M. Esteves, G. Nord
PSEM_2D
A process-based soil erosion model
at the plot scale
DYNAS Workshop
Rocquencourt 6th-8th December 2004
1
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
2
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 basis
PRIM_2D has been validated (Esteves et al., 2000, J. Hyd.,228)
PSEM_2D model is still under evaluation (Nord and esteves,
WRR, submitted)
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
3
DYNAS Workshop, 6th-8th December 2004, INRIA
Presentation outline

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
4
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description
5
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description
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)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : Infiltration
The infiltration algorithm is based on the Green and Ampt
equation (1911)
Ic  K
Z f  h f  h 
Zf
Zf 
I
θ s  θi
In the case of crusted soils the
profile is divided in two layers
Z f  Zc
Ic  Kc
Z f  Zc
Ic  Ke
Ke 
7
Z f  h f  h 
Zf
Zf
Z f  h f  h 
Zf
Zf
Z f  Z c   Z c
Ks
Kc
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : Overland flow
 Fully dynamic two dimensional unsteady flow
equations (Barré de Saint-Venant)
 Continuity equation:
(uh) (vh) h


 R  I ( x, y )
x
y
t
 Momentum equations:
x direction:
u
u
u
 h

u
 v  g   S fx  S ox   0
t
x
y
 x

y direction:
8
g
h
R
I
Sox
Soy
Sfx
Sfy
u
v
gravitational acceleration (m.s-2)
flow depth (m)
rainfall intensity (m s -1)
rate of infiltration (m s -1)
ground slope (x direction)
ground slope (y direction)
friction slope (x direction)
friction slope (y direction)
flow velocity (x direction) (m s -1)
flow velocity (y direction) (m s -1)
 h

v
v
v
 u  v  g   S fy  S oy   0
t
x
y
 y

DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : Flow resistance
 Friction is approximated using the Darcy-Weisbach
equation
x direction:
y direction:
S fx  f
S fy  f
u (u 2  v 2 )
8 gh
v (u 2  v 2 )
8 gh
g
h
Sfx
Sfy
u
v
f
gravitational acceleration (m.s-2)
flow depth (m)
friction slope (x direction)
friction slope (y direction)
flow velocity (x direction) (m s -1)
flow velocity (y direction) (m s -1)
Darcy-Weisbach friction factor
 The Darcy-Weisbach friction factor is constant
9
 For small depth flows (< 0.1 mm) the velocities are
calculated using a kinematic wave approximation
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : soil erosion
Deposition
Dfd < 0
Drd > 0
Detachment and redetachment by raindrop
impact
Dfd > 0
Detachment by
runoff
Transport by
runoff
Entrainment
10
Tc > q s
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
 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:
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DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
 Sediment mass conservation equation (Bennet,1974)
 (hc)  (q x c)  (q y c) 1



( Drd  D fd )
t
x
y
s
h
c
s
qx
qy
Drd
Dfd
water depth (m)
sediment concentration (m3 m-3)
sediment particle density (kg m-3)
unit runoff discharge (x direction) (m2 s-1 )
unit runoff discharge (y direction) (m2 s-1 )
soil detachment rate by rainfall (kg m-2 s-1 )
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)
a 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
13

