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Soil Science Society of America Journal 65:960-961 (2001)
© 2001 Soil Science Society of America

COMMENTS & LETTERS TO THE EDITOR

Comments on "Exact Solution for Horizontal Water Redistributions by General Similarity"

E.G. Youngs

Institute of Water and Environment Cranfield University Silsoe, Bedford, MK45 4DT United Kingdom


   INTRODUCTION
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One of the basic facts of soil water physics is the hysteresis exhibited in soil water relationships, particularly in the relationship between soil water content and soil water pressures (Haines, 1930). However, although this hysteresis has a profound effect on the distribution and movement of water in soils (for example, it plays an important role in retaining infiltration water near the soil surface, impeding downwards movement), it is given scant attention in soil hydrology. The redistribution of soil water after infiltration is the classic example usually cited for hysteretic soil water behavior (Childs, 1969). The note by Shao and Horton (2000) is therefore misleading by ignoring hysteresis in purporting to calculate redistribution profiles in soils. The authors seem to have been inspired by Philip's (1991) analysis of horizontal soil water redistribution from one infinitely long wet column into another infinitely long dry column. This was essentially a consideration of the behavior in a composite porous body consisting of two semi-infinite columns of a soil with different hydraulic properties and so did not address the true complex hysteretic behavior in soils where different parts of the soil profile are wetting and draining down different scanning curves of the soil water characteristic.

Horizontal redistribution soil water profiles after infiltration were presented by Youngs (1958a). He argued that the soil water diffusivity given by the product of the hydraulic conductivity and the slope of the moisture characteristic that was introduced by Childs and Collis-George (1950) in order to put Richards' equation in the form of a more easily solved nonlinear diffusion equation could not be used to analyze the soil water redistribution in such hysteretic situations. The change in slope of the moisture characteristic at a reversal gave a discontinuity in the diffisivity, so the mathematical convenience of introducing the soil water diffusivity is not achieved.

The experimental redistribution profiles presented by Youngs (1958a) showed the importance of hysteisis in their development. The case of the profile development after vertical infiltration is further complicated by the effect of gravity (Youngs, 1958b). In this case, it has been found that two different forms of profile development are possible, depending on the depth of infiltration and also on the texture of the soil. In one the profiles maintain approximately the general shape of the infiltration profile, whereas in the other desaturation at the surface occurs with a step-like advance of the wetting front below. The discussion has been further developed by Youngs and Poulovassikis (1976) and Youngs (1983)(1990).

Shao and Horton (2000) do not consider the situation of the redistribution of an initial infiltration profile but instead that of a given initial hypothetical region of uniform saturation. Even in this simpler case, hysteresis cannot be ignored. Thus it must be concluded that the analysis given in this paper is of little relevance to soil water redistribution but could be of interest in analyzing other processes described by a nonlinear diffusion equation.

Received for publication July 25, 2000.
   REFERENCES
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Response to "Comments on an ‘Exact Solution for Horizontal Redistribution by General Similarity’"

Mingan Shao and Robert Horton

b National Lab of Soil Erosion and Dryland Farming on the Loess Plateau Institute of Soil & Water Conservation, Chinese Academy of Sciences Institute of Soil and Water Conservation, Northwest Agriculture and Forestry University of Sci-Technology, 26 Xinong Road, Yangling, Shaanxi 712100, China
c Department of Agronomy Iowa State University Ames, IA 50011


   INTRODUCTION 
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We thank Youngs (2000) for his interest in our work. His major concern about Shao and Horton (2000) is that hysteresis is not included in the general similarity solution for horizontal water redistribution. A complete analysis of water redistribution in soil should take capillary hysteresis effects into account. Therefore, we agree in principle with Youngs (2000) that hysteresis should be considered in describing the water redistribution process. Currently, only numerical techniques can actually incorporate hysteresis effects into the water flow model that includes the form of potential variables and not the form of a more easily solved non-linear diffusion equation. However, in practice, for some soils the hysteretic effects on water flow processes are relatively minor. Analytical solutions of nonhysteretic flow may still have certain applications to soil water redistribution. In this response we are going to provide some evidence to show that the similarity solution in Shao and Horton (2000) is applicable to soil water redistribution.

Watson and Sardana (1987) conclude that the size of the hysteresis loop decreases as soils become more fine-textured. In Shao and Horton (2000), the D0 value is assumed to be 2 x 10-7 m2s-1. This corresponds to fine-textured soil according to Shao and Horton (1996). Such soil should have a small hysteresis loop. Moreover, both theoretical analysis and experimental evidence show that hysteresis has much less effect on hydraulic properties if they are expressed in water content rather than in pressure head (Mualem and Dagan, 1975; Mualem, 1976). The expression for water diffusivity is in water content, and this makes the hysteresis effect less again. The hysteresis phenomenon primarily affects hydraulic properties of soils in the range of capillarity (Poulovassilis, 1962). Therefore, nonhysteretic solutions still have applications to water redistribution for certain soil water conditions. Such nonhysteretic solutions should be applicable to certain intermediate and low ranges of soil water content. The above reasons make us believe that the general similarity solution for horizontal water redistribution is applicable for some soils. One important application of the solution is to estimate soil water diffusivity. The similarity method for estimating soil water diffusivity only needs information on the advance of wetting front with time to obtain water diffusivity of unsaturated soils.

We performed numerical simulations and column experiments of soil water infiltration and redistribution for silt loam and clay loam. Some of the results are reported in Yang et al. (1999). Numerical simulations of a vertical water redistribution problem were made using a nonhysteretic model, a hysteretic model following Mualem (1984), and a hysteretic model following Kool and Parker (1987). Root mean square error, RMSE (Wilmott et al., 1985), was used to make evaluations of how well the nonhysteretic and hysteretic models described the observed soil water distributions. The results are shown in Table 1.


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  		Table 1. Root mean square error (RMSE) values of water redistribution simulations by nonhysteretic and hysteretic models.

 
From Table 1, one can see that the hysteretic models improve water content predictions for soil water redistribution following infiltration. For both soils, as time increases, hysteresis has fewer effects on water redistribution after infiltration. Including all of the simulations, the hysteretic models increased the average prediction accuracy by 1.3% over the nonhysteretic predictions. We may conclude that neglecting hysteresis produces errors, but not large erors, especially for intermediate and low water contents, and the similarity solution is applicable to water redistribution in some soils.

Received for publication September 12, 2000.


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E.G. Youngs, M. Shao, and R. Horton
Comments on ""Exact Solution for Horizontal Water Redistributions by General Similarity""
Soil Sci. Soc. Am. J., May 1, 2001; 65(3): 960 - 961.
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