Sigmoidal water retention function with improved behaviour in dry and wet soils

de Rooij, Gerrit Huibert; Mai, Juliane; Madi, Raneem

doi:https://doi.org/10.5194/hess-25-983-2021

Articles | Volume 25, issue 2

https://doi.org/10.5194/hess-25-983-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-25-983-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 25, issue 2

Technical note

|

25 Feb 2021

Technical note |

| 25 Feb 2021

Sigmoidal water retention function with improved behaviour in dry and wet soils

Gerrit Huibert de Rooij, Juliane Mai, and Raneem Madi

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Final revised paper (published on 25 Feb 2021)
Supplement to the final revised paper
Preprint (discussion started on 17 Aug 2020)
Supplement to the preprint

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'Review comments on hess-2020-380', Anonymous Referee #1, 04 Oct 2020
- AC1: 'Response to referee 1', Gerrit H. de Rooij, 13 Oct 2020
RC2: 'Review', Anonymous Referee #2, 09 Oct 2020
- AC2: 'Response to referee 2', Gerrit H. de Rooij, 15 Oct 2020

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (further review by editor and referees) (16 Oct 2020) by Roberto Greco

AR by Gerrit H. de Rooij on behalf of the Authors (28 Oct 2020) Author's response Manuscript

ED: Referee Nomination & Report Request started (16 Nov 2020) by Roberto Greco

RR by Anonymous Referee #1 (24 Nov 2020)

RR by Anonymous Referee #2 (22 Dec 2020)

Suggestions for revision or reasons for rejection

The revised article including the new figure 3 has improved and is easy to read. Before publication, some technical aspects related to the hydraulic conductivity function must be clarified.

1) I tried to reproduce some of the plotted K(theta) curves for RIA and VGA model and did not get the same curves. Possibly/probably, I made a typo in the equations and because of that I have different curves. However, as a reviewer (and potential user) I must be sure how the authors computed the curves.
Specifically, for RIA, I implemented eq. (14) using eq. (8) and (9) for beta and h_d, respectively. I tried to compute K(theta) for UNSODA sample 1143 using parameters listed in Table C2. On page 17, lines 298 and 299, it is written “Mualems model for the unsaturated hydraulic conductivity curve was used …” to plot K(theta). So I’m assuming they refer to eq. (14) with gamma=2 and tau = ½. Is that correct?
Given the complexity of the equations, an excel sheet (or a few lines of codes in matlab or python) to enable the user to reproduce a specific example would be helpful (for example as supplementary information file).

2) Similarly, I’m not sure how the conductivity function for the VGA curve was computed. Did the authors apply eq. (11) of Ippisch et al. (2006)? As the authors state on page 24, lines 396-399: “Near saturation, RIA’s K(θ) curve often drops off sharply before leveling off, in stark contrast to that of VGA, which remains high in the wet range. Given the similarity in the θ(h) curves of VGA and RIA, the difference in their K(θ) curves is remarkable.”
The authors do not explore or explain why there is a big difference in K(theta) between VGA and RIA for several cases. It must be possible to explain this from a mathematical point of view. The authors must expand on this (explain the differences between VGA and RIA close to saturation) and must provide the expression for K(theta) they used to plot VGA.

3) In Appendix C, the authors show a comparison of measured and modeled conductivity data. Only in one case the conductivity values were measured in the lab, for all other cases lab-based SWRC parameters inserted into the conductivity function were compared to field measurements (see page 23/24, line 386-388). From my point of view, such a comparison is meaningless and does not help to understand which K(theta) model gives a more realistic description – the results are just dominated by different sample sizes and structures (as the authors know). A more theoretically based description of different K(theta) shapes based on the SWRC parameters would be more insightful.

Another aspect that the authors should explain in more detail is the value of h_d given in eq. (9) (matric potential at which water content reaches zero). Should this value not be universal (as the authors discuss with pF=6.8)? Is this not just the potential to withdraw the last monolayer of water around the particles? How can the authors defend a value of pF = 10.5 as in Figure 1 for clay?

MINOR COMMENTS:

Page 2, line 29: Rephrase or specify “The new curve was more robust than the other two (for more simulation scenarios, convergence to numerical solution was achieved)”

Page 7, lines 133-134: the sentence “Madi et al. ….” is not clear to me. Could the authors specify the constraints and why (and which) usual models are ruled out?

Page 7, lines 141 ff: This paragraph on the hydraulic functions in the wet range is poorly connected to the previous paragraph on dry range. Please rephrase.

Page 8, line 144: I suggest to list the equations of Brooks and Corey and Fayer and Simmons model as well (for example in the Appendix)

Page 11, lines 206 ff: A main benefit of the multimodal curve is to describe the effect of macropores on SWRC; but equation (10) is only valid with the constraint that (1/alpha_i) is larger than |h_ae|. Is this constraint meaningful? Could the authors please comment on that?

Page 12, line 224: The authors state that the primary focus is on SWRC – from my point of view the effect of SWRC on K(theta) or K(h) is as important as well …

Page 12, line 231: define saturation S_e

Page 12, line 233: must be eq. (13), not eq. (12)

Page 14, line 265: what do the authors mean with “sufficient”

Page 15, line 276: for the convenience of the reader, give saturated hydraulic conductivity value as well

Figure 1: Explain in the captions why you stop at pF=6.8 for VGA and VGN

Page 19, line 321: The authors write that RIA has clear advantage compared to RNA and FSB – this is a bit misleading or incomplete, because also VGN and VGA have the same advantage (and perform slightly better than RIA)

Page 28, Summary and conclusions: For the convenience of the reader that are not reading the entire article, explain RIA, VGA and VGN

Page 32, line 534: Do you refer to eq. (14a) and (14b)?

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ED: Publish subject to minor revisions (review by editor) (08 Jan 2021) by Roberto Greco

AR by Gerrit H. de Rooij on behalf of the Authors (11 Jan 2021) Author's response Manuscript

ED: Publish as is (20 Jan 2021) by Roberto Greco

AR by Gerrit H. de Rooij on behalf of the Authors (21 Jan 2021)

Short summary

The way soils capture infiltrating water affects crops and natural vegetation and groundwater recharge. This retention of soil water is described by a mathematical function that covers all water contents from very dry to water saturated. We combined two existing lines of research to improve the behaviour of a popular function for very dry and very wet conditions. Our new function could handle a wider range of conditions than earlier curves. We provide fits to a wide range of soils.