h 
1  
 zm 
Damping effect of the water film at
the soil surface
zm  6.69  R 0.182
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
 Soil detachment by rainfall
After sediment movement
14
Detachment
(kg m-2 s -1)
Re-detachment
(kg m-2 s -1)
e
a
ad
p
h
zm
R
function of the area of the covering layer (0-1)
soil detachability coefficient by rainfall (kg m-2 mm-1)
soil re-detachability coefficient by rainfall (kg m-2 mm-1)
an exponent (1.0)
water depth (m)
the maximum penetration depth of raindrop splash (m)
rainfall intensity (mm h-1)
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]
D fd  (Tc  qs )
(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 the
flow direction (kg m-1 s-1)
 When
• qs<Tc, additional sediment detachment
• qs>Tc, excessive sediment deposition
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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
Entrainment
16
(kg m-2 s -1)
(kg m-2 s -1)
tf is the flow shear stress in the flow direction (Pa)
tc is the critical shear stress of a spherical sediment particle [Yang, 1996] (Pa)
tsoil 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)
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)
j 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 tf (Foster, 1982)
Tc  h(t f  t c )
h
tf
tc
k
k
(kg m-1 s-1)
coefficient of efficiency of sediment transport (m0.5 s2 kg –0.5 )
flow shear stress acting on the soil particles (Pa)
critical shear stress of sediment (Pa)
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
19
 Topographic elevations are re-estimated at each time
step if there is runoff
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Numerical
Model description
methods
Flow chart of PSEM_2D
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).
20
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Initial and boundary conditions
u=0 v=0
dummy cells h=h_inward
c=c_inward
 Boundary conditions
 In the plot version the boundaries are 3
non porous walls and an open boundary
(outlet)
upslope
v=0
 Dummy cells are added to model wall
boundary
 At the outlet no condition is required
because the flow is supercritical
u=0
inward
boundaries
u=0
y
 Initial condition
 At the beginning of the simulation
h(x,y,0) = 0 u(x,y,0) = 0 v(x,y,0) = 0
downslope
c(x,y,0) = 0
21
We consider that rainsplash transportation outside the plot is
balanced by sediment coming from the area surrounding the plot.
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description : Calibrated parameters
Deposition
Drd > 0
Dfd < 0
Detachment and redetachment by raindrop
impact
a
ad
Dfd > 0
Transport by
runoff
Detachment by
runoff
h
tsoil
Kr
22
Entrainment
hf,f
Tc > q s
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 (h,Kr, tsoil, D50)

