carlotta scudeler

Hydrological modeling of coupled surface-subsurfaceflow and transport phenomena: the

CATchment-HYdrology Flow-Transport (CATHY_FT)model

Workshop on coupled hydrological modeling

Carlotta Scudeler, Claudio Paniconi, Mario Putti

Padua, 23-09-2015

�� INTRODUCTION CATHY_FT MODEL PERFORMANCE

Many challenges in improving and testing current state-of-the-artmodels for integrated hydrological simulation

Not so many models address both flow and transport interactionsbetween the subsurface and surface

I am presenting the CATchment-HYdrology Flow-Transportmodel and I am showing its performance under hillslopedrainage, seepage face, and runoff generation

C Scudeler Padua Workshop, Padua, 23-09-2015 2/17

II. CATchment HYdrology Flow

and Transport model

INTRODUCTION�� CATHY_FT MODEL PERFORMANCE

CATchment HYdrology (CATHY) model

Sw Ss∂ψ∂t + φ∂Sw

∂t = −∇ · q + qss

∂Q∂t + ck

∂Q∂s = Dh

∂2Q∂s2 + ck qs

∂θc∂t = ∇ · [−qc + D∇c] + qtss

∂Qm∂t + ct

∂Qm∂s = Dc

∂2Qm∂s2 + ctqts



CATHY Flow-Transport (CATHY_FT) model


∂t = −∇ · q + qss

∂Q∂t + ck

∂Q∂s = Dh

∂2Q∂s2 + ck qs

∂θc∂t = ∇ · [−qc + D∇c] + qtss

∂Qm∂t + ct

∂Qm∂s = Dc

∂2Qm∂s2 + ctqts



Numerical model

Richards’ equation (subsurface flow)


∂t = −∇ · q + qss

∂Q∂t + ck

∂Q∂s = Dh

∂2Q∂s2 + ck qs

∂θc∂t = ∇ · [−qc + D∇c] + qtss

∂Qm∂t + ct

∂Qm∂s = Dc

∂2Qm∂s2 + ctqts

Numerics: P1 Galerkin finite element (FE) model in space and implicit finite differencemodel in time

1. Nodal solution for ψ→ continuous and piecewise linear

2. Elementwise post-computation of the velocity field q from direct application ofDarcy’s law→ elementwise constant, normal flux discontinous and notmass-conservative across every face

3. Larson-Niklasson (LN) velocity field q reconstruction



Numerical model

ADE equation (subsurface transport)


∂t = −∇ · q + qss

∂Q∂t + ck

∂Q∂s = Dh

∂2Q∂s2 + ck qs

∂θc∂t = ∇ · [−qc + D∇c] + qtss

∂Qm∂t + ct

∂Qm∂s = Dc

∂2Qm∂s2 + ctqts

Numerics: High resolution finite volume (for -∇ · qc advective step) and FE (for∇ · (D∇c) dispersive step) combined with a time-splitting technique

1. Advective time-explicit step for the elementwise c

2. Mass-conservative element→node c reconstruction

3. Dispersive time-implicit step for the nodal c

4. Mass-conservative node→element c reconstruction



Numerical model

Surface flow and transport equations


∂t = −∇ · q + qss

∂Q∂t + ck

∂Q∂s = Dh

∂2Q∂s2 + ck qs

∂θc∂t = ∇ · [−qc + D∇c] + qtss

∂Qm∂t + ct

∂Qm∂s = Dc

∂2Qm∂s2 + ctqts

Numerics: Explicit finite difference scheme in space and time for both surface flow andtransport solution



Coupling in CATHY_FT

1 Surface flow 2 Surface transport 3 Subsurface flow 4 Subsurface transport

qsk qts

k

Qk+1,hk+1 Qmk+1,csurf

k+1 ψk+1,qk+1

BC switching

ck+1

BC switchingqssk+1

Atmospheric BCk+1

qssk+1

qtssk+1

qtssk+1

qsk+1 qts

k+1





qsk qts

k


k+1 ψk+1,qk+1

BC switching

Atmospheric BCk+1

ck+1

BC switchingqssk+1

qssk+1

qtssk+1

qtssk+1

qsk+1 qts

k+1





qsk qts

k


k+1

Atmospheric BCk+1

ψk+1,qk+1

BC switching

ck+1

BC switchingqssk+1

qssk+1

qtssk+1

qtssk+1

qsk+1 qts

k+1





qsk qts

k

Qk+1,hk+1

Atmospheric BCk+1

Qmk+1,csurf

k+1 ψk+1,qk+1

BC switching

ck+1

BC switchingqssk+1

qssk+1

qtssk+1

qtssk+1

qsk+1 qts

k+1




1 Surface flow 2 Surface transport 3 Subsurface flow

Atmospheric BCk+1

4 Subsurface transport

qsk qts

k


k+1 ψk+1,qk+1

BC switching

ck+1

BC switchingqssk+1

qssk+1

qtssk+1

qtssk+1

qsk+1 qts

k+1



Model accuracy

Ability of the model to conserve mass



Model accuracy


Sw Ss∂ψ

∂t+ φ

∂Sw

∂t= −∇ · q + qss

→Mass-conservative solutionachieved solving the equation inits ψ− Sw mixed form [Celia et al.,1990]



Model accuracy


∂θc∂t

= ∇ · [−qc + D∇c] + qtss→

HRFV mass-conservative solutionif q is mass-conservative.



