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
( ) ( )( )( ). .s s s
b b b
z z z
w wz z z
ShS S dz h q dz
t tdz∂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 hS S dz S S dz ht t t t
h q dz
dz
dz
∂θ ∂ ∂θ ∂⎛ ⎞ ⎛ ⎞+ θ + θ ∇ − θ ∇⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠
∇ ∇
+ +
θ
+
=−
∫ ∫ ∫
∫ ∫
K
K
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”
• 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
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
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
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
Workshop on coupled hydrological modeling – Padova – September 2015
TentaIve applicaIon – Strengbach catchment
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 be\er spaIally and Imely
distributed source terms