Map of a and ad, ad=10 a

Rainfall (time, intensities)
23
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 (ds=0.047, tsoil 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 h,Kr, tsoil using the ranges
of values found in the literature
WEPP: Water Erosion Prediction Project (US Dept. Agr.)
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DYNAS Workshop, 6th-8th December 2004, INRIA
Applications of
PRIM_2D
25
DYNAS Workshop, 6th-8th December 2004, INRIA
Examples of application PRIM_2D
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
26
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, INRIA
Examples of application PRIM_2D
JAC
20
Sandy mounds
18
Erosion crusts
0.95
16
ERO
12
12
10
10
8
8
6
6
4
4
2
2
28
0
0
0
2
4
0
2
Length (m)
Width (m)
Max slope (x)
Max slope (y)
JAC
14
14
JAC
20.0
5.0
0.19
0.17
4
Soil properties
Soil texture
s sat. W C (-)
hf (m)
Ks (m/s)
Surface properties
Erosion
Zc (m)
hf (m)
Ks (m/s)
f
Sandy mounds
Zc (m)
hf (m)
Ks (m/s)
f
ERO
14.25
5.0
0.12
0.21
ERO
Loamy sand
0.296
1.3795
2.15 E-05
Loamy sand
0.296
1.3795
2.15 E-05
0.005
1.3795
1.70 E-08
0.25
0.005
1.3795
1.70 E-08
0.25
0.05
0.18
1.90 E-06
0.70th th
DYNAS Workshop, 6 -8 December 2004, INRIA
PRIM_2D Validation
An exemple of validation run
160
Discharge and rainfall intensity (mm/h)
140
Rainfall
Observed
120
04 september 94
Calculated
100
80
60
40
20
0
0
29
500
1000
1500
2000
2500
3000
Time (s)
3500
4000
4500
5000
DYNAS Workshop, 6th-8th December 2004, INRIA
PRIM_2D Validation
validation
30
1:1
Calculated (mm)
Calculated (mm)
Runoff depth
calibration
40
20
10
40
calibration
35
validation
30
1:1
Infiltration depth
25
20
15
10
5
0
0
0
5
10
15
20
25
30
35
40
0
5
10
15
calibration
30
35
40
Maximum discharge
200
1:1
Calculated (mm/h)
Calculated (s)
Time to peak
validation
3000
25
Observed (mm)
Observed (mm)
4000
20
2000
1000
175
calibration
150
validation
125
1:1
100
75
50
25
0
0
0
1000
2000
Observed (s)
3000
4000
0
25
50
75
100
125
150
175
200
Observed (mm/h)
30
DYNAS Workshop, 6th-8th December 2004, INRIA
Calculated (s)
PRIM_2D Validation
700
calibration
600
validation
500
1:1
Time to begin runoff
400
300
200
100
0
0
100
200
300
400
500
600
700
Observed (s)
31
DYNAS Workshop, 6th-8th December 2004, INRIA
Plot scale results
Runoff and Rainfall
intensity (mm/h)
160
ERO 25 august 94 20:31:00
140
120
Rainfall
Observed
100
Computed
80
60
40
20
0
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
Time (s)
Runoff and Rainfall
intensity (mm/h)
160
JAC 25 august 94 20:31:00
140
120
Rainfall
100
Observed
80
Computed
60
40
20
0
0
32
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
Time (s)
DYNAS Workshop, 6th-8th December 2004, INRIA
Plot scale results
Plot
ERO obs.
Rain
(mm)
23.9
Ov. flow
(mm)
14.3
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
-
- 5.0 %
+ 0.7 %
+ 5.0 %
Rel. error
Efficiency ERO : 0.879
Peak disch. Infiltration
(mm/h)
(mm)
