the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The contribution of Humboldt Glacier, North Greenland, to sea-level rise through 2100 constrained by recent observations of speedup and retreat
- 1Fluid Dynamics and Solid Mechanics Group, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
- 2Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185, USA
- 3Byrd Polar and Climate Research Center, Columbus, OH, 43210, USA
- 4School of Earth Sciences, Ohio State University, Columbus, OH, 43210, USA
- 1Fluid Dynamics and Solid Mechanics Group, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
- 2Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185, USA
- 3Byrd Polar and Climate Research Center, Columbus, OH, 43210, USA
- 4School of Earth Sciences, Ohio State University, Columbus, OH, 43210, USA
Abstract. Humboldt Glacier, North Greenland, has retreated and accelerated through the 21st century, raising concerns that it could be a significant contributor to future sea-level rise. We use a data-constrained ensemble of three-dimensional higher-order ice sheet model simulations to estimate the likely range of sea-level rise from the continued retreat of Humboldt Glacier. We first solve for basal traction using observed ice thickness, bed topography, and ice surface velocity from the year 2007 in a partial differential equation constrained optimization. Next, we impose calving rates to match mean observed 2007–2017 retreat rates in a transient calibration of the exponent in the power-law basal friction relationship. We find that power law exponents in the range of 1/7–1/5 — rather than the commonly used 1/3–1 — are necessary to reproduce the observed speedup over this period. We then tune an iceberg calving parameterization based on the von Mises stress yield criterion in another transient calibration step from 2007–2017 to approximate both observed ice velocities and terminus position in 2017. Finally, we use the range of basal friction relationship exponents and calving parameter values to generate the ensemble of model simulations from 2007–2100 under three climate forcing scenarios from CMIP5 (two RCP 8.5 forcings) and CMIP6 (one SSP5-8.5 forcing). Our simulations predict 5.5–9.2 mm of sea-level rise from Humboldt Glacier, significantly higher than a previous estimate (~3.5 mm) and equivalent to a substantial fraction of the 40–140 mm predicted by ISMIP6 from the whole Greenland Ice Sheet. Our larger future sea-level rise prediction results from the transient calibration of our basal friction law to match the observed 2007–2017 speedup, which requires a semi-plastic bed rheology. In many simulations, our model predicts the growth of a sizable ice shelf in the middle of the 21st century. Thus, atmospheric warming could lead to more retreat than predicted here if increased surface melt promotes hydrofracture of the ice shelf. Our data-constrained simulations of Humboldt Glacier underscore the sensitivity of model predictions of Greenland outlet glacier response to warming to choices of basal shear stress and iceberg calving parameterizations. Further, transient calibration of these parameterizations, which has not typically been performed, is necessary to reproduce observed behavior. Current estimates of future sea-level rise from the Greenland Ice Sheet could, therefore, contain significant biases.
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Trevor R. Hillebrand et al.
Status: final response (author comments only)
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RC1: 'Comment on tc-2022-20', Anonymous Referee #1, 09 May 2022
Authors present numerical simulations of mass loss from Humboldt Glacier. Historical runs and observations (2007-2017) are used to constrain parameters in the description of basal rheology and the calving law. Optimal model parameters are used to produce projections of mass loss for a range of future forcing scenarios (2017-2100). Results highlight the importance of the basal sliding exponent, and best estimates of mass loss exceed previous projections by about a factor of 2.
The objectives and methodology of this study are clear; the results novel and well-presented; the conclusions well-supported, and overall this work is a good fit to The Cryosphere. I recommend publications with scope for some minor revisions, as outlined below.
The experimental design is mostly straightforward and easy to follow, though I wonder about the need to distinguish between the perturbed parameter ensemble, and the additional sensitivity experiments. After all, these are all sensitivity experiments, and personally I think the distinction overcomplicates the structure of the paper. An overview of the sensitivity to all physical parameters in a single Table would be nice. Some experiments that do not test the significance of physical parameters, such as the mesh resolution and potentially, bed topo, could be included in an Appendix to reduce the amount of information in the main text.
The validation approach is interesting, though I miss a more in-depth description/motivation of the validation criteria. Fig3b suggests that the optimal choice of q is critically dependent on the velocity itself, so why choose 1/5-1/7, which only provides a best match for u>600m/yr? In this regard, you might find the discussion in section 3.3 of [De Rydt et al. 2021] of interest, where authors show that the optimal sliding exponent for Pine Island Glacier is spatially heterogeneous. On a related note, I wonder if you can show the difference between observations and model in Fig3a, rather than the absolute model speed.
