Modelling of water infiltration into water repellent soils
Abstract. Infiltration into water repellent soils has been widely observed, quantified and documented. The modelling of water infiltration into water repellent soils is more rarely taken into account explicitly. In this study, we modelled water infiltration into water repellent soils considering explicitly the contact angle, with the geometrical pore model proposed and validated previously. The applied microscopical approach showed good agreement with macroscopical models and with experimental data. We firstly investigated the case of contact angles lower than 90°, for the cylindrical pore and pearl necklace (PN) models. The cumulative infiltrations were numerically generated versus contact angle and for different pore radii. Then, the modelled infiltration curves were fitted to the two-terms Philip equation and parameters S and A were evaluated versus contact angle. As predicted sorptivity S decreased with increasing contact angle, and the constant infiltration rate A increased with contact angle for both models. Then, the modelled data were fitted to the numerical solution of the Richards equation to derive the equivalent hydraulic parameters assuming van Genuchten model. The results showed that the contact angle decreased the saturated hydraulic conductivity and increased the parameter α. Lastly, our model was used to investigate strong water repellency with contact angles higher than 90°. Cumulative infiltration and related Philip parameters, S and A, were evaluated versus water pressure head at surface h0 and contact angles (between 90° and 96°). Our model may be used to predict water infiltration into water repellent soils for both moderate and strong water repellency, including fingering features
Claude Hammecker et al.
Claude Hammecker et al.
Claude Hammecker et al.
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The grammar needs improvement. Some sentences are cumbersome to read, and commas appear at unexpected places, for instance.
The title is very brief. Please add what type of models you are using and that you are interested in pore-scale and Darcian-scale processes.
The abstract is strictly qualitative and mentions the models that are used in passing. It also staes results that are rather obvious. It can be made more specific, and why not highlight the more interesting stuff?
I missed some relevant literature in the paper. This leads, for instance, to the claim that infiltration into water-repellent soils has not been modeled. See for instance:
Egorov, A.G., R.Z. Dautov, J.L. Nieber, and A.Y. Sheshukov. 2002. Stability analysis of traveling wave solution for gravity-driven flow. In S.M. Hassanizadeh et al. (ed.) Computational methods in water resources. Proc. XIVth Int. Conf. (CMWR XIV), Delft, The Netherlands, Vol. 1. 23–28 June 2002. Elsevier, Amsterdam, The Netherlands.
Egorov, A.G. Stability analysis of gravity-driven infiltrating flow. (9). doi:10.1029/2002WR001886.Water Resour. Res. 2003 39 1266.
Geiger, S.T. Infiltration in homogeneous sands and a mechanistic model of unstable flow. Soil Sci. Soc. Am. J. 2000 64 460– 469. https://doi.org/10.2136/sssaj2000.642460x
Raats, P.A.C. Unstable wetting fronts in uniform and nonuniform soils. Soil Sci. Soc. Am. Proc. 1973 37 681– 685. https://doi.org/10.2136/sssaj1973.03615995003700050017x
Another problem arising from the limited literature review is that no attention is being paid to the temporal dynamics of the contact angle and spatial variation of water repellency. In section 2.1, the dynamics of the contact angle may be of importance, but is not included.
Some (but hardly all) relevant references for this aspect:
Goebel, M.-O., et al., Water potential and aggregate size effects on contact angle and surface energy, Soil Sci. Soc. Am. J. 68, 383-393, 2004.
Leighton-Boyce, G., et al., Temporal dynamics of water repellency and soil moisture in eucalypt plantations, Portugal, Australian J. of Soil Research, 43, 269-280, 2005.
Thwaites, L.A., et al., Near-surface distributions of soil water and water repellency under three effluent irrigation schemes in a blue gum (Eucalyptus globulus) plantation. Agric. Water Managem. 86, 212-219, 2006.
The theoretical analysis of section 2.1 appears to overlap in part with that of Cho et al. (2005), who also invoked the Green-Ampt model. It would be interesting to see how this new analysis compares to this older work.
