New insights into the differences between the dual node approach and the common node approach for coupling surface–subsurface flow

de Rooij, Rob

doi:https://doi.org/10.5194/hess-21-5709-2017

Articles | Volume 21, issue 11

https://doi.org/10.5194/hess-21-5709-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/hess-21-5709-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 21, issue 11

Research article

|

17 Nov 2017

Research article |

| 17 Nov 2017

New insights into the differences between the dual node approach and the common node approach for coupling surface–subsurface flow

Rob de Rooij

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Final revised paper (published on 17 Nov 2017)
Preprint (discussion started on 30 Mar 2017)

Interactive discussion

Status: closed

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

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RC1: 'Review for the article hess-2017-168 : « A consistent implementation of the dual node approach for coupling surface-subsurface flow and its comparison to the common node approach » by Rob De Rooij.', Anonymous Referee #1, 12 May 2017
- AC1: 'Reply to Referee #1', Rob de Rooij, 16 May 2017
RC2: 'Review', Anonymous Referee #2, 16 May 2017
- AC2: 'response to Referee #2', Rob de Rooij, 16 May 2017

Peer-review completion

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

ED: Reconsider after major revisions (further review by Editor and Referees) (06 Jun 2017) by Philippe Ackerer

AR by Rob de Rooij on behalf of the Authors (14 Jul 2017) Manuscript

ED: Referee Nomination & Report Request started (20 Jul 2017) by Philippe Ackerer

RR by Anonymous Referee #1 (05 Sep 2017)

RR by Anonymous Referee #3 (14 Sep 2017)

RR by Anonymous Referee #2 (09 Oct 2017)

Suggestions for revision or reasons for rejection

I think that the manuscript underwent improvements and got more focused, which is good. There are some structural problems (results, discussion, conclusions are in the introduction, see specific comments below) and language problems. In addition some additional clarification would help the reader.
Going back to original publication by Kollet and Maxwell (2006), I feel the paper's important point and novelty was not on a numerical approach (common or dual node or something else). The important point was the realization that the kinematic wave equation can be merged into the top flux boundary condition resulting in a free surface boundary condition at the land surface, very similar to the one used to obtain analytical solutions for a pumping test in unconfined aquifers. I feel this was really the message and as such it can be implemented in a model (numerical, perhaps even semi-analytical and analytical) in a consistent fashion to mathematically close the problem of subsurface flow as the authors wrote. Unfortunately, the numerical implementation is not very clear from the paper, but the sensitivity to the vertical discretization, which clearly is a disadvantage in case of excess infiltration, was transparently reported in the numerical test cases. Yet, this does not detract from the theoretical and practical appeal of the free surface overland flow boundary condition proposed in this paper. I feel that is something that should be pointed out in the ensuing revision of this manuscript. Note also the term “common node” approach was not introduced by Kollet and Maxwell.
I am surprised by the (sometimes) large difference in non-linear iterations, because in principle the common node and dual nodes approach are very similar (which is also the reason why they can be easily switched in the code as described in the manuscript). Which additional nonlinearity is introduced in case of the common node approach? A more satisfactory attempt of explaining this phenomenon would be needed in my opinion.

Provided the general comments above and more specific comments below, I am recommending minor revisions.
68: Is Kollet and Maxwell (2006) and appropriate reference for MODHMS?
100 - 127: These are results and discussion/summary/conclusions and do not belong in the introduction section.
137: ...the mesh...
220: What is fp in the equation?
232: ...dua nodes. The infiltration…
292: I am confused and not sure what the authors wants get at. When qr = I then qr = Kz, thus pss = 0, because there is a unit gradient at the right at the land surface. If pss < 0 then qr < I, contrary to equation 8 because qs is not zero. In case of qr > I, again qs is not equal zero and pss < 0 is wrong in this case. The physics and transient pressure behavior near the surface right at the onset of ponding is more complicated and has been discussed extensively in the literature (Kutilek and Nielsen). Storativity concepts need to be introduced if I remember correctly. If the author wants to look at these processes in the some limit, then this should be done in a mathematically rigorous fashion in my opinion.
376:
380: necessarily
441: Kollet and Maxwell also showed that in their original publication, no?
In figure 4 and 5, it is very difficult to distinguish between the dn and cn results.
Make sure to carefully check language and grammar, especially for typos.

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ED: Publish as is (14 Sep 2017) by Philippe Ackerer

ED: Publish subject to minor revisions (further review by Editor) (09 Oct 2017) by Philippe Ackerer

AR by Rob de Rooij on behalf of the Authors (10 Oct 2017) Author's response Manuscript

ED: Publish as is (11 Oct 2017) by Philippe Ackerer

AR by Rob de Rooij on behalf of the Authors (16 Oct 2017)

Short summary

The dual node and common node approach are widely used to simulate coupled surface–subsurface flows. In this study it is shown that the dual node approach should be conceptualized as a one-sided finite difference approximation of the vertical head gradients at the land surface. This consistent dual node approach can be more accurate as well as as more numerically efficient than the common node approach.