Dear all,

I have a lot of experiences with HYDRUS-1D, but I am relatively new to HYDRUS-2D. Now I am struggling with the correct boundary conditions for an, I think at leat, relative simple problem:

I have a vertical west-east cross section through saturated/unsaturated zone, 650 m long, 3 m thick. There is a (nearly) constant water table of 1.2 m below surface on the western and 0.8 m below surface on the eastern side. The precipitation is about 600 mm/a. This should result in a downward vertical water flow in the unsaturated zone and a slow east-west flow in the saturated zone. Final aim of the simulation is to slightly rise the water table with the help of a impermeable subsurface wall somewhere close to the western boundary which reaches from the bottom of the system up to about 20 cm below the surface.

My problem is now to decide about the the correct boundary conditions:

One option could be: Atmospheric bc at the surface, constant head of 1.8 m with hydraulic equilibrium for all nodes at the eastern boundary, constant head of 2.2 m with hydraulic equilibrium for all nodes at the western boundary, no-flux boundary at the bottom.

Another option could be: Atmospheric bc at the surface, free drainage for all nodes at the eastern and western boundary (free drainage is usually used for lower bc, does it make sense for a vertical boundary?), constant head at the bottom with heads of 2.2 m at the western boundary gradually decreasing to 1.8 m at the eastern boundary. This option, however, seems to be mathematically unstable as the program crashes.

Any help/comment would be highly appreciated! Thank you!

Rudi

## Boundary conditions

### Re: Boundary conditions

This would be fine if you want to fix the position of the water table at the left and right side of the domain (although it may be better to fix this only below the water table (positive pressures) and not in the unsaturated zone, where you may allow changes of pressure heads in response to surface fluxes). However, if you want to allow the water table to fluctuate in response to surface fluxes, you may consider using the gradient BC, which can be activated using the “Boundary Conditions Options” command (and window) and the Edit bar (when BCs are displayed). Then you can specify a gradient parallel with the slope, while GWT is allowed to move up and down. I have implemented this BC for similar problems as yours. J.

### Re: Boundary conditions

Jirka,

thank you very much for the quick and helpful reply. I do understand now the gradient boundary condition and it is working nicely. However, I still have a question with respect to interpretation of the results.

I use a cross vertical section, 650 m long and 3 m thick, with a realistic gradient of 0.0003 m/m, the whole system consists of a standard sand. The recharge (precipitation minus evaporation) is about 200 mm/a. I use a constant flux at the surface (5e-4 m/day corresponding to 200 mm/a), a gradient bc at the left and right side (gradient 0.0003) and a no flux bc at the bottom. As a result, I get a groundwater surface with the given slope, perfect. However, I would expect that after some time (depending on initial heads and recharge), there should be a constant groundwater surface with time. Using standard sand values, however, the profile becomes completely saturated after a few years. Only increasing ks for the sand from about 7 m/day to unreasonable high values of >500 m/day yields the expected results of a constant sloped water table.

I interpret the results, that the recharge on a 650 m transect is higher than the possible lateral flow in a sand which results in steadily increasing water table. Therefore, in reality, there must be some vertical flux leaving the system at the bottom and the no flux lower bc cannot be correct.

If I apply a constant flux at the bottom bc exactly as high as the average annual recharge, I get a constant and sloped groundwater surface. However, I am interested in changes in groundwater surface in the course of the year. Therefore, I applied a constant flux lower bc (200 mm/year) and a time variable flux upper bc (monthly varying fluxes, high in winter and low in summer). This results in a varying groundwater surface in the course of the year. Would this make sense? Would another lower bc would be better? E.g. deep drainage? But where to get the parameters from?

Thank you for a short comment on this. Any help would be highly appreciated!

Rudi

thank you very much for the quick and helpful reply. I do understand now the gradient boundary condition and it is working nicely. However, I still have a question with respect to interpretation of the results.

I use a cross vertical section, 650 m long and 3 m thick, with a realistic gradient of 0.0003 m/m, the whole system consists of a standard sand. The recharge (precipitation minus evaporation) is about 200 mm/a. I use a constant flux at the surface (5e-4 m/day corresponding to 200 mm/a), a gradient bc at the left and right side (gradient 0.0003) and a no flux bc at the bottom. As a result, I get a groundwater surface with the given slope, perfect. However, I would expect that after some time (depending on initial heads and recharge), there should be a constant groundwater surface with time. Using standard sand values, however, the profile becomes completely saturated after a few years. Only increasing ks for the sand from about 7 m/day to unreasonable high values of >500 m/day yields the expected results of a constant sloped water table.

I interpret the results, that the recharge on a 650 m transect is higher than the possible lateral flow in a sand which results in steadily increasing water table. Therefore, in reality, there must be some vertical flux leaving the system at the bottom and the no flux lower bc cannot be correct.

If I apply a constant flux at the bottom bc exactly as high as the average annual recharge, I get a constant and sloped groundwater surface. However, I am interested in changes in groundwater surface in the course of the year. Therefore, I applied a constant flux lower bc (200 mm/year) and a time variable flux upper bc (monthly varying fluxes, high in winter and low in summer). This results in a varying groundwater surface in the course of the year. Would this make sense? Would another lower bc would be better? E.g. deep drainage? But where to get the parameters from?

Thank you for a short comment on this. Any help would be highly appreciated!

Rudi

### Re: Boundary conditions

Rudi,

You can make simple “back-of-the-envelope” calculations to see how much water the profile can transfer laterally using the Darcy’s law, conductivity, thickness of the profile, and gradient.

Bottom BC: You may want to use the Deep Drainage BC since then the bottom flux can vary depending on the position of the BC (higher for higher and vice versa). It should be easy to adjust the two coefficients of the deep drainage functions based on the fluxes that you want to impose (starting with the constant flux you use now and then selecting some other one for another position of GWT).

J.

You can make simple “back-of-the-envelope” calculations to see how much water the profile can transfer laterally using the Darcy’s law, conductivity, thickness of the profile, and gradient.

Bottom BC: You may want to use the Deep Drainage BC since then the bottom flux can vary depending on the position of the BC (higher for higher and vice versa). It should be easy to adjust the two coefficients of the deep drainage functions based on the fluxes that you want to impose (starting with the constant flux you use now and then selecting some other one for another position of GWT).

J.