Great thanks for the author's efforts in deriving a closed-form SWRC with a logarithmic dry branch for addressing dry-range data issues. This is particularly helpful when the SWRC is parameterized (within a physical range) for soils in arid and semi-arid areas, for which the numerical solution of Richards equations can easily crash. This reviewer is very interested by the proposed model, and had tried out the code with the example input and obs data as provided. Although this reviewer recommended the acceptance of this manuscript, there are a few technical comments for the author's considerations as below:

1. The model seems not working well for soil C2 and C4 soils. This reviewer is wondering if the author could help explain or hypothesize the relevant potential physical mechanisms behind it?

2. This reviewer appreciates very much the author for sharing his data/code/manual. And it is very well documented as well. Just a trial to make the applications easier for various users, and for their understanding, perhaps it would be nice to indicate a few places (in the code) to which equations  (as numbered in the manuscript) the code are corresponding.

Some minor technical adjustments are attached.

de Rooij’s submission aims primarily at presenting some adjustments to a previously developed sigmoid-logarithmic soil-water retention function (WRF) and evaluates the new parametric relationship in terms of better describing the dry range of WRF. Specifically, this technical note is an extension of previous works by Prof. de Rooij’s group on the subject and deals with a slightly different parameterization of de Rooij et al.’s (2021) WRF which places greater emphasis on the role exerted by the “alpha” parameter of the sigmoid component of this analytical relation.

The text reads well and is properly organized, although some parts of Sections #2 and #3 seem too wordy for a technical note. The figures and tables are satisfactory, but I suggest improving the readability of Figs. #2, #3, and #5 (and subsequent) by enlarging a bit more the fonts of the numbers.

I have some criticisms and concerns that offer to the author for possible revision of the original submission. As a comment to the editor in charge, I shall make my opinion clearer below that the topic of this manuscript might be of scant interest to the HESS readership. Therefore, this paper should not be accepted in its current form, requires major revisions, or should be rejected altogether.

1) The author should, first of all, explain well and in detail to the reader why he feels the need to present this parametric analysis only on the analytical expression of the water retention function. Nowadays, it is quite clear that the real advantage of using a relatively simple or more comprehensive closed-form WRF is to infer the hydraulic conductivity function (HCF). I believe it might be worth putting one's attention to only a better (one expects) analytical description of the measured water retention data-points whether one employs the WRF for a certain scope (e.g. to get a better estimation of the water content at the condition of field capacity, or to better compute the integral of WRF).

2) P.3, L.60. On the subject of “hydraulic equilibrium” and relevant constraints on the soil hydraulic parameters, the author can find useful inputs if the review paper by Assouline and Or (2013).

3) P.4, L.80. Here one should warn the reader that the reported range of the “alpha” parameter depends on the parametric relation used to describe the WRF.

4) P.5, L.106. Strictly speaking, if the first derivative is zero, this is a necessary, yet not sufficient, condition for a minimum (or a maximum). In a view of the detailed parametric evaluation carried out in this article, one should also discuss the likely presence of relative minima and global minimum.

5) P.9, Section 3, L.206. I believe the author emphasizes too much the role that the various soil textural classes exert on WRF. Of course, soil texture is important, but other soil characteristics play a role in determining the shape of the WRF and often also have dominant effects, such as the oven-dry soil bulk density, the organic carbon content, and soil aggregate composition and aggregate-size distribution.

6) This comment is somehow linked to the previous point -5-. Some water retention data-points used in this technical note (especially those shown in Fig.8) seem better described by a bimodal (or multi-modal) water retention relationship. Firstly, coarse-textured soils can have a bimodal retention behavior as happens in the cases of some volcanic soils (e.g. Romano et al., 2011). It should also be considered whether other parametric relations, perhaps even simpler (e.g. just a simply bimodal relation linked somehow to the final matric pressure head Hd) than those proposed in this article, can give equally satisfactory or even better results.

7) As a final comment and allowing for HESS’s aims and scope, if I were a reader of this journal, I would probably find this article of little use. This is definitely not because the analytical developments are not interesting, but mainly because I think it is more effective here to discuss a functional evaluation rather than a parametric one (see, for example, the paper by Iden et al, 2021). This article can be more profitably submitted to a soil physics journal.

Reference cited.

Assouline, S., D. Or, 2013. Conceptual and parametric representation of soil hydraulic properties: A review. Vadose Zone J., 12, doi:10.2136/vzj2013.07.0121.

