Intercomparison of surface meltwater routing models for the Greenland ice sheet and influence on subglacial effective pressures

Yang, Kang; Sommers, Aleah; Andrews, Lauren C.; Smith, Laurence C.; Lu, Xin; Fettweis, Xavier; Li, Manchun

doi:https://doi.org/10.5194/tc-14-3349-2020

Articles | Volume 14, issue 10

https://doi.org/10.5194/tc-14-3349-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-14-3349-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 14, issue 10

Research article

|

07 Oct 2020

Research article |

| 07 Oct 2020

Intercomparison of surface meltwater routing models for the Greenland ice sheet and influence on subglacial effective pressures

Kang Yang, Aleah Sommers, Lauren C. Andrews, Laurence C. Smith, Xin Lu, Xavier Fettweis, and Manchun Li

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Final revised paper (published on 07 Oct 2020)
Supplement to the final revised paper
Preprint (discussion started on 04 Nov 2019)
Supplement to the preprint

Interactive discussion

Status: closed

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

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RC1: 'Review to the paper entitled "Inter-comparison of surface meltwater routing models for the Greenland Ice Sheet and influence on subglacial effective pressures"', Basile de Fleurian, 06 Dec 2019
- AC1: 'Response to Reviewer 1', Kang Yang, 19 Jan 2020
RC2: 'Reviewer comments', Anonymous Referee #2, 19 Dec 2019
- AC2: 'Response to Reviewer 2', Kang Yang, 19 Jan 2020

Peer-review completion

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

ED: Publish subject to revisions (further review by editor and referees) (13 Feb 2020) by Elizabeth Bagshaw

AR by Kang Yang on behalf of the Authors (05 Mar 2020) Author's response Manuscript

ED: Publish subject to revisions (further review by editor and referees) (18 Mar 2020) by Elizabeth Bagshaw

ED: Referee Nomination & Report Request started (19 Mar 2020) by Elizabeth Bagshaw

RR by Basile de Fleurian (01 Apr 2020)

RR by Anonymous Referee #2 (15 Apr 2020)

RR by Anonymous Referee #3 (23 Jun 2020)

Suggestions for revision or reasons for rejection

This paper addresses a great problem and has more than enough good content to make it a useful and worthy contribution to TC. Recognizing that this paper has already been through review and revision, I will focus specifically on what I think could be a contentious element of the revised manuscript.

The primary contribution of this study is the inter-comparison of three methods used for surface meltwater routing to moulins. All three schemes are forced by the same RCM (MAR), and all three results are used to drive the same subglacial drainage model SHAKTI. The routing is tested on four internal catchments on the western margin of the Greenland ice sheet, where surface water feeds a network of supraglacial streams that presumably terminates in a single moulin. The underlying motivation for the study is the importance of distributed versus punctual water input to the basal drainage system and its influence on basal effective pressure, and therefore ice dynamics (via sliding). I think there is a strong observational and theoretical case for pursuing a better understanding and representation of meltwater routing to surface portals in the ice sheet, as is done in this paper. As an aside, I do not see a problem with investigating the precision of different approaches even in the absence of assessing accuracy by making comparisons with observations.

In principle, I can understand why the authors chose to follow this line of inquiry all the way through to the subglacial drainage model (and can anticipate the rebuttal to my suggestions below). However, a tidier and more useful study, in my mind, would omit the subglacial modelling and instead focus on everything upstream. Ideally, this might include the use of two RCMs instead of one, and/or a wider variety of test catchments (perhaps of different sizes, as elevation is varied in this study but not size). Text saved by omitting the subglacial drainage model could be dedicated to a more thorough statistical and descriptive characterization of the modelled moulin input hydrographs, and perhaps even the proposal of useful parameterizations or short-cuts. Qualitative statements about the anticipated influence these input hydrographs would have on modelled subglacial drainage variables could still be made, but more detailed and realistic modelling thereof left for another study.

The ambivalence I have about the usefulness of the subglacial drainage modelling component of the study has nothing to do with the particular model itself: SHAKTI is one of the better models out there. Rather it stems from (1) the age-old dependence of model results on poorly constrained model parameters and (2) the way in which the model tests were executed. For readers familiar with subglacial drainage modelling, it might be straightforward to discriminate between a particular model result and generalizations about the *actual* behaviour of the subglacial drainage system; for other readers, this line might be fuzzy.

The first concern relates to the dependence of the model on uncertain parameter values. For example, the propensity for distributed/cavity-system-like model behaviour (and hence tendency toward lower effective pressures) would be influenced by prescribed bed properties (e.g. height and wavelength of bedrock obstacles: br, lr), sliding and the coefficient A. br, lr and A are prescribed. Although SHAKTI has been described in other publications, the implications of these chosen parameter values should be addressed in this paper. For example, to what extent can channel-like (efficient drainage) behaviour be enhanced or supressed with plausible variations in br, lr, A? On sliding: I may have missed it, but is two-way coupling between SHAKTI and ISSM included such that enhanced sliding caused by low effective pressure feeds back on gap height? This has been shown to be an important negative feedback excluded from most drainage models by Hoffman and Price (as sliding is often prescribed, or if not prescribed, the full feedback not included). The authors can probably add some text to the manuscript to reassure readers that the values of br, lr, A and treatment of sliding have a strong basis, or that their specific values/treatment are not critical to the model results.