Model accuracy


∂θc∂t

= ∇ · [−qc + D∇c] + qtss→

HRFV mass-conservative solutionif q is mass-conservative.P1 Galerkin q is notmass-conservative



Model accuracy


∂θc∂t

= ∇ · [−qc + D∇c] + qtss→


To make q mass-conservative:

change the numerical scheme from FE =⇒ High computational costto Mixed Hybrid Finite Element (MHFE)

or

add mass-conservative velocity field =⇒ Low computational costreconstruction



Model accuracy


∂θc∂t

= ∇ · [−qc + D∇c] + qtss→


To make q mass-conservative:

change the numerical scheme from FE =⇒ High computational costto Mixed Hybrid Finite Element (MHFE)

or

add mass-conservative velocity field =⇒ Low computational costreconstruction

In CATHY_FT: FE =⇒ FE+Larson-Niklasson (LN) post-processing technique



Larson-Niklasson technique

Domain discretized by ne tetrahedral elements and n nodes

At each time step

qe is the non mass-conservative element velocity

Rei is the element residual associated to each node i

~n is the vector normal to each element faces

qeLN is the mass-conservative element velocity





At each time step

CATHY solution

· ψ nodal solution· qe non mass-conservative

where:qe is the non mass-conservative element velocity








At each time step

CATHY solution


· Rei

· ~q·~n









At each time step

CATHY solution


· Rei

· ~q·~n Larson-Niklasson

· new ~qLN ·~n· new mass-conservative qe

LN







LN velocity reconstruction results

1. Convergent streamlines towards an outlet

2. High streamline curvatures due to heterogeneity





D=50 mD=0 m

qN=0 m/scin=1





0 1 2 3 4Time (h)

25

50

75

100

Mass(%)

Mst- P1 Mout- P1 Err - P1

Mst → mass storedMout → cumulative mass flown out

Min → mass initially in the systemErr=Min − Mst − Mout





0 1 2 3 4Time (h)

25

50

75

100

Mass(%)

Mst- P1 Mout- P1 Err - P1

Mst → mass storedMout → cumulative mass flown out

Min → mass initially in the systemErr=Min − Mst − Mout

At the end Mout 6= Min ⇒ P1 Galerkin q exits from the 0 flux boundary





0 1 2 3 4Time (h)

25

50

75

100

Mass(%)

Mst- LN M

out- LN





0 1 2 3 4Time (h)

25

50

75

100

Mass(%)

Mst- LN M

out- LN

Velocities reconstructed with LN do not violate the 0 flux boundaries






D=50 mD=0 m

qN=0 m/scin=1

Ks (m/s)2x10-4

2x10-12






0 2 4 6 8 10Time (h)

Mst- LN M

stf- LN

0 2 4 6 8Time (h)

25

50

75

100

Mass(%)

Mst- P1 M

stf- P1

Mstf → mass stored in the unpermeable soil Mst → mass stored






0 2 4 6 8 10Time (h)

Mst- LN M

stf- LN

0 2 4 6 8Time (h)

25

50

75

100

Mass(%)

Mst- P1 M

stf- P1

Mstf → mass stored in the unpermeable soil Mst → mass stored

At the end for P1 Mstf = Mst 6=0 ⇒ Solute mass get trapped in the unpermeable soil

At the end for LN Mstf = Mst =0 ⇒ Solute mass slightly crosses the unpermeable soil


III. Testing CATHY_FT at the

Landscape Evolution

Observatory (LEO)

INTRODUCTION CATHY_FT�� MODEL PERFORMANCE

The Landscape Evolution Observatory (LEO)

LEO, Biosphere 2, Oracle,Arizona, U.S.A.

3 convergent landscapes30 m long, 11.5 m wide

dense sensor and samplernetwork

rainfall simulator (3-45mm/h)

View of one of the threehillslopes from top

Tipping bucket for low seepageface flow

Rainfall simulator



The Landscape Evolution Observatory (LEO)

LEO, Biosphere 2, Oracle,Arizona, U.S.A.

