Approximate expansions for water infiltration into dual permeability soils

The understanding of hydrological processes requires the investigation of preferential flows. In particular, the infiltration compartment is strongly affected by preferential flows. Recently, Lassabatere et al. (2014) proposed a model for the analytical modelling of the infiltration impacted by preferential flow. These authors extended the model developed by Haverkamp et al. (1994) for single permeability soils to the case of dual permeability soils. However, this model remains implicit, requiring an inversion procedure for the quantification of the bulk cumulative infiltration. Such an implicit feature prevents from direct computation and may annoy any fellow who wants a direct and simple computation procedure. In this paper, we develop two approximate expansions for both transient and steady states. For that, we use the expansions proposed by Haverkamp et al. (1994) for single permeability systems. These expansions are written for each compartment of the dual permeability soils, i.e. the matrix and the fast-flow regions and are combined for the computation of the bulk infiltration. After formulation of these expansions, these are assessed in terms of their capability to accurately reproduce the complete implicit model. Their validity time intervals are also determined and discussed. The main limitation for the use of these expansions results from the fact that the time intervals that define the transient and steady states are contrasted between the matrix and the fast-flow regions. However, some domain of validity can be defined allowing the use of these approximate expansions.Haverkamp, R., Ross, P. J., Smettem, K. R. J. and Parlange, J. Y.: 3-Dimensional analysis of infiltration from the disc infiltrometer .2. Physically-based infiltration equation, Water Resour. Res., 30(11), 2931–2935, 1994.Lassabatere, L., Angulo-Jaramillo, R., Soria-Ugalde, J. M., Simunek, J. and Haverkamp, R.: Numerical evaluation of a set of analytical infiltration equations, Water Resour. Res., 45, W12415, doi:doi:10.1029/2009WR007941, 2009.