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Transcript of 1 DYNAS Workshop, 6 th -8 th December 2004, INRIA M. Esteves, G. Nord PSEM_2D DYNAS Workshop...
1
DYNAS Workshop, 6th-8th December 2004, INRIA
M. Esteves, G. NordM. Esteves, G. Nord
PSEM_2D
DYNAS Workshop
Rocquencourt 6th-8th December 2004
A process-based soil erosion model at the plot scale
2
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 designed to dynamically couple hydrological and soil
erosion processes to predict the spatial pattern of overland flow
hydraulics to predict the spatial pattern of soil erosion to be used in natural slopes conditions to 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 are to 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
Description of PRIM_2D and PSEM_2D
Applications of PRIM_2D Validation 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
Presentation outline
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description Model description
6
DYNAS Workshop, 6th-8th December 2004, INRIA
The model has three major components Overland 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
7
DYNAS Workshop, 6th-8th December 2004, INRIA
The infiltration algorithm is based on the Green and Ampt equation (1911)
f
ff hh
Z
ZKIc
is
Zθθ
If
f
ff hh
Z
ZKI cc
cf ZZ
In the case of crusted soils the profile is divided in two layers
cf ZZ f
ff hh
Z
ZKI ec
c
c
s
ce
KZ
KZZZ
K
f
f
Zf
Model description : Infiltration
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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:
),()()(
yxIRt
h
y
vh
x
uh
0
oxfx SSx
hg
y
uv
x
uu
t
u
0
oyfy SSy
hg
y
vv
x
vu
t
v
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)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Friction is approximated using the Darcy-Weisbach equation
The Darcy-Weisbach friction factor is constant
For small depth flows (< 0.1 mm) the velocities are calculated using a kinematic wave approximation
gh
vuufS fx 8
)( 22
gh
vuvfS fy 8
)( 22
Model description : Flow resistance
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
Sediment mass conservation equation (Bennet,1974)
Model description: Soil erosion
)(1)()()(
fdrds
yx DDy
cq
x
cq
t
hc
h water depth (m)c sediment concentration (m3 m-3)s 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)
mz
h1 Damping effect of the water film
at the soil surface
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)
where
182.069.6 Rzm
Before sediment movement
(kg m-2 s -1)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
Soil detachment by rainfall
function of the area of the covering layer (0-1) soil detachability coefficient by rainfall (kg m-2 mm-1)d 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)
(kg m-2 s -1)
(kg m-2 s -1)Detachment
Re-detachment
After sediment movement
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DYNAS Workshop, 6th-8th December 2004, INRIA
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)
Model description: Soil erosion
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
When Tc>qs (Dfd>0) net erosion occurs and the detachment and entrainment rates are given by:
(kg m-2 s -1)
(kg m-2 s -1)Detachment
Entrainment
f is the flow shear stress in the flow direction (Pa)c is the critical shear stress of a spherical sediment particle [Yang, 1996] (Pa)soil 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)
Model description: Soil erosion
17
DYNAS Workshop, 6th-8th December 2004, INRIA
When Tc<qs (Dfd<0) net deposition occurs and the deposition rates is given by [Foster et al., 1995]:
(kg m-2 s -
1)
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)
Model description: Soil erosion
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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 f (Foster, 1982)
coefficient of efficiency of sediment transport (m0.5 s2 kg –0.5 ) f flow shear stress acting on the soil particles (Pa)c critical shear stress of sediment (Pa) k an exponent taken as 1.5 (Finkner et al.,1989)
kcfcT )( (kg m-1 s-1)
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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 conditions In 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 condition At 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 is balanced by sediment coming from the area surrounding the
plot.
22
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
soil
Kr
d
hf,f
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DYNAS Workshop, 6th-8th December 2004, INRIA
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 (,Kr, soil, D50)
Map of and dd=10
Rainfall (time, intensities)
Model description: Data
24
DYNAS Workshop, 6th-8th December 2004, INRIA
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 (s=0.047, soil 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 ,Kr, soil using the ranges of values found in the literature
Model description: Parameter identfication
WEPP: Water Erosion Prediction Project (US Dept. Agr.)