3 convergent landscapes30 m long, 11.5 m wide

dense sensor and samplernetwork

rainfall simulator (3-45mm/h)

In Figure:

View of one of the threehillslopes from top

Tipping bucket for low seepageface flow

Rainfall simulator



Test case

Computational domain60 x 22 grid cells

30 layers; more refined close to thesurface and at bottom



Test case



Material model:

homogeneity with Ks=1×10−4 m/sand φ=0.39

Van Genuchten parametersnVG=2.26, θres=0.002, ψsat =-0.6 m



Test case



Material model:



Model performance for Subsurface-Surface flow and transport



Test case



Material model:




1) Rainfall



Test case



Material model:




1) Rainfall2) Seepage face flow



Test case



Material model:





3) Drainage under variably saturated conditions



Test case



Material model:





3) Drainage under variably saturated conditions4) Surface flow



Test case

Seepage Face

Outlet



Material model:





3) Drainage under variably saturated conditions4) Surface flow



Input

Water and solute mass inflow Cumulative volume and mass

0.005

0.01

0.015

Qr(m

3 /s)

0 6 12 18 24 30 36 42 48Time (h)

0.005

0.01

0.015

Qm(mg/s)

15

30

45

60

Vr(m

3 )

0 6 12 18 24 30 36 42 48Time (h)

15

30

45

60

Min(mg)

Initial conditions: 119 m3 of water initially present in the system (water table set at 0.4 mfrom bottom) and 0 solute mass

Flow input : pulse of homogenous rain Qr =0.012 m3/s for 1 h→ cumulative volumeinjected Vr =40.4 m3

Transport input : solute injection with c=1 mg/m3 of rain pulse→ mass inflow Qm=0.012mg/s and cumulative mass injected Min=40.4 mg



Input


0.005

0.01

0.015

Qr(m

3 /s)

0 6 12 18 24 30 36 42 48Time (h)

0.005

0.01

0.015

Qm(mg/s)

Qr=0.012 m3/s

15

30

45

60

Vr(m

3 )

0 6 12 18 24 30 36 42 48Time (h)

15

30

45

60

Min(mg)

Vr=40.4 m3






Input


0.005

0.01

0.015

Qr(m

3 /s)

0 6 12 18 24 30 36 42 48Time (h)

0.005

0.01

0.015

Qm(mg/s)Qm=0.012 mg/s

15

30

45

60

Vr(m

3 )

0 6 12 18 24 30 36 42 48Time (h)

15

30

45

60

Min(mg)

Min=40.4 mg






Results

Water balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

Vr − ∆Vst − Vsf − Vout = Flow Error

Min − ∆Mst − Msf − Mout = Transport Error



Results

Water balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

Vr=100% 4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

Vr − ∆Vst − Vsf − Vout ⇒100




Results

Water balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

-48.17%∆Vst=

4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

Vr − ∆Vst − Vsf − Vout ⇒100+48.17




Results

Water balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

Vsf=77.62%

4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

Vr − ∆Vst − Vsf − Vout ⇒100+48.17-77.62




Results

Water balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

Vout=70.58%

4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

Vr − ∆Vst − Vsf − Vout ⇒100+48.17-77.62-70.58=o(0.01)%




Results

Mass balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

Min=100%

Vr − ∆Vst − Vsf − Vout ⇒100+48.17-77.62-70.58=o(0.01)%

Min − ∆Mst − Msf − Mout ⇒100



Results

Mass balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

∆Mst=28.62%

Vr − ∆Vst − Vsf − Vout ⇒100+48.17-77.62-70.58=o(0.01)%

Min − ∆Mst − Msf − Mout ⇒100-28.62



Results

Mass balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

Msf=6.86%

Vr − ∆Vst − Vsf − Vout ⇒100+48.17-77.62-70.58=o(0.01)%

Min − ∆Mst − Msf − Mout ⇒100-28.62-6.86



Results

Mass balance

4080

Vr(%)

-4004080

∆Vst(%)

4080

Vsf(%)

0 6 12 18 24 30 36 42 48Time (h)

4080

Vout(%)

4080

Min(%)

10203040

∆Mst(%)

5

10

Msf(%)

0 6 12 18 24 30 36 42 48Time (h)

306090

Mout(%)

Mout=64.42%

Vr − ∆Vst − Vsf − Vout ⇒100+48.17-77.62-70.58=o(0.01)%

Min − ∆Mst − Msf − Mout ⇒100-28.62-6.86-64.42=o(0.1)%


INTRODUCTION CATHY_FT MODEL PERFORMANCE

Conclusions

1. P1 Galerkin solution is mass-conservative while the velocities arenot; this causes problems for transport simulations. This requires apost-processing technique to ensure mass-conservation

2. Results so far indicate that LN reconstructed velocities are asaccurate as MHFE velocities and achieve much better computationalefficiency

3. Exchange processes in integrated surface-subsurface models arehighly complex and need to be carefully formulated and resolved


Thanks for your attention

carlotta scudeler

Science