91.6
9.6
Efficiency JAC : 0.913
33
DYNAS Workshop, 6th-8th December 2004, INRIA
Distributed results
Time 789 s
(max discharge)
20
JAC
18
14
14
12
JAC
Velocities (m/s)
18
0.5
Water
depth (m)
16
20
16
ERO
14
14
12
12
12
10
10
10
8
8
8
6
6
6
4
4
4
2
2
2
ERO
0.01
10
0.009
0.008
8
0.007
0.006
6
0.005
0.004
4
0.003
0.002
2
0.001
34
0
0
0
1
2
3
4
5
0
0
0
0
1
2
3
4
5
0
0
1
2 2004,
3
4
5
1
2Workshop,
3
4
DYNAS
65 th-8th December
INRIA
Distributed results
JAC
Time 789 s
20
Infiltration
depth (m)
18
JAC
20
Shear velocities
(m/s)
18
ERO
16
16
ERO
0.098
14
14
14
14
12
12
12
0.093
0.088
12
0.06
0.083
10
0.078
0.073
8
0.045
10
10
0.0445
8
0.05
8
0.04
8
6
0.03
6
0.068
6
0.063
0.058
4
6
0.044
0.048
35
0.043
0
0
1
2
3
4
5
0.02
4
4
0.053
2
10
0.0435
0.01
2
2
2
4
0
0.043
0
0
1
2
3
4
5
0
0
1DYNAS
2
3Workshop,
4
5
0
0
1 2004,
2
3 INRIA
4
5
6th-8th December
Point results
(m /s )
Velocities
20
0 .3
0 .2
0 .1
0
18
A small pond
16
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
0
500
1000
1500
2000
2500
Water depth 0 .0 1
(m )
0 .0 0 7 5
14
0 .0 0 5
0 .0 0 2 5
0
12
Shear
velocities
C rill
10
8
0.06
(m /s )
B rill
0.04
0.02
0
D top
6
1500
4
mm/h
150
2
36
Rainfall
100
500
50
0
0
0
0
0
2
4
Reynolds
1000
0
500
1000
1500
2000
2500
500
1000
1500
2000
2500
T im e (s)
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
37
DYNAS Workshop, 6th-8th December 2004, INRIA
Runoff and Rainfall
intensity (mm/h)
Effect of the microtopography
100
90
80
70
60
50
40
30
20
10
0
25 august 94 20:31:00
Observed
Computed Plan.
Computed Topo.
0
200
400
Simulation
600
Rain
(mm)
Topography 23.9
800
1000
1200
Time (s)
Ov. flow
(mm)
11.3
1400
1600
1800
2000
2200
2400
Peak disch. Infiltration
(mm/h)
(mm)
69.2
12.6
Plane
23.9
11.1
73.0
12.8
Diff.
-
- 1.8 %
+ 5.5 %
+ 1.6 %
38
DYNAS Workshop, 6th-8th December 2004, INRIA
Effect of the microtopography
JAC
PLAN
JAC
Distributed results
Time 789 s
20
Water
depth (m)
18
16
14
Vel. (m/s)
0.5
20
20
20
18
18
18
16
16
16
14
14
14
12
12
12
10
10
10
8
8
8
6
6
6
4
4
4
2
2
2
PLAN
0.01
12
0.009
0.008
10
0.007
8
0.006
0.005
6
0.004
4
0.003
2
0.002
39
0.001
0
0
1
2
3
4
5
0
0
0
0
0
2
4
0
DYNAS
2004,
INRIA
0
2
4
1 2 Workshop,
3 4 5 6th-8th December
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
40
DYNAS Workshop, 6th-8th December 2004, INRIA
Runoff and Rainfall
intensity (mm/h)
Effect of the surface features distribution
100
90
80
70
60
50
40
30
20
10
0
25 august 94 20:31:00
Observed
Computed 1 SF
Computed 2 SF
0
200
Simulation
41
400
600
800
1000
1200
1400
Time (s)
1600
1800
2000
2200
2400
2 Surf. feat.
Rain
(mm)
23.9
Ov. flow
(mm)
11.3
1 Surf. Feat.
23.9
14.4
84.6
9.5
-
+ 27.4 %
+ 22.3 %
- 24.6 %
Diff.
Peak disch. Infiltration
(mm/h)
(mm)
69.2
12.6
DYNAS Workshop, 6th-8th December 2004, INRIA
Effect of the surface features distribution
20
JAC 1 SF
JAC 2 SF
20
Time 589 s
 For this storm the
time to ponding is
18
18
Water
depth (m)
16
16
14
14
12
12

