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

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?