25
DYNAS Workshop, 6th-8th December 2004, INRIA
Applications of PRIM_2DApplications of PRIM_2D
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DYNAS Workshop, 6th-8th December 2004, INRIA
Two runoff plots located on the same hillslope Homogeneous 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
Examples of application PRIM_2D
27
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)
28
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
J AC ERO
Soil properties
Soil texture Loamy sand Loamy sand s sat. W C (-) 0.296 0.296
hf (m) 1.3795 1.3795 Ks (m/ s) 2.15 E-05 2.15 E-05
Surf ace 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
J AC ERO
Length (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
29
DYNAS Workshop, 6th-8th December 2004, INRIA
04 september 94
0
20
40
60
80
100
120
140
160
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000Time (s)
Dis
charg
e a
nd r
ainf
all
inte
nsit
y (m
m/h
)
Rainf all
Observed
Calculated
PRIM_2D Validation
An exemple of validation run
30
DYNAS Workshop, 6th-8th December 2004, INRIA
0
10
20
30
40
0 5 10 15 20 25 30 35 40
Observed (mm)
Calc
ulat
ed (
mm
)
calibration
validation
1:1
Runoff depth
PRIM_2D Validation
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 35 40
Observed (mm)
Cal
cula
ted (
mm
)
calibration
validation
1:1
I nfi ltration depth
0
1000
2000
3000
4000
0 1000 2000 3000 4000
Observed (s)
Cal
cula
ted (
s)
calibration
validation
1:1
Time to peak
Cal
cula
ted (
mm
/h)
0
25
50
75
100
125
150
175
200
0 25 50 75 100 125 150 175 200
Observed (mm/ h)
calibration
validation
1:1
Maximum discharge
31
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)
Cal
cula
ted (
s)
calibration
validation
1:1
Time to begin runoff
32
DYNAS Workshop, 6th-8th December 2004, INRIA
ERO 25 august 94 20:31:00
0
20
40
60
80
100
120
140
160
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
0
20
40
60
80
100
120
140
160
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
Plot scale results
33
DYNAS Workshop, 6th-8th December 2004, INRIA
Plot Rain(mm)
Ov. flow(mm)
Peak disch.(mm/ h)
I nfi ltration(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 %
J AC Obs. 23.9 11.9 68.7 12.0
J AC 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
Plot scale results
34
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
ERO
Water depth (m)
Time 789 s(max discharge)
Distributed results
35
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
ERO
Infiltration depth (m)
Shear velocities(m/s)
Time 789 s
Distributed results
36
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
37
DYNAS Workshop, 6th-8th December 2004, INRIA
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
Effect of the microtopography
38
DYNAS Workshop, 6th-8th December 2004, INRIA
25 august 94 20:31:00
010
20304050
607080
90100
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400Time (s)
Run
off
and
Rai
nfal
l in
tens
ity (
mm
/h) Observed
Computed Plan.
Computed Topo.
Simulation Rain(mm)
Ov. flow(mm)
Peak disch.(mm/ h)
I nfi ltration(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 %
Effect of the microtopography
39
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 PLANPLANJAC
Water depth (m)
Distributed results Time 789 s
Effect of the microtopography
40
DYNAS Workshop, 6th-8th December 2004, INRIA
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
Effect of the surface features distribution
41
DYNAS Workshop, 6th-8th December 2004, INRIA
Simulation Rain(mm)
Ov. flow(mm)
Peak disch.(mm/ h)
I nfi ltration(mm)
2 Surf . f eat. 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 %
25 august 94 20:31:00
010
2030
4050
6070
8090
100
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400Time (s)
Run
off
and
Rai
nfal
l in
tens
ity (
mm
/h)
Observed
Computed 1 SF
Computed 2 SF
Effect of the surface features distribution
42
DYNAS Workshop, 6th-8th December 2004, INRIA
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
Effect of the surface features distribution
43
DYNAS Workshop, 6th-8th December 2004, INRIA
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
Key results
44
DYNAS Workshop, 6th-8th December 2004, INRIA
PSEM_2D EvaluationPSEM_2D Evaluation
45
DYNAS Workshop, 6th-8th December 2004, INRIA
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.