I think some further details about the melting and calving paramterization would be instructive for readers less familiar with the different (model) approaches. For example, in line 151: can you be more explicit about what you mean by ‘if there is no floating ice’, line 146-150 and 160-170: how does this discussion relate to quantities displayed in figure 2 (e.g. I’m unsure how ‘mean ocean thermal forcing’ is translated into a depth-dependent parameterization of melt), section 2.5: how is the calving front tracked in the model, and what happens to ice that has calved – is a minimum ice thickness applied?
Line 274 you refer to Table 1 here, but this table does not contain any information on SLR. Also, is there a reason why \sigma_max for q=1/7 in Table 1 is different between MIROC5 and the other forcing scenarios?
Line 427 I assume you are using annually averaged velocities, rather than seasonal products, for the 2007 initialization and 2017 validation? Given the large amplitude of seasonal speed-up/slow-down along this section of Greenland’s margin, how important is the choice of velocity product? In lines 590-595 you allude to possible important implications, but can you provide quantitative insights in how alternative intialization approaches (e.g. by using summer-only values of surface speed) might alter/bias your results?
FigS1. Can you provide a legend for the different colours please?
Ref.
De Rydt, J., Reese, R., Paolo, F. S., and Gudmundsson, G. H.: Drivers of Pine Island Glacier speed-up between 1996 and 2016, The Cryosphere, 15, 113–132, https://doi.org/10.5194/tc-15-113-2021, 2021- AC1: 'Reply on RC1', Trevor Hillebrand, 29 Jun 2022
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RC2: 'Comment on tc-2022-20', Anonymous Referee #2, 01 Jun 2022
In this work the authors investigate the contribution to sea-level rise of the Humboldt Glacier (North Greenland) for the next century. The model initial conditions are optimised through a three step procedure: first, the basal friction coefficient is optimised from surface velocity inversion at 2007; second, the basal friction exponent is tuned through imposed calving rates to match the observed ones for 2007-2017 and velocities for 2017-2018; third, the calving retreat parameterisation is tuned to match calving front positions and velocities for 2017-2018. The resulting initialisation is then used to launch an ensemble of model simulations for the period 2007-2100 and estimate sea-level rise due to future glacier retreat.
Overall I find this a very interesting work. It is well framed, the experimental design is novel and clever, and the results are comparable to previous estimates, although higher. I think this work suits very well the scope of The Cryosphere. Yet, I am not 100% convinced about the initialisation procedure that led to such results. Since your estimated SLR contributions are considerably higher than previous estimates and you attribute this “primarily to calibration of the basal friction law to match observed surface velocity changes”, I am wondering to what extent the validation procedure you apply in the optimisation+tuning experiments does affect the choice of the basal friction exponent, and so your final SLR estimates. I think that the strength of your results must be proven with some further verification of the tuning procedure for the historical runs. Moreover, I think section 2.3, as it is now, is missing some important clarifications. Therefore I suggest major revisions before publication.
Most of my comments concern the tuning of basal friction parameters in the initialisation procedure. I outline them here:
- Could you explain better how the effective pressure N is calculated in your basal friction law (line 95)? From what you write I understand it is rho_i g H - rho_w g z_bed, right? How is N treated during the basal friction coefficient optimisation? Is it kept fixed to initial values for the whole procedure assuming that ice thickness doesn’t change? See also next point.
- The relationship used to tune the basal friction exponent (line 129, µ = µ_opt |u_opt|^(1/3-q)) should be explained more in detail. To my understanding, you derived it by solving the equation N*µ*|u_opt|^(1/3-1) = N*µ_opt*|u_opt|^(q-1), having assumed same basal friction and velocity from the inversion procedure. However, this relationship is defined under some important assumptions that should be explained. You assume that the effective pressure is the same between the optimisation and the tuning procedure, but I would expect the ice thickness has varied between 2007 and 2017 due to margin retreat, and so did N. This argument is also valid for surface velocities. How did you account for velocity changes that come out due to glacier retreat in your tuning procedure? I would expect that the choice of the best basal friction exponent ultimately depends on these assumptions. Since your results strongly depend on the value of q (Fig. 5), to what extent do you think these assumptions affect your sea-level contribution for year 2100? What happens if the relationship you wrote is not supported, i.e. the N and velocities are not constant and, still assuming that the basal friction is the same for optimisation and tuning, you have this relationship instead: µ = N(2007) / N(2017) * µ_opt * |u_opt|^(1/3-q) * u_obs(2007)/u_mod(2017) ? Also, have you tried to do the inversion with 1/7<q<1/5 to corroborate your tuning procedure?
