Modeling cumulative infiltration into dual-permeability soils

Preferential flow is the rule rather than the exception, which questions the applicability of homogeneous models to simulate flows accurately. Gerke and van Genuchten (1993) developed the dual-permeability (DP) approach to account for preferential flow. This approach describes the soil as a combination of the fast-flow and the matrix regions. It defines a set of partial differential equations based on the application of Richards' equation to each region, in combination with an additional equation to govern water exchange between the two regions. In this study, we propose a strategy to model cumulative infiltration into DP soils considering the magnitude of the water exchange between the two regions.

In the absence of water exchange, infiltration can be considered independently in each region (Lassabatere et al., 2014). Consequently, the bulk infiltration at the soil surface equals the sum of the infiltration into the two independent regions weighted by their volumetric fractions. For this reason, the quasi-exact implicit (QEI) analytical model developed by Haverkamp et al. (1994) for single permeability (SP) Darcian soils can be applied to each region, and the two separate infiltrations can be summed to compute the bulk infiltration. The resulting QEI-Σ model was already detailed in Lassabatere et al. (2014). In the case of instantaneous water exchange, the water pressure head equilibrates instantaneously between the two regions. At any water pressure head, the bulk soil water retention and unsaturated hydraulic conductivity equal the combination of these hydraulic functions for the two regions. On a physical basis, the soil behaves as a Darcian soil with bimodal hydraulic functions, and water infiltration can be quantified by solving Richards’ equation considering bimodal hydraulic functions. Consequently, the QEI model can be used with the "bimodal" sorptivity computed from the bimodal hydraulic functions to depict the QEI-S2K model. Between these two limiting scenarios (i.e., zero versus instantaneous water exchange between the two regions), the problem must be solved numerically.

In this study, we modeled water infiltration into DP soils for various scenarios between the two extreme cases of zero and instantaneous water exchange. We used the two limiting models, QEI-Σ and QEI-S2K, to compare the cumulative infiltration for zero versus instantaneous water exchange. We used numerical simulation with HYDRUS-1D to solve the same scenario and compared it with the analytical models. Then, we modeled the cases with intermediate magnitudes of water exchange to characterize the progression from one extreme to the other. We then varied the value of the hydraulic conductivity of the interface between the two regions, with null values corresponding to zero water exchange, and quasi-infinite values corresponding to instantaneous water exchange. Our findings participate in the optimization of direct and inverse modeling procedures for preferential flow and their contributions to water infiltration into soils.

Gerke, H.H., van Genuchten, M.T., 1993. Water Resources Research 29, 305–319.

Haverkamp, R., Ross, P.J., Smettem, K.R.J., Parlange, J.Y., 1994. Water Resources Research 30, 2931–2935.

Lassabatere, L., Yilmaz, D., Peyrard, X., Peyneau, P.E., Lenoir, T., Šimůnek, J., Angulo-Jaramillo, R., 2014. Vadose Zone Journal 13.