Psem_2D Evaluation : Experimental data
46
DYNAS Workshop, 6th-8th December 2004, INRIA
Kilinc and Richardson (1973) experimental data
The 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.
Psem_2D Evaluation : Experimental data
47
DYNAS Workshop, 6th-8th December 2004, INRIA
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)
Psem_2D Evaluation : Experimental data
48
DYNAS Workshop, 6th-8th December 2004, INRIA
0
0.01
0.02
0.03
0.04
0.05
0 10 20 30 40 50 60
Time (min)
Sed
imen
t di
scha
rge
(kg/
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
Rain intensity, 93 mm h-1. Slopes, 15, 20, and 30 %
Psem_2D Evaluation : Results
49
DYNAS Workshop, 6th-8th December 2004, INRIA
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 10 20 30 40 50 60
Time (min)
Se
dim
en
t d
isch
arg
e (
kg/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
Rain intensity, 117 mm h-1. Slopes, 15, 20, and 30 %
Psem_2D Evaluation : Results
50
DYNAS Workshop, 6th-8th December 2004, INRIA
0
5
10
15
20
25
30
35
40
45
50
0 5 10 15 20 25 30 35
Time (min)
Se
dim
en
t co
nce
ntr
atio
n (
g/l)
Observed, 50 mm/h Observed, 100 mm/h
PSEM_2D, 50 mm/h (calibrated) PSEM_2D, 100 mm/h
Govindaraju and Kavvas [1991], 50 mm/h Govindaraju and Kavvas [1991], 100 mm/h
Singer and Walker [1983] experiment Slope 9%
D50 of the soil: 2. 10-5 m
Psem_2D Evaluation : Results
51
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
-200
-100
0
100
200
300
400
500
-500 0 500 1000 1500 2000 2500
parameter variation (in %)
C v
ari
atio
n (
in %
)
s
Kr
f
D50
soil
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
Psem_2D Evaluation : Sensitivity analysis
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DYNAS Workshop, 6th-8th December 2004, INRIA
PSEM_2D ApplicationsPSEM_2D Applications
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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
0
20
40
60
80
100
120
140
160
180
2000 20 40 60 80 100 120 140
time (min)
rain
fall in
ten
sit
y (
mm
/h)
0
20
40
60
80
100
120
140
160
180
200
wate
r d
isch
arg
e (
mm
/h)
an
d s
ed
imen
t con
cen
trati
on
(g
/L)
rainfallwater dischargesediment concentration
sediment concentration (without the first rainfall event)D50 = 20 µm
Psem_2D application: Effect of initial condition
Effect of the formation of a deposited layer before the rainfall
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DYNAS Workshop, 6th-8th December 2004, INRIA
-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
Erosion and deposition pattern on the plot at the end of the two consecutive rainfall events (time = 135 min
after the beginning of the simulation)
Deposition
Erosion
Psem_2D application
D50 = 20 µm
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DYNAS Workshop, 6th-8th December 2004, INRIA
0 m
0 . 0 0 0 4 m
0 . 0 0 0 8 m
0 . 0 0 1 2 m
0 . 0 0 1 6 m
0 . 0 0 2 m
0 . 0 0 2 4 m
0 . 0 0 2 8 m
0 . 0 0 3 2 m
0 . 0 0 3 6 m
0 . 0 0 4 m
Computed flow depths
0 m
0 . 0 0 0 4 m
0 . 0 0 0 8 m
0 . 0 0 1 2 m
0 . 0 0 1 6 m
0 . 0 0 2 m
0 . 0 0 2 4 m
0 . 0 0 2 8 m
0 . 0 0 3 2 m
0 . 0 0 3 6 m
0 . 0 0 4 m
Psem_2D application
time = 124 mintime = 27 min
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DYNAS Workshop, 6th-8th December 2004, INRIA
Hydrograph and related sedimentographs for different particle
size diameter0
20
40
60
80
100
120
140
160
180
2000 20 40
time (min)
rain
fall
in
ten
sity
(m
m/h
)
0
20
40
60
80
100
120
140
160
180
200
wat
er d
isch
arg
e (m
m/h
) an
d
sed
imen
t c
on
cen
tra
tio
n (
g/L
)
rainfall water dischargesediment concentration D50=12µm sediment concentration D50=20µmsediment concentration D50=100µmsediment concentration D50=200µmsediment concentration D50=500µmsediment concentration D50=1000µm