Cho, H., de Rooij, G.H., and Inoue, M.: The pressure head regime in the induction zone during ubnstable nonponding infiltration: Theory and experiments. Vadose Zone J. 4, 908-914, 2005, https://doi.org/10.2136/vzj2004.0158.
In Section 2.2, include a reference to Fig. 1. In figure 1, include all the terms you used in Section 2.2 to create an solid connection between the text and the figure.
In Section 3, I think the clarity of the figures would benefit from using colour. I had to magnify some of the figures a lot so I could read them.
At line 187 you state that the observed relationship between the contact angle and the sorptivity was unexpected, but why was it? Although it may be possible to derive such a relationship in the theory section, you did not pursue this there, although it would add an interesting element to the paper. Without a theoretical expression for the sorptivity as a function of the contact angle, I find it hard to see why the relationship you established through the simulations would be unexpected. Indeed, the correction you propose does not seem to be consistent with the rather complicated role of hf in Eq. (10). As it is, the correction proposed in line 188 has no connection with the equations developed earlier in the paper. I therefore think it may be possible to explore this more thoroughly in the theory section. You could do so directly by moving Eqs. (21) and (22) to the theory section, thereby establishing a hypothetical correction of S. The simulations can then be used to test this hypothesis, and you end up with a more neatly organized paper that confirms a theoretically derived hypothesis.
If you decide to do so, as I hope you will, it would be very helpful to modify the theory section so that the sorptivity actually appears in some of the equations.
Your conclusion in lines 204-206 is nice. Once you think about it it is easy to understand, but I share your view that it is good to mention.
In Fig. 4, does the dashed line in the top panel indicate the 1:1 line and does the same dashing in the bottom panel denote the cylindrical model? That is a bit confusing. Colour could help.
I think the effect of time on A reflects the decreasing validity of the two-term approximation of the full series with increasing time. As time progresses the importance of capillarity wanes and that of gravity grows (in Philip’s own terminology), which explains why the effect on S is much smaller than that on A.
The word ‘sorptivity’ conveys the tendency of a soil to absorb water. If the contact angle exceeds 90 degrees, this tendency is zero. Reporting positive sorptivities for such soils sounds contradictory.
The caption and legend of Fig. 7 do not explain r and the contact angles. For A/A0 I cannot see to which radius a curve belongs.
Particularly in strongly hydrophobic soils, which are the focus of this section, the tendency of the contact angle to decrease when the soil is exposed to water has dramatic effects on infiltration and the formation of preferential flow paths. Although this is a long section, this aspect is not addressed at all, in fact, it is not even mentioned. I can follow the analysis and its internal logic, but nevertheless it seems beside the point because it ignores the most important factor governing infiltration in such soils, which is the persistence of hydrophobicity under wet conditions.
Figure 12 c incorrectly represents a finger. As soon as a slight instability develops (termed a proto-finger in some of the references mentioned above), the pressure head near the proto-finger tip will be slightly larger than at the rest of the wetting front, accelerating the infiltration rate at that finger tip. This creates a positive feedback loop that lets the ‘winning’ protofingers grow while the ‘losers’ stop advancing. In the shallow wet layer of the top soil, flow will be directed horizontally towards the growing fingers. Because these take all the water, the wetting front stagnates everywhere else. The wet lobe to the left of the finger that is shown in the figure therefore will not develop. Some podzolic soils show evidence of very long persistence of preferential flow paths in the pattern of the brown organic matter band that is leached from the A horizon and deposited in the B horizon. I have never seen such a lobe next to a finger in the literature.
All in all, the theoretical analysis is interesting and offers some new insights. It needs to be better embedded in the literature because there are previous uncited analyses available that are not compared with the work reported here. As indicated above, I think there is potential for a more thorough analysis of the relation between the sorptivity and the contact angle that, to my knowledge, has not been explored before. The inclusion of results obtained with a Richards solver (Hydrus-1D) is interesting, but it can be better clarified in the text that these simulations either apply to the very early stage of infiltration when the induction zone (terminology adopted from the references above) is formed and preferential flow paths have not yet developed, or to flow in a single preferential flow path without interaction with the dry soil surrounding it.
Some minor comments were made directly in the text.