Dual-Permeability Model and Atmospheric Boundary Condition with Surface
Water Layer
Jirka Šimůnek
Department of Environmental Sciences
University of California Riverside

Example presented in Figure 5 of Šimůnek et al. (2003) was rerun with the atmosphericboundary condition, which considered the surface water layer. In this example we assume thatwater initially infiltrates into the matrix at a rate that is equal to precipitation. Once the ponding
is reached, the boundary condition is switched from the flux boundary condition to the variable
pressure head boundary condition, and all excess water (difference between precipitation andinfiltration) accumulates at the surface until the thickness of the water layer reaches themaximum allowed value (1 cm). Only at this moment the excess water starts flowing into thefracture domain. Once precipitation stops, the thickness of the water layer decreases below thecritical thickness (1 cm), and flow into the fracture domain stops. Water accumulated at the soil
surface infiltrates into the matrix domain, until all water is used up.

1.2

Thickness [cm]10.8

Surface Water Layer

0.6
0.4
0.2
00

0.1

0.2

0.30.4

Time [d]Figure 1 shows the thickness of the surface water layer. It is shown that ponding develops atabout 0.005 d, the critical thickness of the water layer (1 cm) when water starts flowing to thefracture domain is reached at about 0.036 d. The critical thickness of the water layer remains tillthe end of the precipitation event (i.e., 0.08 d). After that, water keeps on infiltrating into thematrix domain (not anymore to the fracture domain since the thickness of the water layer issmaller than the critical value) until 0.3 d, when all water infiltrates.

60

Flux [cm/d]

50
Precipitation
Infiltration
Fracture FluxMatrix Flux
Mass Transfer

40302010000.1

0.2

0.3

0.4

Time [d]Figure 2 shows various fluxes. The precipitation event lasts for 0.08 d and has an intensity of 50
cm/d (blue line). After ponding is reached at about 0.005 d, infiltration flux into the matrix(black line) decreases dramatically. The excess water, i.e., the difference between precipitationand infiltration is stored in the surface water layer (see Figure 1, which shows increasing
thickness of the water layer). After the critical thickness of the surface water layer is reached(0.036 d), water starts flowing into the fracture domain (red line). The overall infiltration (greenline), i.e., infiltration into both matrix and fracture domains, is again equal to precipitation. Once
precipitation stops, the thickness of the surface water layer decreases below the critical value andflow into the fracture domain stops. However, infiltration into the matrix domain continues until
all water from the surface water layer infiltrates (0.3 d). Once water starts infiltrating into thefracture domain, there is also the mass transfer between the fracture and matrix domains (dashedline).

4.5
Cumulative Flux [cm]

43.5
3
2.5
2
1.5

Cumulative Precipitation
Cumulative Infiltration
Fracture FluxMatrix Flux
Mass Transfer

10.5
000.2

0.4

0.6

Time [d]Figure 3 shows cumulative fluxes and it basically provides the same information as Figure 2.
Notice the parallel blue and green lines representing cumulative precipitation and infiltration.
The difference between these two lines reflect the amount of water in the surface water layer.
The difference increases between 0.005 and 0.036 d, i.e., between ponding and when the critical
thickness of the surface water layer is reached. It remains constant after that until precipitation
stops. Then the difference decreases as water infiltrates into the matrix domain. Note again, thatinfiltration into the fracture domain is active only when the thickness of the surface water layer isat its critical level.
Šimůnek, J., N. J. Jarvis, M. Th. van Genuchten, and A. Gärdenäs, Review and comparison ofmodels for describing non-equilibrium and preferential flow and transport in the vadose zone,
Journal of Hydrology, 272, 14-35, 2003.
Šimůnek, J. and M. Th. van Genuchten, Modeling nonequilibrium flow and transport with
HYDRUS, Vadose Zone Journal, doi:10.2136/VZJ2007.0074, Special Issue “Vadose Zone
Modeling”, 7(2), 782-797, 2008.