- In the basal friction exponent tuning experiment you compared modelled to observed velocities only for year 2017-2018. Why didn’t you test your velocities for the whole historical period (2007-2017) and choose the q that best matches the velocities on a 10yr mean? Also, would considering seasonal velocities instead of annual mean lead to a different q? Would in these cases the choice of 1/7<q<1/5 still be confirmed and so your SLR estimates?
- How did you impose the calving front retreat rates for years 2007-2018 (line 131)? To my understanding the calving tuning procedure described in section 2.5 is done after the basal friction optimisation. How did you calculate the calving rate then? Also, is the submarine melt taken into account for such tuning tests?
Regarding the structure of the manuscript, I don’t really understand why you separate the perturbation from the sensitivity tests. In fact, their design is comparable (you fix some parameters and perturbed some others) and they all contribute to build the uncertainty range of sea-level rise due to glacier retreat. To lighten the structure of the paper, I would suggest to include all sensitivity tests into the perturbation experiments and introduce a summary table describing the whole experimental design (which parameters are varied and which are fixed for each run). I suggest also to mark out those tests do not take part in the final estimates of sea-level contribution (e.g. tests for q=1, calving rate limit > 5km/yr). Finally, I would suggest to leave the mesh convergence test to the supplementary material, since it is more a precondition for your tests rather than a functional part of the study, and the bedrock sensitivity test too, since it does not involve any change in physical variables.
Specific Comments
- Figure 1: is this the Humboldt Glacier or the regional model domain? To me that is the catchment containing the Humboldt glacier. Also, I suggest to make the black rectangle in a) with a bigger line and with a different colour. I would add the modelled effective pressure and instead of panel b) and d) I would only show the velocity difference (modelled velocity - observed velocity).
- Line 128: do you mean q instead of m? Also, “to find the appropriate range of values of q in the basal friction relationship, we recalculate the friction parameter ð…” is misleading. You should add you did that to match the velocities upon retreat.
- Line 132: Do you mean 2017 instead of 2018? Generally, I found quite confusing the definition of the period used for hindcast, which sometimes ends in 2017, sometimes in 2018. Please check that in the whole manuscript.
- Line 156: Please change to “Connectivity Temperature Depth (CTD) and Airborne eXpendable Connectivity Temperature Depth (AXCTD)”.
- Line 207: where does this SMB forcing come from? From which model? And why did you choose this period, and not a climatology close to year 2000 since you initialise the model at 2007? To what extent might the choice of a more recent climatology for the control run affect your results and reduce your estimated sea level contributions?
- Line 274: Table 1 does not show the results, rather summarises the experimental design. I think that table is missing.
- Line 281: where does the upper bound of SLR for the 2017 Calving front experiment (6.7 mm) come from? Is HadGEM 2 predicting ~6.5 or 6.7mm?
- Line 286: with “variability due to … climate forcing” you include also the variability in submarine melting, right? Could you be more precise since the choice of the oceanic thermal forcing influences your results?
- Line 304: looking at Fig. 2c it seems that CNRM-CM6 has a higher ocean thermal forcing than HadGEM2. So why does only the latter lose all the ice shelves within 2100?
- Line 321: could you introduce the undercutting already in the submarine melting parameterisation section since you have a precise parameterisation for it?
- Line 366: why not repeating the experiment also for MIROC for consistency with the other tests?
- Figure 9: could you plot also the change in volume above flotation and compute the associated sea-level contribution?
- I am missing a Figure summarising the sea-level contribution from all sensitivity/perturbation experiments compared to previous estimates. For example, you could plot the latter as superimposed to the uncertainty range in SLR raised from your runs. I think it would help the reader to have your results recapped in one plot.
- Figure S3, S4: don’t think you really need to show the bathymetry here. In case you want to keep it, please change the colour palette to a scale of greys. Also, specify that grounding line colours follow legend of Fig.4. Finally, please change the colour of small areas with speed>3km/yr to red or green.
- AC2: 'Reply on RC2', Trevor Hillebrand, 29 Jun 2022
Trevor R. Hillebrand et al.
Data sets
MPAS-Albany Land Ice model simulations of Humboldt Glacier, North Greenland, from 2007–2100 Trevor R. Hillebrand, Matthew J. Hoffman, Mauro Perego, Stephen F. Price https://doi.org/10.5281/zenodo.6338400
Model code and software
MPAS-Albany Land Ice model simulations of Humboldt Glacier, North Greenland, from 2007–2100 Trevor R. Hillebrand, Matthew J. Hoffman, Mauro Perego, Stephen F. Price https://doi.org/10.5281/zenodo.6338400
Trevor R. Hillebrand et al.
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