European Journal of Soil Science, December 2010, 61, 1113–1117 doi: 10.1111/j.1365-2389.2010.01285.x Letter to the Editor Comments on ‘General scaling rules of the hysteretic water retention function based on Mualem’s domain theory’ by Y. Mualem & A. Beriozkin Our comments on Mualem & Beriozkin (2009) have two main points. The first concerns Parlange (1976) and the two papers applying this method directly (Hogarth et al., 1988; Braddock et al., 2001). The discussion by Mualem & Beriozkin (2009) regarding those papers seems somewhat misleading: the papers emphasize that the use of a drying curve rather than a wetting curve is recommended. Indeed, Mualem & Beriozkin (2009) state quite correctly ‘Viaene et al. (1994) properly followed Parlange’s (1976) recommendation to calibrate the model by the main drying curve for predicting the main wetting curve’. Of course, when both the main drying and wetting curves are measured, one should expect that interpolation models will be more accurate than extrapolation models requiring only one boundary (Bachmann & van der Ploeg, 2002; Pham et al., 2005; Wei & Dewoolkar, 2006). In fact, both curves are rarely measured, especially in the field, and because ‘such a complete set is seldom available’ (Nimmo, 1992), ‘it restricts the usefulness of these models’ that require two curves (Jaynes, 1992). We might add that a major difficulty in obtaining main wetting curves is that for infiltration experiments, the wetting fronts can be too abrupt to obtain accurate data, whereas, drying curves relying on drainage experiments do not present the same difficulty (Selker et al., 1992a,b; Liu et al., 1995). Thus, the advantage of our branch model is based on ‘the main drying branch of the water retention curve because this is the most commonly measured soil hydraulic property’ (Perfect, 2005). As stated by Viaene et al. (1994) ‘In those cases, the model presented by Parlange (1976) seems to be the best choice’. This conclusion seems to hold in more recent studies (Si & Kachanoski, 2000; Ma et al., 2008). Mualem & Beriozkin (2009) agree with the conclusion of Viaene et al. (1994) when using the main drying curve for a one-branch model. However, they criticize studies for not using the main wetting curve. Given the lack of data for this curve, especially in the field, this criticism seems misleading. The fundamental theoretical difficulty, if one wants to start with a wetting curve, is that it enters the model through its derivative (Parlange, 1976, 1980). Thus, not only are wetting curves hard to measure, but the difficulty is compounded as estimating derivatives numerically usually requires very good data. In particular, the model cannot handle an inflection point on the wetting curve (Mualem & Beriozkin, 2009) as is obtained, for instance, with a van Genuchten (1980) water-retention model. Braddock et al. (2001) looked at this problem at great length when they used a van Genuchten rather than a Brooks & Corey (1964) model to describe the drying curve accurately (also suggested by Appelbe et al., 2009). Braddock et al. (2001) pointed out that to use the model by starting with a wetting curve would require limiting oneself to matric potentials greater than the potential of the inflection point. This is equivalent to replacing the wetting curve below the potential of the inflection point by the tangent at that point, so that the corresponding drying curve would have an entry value equal to that potential, making it look like a Brooks & Corey (1964) curve. Doing so would eliminate the mathematical difficulty of the inflection (Pham et al., 2005). As this construction is possible, but not necessary, we rather recommend, as we have in the past, that our model be used starting with a drying curve only, which, again, corresponds closely to what is accurate experimentally. The second point concerns some work not discussed by Mualem & Beriozkin (2009). A recent study by Canone et al. (2008) was based on the model by Haverkamp et al. (2002) using the concepts of Parlange (1976) but removing its theoretical difficulty. Canone et al. (2008) used Parlange (1976) to derive parameters for a suitable hysteresis prediction model based on the concept of rational extrapolation. Starting with a normalized water retention equation valid for all wetting and drying curves whatever their scanning order, they considered the equation to be described by three parameters, the first defining the shape of the curve and the other two scaling the soil-water pressure head and volumetric soil- water content. Three geometrical scaling conditions were derived. The first condition determines a shape parameter that is identical for all wetting and drying curves and independent of their scanning order; the second defines the relationship between the pressure head scale and the water content scale specific to each curve in wetting or drying; and the third condition determines specific water content scale parameters according to the points of departure and arrival of each scanning curve. Equations necessary for the calculation of the different scale parameters were derived. Canone et al. (2008) and Haverkamp et al. (2002) showed that given the saturated water content, all main, primary and higher order scanning curves can be predicted from knowledge of only one curve, although in practice, knowledge of a main or primary curve is desirable. Constraints such as the need for scanning curves to be closed and to lie inside curves of a lower scanning order are automatically satisfied. The method using the van Genuchten water retention function was tested by Canone et al. (2008) on more than 23 soils (from the field and laboratory) of different texture ranging from sandy to silt. The results showed very good agreement with nearly all the experimental data. The results also showed that knowledge of water retention in the field is often hampered by uncertainty in the hysteresis history of the soil, © 2010 The Authors Journal compilation © 2010 British Society of Soil Science 1113