This document discusses preparatory work for coupling reactive solute transport modeling with flow modeling in the Cathy model. The objectives are to develop a 3D coupled surface and subsurface flow and reactive solute transport model based on Cathy, validate it using field data from two hillslopes in France, and upscale the model from hillslope to catchment scale. An existing subsurface flow model (Cathy) and solute transport model (Tran3d) will be merged to allow modeling of non-steady state cases. The merged model will be validated using two test cases from literature and applied to a site in Beaujolais, France.

1. 1
Modeling reactive solute transport
coupled with flow in Cathy :
preparatory work.
Laura Gatel (Irstea Lyon, France)
23 septembre 2015

2. 2
Context
Flow and solute pathways in agricultural hillsopes are complex to
precisly caracterize, particularly for what concerns surface/subsurface
exchanges and lateral transfers.
Modelisation can help, and in order to obtain accurate results on those
kind of domains, the use of a physically-based model is required.
Study site at the Morcille
catchment (Beaujolais)
First work centered on vagatative buffer strip zones :
Those areas are a way to limit solute transfers from the field
to aquatic environments and particularly activ for what
concerns water infiltration.
→ About the influence of soil heterogeneity on surface and
subsurface flow
Example of 3 saturated conductivity statistical fields
Generation of statistical fields with variable
characteristics (correlation, enforcement
with measured conductivity values, ... )
Comparison of the runoff and
subsurface patways with field
data on three events
→ Results are very sensitive to the conductivity dictributions
→ Generated hydrodynamic parameters with enforcement are quite close to data
→ Need to take into account microtopography

3. 3
Objectives
3-years PhD objectives :
● To develop a coupled surface / surbsurface flow and solute reactive transport model in 3D
based on the Cathy model.
● Validate the model at the hillslope scale with a global sensitivity analysis and the comparison
with field data (large database from Irstea Lyon on two hillslopes of the Morcille catchment,
Beaujolais, France)
● Upscaling from hillslope to catchment
INRS summer 2015 session obectives :
● Merge a calculation flow model and a reactive transport model
● Compare the results of this new model with two litterature examples and control the mass
balance.

4. 4
Existing tools
Cathy flow
Coupled subsurface flow (FLOW3D)
and surface routing
(SURF_ROUTE) model
Variably saturated flow
3D
subsurface calculation : finite
elements (FLOW3D)
Tran3d
Solute transport model with decay
and linear sorption
Variably saturated flow
3D
Advection, sorption and decay
resolved with finite elements
BUT no flow calculation
→ steady state cases only

5. 5
Context
Flow and solute pathways in agricultural hillsopes are complex to
precisly caracterize, particularly for what concerns surface/subsurface
exchanges and lateral transfers.
Modelisation can help, and in order to obtain accurate results on those
kind of domains, the use of a physically-based model is required.
Study site at the Morcille
catchment (Beaujolais)
First work centered on vagatative buffer strip zones :
Those areas are a way to limit solute transfers from the field
to aquatic environments and particularly activ for what
concerns water infiltration.
→ About the influence of soil heterogeneity on surface and
subsurface flow
Example of 3 saturated conductivity statistical fields
Generation of statistical fields with variable
characteristics (correlation, enforcement
with measured conductivity values, ... )
Comparison of the runoff and
subsurface patways with field
data on three events
→ Results are very sensitive to the conductivity dictributions
→ Generated hydrodynamic parameters with enforcement are quite close to data
→ Need to take into account microtopography

6. 6
Method
- Two study cases from the
literature (Gureghian 1983
and Huyakorn et al. 1985)
Merging of the two models
Validation
Application to a real hillslope
(Beaujolais, France)
Massbalance
calculation

7. 7
Merging of the two model
Merged model
- Initialisation of surface and flow calculation
- Initialisation of reactive transport calculation
Beginning of the time loop
- Surface flow calculation
- Subsurface flow calculation
Backstepping if necessary
- Reactive transport calculation (only one
resolution for advection, sorption and decay)
End of the time loop
Tran3d :
- Initialisation of reactive transport calculation
- Integration of steady-state results
Beginning of the time loop
- Reactive transport calculation (only one
resolution for advection, sorption and decay)
End of the time loop
Cathy flow :
- Initialisation of surface and flow calculation
Beginning of the time loop
- Surface flow calculation
- Subsurface flow calculation
End of the time loop
At each time step, reactive transport calculation is based on the flow
calculation results : the merging allows the study of no-steady state cases
● At each step, flow and transport are calcultated with the same Δt (if necessary, backsteping occurs after
subsurface flow and before transport)
● Surface transport isn't take into account.

