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Claude Mugler

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Darcy multi-domain approach for coupling surface-subsurface flows: Application to benchmark problems

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Claude Mugler

  1. 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. 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. 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. 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. 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. 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 6/17
  7. 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. 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. 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. 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. 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. 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. 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. 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. 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. 16. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE The Superslab test case: Cast3M results (2/2) 16/17
  17. 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 17/17
  18. 18. Workshop on coupled hydrological modeling, Padova, September 23-24, 2015LSCE Thank you for your attention

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