow(mm)
Peak disch.(mm/h)
Infiltration(mm)
Topography 23.9 11.3 69.2 12.6
Plane 23.9 11.1 73.0 12.8
Diff. - - 1.8 % + 5.5 % + 1.6 %
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DYNAS Workshop, 6th-8th December 2004, INRIA0 1 2 3 4 50
2
4
6
8
10
12
14
16
18
20
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Vel. (m/s)
0.5
0 1 2 3 4 50
2
4
6
8
10
12
14
16
18
20
0 2 40
2
4
6
8
10
12
14
16
18
20
0 2 40
2
4
6
8
10
12
14
16
18
20
JAC PLAN PLANJAC
Water depth (m)
Distributed resultsTime 789 s
Effect of the microtopography
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DYNAS Workshop, 6th-8th December 2004, INRIA
Effect of the surface features distribution
The soil surface features are represented by
the soil surface feature map (JAC)
the dominant surface feature (erosion crust)
All the other parameters are the same
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DYNAS Workshop, 6th-8th December 2004, INRIA
Effect of the surface features distribution
25 august 94 20:31:00
0102030405060708090
100
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400Time (s)
Run
off a
nd R
ainf
all
inte
nsity
(mm
/h)
Observed Computed 1 SF Computed 2 SF
Simulation Rain(mm)
Ov. flow(mm)
Peak disch.(mm/h)
Infiltration(mm)
2 Surf. feat. 23.9 11.3 69.2 12.6
1 Surf. Feat. 23.9 14.4 84.6 9.5
Diff. - + 27.4 % + 22.3 % - 24.6 %
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DYNAS Workshop, 6th-8th December 2004, INRIA
Effect of the surface features distribution
JAC 2 SF JAC 1 SF
0 2 40
2
4
6
8
10
12
14
16
18
20
0 2 40
2
4
6
8
10
12
14
16
18
20
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Water depth (m)
Time 589 s
For this storm the time to ponding is
390 s for erosion crust
625 s for sandy mounds
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DYNAS Workshop, 6th-8th December 2004, INRIA
Key results
Even in low relief plots, OF is not a sheet of flowing water, uniform in depth and velocity across the slope. OF concentrates downslope into deeper flow pathways
Small surface feature may play a major role in the OF production from a plot
A good reproduction of discharges at the outlet of a plot does not imply that OF hydraulics is correctly simulated
Infiltration is not homogeneous all over the plot which is partly due to the effect of micro-topography
Large variations in the OF hydraulics are due to the variable rainfall rates and to the characteristics of the uphill areas
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DYNAS Workshop, 6th-8th December 2004, INRIA
PSEM_2D EvaluationPSEM_2D Evaluation
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Experimental data
Kilinc and Richardson (1973) experimental data
A 1.52 m wide × 4.58 m long flume with an adjustable slope and a rainfall simulator. Each run was one hour long
The flume was filled with compacted sandy soil composed of 90 % sand and 10 % silt and clay.
The soil had a non-uniform size distribution with a median diameter D50 of 3.5 × 10-4 m.
The soil surface was levelled and smoothed before each run.
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Experimental data
Kilinc and Richardson (1973) experimental dataThe major controlled variables were rainfall intensity and soil surface slope.
Infiltration and erodibility of surface were supposed constant.
Six slopes (5.7, 10, 15, 20, 30, and 40 %) were tested
Four rainfall intensities (32, 57, 93, and 117 mm h-1).
Calibration was carried out using a run with 20 % slope and 93 mm h-1 rainfall intensity.
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Experimental data
Data available
• Flow discharge at the outlet of the flume
• Mean sediment concentration in the flow at the outlet
• Mean infiltration rate
• No data were collected on microtopography and Overland flow hydraulics (water depth, velocity)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Results
Rain intensity, 93 mm h-1. Slopes, 15, 20, and 30 %
0
0.01
0.02
0.03
0.04
0.05
0 10 20 30 40 50 60
Time (min)
Sed
imen
tdis
char
ge(k
g/m
/s)
Observed, 30 % slope
PSEM_2D, 30 % slope
Govindaraju and Kavvas[1991], 30 % slope
Observed, 20 % slope
PSEM_2D, 20 % slope(CALIBRATED)
Govindaraju and Kavvas[1991], 20 % slope
Observed, 15 % slope
PSEM_2D, 15 % slope
Govindaraju and Kavvas[1991], 15 % slope
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Results
Rain intensity, 117 mm h-1. Slopes, 15, 20, and 30 %
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 10 20 30 40 50 60
Time (min)
Sed
imen
t dis
char
ge (k
g/m
/s)
Observed, 30 % slope
PSEM_2D, 30 % slope
Govindaraju and Kavvas[1991], 30 % slope
Observed, 20 % slope
PSEM_2D, 20 % slope
Govindaraju and Kavvas[1991], 20 % slope
Observed, 15 % slope
PSEM_2D, 15 % slope
Govindaraju and Kavvas[1991], 15 % slope
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Results
0
5
10
15
20
25
30
35
40
45
50
0 5 10 15 20 25 30 35Time (min)
Sed
imen
t con
cent
ratio
n (g
/l)
Observed, 50 mm/h Observed, 100 mm/hPSEM_2D, 50 mm/h (calibrated) PSEM_2D, 100 mm/hGovindaraju and Kavvas [1991], 50 mm/h Govindaraju and Kavvas [1991], 100 mm/h
Singer and Walker [1983] experimentSlope 9%
D50 of the soil: 2. 10-5 m
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Sensitivity analysis
The range of variation of the parameters calibrated with the data of Singer and Walker [1983]
9 % slope and 50 mm h-1 rainfall intensity.
