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Sylvain Weill

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A dimensionally-reduced approach for coupled river-subsurface flow modeling

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Sylvain Weill

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 12. Workshop  on  coupled  hydrological  modeling  –  Padova  –  September  2015   Inter-­‐comparison  with  CATHY  
  13. 13. Workshop  on  coupled  hydrological  modeling  –  Padova  –  September  2015   TentaIve  applicaIon  –  Strengbach  catchment  
  14. 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. 15. Workshop  on  coupled  hydrological  modeling  –  Padova  –  September  2015   Proposal  for  the  next  workshop  (2017?)  !  To  be  held  in   Strasbourg?    

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