Dear Reviewer,

The authors warmly thank you for the time dedicated to reviewing our paper and his positive feedback. The authors will check for typos carefully. They will add a few sentences in the introduction about the alternative flux concentration functions available for the computation of sorptivity. In this paper, the authors considered Parlange’s equation for the flux concentration function. However, other flux concentration functions may be used in the integral that defines the sorptivity, like those proposed by Crank (1979), Philip and Knight (1974), Parlange (1975), Brutsaert (1976).

The authors intend to deal with the sensitivity of the computation of sorptivity with regard to the choice of the flux concentration function. The authors will also discuss the proper selection of these functions with regard to the type of soil. All those topics will be the subject of another paper.

Best regards,

Laurent Lassabatere on behalf of the authors.

Brutsaert, W. 1976. The concise formulation of diffusive sorption of water in a dry soil, Water Resources Research, 12(6), 1118–1124.

Crank, J. 1979. The mathematics of diffusion, Oxford university press.

Philip, J. R. a and Knight, J. H. 1974: On solving the unsaturated flow equation: 3. new quasi-analytical technique, Soil Science, 117(1), 1–13, 1974.

Parlange, J.-Y. 1975. On Solving the Flow Equation in Unsaturated Soils by Optimization: Horizontal Infiltration, Soil Science Society Of America Journal, 39(3), 415–418, 1975.

Dear Reviewer,

The authors thank you for your very positive review and the time dedicated to reviewing the paper.

Detailed answers to comments.

Regarding the two main comments, we will revise the paper to make it clear that sorptivity has two parts, the unsaturated sorptivity that corresponds to cp’ and the saturated part that corresponds to 2|ha*|. The saturated part is related to the air-entry water pressure head |ha*| that equals unity only for the Delta and the BC functions. In that case, the saturated part equals 2*|ha*|=2. Note that by convention, for the Delta and BC functions, the scale water pressure head, hg, is taken equal to the air entry pressure head, so that |ha*|=1. For the other hydraulic functions, |ha*| = 0, and the saturated part of sorptivity is null. We will implement the reviewer's suggestions on discussing both parts of the sorptivity as a function of the shape indexes and revise Figure 3.

Comment 1 by Reviewer RC2. Eq. (22) gives rise to contrasting values of sorptivity for the different hydraulic conductivity functions. The authors attribute this difference to the dependence of the parameter cp on the hydraulic functions (see section 4.4). However, sorptivity as defined in Eq 22 also varies with |hg| and 2 |ha*|. Indeed, the authors defined a variable cp' = cp-2 |ha*|. Therefore, consider deriving shape indices for cp'.

Authors’ answer: In the result section (section 3.2), we plotted the scaled dimensionless sorptivity, cp, as a function of shape indexes. For the Delta and BC functions, the scaled sorptivity lumps the saturated parts, equal to 2 |ha*| = 2 plus the unsaturated part, cp’. For the other functions, the scaled sorptivity corresponds directly to the unsaturated part, cp’, since |ha*| and the saturated part of sorptivity are null. We will insist on this point and discuss the evolution of the unsaturated part cp’ as a function of the shape index, as suggested by the reviewer. Note that the computation of dimensional sorptivity with equation 22 requires both the saturated and unsaturated parts of sorptivity.

Comment 2 by Reviewer RC2. What is the value of ha? I suspect it is equal to hg for the Delta and BC models and zero for the others. If that is the case, |ha*| = 1 for the former two and 0 for the others (see the top of Page 5). Thus, cp' = cp - 1 or cp' = cp. If you plot cp', the curves for cp,d' and cp, BC' in Figure 3 would be lowered by 1 and the in (a) and (c). This would reduce the dissimilarity between the various hydraulic functions a bit.

Authors’ answer: The reviewer is correct to state that |ha*| = 1 by convention for the Delta and BC functions and zero for the other hydraulic functions. Thus, the unsaturated part of the sorptivity equals cp' = cp – 2 for the Delta and BC functions and cp' = cp for the others. We will add cp' for the BC hydraulic functions in Figure 3a and discuss this point in the revised version of the paper.

Detailed answers to the reviewer’s suggestions.

We will carefully search for typos and revise the manuscripts. We will rewrite the inappropriate sentences. More importantly, the reviewer suggested changing the structure of section 2.1 with the presentation of first all the dimensional equations before the scaling procedure. The authors will investigate his proposal and attempt to revise this section.

• Reviewer: In the first line of the introduction, verify if sorptivity is actually used for desorption. Authors: Regarding sorptivity and its definition (line 22 of the manuscript), it corresponds to the following description of sorptivity proposed by Minasmy and Cook (2011): “Sorptivity is a measure of the capacity of the medium to absorb or desorb liquid by capillarity.” The concept of sorptivity can be considered regarding the two sides of the same coin, i.e., water adsorption and desorption, with hysteresis effects.
• Reviewer: Eq (4), Eq (5), and elsewhere there is no need to show the detailed step-by-step derivation of straightforward algebraic manipulations. Authors: We will carefully look at equations and simplify them when necessary. Our goal is to help the reader to retrieve all equations and derivations. When the derivations were relatively simple, all the steps were kept. When derivations were more complicated, we tried to keep only the main steps.
• Reviewer: (i) In the last paragraph of Page 3, rewrite the sentence that starts with "Secondly, ..." // (ii) In the same paragraph as above, define "BEST." // (iii) In the same paragraph as above, introduce hydraulic functions starting with the delta function to be consistent with how the equations are presented. Authors: we will rewrite this paragraph and address these points.
• Reviewer: Rewrite equation (6) using the Heaviside function since H is defined underneath and later references use H as well. Authors: we will rewrite the equation accordingly.
• Reviewer: (i) Postpone the introduction of the scaling parameters section 2.1, where they are used // (ii) Consider moving Eq (23) (definition of cp) to just after Eq (15), where cp is initially introduced. Also, provide more information of what assumptions were used by Haverkamp et al. in deriving cp. Authors: we will rewrite section 2.1 accordingly.
• Reviewer: Edit the incomplete first sentence of section 2.2.2. Authors: we will rewrite the sentence.

Again, the authors thank the reviewer for his suggestions and contributions.

Best regards,

Laurent Lassabatere on behalf of the authors.