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Sylvain Weill
- 1. Workshop on coupled hydrological modeling – Padova – September 2015 A dimensionally-‐reduced model for coupled river-‐ subsurface flow modeling Yi Pan, Sylvain Weill, Philippe Ackerer, Frederick Delay Laboratory of Hydrology and Geochemistry of Strasbourg (LHyGeS)
- 2. Workshop on coupled hydrological modeling – Padova – September 2015 Outlines • Context / MoIvaIon • Models: – The dimensionally-‐reduced subsurface model – The coupled model • Dimensionally-‐reduced subsurface model “validaIon” • Inter-‐comparison with CATHY (Fully dimensioned Model) • First tests on the Strengbach catchment
- 3. Workshop on coupled hydrological modeling – Padova – September 2015 Context / MoIvaIon • The Strengbach catchment : – Instrumented and surveyed for more than 25 years by the LHyGeS’ staff – Mountainous catchment – steep slopes ( 30°) – Assumed deep bedrock (> 150 m depth at the ridge) – Needs for integrated simulaIon to beer characterize flow pathways and residence Imes • Not easy to simulate this catchment with integrated tools based on the 3D Richards equaIon for subsurface flow è Development of a simpler approach which remains physically-‐ based, distributed and integrated
- 4. Workshop on coupled hydrological modeling – Padova – September 2015 The dimensionally-‐reduced subsurface model • Basic idea : to develop a dimensionally-‐reduced subsurface model accounIng for both saturated and unsaturated flow processes • IntegraIon of the 3D Richards equaIon in a direcIon perpendicular to the bedrock from bedrock zb to land surface zs elevaIons • Splibng the integral by introducing the water table elevaIon zw results in ( ) ( )( )( ). . s s s b b b z z z w w z z z S h S S dz h q dz t t dz ∂θ ∂⎛ ⎞ + θ ∇ − θ ∇ ∂⎝ =⎟ ∂ +⎜ ⎠ ∫ ∫ ∫K ( ) ( ) ( )( )( ) ( )( )( ) . . . . w s w b w b s s w b z z z S w S w w z z z z z z z h h S S dz S S dz h t t t t h q dz dz dz ∂θ ∂ ∂θ ∂⎛ ⎞ ⎛ ⎞ + θ + θ ∇ − θ ∇⎜ ⎟ ⎜ ⎟ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ∇ ∇ + + θ + =− ∫ ∫ ∫ ∫ ∫ K K
- 5. Workshop on coupled hydrological modeling – Padova – September 2015 The dimensionally-‐reduced subsurface model • SimplificaIons : – In the saturated zone : – In the vadose zone : • Further assumpIons : – Flow is mainly parallel to the bedrock – Pressure profile in the vadose zone is hydrostaIc ( )( ) ( ) , , ( ) ( , ) ( ) ( ) . . s w s w x y x y w z z z z S h Ssat h h S h h Q with t h dz C h dz h θ ⎧ = + ∂ ⎪ +∇ − θ ∇ = ⎨ ∂ ⎪ + θ ⎩ = ∫ ∫ T Ksat KT ( )S wS S t ∂θ >> θ ∂ ( )0 1wand S t ∂θ = θ = ∂
- 6. Workshop on coupled hydrological modeling – Padova – September 2015 The coupled model • Subsurface equaIon : • Surface equaIon for 1D river flow : diffusive wave • Coupling : first order law • ResoluIon : – Fully implicit – Mixed Hybrid Finite Elements (Subsurface) – Finite element (Surface) – Picard algorithm + mass lumping + adapIve Ime step ( )( ), ,( ) . .x y x y w h S h h Q t ∂ +∇ − θ ∇ = ∂ T ( ) ( ) 2 3 1 2 . 'h x x r Man x r A R A h z l q t N h z ⎛ ⎞∂ ⎜ ⎟−∇ ∇ + = ⎜ ⎟∂ ∇ +⎝ ⎠
- 7. Workshop on coupled hydrological modeling – Padova – September 2015 Dimensionally-‐reduced subsurface model “validaIon” • Inter-‐comparison between the dimensionally-‐reduced model and a classical Richards based model on a 2D verIcal cross secIon (Weill et al, Hydrological Processes, submiAed) • Geometry inheriIng of the Strengbach catchment è 176 000 elements for Richards / 12 000 elements for the dimensionally-‐reduced model
- 8. Workshop on coupled hydrological modeling – Padova – September 2015 Dimensionally-‐reduced subsurface model “validaIon” • 4 subsurface configuraIons : – Homogeneous – 3 layers – 30 layers / constant VG parameters – Random field of saturated hydraulic conducIvity/ constant VG parameters • IniIal and boundary condiIons : – Water table located 3 m below land surface iniIally – Dirichlet BC downstream – Rainfall rate of 100 mm/day during 5 days, over a line between x = 0 and 50 m (upstream) aker 11 days of simulaIon Ksat (m/ day) ω (-‐) θr (-‐) α (m-‐1) n (-‐) Depth (m) 10 0.1 0.0106 2 2 0 – 3 1 0.1 0.0106 1.5 1.8 3 – 4 0.1 0.1 0.0106 1.05 1.4 4 – 5
- 9. Workshop on coupled hydrological modeling – Padova – September 2015 Results – homogeneous configuraIons Section 1 – x = 150 m Section 1 – x = 150 m Section 2 – x = 300 m Section 3 – x = 425 m
- 10. Workshop on coupled hydrological modeling – Padova – September 2015 Results – Random saturated conducIvity Section 1 – x = 150 m Section 2 – x = 300 m Section 3 – x = 425 m Section 1 – x = 150 m
- 11. Workshop on coupled hydrological modeling – Padova – September 2015 Inter-‐comparison with CATHY • Pan et al, Journal of Hydrology, accepted • IniIal / Boundary condiIons : – IniIal water table 1m below land surface – Imposed discharge upstream / No-‐flow for the subsurface 1D link cons+tuing the river CATHY model VIC model 10 m deep aquifer Sx = 0.05 2D meshes cons+tuing the river
- 12. Workshop on coupled hydrological modeling – Padova – September 2015 Inter-‐comparison with CATHY
- 13. Workshop on coupled hydrological modeling – Padova – September 2015 TentaIve applicaIon – Strengbach catchment
- 14. Workshop on coupled hydrological modeling – Padova – September 2015 Conclusions • Reminder – Dimensionally-‐reduced subsurface model seems a relevant approach – First tests and applicaIons of the coupled model are not flawed • LimitaIons – HydrostaIc pressure profile – No 2D overland flow – Impossible to describe Horton’s runoff • PerspecIves – Add 2D overland flow – Work on transport processes – Coupling with vegetaIon/atmosphere models for beer spaIally and Imely distributed source terms
- 15. Workshop on coupled hydrological modeling – Padova – September 2015 Proposal for the next workshop (2017?) ! To be held in Strasbourg?