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Sensitivity analysis
-200
-100
0
100
200
300
400
500
-500 0 500 1000 1500 2000 2500
parameter variation (in %)
C v
aria
tion
(in %
)
δs
Kr
f
D50
τsoil
α
η
ld_initia l = 0.01 m
Variations in percentage of the mass sediment concentration versus variations in percentage of each tested parameter, all the
other parameters keeping the calibrated value
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DYNAS Workshop, 6th-8th December 2004, INRIA
PSEM_2D PSEM_2D ApplicationsApplications
54
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Plot 5 by 15 m a grid of 0.2 by 0.2 m
Parameter values of Singer and Walker experiment
Average slopes are 0.02 and 0.06 in the x and y directions.
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application: Effect of initial condition
Effect of the formation of a deposited layer before the rainfall
0
20
40
60
80
100
120
140
160
180
2000 20 40 60 80 100 120 140
time (min)
rain
fall
inte
nsi
ty(m
m/h
)
0
20
40
60
80
100
120
140
160
180
200
wat
erdi
sch
arge
(mm
/h)
and
sedi
men
tco
nce
ntr
atio
n (
g/L)
rainfallwater dischargesediment concentrationsediment concentration (without the first rainfall event) D50 = 20 µm
56
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Erosion and deposition pattern on the plot at the end of thetwo consecutive rainfall events (time = 135 min after the
beginning of the simulation)
-0.007 m
-0.006 m
-0.005 m
-0.004 m
-0.003 m
-0.002 m
-0.001 m
0 m
0.001 m
0.002 m
0.003 m
0.004 m
0.005 m Deposition
D50 = 20 µm
Erosion
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Computed flow depths
time = 124 mintime = 27 min
0 m
0.0004 m
0.0008 m
0.0012 m
0.0016 m
0.002 m
0.0024 m
0.0028 m
0.0032 m
0.0036 m
0.004 m
0 m
0.0004 m
0.0008 m
0.0012 m
0.0016 m
0.002 m
0.0024 m
0.0028 m
0.0032 m
0.0036 m
0.004 m
58
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Hydrograph and related sedimentographs for different particle size diameter
020406080
100120140160180200
0 20 40time (min)
rain
fall
inte
nsity
(mm
/h)
0
20406080100120140160180200
wat
erdi
scha
rge
(mm
/h) a
ndse
dim
entc
once
ntra
tion
(g/L
)
rainfall water dischargesediment concentration D50=12µm sediment concentration D50=20µmsediment concentration D50=100µm sediment concentration D50=200µmsediment concentration D50=500µm sediment concentration D50=1000µm
59
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Contribution of the different processes to the sediment yield
-40
-20
0
20
40
60
80
12µm 15µm 20µm 100µm 200µm 500µm 1000µm
Median diameter D50
mas
s (k
g)
EntrainmentF Detachment
R Re-detachmentR Detachment
Deposition
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Interrill versus Rill erosion: what does it change in terms of processes ?
Hyetograph
0
20
40
60
80
100
120
140
160
180
2000 20 40
time (min)
rain
fall
inte
nsity
(mm
/h)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Comparaison interrills rills contributing processes to the total sediment yield
plot size0%
20%
40%
60%
80%
100%
1m*1m plot 15m*5m plot
Tota
l sed
imen
tm
ass
EntrainmentF Detachment
R Re-detachmentR Detachment
29 %
95 %64 %
Deposition represents 11.4 % of the total mass eroded
Deposition represents 0.7 % of the total mass eroded
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DYNAS Workshop, 6th-8th December 2004, INRIA
Some key issues Runoff production limited to excess rainfall
Sources and sinks of sediment vary with the magnitude of the events
The soil erodibility coefficients have not yet been quantitatively related to a measurable soil property and must therefore be determined empirically or calibrated
Model calibration, a lot of parameter to determine
More complex models increase data requirement and …
Increase data and model uncertainty, which affects model results
Propagation of errors in input data
Model structural errors
Uncertainty associated with evaluation of model parameters
Problem of the model evaluation (spatial field data) “the right answer for the wrong reason”
63
DYNAS Workshop, 6th-8th December 2004, INRIA
As a conclusion Future research
Overland flow hydraulicsTo improve the prediction of the flow resistance from surface roughness To analyse the respective effects of roughness and micro topography
Modelling erosionTo validate the model for complex microrelief and natural rainfall events : new experimentsTo improve the representation of the flow detachment at the subgrid level To implement a multiclass sediment representationTo test alternative parametrisation of the transport capacity
Unit stream powerGovers equation (1990)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Thank you for your
attention