390 s for erosion crust

625 s for sandy mounds
0.007
10
0.006
0.005
8
10
8
0.004
6
6
0.003
4
4
0.002
0.001
2
42
2
0
0
0
0
2
4
0
2
4
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
43
variable rainfall rates and to the characteristics of the
uphill areas
DYNAS Workshop, 6th-8th December 2004, INRIA
PSEM_2D Evaluation
44
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.
45
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Experimental data
 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.
46
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)
47
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Results
Rain intensity, 93 mm h-1. Slopes, 15, 20, and 30 %
0.05
Observed, 30 % slope
PSEM_2D, 30 % slope
Sediment discharge (kg/m/s)
0.04
Govindaraju and Kavvas
[1991], 30 % slope
Observed, 20 % slope
0.03
PSEM_2D, 20 % slope
(CALIBRATED)
Govindaraju and Kavvas
[1991], 20 % slope
0.02
Observed, 15 % slope
PSEM_2D, 15 % slope
0.01
Govindaraju and Kavvas
[1991], 15 % slope
0
48
0
10
20
30
40
50
60
Time (min)
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Results
Rain intensity, 117 mm h-1. Slopes, 15, 20, and 30 %
0.07
Observed, 30 % slope
Sediment discharge (kg/m/s)
0.06
PSEM_2D, 30 % slope
Govindaraju and Kavvas
[1991], 30 % slope
0.05
Observed, 20 % slope
0.04
PSEM_2D, 20 % slope
Govindaraju and Kavvas
[1991], 20 % slope
0.03
Observed, 15 % slope
0.02
PSEM_2D, 15 % slope
0.01
Govindaraju and Kavvas
[1991], 15 % slope
0
49
0
10
20
30
40
50
60
Time (min)
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Results
Singer and Walker [1983] experiment
Slope 9%
D50 of the soil: 2. 10-5 m
50
Sediment concentration (g/l)
45
40
35
30
25
20
15
10
5
0
0
5
10
15
20
25
30
35
Time (min)
50
Observed, 50 mm/h
PSEM_2D, 50 mm/h (calibrated)
Observed, 100 mm/h
PSEM_2D, 100 mm/h
Govindaraju and Kavvas [1991], 50 mm/h
Govindaraju and Kavvas [1991], 100 mm/h
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.
51
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Sensitivity analysis
Variations in percentage of the mass sediment concentration
versus variations in percentage of each tested parameter, all the
other parameters keeping the calibrated value
ds
500
Kr
f
400
D50
tsoil
300
C variation (in %)
a
200
h
ld_initia l = 0.01 m
100
0
-500
0
500
1000
1500
2000
2500
-100
52
-200
parameter variation (in %)
DYNAS Workshop, 6th-8th December 2004, INRIA
PSEM_2D
Applications
53
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.
54
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application: Effect of initial condition
0
200
20
180
40
160
60
140
80
120
100
100
120
80
140
60
160
40
180
20
200
55
0
20
40
60
80
time (min)
100
rainfall
water discharge
sediment concentration
sediment concentration (without the first rainfall event)
120
0
140
water discharge (mm/h) and sediment
concentration (g/L)
rainfall intensity (mm/h)
Effect of the formation of a deposited layer before the rainfall
D50 = 20 µm
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
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)
0.005 m
Deposition
0.004 m
0.003 m
0.002 m
0.001 m
0m
-0.001 m
D50 = 20 µm
-0.002 m
-0.003 m
-0.004 m
-0.005 m
-0.006 m
-0.007 m
Erosion
56
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Computed flow depths
time = 124 min
time = 27 min
0.004 m
0.004 m
0.0036 m
0.0036 m
0.0032 m
0.0032 m
0.0028 m
0.0028 m
0.0024 m
0.0024 m
0.002 m
0.002 m
0.0016 m
0.0016 m
0.0012 m
0.0012 m
0.0008 m
0.0008 m
0.0004 m
0.0004 m
0m
0m
57
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
0
200
20
180
40
160
60
140
80
120
100
100
120
80
140
60
160
40
180
20
200
0
0
20
time (min)
rainfall
sediment concentration D50=12µm
sediment concentration D50=100µm
sediment concentration D50=500µm
40
water discharge (mm/h) and
sediment concentration (g/L)
rainfall intensity (mm/h)
Hydrograph and related sedimentographs for
different particle size diameter
water discharge
sediment concentration D50=20µm
sediment concentration D50=200µm
sediment concentration D50=1000µm
58
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
mass (kg)
Contribution of the different processes to
the sediment yield
R Re-detachment
80
R Detachment
Entrainment
60
F Detachment
Deposition
40
20
0
-20
-40
59
12µm
15µm
20µm
100µm
200µm
500µm
1000µm
Median diameter D50
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
rainfall intensity (mm/h)
40
60
80
100
120
140
160
180
200
0
20
time (min)
40
60
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D application
Comparaison interrills rills contributing processes to
the total sediment yield
Total sediment mass
100%
80%
29 %
R Detachment
Entrainment
F Detachment
60%
40%
R Re-detachment
95 %
64 %
20%
0%
61
1m*1m plot
plot size
Deposition represents 0.7 %
of the total mass eroded
15m*5m plot
Deposition represents 11.4 %
of the total mass eroded
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”
62
DYNAS Workshop, 6th-8th December 2004, INRIA
As a conclusion Future research

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

63

Unit stream power
Govers equation (1990)
DYNAS Workshop, 6th-8th December 2004, INRIA
Thank you for
your
attention
64
DYNAS Workshop, 6th-8th December 2004, INRIA
Expériences utilisées
pour le
calibrage et: l’évaluation
du modèle
Psem_2D
Evaluation
Experimental
data
 Singer and Walker (1983) experimental data
65
 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
DYNAS Workshop, 6th-8th December 2004, INRIA
Model description: Soil erosion
 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 tc is that of a spherical
sediment particle expressed as [Yang, 1996]:
66
ds is the the critical dimensionless shear stress of the particle
DYNAS Workshop, 6th-8th December 2004, INRIA
Psem_2D Evaluation : Model parametrisation
Values of the parameters
67
DYNAS Workshop, 6th-8th December 2004, INRIA