Workshop on coupled hydrological modeling – Padova – September 2015 A dimensionallyreduced model for coupled river subsurface flow modeling Yi Pan, Sylvain Weill , Philippe Ackerer, Frederick Delay Laboratory of Hydrology and Geochemistry of Strasbourg (LHyGeS)
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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)
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
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 be\er 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
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
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
zS h Ssat hhS h h Q with
t h dz
C h dz
h θ
⎧ = +∂ ⎪
+∇ − θ ∇ = ⎨∂ ⎪ + θ
⎩= ∫
∫T
Ksat KT
( )S wS St∂θ
>> θ∂
( )0 1wand St∂θ
= θ =∂
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 whS h h Qt∂
+∇ − θ ∇ =∂
T
( )( )
2 3
1 2. 'hx x r
Man x r
A RA h z l qt N h z
⎛ ⎞∂ ⎜ ⎟−∇ ∇ + =⎜ ⎟∂ ∇ +⎝ ⎠
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
Workshop on coupled hydrological modeling – Padova – September 2015
Dimensionally-‐reduced subsurface model “validaIon”