8. 8
Validation
Test case 1 (Huyakorn et al. 1985) : case description
Transport of non-conservative solute in a unsaturated soil.
3D mesh as modelised in the merged model
(surface of 10 cm * 15 cm and 10 cm deep)
with steady-state pressure in the domain.
Boundary conditions used for the test case.
2D mesh (15 cm wide and 10 cm deep).
Reactive transport :
Dispersion αL
= 1 cm αT
= 0
Diffusion 0,01 cm²/d
Sorption Rd = 2
Decay 0,001 d-1

9. 9
Validation
Tran3d
Mergedmodel
0,053 d (1 h 15 min)0,165 d (4 h) 0,508 d (12 h)
Test case 1 (Huyakorn et al. 1985) : results
Concentration contours
Mass balance :
For each time step of this run, mass balance
error stayed between 0,01 % and 1 %

10. 10
Validation
Vertical concentration
profiles at x = 3 cm and
three different times
Horizontal concentration
profiles at z = 10 cm and
three different times
t = 0,053 d
t = 0,165 d
T = 0,508 d
Tran3dMerged model
Test case 1 (Huyakorn et al. 1985) : results
Relative concentration

11. 11
Validation
Test case 2 (Gureghian 1983) : case description
Flow and transport in a ditch-drained aquifer with incident steady rainfall and infiltration of solute
3D mesh as modelised in the merged model
(surface of 10 cm * 15 cm and 10 cm deep)
with steady-state pressure in the domain.
→ 176 nodes for the plan (XZ)
Boundary conditions used for the test case.
2D mesh ( 100 cm wide and 50 cm deep).
→ 176 nodes
The mesh is not exactly reproduced, because
Cathy flow does not allow unregular mesh.
Reactive transport :
Dispersion αL = 0,5 cm αT = 0,1 cm
Diffusion 1e-5 cm²/d
Sorption -
Decay -

12. 12
Validation
Test case 2 (Gureghian 1983) : results
Concentration contours
Tran3dCombined model
15 days
45 days

13. 13
Validation
Test case 2 (Gureghian 1983) : results
Concentration contours
Tran3dMerged model
→ Little differences observed between tran3d and merged model results in the shape of the non-zero
concentration zone.
In this case, the slightly different used mesh could explain this variations.
90 days
120 days

14. 14
Validation
Test case 2 (Gureghian 1983) : results
Mass balance
Inside mass
Entering mass
Exiting mass
d = 15
Solute infiltartion stops
d ~ 70
Solute shape reaches
seepage faces
If we continue the run until 600 d ...

15. 15
Discussion
Even if there is little unexplained differences in the results of case 1, and inconsistent mass
balance for seepage faces, the coupled model gives good results on those two simple examples.
But in other situations, when concentration evolutions are less « smooth » (less or no dispersion
or diffusion for example), the model becomes unstable and the user have to carrefully choose the
time stepping to avoid concentration explosions.
→ It will not be enough stable to modelise complex hillslopes caracterized by important
heterogeneity (with no string conditions on mesh or time steps)
Solution : separate advection and reaction parts and calculate advection as finite volumes (see
S. Weill et al. 2011).

16. 16
Perspectives
Short-term objective :
From the last version of Cathy with non-reactive transport (probably Carlotta's
version with velocity fields reconstruction), integrate sorption and decay equations.
Construction scheme of the last version of transport on Cathy :
Initialisation
Beginning of the time loop
Surface flow
Surface transport
Subsurface flow
Subsurface transport
- advective part → finite volume
- reactive part (for now, only dffusion and dispersion) → finite elements
End of the time loop
Addition of linear sorption
and first order decay

17. 17
Perspectives
Mid-term objective :
● Validation :
1- Apply the new model to a hillslope (Morcille's
catchment, Beaujolais). The site is instrumented since more
than a decade → a large database to compare with the model.
2- Global sensitivity analysis
• Upscaling :
Apply the model to the entire Morcille catchment
and compare results with actual data (all in all 3
sites instrumented sites on the catchment).
Rabiet et al. (2015)
Boivin(2007)
St-Joseph site on the Morcille Catchment

18. 18
Thank you for your attention !
References :
Camporese M., Paniconi C., Putti M., and Orlandini S. (2010). Surface and subsurface flow modeling with path-based runoff routing, boundary
condition-based coupling, and assimilation of multisource observation data. Water Resources Research, 46(2).
Gambolati G., Pini G., Putti M. and Paniconi C. (1994). Finite element modeling of the transport of reactive contaminants in variably saturated soils
with LAE and non LEA sorption. Environmental Modeling vol. 2, ch. 7, pp. 173-212.
Paniconi C., Wood E. (1983). A detailed model for simulation of catchment scale subsurface hydrologic processes. Water resources Research,
29(6):1601-1620.
Weill S., Mazzia A., Putti., Paniconi C. (2011). Coupling water flow and solute transport into a physically-based surface-subsurface hydrological
model. Advances in Water Resources vol 34, pp 128-136.