Iden, S.C., J.R. Blöcher, E. Diamantopoulos, W. Durner, 2021. Capillary, film, and vapor flow in transient bare soil evaporation (1): Identifiability analysis of hydraulic conductivity in the medium to dry moisture range. Water Resour. Res., 57, e2020WR028513.

Romano, N., P. Nasta, G. Severino, J.W. Hopmans, 2011. Using bimodal log-normal functions to describe soil hydraulic properties. Soil Sci. Soc. Am. J. 75:468-480.

The author proposes an adaptation to the new analytical relation presented by de Rooij (2021) to describe the water retention curve in a full matric head range. The analytical expression was tested on 21 soil samples taken from UNSODA database.

The evaluation of this manuscript is based on the following questions:

• Is it a novel work based on a reliable scientific technique?
• Is it clearly structured and well-written?
• Are the experimental design and analysis of data adequate and appropriate to the investigation?

Generally speaking, I would like to state that HESS is a high-ranked Journal and should receive novel, robust, scientifically-sound applications based on big data. This technical note does not fit in HESS for the following reasons:

• A new, or an adaptation of a new, analytical expression should be tested on ad-hoc water retention measurements to resolve the data fitting in the dry region. The soil sampling should cover all texture classes. The author took only 21 soil samples from the UNSODA. This number is not sufficient to draw strong conclusions. Moreover, the new expression should be compared to the existing expressions (van Genuchten, Brooks and Corey, Kosugi, to mention a few) by considering performance indexes like RMSE, R2, KGE and especially AIC (that penalizes the performance if the number of parameters is too high).
• The parameter fitting optimizes five water retention curve parameters on six to fourteen data pairs (Fig. 5) which are unable to provide basic information on the water retention curve. The author should show the uncertainty bands around the optimized curve and other performance indicators. I would be curious to see the parameter cross-correlation for each soil sample in Supplemental Material. What are the parameter ranges?
• This technical note resolves the fitting only for the water retention function by ignoring the hydraulic conductivity function that represents an essential prerequisite to solve the Richards equation in process-oriented hydrological models
• The author should convince the readers the advantage in using this equation and the disadvantage in using the most widespread equations. The three above mentioned analytical relations (and others) provide a closed-form expression for the hydraulic conductivity curve and for this reason are widely used by the hydrology community
• The RMSE is calculated on soil water content data (line 219)? If so, the RMSE values (the author should report the units) in Table 1 are dramatically high. In line 276, the author states that maximum allowed RMSE is 0.1 but in Table 1 I see many values higher than 0.1
• The text is too long for a technical note. There are too many figures that can be moved in Supplemental Material. The title should be concise and line numbering should be continuous for all lines. Figures must be improved consistently (enlarge fontsize, add grid, clarify axis titles by adding symbols and units)

This technical note should be rejected in this present form. I suggest to revise it thoroughly and re-submit

This manuscript presents the improved parameterization of SWRC in the dry range based on the author’s previously developed logarithmic-sigmoid SWRC model (published in HESS). Specifically, as  formulated in the previous paper is expressed as a function of other parameters that were fitted, this may lead to the obtained  not in the reasonable range. To solve this issue, the author focuses on regarding the shape parameter  instead of  as a derived parameter. By using the positive characteristic of  and the minimum value of  for any  through the partial derivative of  with respect to , the author quantified the corresponding upper and lower limits imposed on , then  as a fitting parameter is eliminated and replaced by its upper limit that is determined by both  and , given all fit points fell on the upper limit. As such, the obtained entire parameter space is valid, which is quite good. On the other hand, the author found that the sigmoid branch of the SWRC could be simplified to the commonly used power law as  is very large. This further guarantees the rationality of emphasizing on  fitting and the newly found parametric relationship.  

The reviewer thinks that the SWRC formulated with the parameters that are suggested being better fitted or derived, are useful to be applied in soil moisture and temperature and land surface fluxes modeling especially for arid and semi-arid regions. On the other hand, the calculated fractions of capillary-bound water and adsorption water using functions in this paper may be useful in investigating microwave dielectric properties of dry soil and associated soil backscatter. The paper is well written and organized. The reviewer appreciates the author making the hand-on script and manual public, which is encouraging and makes readers and peers benefit. The reviewer suggests the acceptance of this paper with minor revisions, especially improving the resolutions of Figures 5-8. For other minor comments please see them in the .pdf.