Preferential Flow in Hillslope

This last month was partially spent in reviewing Grigoris Anagnostopoulos Ph.D. thesis about subsurface hillslope modelling and landsliding. Among the topics he faced, one of particular interest is the one of preferential flow. This have been largely debated in literature since the 1982 work by German and Beven (great to address the issue, less fundamental in getting a solution, as well as the 2013 recent effort by the same authors).  Grigoris writes:

“Natural soils normally exhibit a high degree of heterogeneity due to macropores, fissures, cracks and root holes, which are the result of soil forming processes and biological activity. The existence of these structural heterogeneities result in the non- uniformity of the pressure potential making the infiltration front to move faster to greater depths using the macropore space without passing through the soil matrix. 

..

Several studies showed that the contribution of preferential flow paths to hillslope water regime and catchment response can be substantial [Weiler and Naef , 2003a, b; Jones, 2010]. “

Here I would add the studies by Flury et al, 1990, and other Juris work (e.g  Godhrati, 1990), Jeff McDonnell [e.g McDonnell, 1990], Andreini and Steenhuis, 1990, to name a few.

What has been elusive for years (and still is) is the way to simulate it [e.g. Simunenk, et al, 2003]. Grigoris gives a simple and clear summary:

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“The simplest way to describe preferential flow is to use Richards’ equation coupled with piecewise continuous soil water retention and hydraulic conductivity functions that take into account the increase in hydraulic conductivity near saturation, due to the existence of macropores [Mohanty et al., 1997; Schaap and van Genuchten, 2005; Børgesen et al., 2006]. “

He also comments:

“This approach, although it is very easy to implement and takes into account successfully the substantial increase in the hydraulic conductivity near saturation, cannot describe the non-equilibrium mechanisms of flow that the existence of macropores implies.

Furthermore … more rigorous approaches for modelling preferential flow through soil have been proposed the last decades, ranging from single-porosity non equilibrium flow models to dual-porosity and dual-permeability models. 

Single porosity non equilibrium models [Ross and Smettem, 2000; Diamantopoulos et al., 2012] make the assumption that water content in not a function of the pressure head and the SWRC in not used any more for its computation. Instead, a kinematic approach is used to describe the water content’s evolution towards equilibrium. 

The implementation of the aforementioned approach in existing numerical codes based on the mixed form of Richards’ equation is easy and straightforward. (N.o.B. - straightforward is usually not so)

Dual-porosity models [Philip, 1968; van Genuchten and Wierenga, 1976] divide the soil media into two distinct domains: the macropore domain and the soil matrix domain. Water is assumed to flow only through the macropores and the soil matrix is used to store and exchange water with the macropore domain without permitting the development of convective flow. 

In dual-permeability models, two separate Richard’s equation are used to simulate water flow through the two distinct pore regions described above [Gerke and van Genuchten, 1993a, b, 1996]. 

The basic drawback of this approach is that it requires the determination of many parameters because of the fact that sepa- rate soil water retention and hydraulic conductivity functions are used for the two pore regions and the interface between them.

During the last decades many hillslope-scale experiments were carried out in several places around the world [Tsuboyama et al., 1994; Uchida et al., 2002; Weiler and Naef, 2003a; Uchida et al., 2005] trying to shed light on many qualitative and quantitative characteristics of preferential flow phenomena and their implications in subsurface flow and catchment response. Several researchers [Beckers and Alila, 2004; Weiler, 2005; Weiler and McDonnell, 2007] proposed simple models for the description of preferential flow, trying to incorporate all the knowledge acquired from the observed characteristics from the field experiments. 

The problem of this kind of approaches arises from their lack of generality, because they are founded and tested with the data from a specific test site, making them not easily transferable to other locations.”

So I thanks Grigoris of the little review and I hope he does not blame me if I reproduced here part of his thesis, and added some bibliography.  With a good luck for his carrier.

References

MS Andreini, TS Steenhuis - Preferential paths of flow under conventional and conservation tillage, Geoderma, 1990, http://dx.doi.org/10.1016/0016-7061(90)90009-X

Beven, K.J., Germann, P F. 1982. Macropores and water flow in soils, Water Resources Research, 18(5), 1311‐1325.

