The paper is generally well-written and clear, and the contribution to soil physics is relevant and suitable for HESS. Below are a few (somewhat) major comments. These, in addition to minor comments, also appear in the annotated manuscript.

The Introduction is well-written and convincingly argued. I think the paper can be embedded in the literature a bit better. I provide two additional references that themselves have additional references that may be worthy of inclusion. I have been following the work of some of the authors, so I know they are well aware of developments in the literature. Perhaps they can use the depth of that awareness to add a few relevant papers. There is no need for a full-blown review though.

L. 201-202

Does the hypothesis of a mildly varying tau_sub_s not implicitly require that the conductivity of a soil that is so wet that all but the largest pores (whose size and shape are determined almost entirely by the soil macrostructure) are filled does not vary much for different textures? I am not convinced that is the case, but have to admit that my reservations are based more on intuition than hard data. I understand the proof will come later in the paper.

Still, I would be interested in a more elaborate treatment of the implications of the range of tau_sub_s for the range of Ksc in Eq. (20). It seems to me that the additional variability in Ks must stem from the other terms in Eq. (20) except the constant beta. Perhaps dot plots of those terms for the soils for which you predicted Ksc could help. I am not sure if that is the best way to explore this, but the interaction between the three non-constant terms in Eq. (20) is of interest but largely neglected.

Eq. (20)

The presence of a residual water content confuses me a little given the tendency in the past 10 - 15 years or so to get rid of it. As a case in point, you quote Schneider and Goss, who provided a finite matric potential for oven-dryness. Does this not contradict the existence of a non-zero residual water content?

L.228

Please add some explanation for your choices for the capillary saturation functions. There are many alternatives, some of which are part of a set of curves that  distinguish between adsorbed water and capillary-bound water. There are also versions without asymptote at zero or a non-zero residual water content. Given the argumentation in the Introduction, I did not expect equations with an asymptote to be included. Perhaps you indeed used the non-asymptotic version of Fredlund and Xing? If I recall correctly, they propose several functions, some of which have an asymptote at zero water content.

L. 263

Basically, you fit tau-s instead of Ks to fit the data everywhere except in the range near saturation. In effect you are still scaling a conductivity curve, you just call the scaling parameter something else.

The new element is that you use the fitted value as a predictor for soils where you did not fit it to. These soils each have their own values of the residual and saturated water contents, F(1), and F(Gamma-0), from which emerges an individual value of Ksc using Eq. (20).

Is this a correct description of the procedure? If so, it makes any relationships/correlations between the three non-constant terms of Eq. (20) even more interesting (see my earlier comment).

Figs. 5 and 6

Due to ‘space limitations’ you present only 6 of the predicted curves. Particularly in the box plots of Figs. 5 and 6, there seems to be plenty of space for more red dots. I would not mind seeing a few more, perhaps even all of them. But what is the meaning of the red cross in the vGc column of the left panel in Fig. 5?

Review by John Nimmo.

This paper addresses a very important longstanding problem. The prediction of unsaturated hydraulic conductivity from soil water retention measurements requires specific hydraulic conductivity information in addition to the retention data. The authors correctly explain that in practice the required information is unavailable or is available only in a form, for example a measurement of saturated hydraulic conductivity, that is inappropriate for this use and thus produces erroneous results.

The main innovation here leading to an absolute hydraulic conductivity curve (HCC) is what the authors call an absolute tortuosity coefficient. A second necessary element is their finding that a universal value of a saturated tortuosity factor can be suitable for a wide range of soil types. Together with a well-known relation put forth by Mualem (1976), these permit establishment of an unsaturated HCC without requiring hydraulic conductivity measurements. It is a very useful contribution that the proposed model is formulated in such a way that it can utilize an approximate though adequately representative universal value of an appropriate parameter.

This paper’s treatment of the problem and the conclusions drawn are sound. The results have real utility for scientists working with water flow in soils. The text is easy to understand. With revision this can be a strong contribution to be published in HESS. Below I recommend some important clarifications and modifications to be made.

Noncapillary:

Use of the term “noncapillary water” raises some problems. There is a need to recognize the effects of noncapillary processes at the wet end of the unsaturated range. I see the chief issues as these: Being inversely proportional to pore radius, capillary force in the largest pores is so weak as to be dominated by gravity and instability of air-water interfaces. Consequently, in soil that is nearly saturated, some of the water in large pores is present not because it is held by capillary forces but because it is supplied by water flowing from a copious supply, typically driven by gravity. Such water can be considered an aspect of nonequilibrium flow (e.g. Jarvis, 2007, European Journal of Soil Science, 58:523–546). Capillarity, exemplified by such phenomena as capillary rise, is inherently an equilibrium concept and thus is inappropriate as a classification for the soil water near saturation that is in a nonequilibrium state. This is a major factor underlying a central problem that this paper addresses, that measurements of saturated hydraulic conductivity, normally made under ponded or nearly-ponded conditions, are not suitable for use as a matching factor when predicting unsaturated hydraulic conductivity from retention data. Values obtained in such measurements are reflective largely of flow through pores that are filled not by capillarity but by the dynamics of inflowing water. Thus they have an incompatible mismatch with information from capillary-based water retention data.

