EGU2020-5172
https://doi.org/10.5194/egusphere-egu2020-5172
EGU General Assembly 2020

# Approximate expansions for water infiltration into dual permeability soils

Laurent Lassabatere et al.

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.

How to cite: Lassabatere, L., Di prima, S., Iovino, M., Bagarello, V., and Angulo-Jaramillo, R.: Approximate expansions for water infiltration into dual permeability soils, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5172, https://doi.org/10.5194/egusphere-egu2020-5172, 2020

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displays version 1 – uploaded on 25 Apr 2020
• CC1: Comment on EGU2020-5172, Horst H. Gerke, 05 May 2020

Dear Laurent and colleagues: Very nice work! It is good and useful to have analytical solutions - still I have not understood how you treat the mass exchange term.

• AC1: Reply to CC1, Laurent Lassabatere, 05 May 2020

dear Horst,

these analytical solutions assume that there is no mass exchange. In fact, in Lassabatere et al. (2014), we demonstrated that the cumulative infiltrations into dual permeability soil did not depend on Ksa (water exchange) and corresponded to that with no exchange. We then considered the easiest case (no exchange) which allowed us to simply add cumulative infiltrations related to each domain. We then obtained a complex formulation  (see Eq. [8] in Lassabatere et al., 2014). In this study, we simplify the expression, by analogy with Haverkamp et al. (1994). All that is really far from reality ;)

Best,

Laurent

Lassabatere, L., Yilmaz, D., Peyrard, X., Peyneau, P. E., Lenoir, T., Šimůnek, J. and Angulo-Jaramillo, R.: New analytical model for cumulative infiltration into dual-permeability soils, Vadose Zone Journal, 13(12), 1–15, doi:, 2014.

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 Resources Research, 30(11), 2931–2935, 1994.