claude mugler
TRANSCRIPT
Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
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
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
Summary
• The integrated model: Description and validation
• Integrated Hydrologic Model Intercomparison • Conclusion
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
– 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
)))((.()( zhhKthhC ∇+∇∇=
!!!
∂∂
))(.( zhKthS sat ∇+∇∇=
!!!
∂∂
⎩⎨⎧
=∂
∂=
SZinSUZinhC
hhC sub
sub
)()( θ
h 0
Ksub(h)
Csub(h)
⎩⎨⎧
=SZinKUZinhK
hKsat
sub
)()(
Ksat
K(h)
C(h)
S
Subsurface Model
Le Potier, CMWR XII (1998)
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
diffusive wave + Manning formula
))((3/5
sss
ss zhxSn
hxt
h+
∂∂
∂∂
=∂∂ hs = runoff water depth
zs = soil surface elevation n = Manning’s coefficient Ss = soil slope
Surface-subsurface coupling: Introduction of runoff
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
diffusive wave + Manning law
))((3/5
sss
ss zhxSn
hxt
h+
∂∂
∂∂
=∂∂ hs = runoff water depth
zs = soil surface elevation n = Manning’s coefficient Ss = soil slope
Surface-subsurface coupling: Introduction of runoff
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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)
Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
• Unified equation
)())(.()( zhHqHHKtHHC uniuniuni +==∇−∇−
!!
∂∂
Integrated model: Darcy multidomain
• Physical laws for the whole domain
⎪⎩
⎪⎨⎧
=surfacehK
subsurfacehKHK
ss
subuni )(
)()(
⎩⎨⎧
=surfacehsubsurfaceh
Hss
subuni )(
)()(
θ
θθ
hHC uni
uni ∂θ∂
=)( with
A single equation describes the whole set of surface & subsurface processes and their interactions
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
• 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
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
● 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
))(.()( 1,11,1
1,1,1 zhK
tHHhC in
in
ninin ∇+∇∇=
Δ− ++
++
+++
!!!
)10()()1()( 1,1,11,1 <<−+= −++++ ααα ininin hKhKK
Integrated model: Numerics
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
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
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Weill, PhD thesis (2008); Weill et al., J. Hydrol. (2009)
Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
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)
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
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
Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
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
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
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
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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
Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
Initial conditions: Water table 5 m below land surface, and hydrostatic conditions vertically
The Superslab test case: Configuration (2/2)
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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
Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE Saturation
Rainy period Rainy period Recession period
The Superslab test case: Cast3M results (1/2)
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
The Superslab test case: Cast3M results (2/2)
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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
● 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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Workshop on coupled hydrological modeling, Padova, September 23-24, 2015 LSCE
Thank you for your attention