These considerations point to a feature of the PDI model system, that it presumes the capillary range extends up to saturation. It should be revised, but revision of the PDI system is not the point of this paper, and I am not recommending an extension of scope for it to additionally evaluate the matter of noncapillary water at the wet extreme. That would be a substantial topic suitable on its own for future research papers. I also recognize that the main body of the work here is in harmony with the basic understanding I’ve described above. The statement in lines 221-224 in effect acknowledges this point. The paper appropriately refers to an emphasis on properties of soil matrix material (e.g. lines 23, 150, 369, and elsewhere in section 4.4), where capillarity is a dominant controlling factor. What I do recommend is that there be direct acknowledgement and description, early in the introduction, of what could also be termed noncapillary water at the wet extreme (or alternatively called “nonequilibrium water” or some other term).

Tortuosity:

Path extension, as implied by the term “tortuosity”, is not the sole cause of deviations from a straight-tube model. This is well stated in 215-217. It would be good to give this concept more prominence, for example mentioning it when tortuosity is first discussed quantitatively with eq. 11.

Support for near constancy of τ_s is from results in Fig. 3. The key fact is in line 315, that even though 1.5 orders of magnitude may sound like much, it is small compared to the variability of K_s among soils. The K_s variability among soils, however, is based on a large number of measurements, many of which are dominated by effects of pores larger than about 0.5 mm in diameter. This fact would be worth pointing out, perhaps noting that the procedure used here may provide a result similar to what would result from excluding K_s data from soils with large pores from use as a K matching factor.

Deletion and additions:

The specific values of fitted parameters, τ_s, and goodness-of-fit values for all tested soils would be very useful for understanding and evaluating the proposed models. These values should be included in a table in the main text. One particular benefit from such a table is that it would allow the reader to assess possible trends with soil type in the spread in τ_s values seen in Fig. 4. Similar reasoning applies to figs. 5 and 6.

The value of section 4.3 is doubtful. I recommend omitting it. The statement in 349-350, which suggests the new prediction scheme is worthwhile only for the case of unavailable or insufficient conductivity information, understates its value. Even though they are widely used for this purpose, saturated hydraulic conductivity measurements are in general inappropriate for use in predicting conductivity in the capillary range, and this new scheme usefully provides a way to avoid using them. I also do not see value in attempting to predict saturated hydraulic conductivity, as in Fig. 8, with the approach developed here. This approach is closely tied to capillary phenomena, which are not what dominates saturated hydraulic conductivity in the most general case. One additional point is that I don’t think this paper is a good place to mention possible adjustments of Mualem’s 𝜆 parameter. With his recommendation of setting 𝜆 at 0.5, Mualem saw the value in recognizing what can be regarded as essentially the same for a range of situations. This was a positive development analogous to the present work’s recognition of a universal value of τ_s.

As the authors note (lines 383-384), the development in Section 4.4 has potential value for improving the performance of numerical models if near-saturated conditions are important. This is an appropriately modest objective, given that this development is based mainly on mathematical convenience, with attention to physical plausibility, and has extremely little support from measurements. Even so, it should explain what need there is for a nonzero h_s value and the reasons for assigning it a value of 0.006 m.

Minor comments:

100: “The total hydraulic conductivity function . . .” Here, “total” is potentially misleading.  Better would be “The unsaturated hydraulic conductivity function . . .” or more vague wording.

120: A commendable example of terminology that improves on most unsaturated zone literature is the definition of 𝜃_r as the “maximum adsorbed water content”, as opposed to the undefined “residual water content”.

160: Missing word “conductivity.”

174: Clearer wording would be “Since the degree of capillary saturation . . .”

196: Clarify “(occurring in Equation (16) in Equation (12),”

256: Jarvis (2007)

262-263: How is τ_s determined, when it does not appear in the WRC equations that are fitted?

Fig. 2: Scale and other design elements are inappropriate. Fitted curves fall largely on top of each other. Moreover, the differences in color are subtle and hard to distinguish. All graphs need to be much larger. I recommend choosing only one soil for this figure and putting the rest in supplementary material.

350: Awkward wording. I suggest “. . . if conductivity information is unavailable or insufficient . . .”

400: Qualifier needed: “. . . such predictions mostly use . . .”

406-411: Confusing use of the term “tortuosity.” I suggest presenting facts in this order: (1) Pore bundles do not in themselves account for important characteristics such as path elongation due to tortuosity, physical properties of the liquid phase, . . . . (2) These effects can be accounted for with a parameter that here is called a tortuosity coefficient. (3) We separate this parameter into two factors, a relative and a saturated tortuosity factor. (4) The saturated tortuosity factor is shown to vary little among different soils, and we have determined a universal value empirically from data.

412: This would be a good place to point out that the saturated tortuosity factor with an assigned universal value provides the basis for estimating conductivity from retention data without a matching factor that can only be determined from a measured conductivity value. The last two paragraphs of the abstract did this very well.

431-491: I do not find the appendices to be strictly necessary but they may serve as a convenience to some readers.