claude mugler

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

1/17


Summary

•  The integrated model: Description and validation

•  Integrated Hydrologic Model Intercomparison •  Conclusion

2/17


–  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)

3/17


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

4/17


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

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)


•  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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•  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


●  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

8/17


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)


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


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


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


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


Cross-section: different colors indicate different hydraulic conductivities and VG parameters

80m

20m

8m

12/17


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


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)

15/17


The Superslab test case: Cast3M results (2/2)

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●  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

17/17


Thank you for your attention