Psem_2D application
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DYNAS Workshop, 6th-8th December 2004, INRIA
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
mass (
kg
)
Entrainment
F Detachment
R Re-detachment
R Detachment
Deposition
Psem_2D application
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DYNAS Workshop, 6th-8th December 2004, INRIA
Interrill versus Rill erosion: what does it change in terms of processes ?
Hyetograph
0
20
40
60
80
100
120
140
160
180
200
0 20 40time (min)
rain
fall
inte
nsi
ty (
mm
/h)
Psem_2D application
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DYNAS Workshop, 6th-8th December 2004, INRIA
Comparaison interrills rills contributing processes to the total sediment yield
plot size
Deposition represents 0.7 % of the total mass
eroded
Deposition represents 11.4 % of the total mass eroded
Psem_2D application
0%
20%
40%
60%
80%
100%
1m*1m plot 15m*5m plot
Tota
l sed
imen
t m
ass
Entrainment
F Detachment
R Re-detachment
R Detachment29 %
95 %64 %
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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”
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DYNAS Workshop, 6th-8th December 2004, INRIA
Overland flow hydraulics To improve the prediction of the flow resistance
from surface roughness To analyse the respective effects of roughness
and micro topography Modelling erosion
To validate the model for complex microrelief and natural rainfall events : new experiments
To improve the representation of the flow detachment at the subgrid level
To implement a multiclass sediment representation
To test alternative parametrisation of the transport capacity
Unit stream power Govers equation (1990)
As a conclusion Future research
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DYNAS Workshop, 6th-8th December 2004, INRIA
Thank you for your
attention
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DYNAS Workshop, 6th-8th December 2004, INRIA
Expériences utilisées pour le calibrage et l’évaluation du modèle
Singer and Walker (1983) experimental data The experiment set up was a laboratory flume (3.0 by 0.55 m)
and a rainfall simulator. The flume was filled with 200 kg of compacted moist fresh soil
to produce a 0.08 m thick bed. The soil was a fine sandy loam with a clay content of 13.9 %
and a high amount of silt plus very fine sand (59.2 % in the range 2.10-6 –1. 10-4 m).
The D50 of the soil was 2. 10-5 m. The final soil surface was smooth and hard to the touch.
The slope was constant and equal to 9 %. The major control variable was rainfall intensity. Bare soil surfaces were tested with two rainfall intensities (50
and 100 mm h-1) constant during 30 minutes. Calibration of soil erosion parameters 50 mm h-1
Données disponiblesDébit d’écoulement à l’exutoire Concentration moyenne de sédiments dans l’écoulement à l’exutoire
Psem_2D Evaluation : Experimental data
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DYNAS Workshop, 6th-8th December 2004, INRIA
The sediment discharge per unit flow width in the flow direction qs is defined by:
The flow shear stress in the flow direction is expressed as:
The critical shear stress c is that of a spherical sediment particle expressed as [Yang, 1996]:
s is the the critical dimensionless shear stress of the particle
Model description: Soil erosion
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DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Model parametrisation
Values of the parameters