Beven, K., and P. Germann (2013), Macropores and water flow in soils revisited, Water Resour. Res.,49, 3071–3092, doi:10.1002/wrcr.20156

Børgesen, C. D., O. H. Jacobsen, S. r. Hansen, and M. G. Schaap, Soil hydraulic properties near saturation, an improved conductivity model, Journal of Hydrology, 324, 40–50, 2006.

Diamantopoulos, E., S. C. Iden, and W. Durner, Inverse modeling of dynamic nonequilibrium in water flow with an effective approach, Water Resources Research, 48, 1–16, 2012.

Flury, M., H. Flühler, W. A. Jury, and J. Leuenberger (1994), Susceptibility of soils to preferential flow of water: A field study, Water Resour. Res., 30(7), 1945–1954, doi:10.1029/94WR00871.

http://akasha.wsu.edu/~flury/theses_articles/screening.pdf

Gerke, H., and M. T. van Genuchten, A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media, Water Resources Research, 29, 305–319, 1993a.

Gerke, H. H., and M. T. van Genuchten, Evaluation of a First-Order Water Tranfer Term for Variably Saturated Dual-Porosity flow Models, Water Resources Research, 29, 1225–1238, 1993b.

Gerke, H. H., and M. T. van Genuchten, Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media, Advances in Water Resources, 19, 343–351, 1996

Ghodrati, M. and Jury, William A.  A Field Study Using Dyes to Characterize Preferential Flow of Water, SSSAJ, Vol. 54 No. 6, p. 1558-1563, Nov, 1990, doi:10.2136/sssaj1990.03615995005400060008x

Hencher, S. R., Preferential flow paths through soil and rock and their association with landslides, Hydrological Processes, 24, 1610–1630, 2010.

Jones, J. A. A., Soil piping and catchment response, Hydrological Processes, 24, 1548– 1566, 2010.

McDonnell, J. J. (1990), A Rationale for Old Water Discharge Through Macropores in a Steep, Humid Catchment, Water Resour. Res., 26(11), 2821–2832, doi:10.1029/WR026i011p02821. 

Mohanty, B., R. Bowman, J. M. H. Hendrickx, and M. T. van Genuchten, New piecewise-continuous hydraulic functions for modeling preferential flow in an intermittent-flood-irrigated field, Water Resources Research, 33, 2049–2063, 1997.

Philip, J., The theory of absorption in aggregated media, Australian Journal of Soil Research, 6, 1–19, 1968.

Ross, P., and K. Smettem, A Simple Treatment of Physical Nonequilibrium Water Flow in Soils, Soil Science Society of America Journal, 64, 1926–1930, 2000.

Schaap, M. G., and M. T. van Genuchten, A Modified Mualem-van Genuchten For- mulation for Improved Description of the Hydraulic Conductivity Near Saturaion, Vadose Zone Journal, 5, 27–34, 2005.

Simunek, J., Jarvis, N.J., van Genuchten, M.Th. , and Gardena, A., Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone, Journal of Hydrology 272 (2003) 14–35

Uchida, T., K. Kosugi, and T. Mizuyama, Effects of pipeflow on hydrological process and its relation to landslide: a review of pipeflow studies in forested headwater catchments, Hydrological Processes, 15, 2151–2174, 2001.

Uchida, T., K. Kosugi, and T. Mizuyama, Effects of pipe flow and bedrock groundwater on runoff generation in a steep headwater catchment in Ashiu, central Japan, 38, 1119–1133, 2002.

Uchida, T., I. T.-v. Meerveld, and J. J. Mcdonnell, The role of lateral pipe flow in hillslope runoff response : an intercomparison of non-linear hillslope response, Journal of Hydrology, 311, 117–133, 2005.

van Genuchten, M., and P. Wierenga, Mass Tranfer Studies in Sorbing Porous Media I. Analytical Solutions, Soil Science Society of America Journal, 40, 473–480, 1976.

Weiler, M., and F. Naef, An experimental tracer study of the role of macropores in infiltration in grassland soils, Hydrological Processes, 17, 477–493, 2003a.

Weiler, M., and F. Naef, Simulating surface and subsurface initiation of macropore flow, Journal of Hydrology, 273, 139–154, 2003b.