Sylvain Weill

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)


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


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


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


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 =∂


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

⎛ ⎞∂ ⎜ ⎟−∇ ∇ + =⎜ ⎟∂ ∇ +⎝ ⎠


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


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


Results – homogeneous configuraIons

Section 1 – x = 150 m Section 1 – x = 150 m



Results – Random saturated conducIvity

Section 1 – x = 150 m


Section 1 – x = 150 m


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


Inter-‐comparison with CATHY


TentaIve applicaIon – Strengbach catchment


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


Proposal for the next workshop (2017?) ! To be held in Strasbourg?

Science

Sylvain Weill