This document summarizes work on developing an integrated surface-subsurface hydrological model using a Darcy multi-domain approach. It describes the model, its validation using benchmark problems, and participation in an international model intercomparison project. The integrated model couples surface and subsurface flows using a single pressure head equation. It was able to successfully simulate several benchmark problems, including a superslab test case with heterogeneous soils, though very small grid cells and many iterations were required.

1. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
Darcy multi-domain approach for
coupling surface-subsurface flows:
Application to benchmark problems
Claude MUGLER, Emmanuel MOUCHE
Laboratoire des Sciences du Climat et de l’Environnement
UMR 8212 CEA/CNRS/UVSQ, Orme des Merisiers,
91191 Gif-sur-Yvette, France
1/17

2. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
Summary
• The integrated model: Description and validation
• Integrated Hydrologic Model Intercomparison
• Conclusion
2/17

3. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
– Unsaturated Zone (UZ): Richards equation
– Saturated Zone (SZ): Darcy equation
Pressure head h as the main variable
è unified description of flow in the UZ and SZ
)))((.()( zhhK
t
h
hC ∇+∇∇=
!!!
∂
∂
))(.( zhK
t
h
S sat ∇+∇∇=
!!!
∂
∂
⎩
⎨
⎧
=
∂
∂
=
SZinS
UZinhC
h
hC sub
sub
)(
)(
θ
h0
Ksub(h)
Csub(h)
⎩
⎨
⎧
=
SZinK
UZinhK
hK
sat
sub
)(
)(
Ksat
K(h)
C(h)
S
Subsurface Model
Le Potier, CMWR XII (1998)
3/17

4. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
diffusive wave + Manning formula
))((
3/5
ss
s
ss
zh
xSn
h
xt
h
+
∂
∂
∂
∂
=
∂
∂ hs = runoff water depth
zs = soil surface elevation
n = Manning’s coefficient
Ss = soil slope
Surface-subsurface coupling:
Introduction of runoff
4/17

5. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
diffusive wave + Manning law
))((
3/5
ss
s
ss
zh
xSn
h
xt
h
+
∂
∂
∂
∂
=
∂
∂ hs = runoff water depth
zs = soil surface elevation
n = Manning’s coefficient
Ss = soil slope
Surface-subsurface coupling:
Introduction of runoff
5/17
è same type of equation as Richards and Darcy equations
è Runoff modeled as Darcean flow in a porous layer
Weill, PhD thesis (2008)
Weill et al., J. Hydrol. (2009)

6. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
• Unified equation
)())(.()( zhHqHHK
t
H
HC uniuniuni +==∇−∇−
!!
∂
∂
Integrated model: Darcy multidomain
• Physical laws for the whole domain
⎪⎩
⎪
⎨
⎧
=
surfacehK
subsurfacehK
HK
ss
sub
uni
)(
)(
)(
⎩
⎨
⎧
=
surfaceh
subsurfaceh
H
ss
sub
uni
)(
)(
)(
θ
θ
θ
h
HC uni
uni
∂
θ∂
=)( with
A single equation describes the whole set of surface & subsurface
processes and their interactions
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7. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
• Resolution of a single nonlinear system with domain dependent
parameters (Darcean continuum)
• Natural continuity of pressure and flux at the soil surface
• Runoff / infiltration partitioning naturally controlled by pressure
at the soil surface
• Same formalism to describe runoff and streams
• Can take into account any friction law
Integrated model: Advantages of the approach
7/17

8. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
● Cast3M simulation platform (www-cast3m.cea.fr)
● Spatial scheme:
- Mixed Hybrid Finite Elements
- Finite Volumes
● Time scheme:
- Iterative Picard algorithm for nonlinear terms
(n: time index, i: iteration index)
- Underrelaxation for nonlinear laws
))(.()( 1,1
1,1
1,1
,1
zhK
t
HH
hC in
in
nin
in
∇+∇∇=
Δ
− ++
++
++
+
!!!
)10()()1()( 1,1,1
1,1 <<−+= −++
++ ααα inin
in hKhKK
Integrated model: Numerics
8/17

9. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
Abdul and Gillham (WRR, 1984)
Ogden and Watts (WRR, 2000)Govindaraju and Kavvas (WRR, 1991)
Di Giammarco et al (J Hydrol 1996)
Mugler et al ( sub. J Hydrol)
Vauclin et al (WRR, 1978)
Subsurface flow and transport
Overland flow model
Integrated surface/subsurface model
outlet
saturated zone
unsaturated
zone
Rainfall
prescribed head boundary
no flow boundaries
saturated length
3D configuration
Validation & Application
9/17
Weill, PhD thesis (2008); Weill et al., J. Hydrol. (2009)

10. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
2nd phase of the « Integrated Hydrologic Model Intercomparison Project »
Maxwell et al., WRR 2014; Kollet et al., EGU 2015; www.hpsc-terrsys.de/intercomparison-project
- Organizers: S. Kollet (Forschungszentrum Jülich GmbH),
R. Maxwell (Colorado School of Mines),
M. Putti (Univ. of Padova),
C. Paniconi (Univ. of Québec)
- Models: CATHY, Cast3M, HydroGeoSphere,
OpenGeoSys, MIKE SHE,
ParFlow, PAWS, PIHM
- Focus: - 3D surface-subsurface flow interactions
- more complex heterogeneity
- a field experiment
Bonn meeting, 2013
Application to benchmark problems (1/2)
10/17

11. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
1 Tilted v-catchment: 3D, homogenous subsurface, recession and rain/recession
3 Borden field experiment: 3D, real
topography, rain/recession experiment
2 Superslab: 2D, heterogeneous subsurface,
rain/recession
Application to benchmark problems (2/2)
Cross-section: different colors indicate different hydraulic
conductivities and VG parameters
80m
20m
8m
80m
(from Kollet et al., EGU 2015)
11/17
(Abdul &
Gillham, 1989)
4 scenarios:
recession,
rainfall,
various nManning
1 scenario:
50’ rainfall,
50’ recession

12. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
1 Tilted v-catchment: 3D, homogenous subsurface, recession and rain/recession
3 Borden field experiment: 3D, real
topography, rain/recession experiment
2 Superslab: 2D, heterogeneous subsurface,
rain/recession
Application to benchmark problems (2/2)
Cross-section: different colors indicate different hydraulic
conductivities and VG parameters
80m
20m
8m
12/17

13. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
The Superslab test case: Configuration (1/2)
Geometry and parameters:
Domain:
Lx×Lz=100 m×5 m
Ksat=10 m/h
(n,α,θres,θsat)=(2,6,0.02,0.1)
Slab1:
Lx×Lz=42 m×0.4 m
Ksat=0.025 m/h
(n,α,θres,θsat)=(3,1,0.03,0.1)
Slab2:
Lx×Lz=20 m×1.3 m
Ksat=0.001 m/h
(n,α,θres,θsat)=(3,1,0.03,0.1)
Manning: nc=3.6×10-3 s/m1/3
Sf,x=0.1, Sf,z=0
13/17
Domain:
Ksat=200×R
R = 0.05 m/h
Slab1: Ksat=0.5×R
100 m
5 m
10 m
Saturation
Initial conditions: - Water table depth = 5 m
- Hydrostatic conditions vertically
Boundary conditions: - No flow along the sides and bottom
- 3 hours of rain followed by 9 hours of recession

14. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
Initial conditions: Water table 5 m below land surface, and hydrostatic conditions vertically
The Superslab test case: Configuration (2/2)
14/17
Heterogeneous properties:
1 m
20 cm
Very small grid cells required in Cast3M: 5×10-5 m < Δz < 5×10-2 m
with Δx=1 m, Nx×Nz=100×2015 cells
αVG = 1 m-1 in the slabs
αVG = 6 m-1 in the domain
Lc ~ 1 m in the slabs
Lc ~ 20 cm in the domain
van Genuchten parameters
in the slabs and domain:
Water retention curve for the slabs and the domain

15. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE Saturation
Rainy period Rainy period Recession period
The Superslab test case: Cast3M results (1/2)
15/17

16. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
The Superslab test case: Cast3M results (2/2)
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17. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
● Development and validation of an integrated model
A single equation for surface and subsurface flows
● Participation to an intercomparison
Advantages of our model: All benchmarks simulated with success,
but very small grid cells and many iterations needed to reach
convergence à long calculations
Conclusion
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18. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE
Thank you for your attention