The more serious concern I have is the way in which the model tests were conducted: on a square 1-km domain, where it is difficult to image the (necessary but uncertain and possibly unrealistic) boundary conditions not having an undue influence on the results. I gather the authors reran all the simulations with Pw=0.5Pi as the left (~downstream) boundary condition for the revised manuscript, rather than Pw=0. I agree that Pw=0 seems very hard to justify, especially considering that the same boundary conditions are being applied to all four domains (correct?), which span a range of elevations and ice thicknesses. Pw=0.5Pi seems marginally better, but still: boundary conditions, especially when boundaries are close to the region of interest (within 500m of the moulin in this case), can dictate the results. I fear that the similarity of results between all four IDCs may be a function of the uniform boundary conditions being applied to each. IDC4 is 100km from the ice-sheet margin, with a surface elevation > 1600m and ice thickness > 1400m. Could the water pressure 500m from this moulin really be the same as that for IDC1? With three no-flow boundaries (aside: I interpret “zero flux pressure boundaries” to mean “zero flux boundaries” (i.e. Neumann), correct?) and one low-pressure (Dirichlet) boundary, it seems a foregone conclusion that preferential flow will develop from the point of water injection to the boundary. The no-flow boundary conditions at the upstream end of the domain seem equally problematic to the pressure boundary condition at the downstream end. In the subglacial drainage system, water would be flowing across these domains defined on the basis of small supraglacial catchments. My sense is that a square 1-km domain is too small to say with confidence that boundary conditions are not dictating the solution.

I suspect this model set-up was adopted based on CPU considerations. That aside, if I were to imagine the ideal test, it would be one in which there were a quasi-realistic control simulation to which the various moulin-injection simulations could be compared. For example, the control simulation could be a catchment-wide steady state forced by distributed water input. The moulin input could then be introduced to this catchment-wide steady state. Simulating the entire catchment would solve the boundary-condition problem but be much more computationally expensive. Without going to this trouble I can imagine some alternatives: (1) increase the size of the domain by an order of magnitude and observe how results change, (2) keep the domain size the same but prescribe uniform boundary conditions on all four sides (e.g. Pw=0.5Pi, Pw=0.9Pi, Pw=Pi) and observe how results change.

So what are the options?

1. Omit the subglacial drainage modelling from the paper. I can imagine most or all of the reasons the authors might argue strongly against this.

2. Perform additional model tests (see text above) to assess the role of parameter choices and boundary conditions in determining the model results and revise accordingly. One would like to see that the similarities/differences between the tests with different surface water routing schemes is robust to uncertain model parameter values and treatment of boundary conditions on the subglacial drainage model. This may involve replacing the current results in the paper with updated results.

3. Change none of the model results but revise the text to dial-down results/conclusions about subglacial hydrology. This option would still benefit from additional model tests being done (even if not shown), to increase the readers’ confidence in the robustness of the results/conclusions. As I imagine this is the most appealing option, I will be specific. The following statements are examples of results/conclusions that are difficult to buy into without additional information related to the boundary-condition issue described above, and to a lesser extent, the parameter choices:

“In all cases a clear preferential pathway develops from the moulin location to the outflow at the left edge of the domain.”

“the overall channelization behaviour and temporal mean effective pressure over the 31-25 day simulations are relatively consistent between models”

“different routing methods may not produce significantly different cumulative or time-averaged effects in effective pressure for simulation time scales longer than daily.”

“The subglacial model domain and duration were chosen to illustrate the impact of the chosen supraglacial routing model on local subglacial hydrology in the vicinity of a moulin input at the bed.” (Though I understand the idea here, I’m not sure this can be done without realistic boundary conditions.)

Finally, I found this a really useful and interesting conclusion of the study as it relates to methodological/numerical aspects of subglacial drainage modelling: “Our results demonstrate that the supraglacial hydrologic system acts as short-term storage for surface-derived meltwater, as exhibited by the time lag of moulin inputs between models; therefore, application of an appropriate surface meltwater routing scheme may reduce the dependence of some subglacial models on a somewhat arbitrary englacial storage term to produce realistic diurnal effective pressure variations and timing lags”

The authors have done some great work on an important problem that merits publication. I appreciate their efforts to follow the water all the way into the subglacial drainage system in order to figure out whether/how surface water routing matters to hydrologically forced ice dynamics. If greater confidence in the robustness and realism of the subglacial drainage modelling results can be established with further (even somewhat minor) revision to the paper, I think the impact of this work will be amplified and more persistent.

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ED: Publish subject to revisions (further review by editor and referees) (28 Jun 2020) by Elizabeth Bagshaw

AR by Kang Yang on behalf of the Authors (23 Jul 2020)

ED: Publish subject to technical corrections (17 Aug 2020) by Elizabeth Bagshaw

AR by Kang Yang on behalf of the Authors (20 Aug 2020) Author's response Manuscript

Short summary

This study compares hourly supraglacial moulin discharge simulations from three surface meltwater routing models. Results show that these models are superior to simply using regional climate model runoff without routing, but different routing models, different-spatial-resolution DEMs, and parameterized seasonal evolution of supraglacial stream and river networks induce significant variability in diurnal moulin discharges and corresponding subglacial effective pressures.