the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Mar 2026
Random forest parameterization of Antarctic subglacial hydrology for coupled ice-flow modelling
Abstract. Antarctic ice-sheet flow is sensitive to changes in basal friction. These frictional changes are modulated by the effective pressure in the subglacial drainage system in response to changes in ice thickness, basal melt, and slip rates. To overcome the computational burden of coupled modelling of the ice sheet and the subglacial drainage system, we develop and evaluate a machine-learning parameterization of basal effective pressure. The parameterization, consisting of a random forest regression model, is trained to predict continent-wide effective pressure based on ensembles of simulations with the physics-based Glacier Drainage System (GlaDS) model in seven major ice-flow basins. The ensembles vary the values of five subglacial drainage model parameters, allowing the parameterization to predict how effective pressure varies across parameter space. The random forest parameterization explains 65 % of the variance of the effective pressure predicted by the numerical model, but 99 % of the variance in ice speed when coupled to the ice-flow solver in the Ice-Sheet and Sea-level System (ISSM) model. We assess the influence of effective pressure on future flow speeds by imposing plausible ice-sheet thickness changes drawn from ice-sheet model projections. Using the random forest parameterization instead of the numerical subglacial drainage model results in differences in grounding line speed of 127–311 m a-1 (2.1–10 %). Other approaches, such as holding effective pressure constant in time or assuming ocean connectivity, result in larger grounding-line speed differences of 441–2199 m a-1 (8.5–74 %). These results suggest that the random forest parameterization for effective pressure can be used to add active subglacial hydrology to ice-sheet modelling with higher fidelity than other effective-pressure parameterizations while reducing computation time from as long as 16 days to 0.5 seconds.
- Preprint
(7379 KB) - Metadata XML
- BibTeX
- EndNote
Status: open (until 22 May 2026)
- RC1: 'Comment on egusphere-2026-343', Anonymous Referee #1, 15 Apr 2026 reply
-
RC2: 'Comment on egusphere-2026-343', Anonymous Referee #2, 16 Apr 2026
reply
This manuscript (MS) presents and discusses a new, statistical parametrisation of subglacial drainage. The statistical model is a Random Forest (RF) model trained on flotation fraction outputs of an ensemble of Glads model runs of seven large Antarctic catchments. The model is evaluated in terms of its capability to reproduce flotation fraction, effective pressure as well as ice flow speeds calculated with a one-way-coupled SSA ice flow model (using a Budd sliding law). The evaluation is done both for present day and in future configurations of Antarctica (2050 for West Antarctica and 2300 for East Antarctica). The ice flow outputs are also compared against SSA model runs using a sliding relation fed by Glads and by a perfect ocean connection (POC) subglacial drainage model runs.
The tuned RF model performs well in reproducing flotation fraction as modelled by Glads, a bit less well for effective pressure, but well also when coupled to ice flow. The MS shows that for future ice flow predictions the choice of model for effective pressure matters and that this RF of model could be useful for such simulations.
Unfortunately, the MS suffers from a incomplete presentation of the methods, too many model runs and, hence, results which are difficult to follow. It thus needs to be streamlined considerably before publication. In particular, the methods do not fully describe the RF model nor how it is evaluated against other models. For instance, the RF model needs to be described fully (e.g. number of trees, levels, total number of parameters) and what cost function it aims to minimise. Many methods applied are not defined, for instance what "mean" in various context means, what "perturbed parameters" are, what "cross-validation" is, etc. Last, there was not enough selection of which of the many performed model runs are presented. In the Results section, in many subsections a new set of model runs are presented and discussed without ever being specified accurately.
Concluding, the manuscript presents an interesting and potentially very useful subglacial drainage parametrisation. However, the confusing presentation of both methods and results lead me to not fully understand what the authors present and to a quite difficult time reading the MS. I suggest that (I) the methods are updated to carefully define the RF model, all the model runs (Glads, RF, POC, SSA), the calibrations and the evaluations, (II) the numbers of presented results is reduced to what is needed to support the main results (which should probably be: RF works well and RF potentially useful for predictive ice flow modelling). Point I is necessary whereas II would be nice-to-have.
Major comments
The issues mentioned above (and below) with the Methods and Results section.
The paper by Brinkerhoff et al 2021 is not cited nor discussed. This was the first paper doing subglacial drainage system emulation and ice flow, thus this is an important context which is missing.
What are the Glads parameters corresponding to the mean simulation? In fact, they don't exist as the mean of an ensemble of Glads runs is unlikely a result which could be (re)produced by a Glads-run with some suitable parameters. I don't think this is an issue as, likely, the mean would not be too far off a realisable Glads run with parameters close to some mean of the parameters. So, no need to change the methodology for this but it should be acknowledged.
It could be interesting to plot the RF predicted values of floatation-fraction for that median set of Glads parameters (or the mean of all) versus thickness and bed elevation (the two most important parameters), maybe as a contour plot. This could give some insights what kind of function the RF encodes and how smooth it is.
Model/calibration runs mentioned in the Results
To aid to resolve my confusion I made a summary of the model runs encountered in the Resutls section. Many of them are not described in the Methods section (which would be the classic paper-structure). I indicate with "(...)": where model run was introduced and with "[...]" recommendation for update.
3.1 Glads present day ensembles (in Methods) []
3.2 RF trained on mean (new) [is this really necessary?]
3.2.1 method-like description of RF geometry-parameter selection (new) [importance scoring should be described in the Methods]; new "production" RF model fitted on only four geometric variables (partially mentioned in methods)
3.2.2 (1) RF retrained with leaving basins out (new) [Needs mention in Methods. "cross-validation exercise" is not defined anywhere]
3.2.2 (2) RF retrained taking "subsets of the training data" (new) [not clear to me what is done exactly. Needs mention in Methods]
3.3 Here, I think, the retrained RF of 3.2.1 is used (previously defined) [be clear what is used]
3.4 Here RF is run at 2300 for all of Antarctica, which is slightly confusing as before it was said that West Antarctica is only run in 2050.
3.5.1 (1) describes inversion for ice flow modelling, which is at least partially described in the Methods already (previously defined) [only describe in one place]
3.5.1 (2) forward simulations with using different C and N
3.5.2 future simulations: unclear what glads parameters are used. Figure 7 suggests it's the ensemble of of all. In all it seems 2x2 simulations for the two ensembles and then 2 simulations for POC. Additionally there is the RF trained on mean simulation mentioned in the last sentence.
3.5.3 It seems to me that the simulations described in the first sentence are the same as in 3.5.2. If so this is a bit confusing as it sounds like a new set of simulations is done.
I recommend that the all the model runs and calibrations are at least mentioned in the Methods and that at least the ones which feature several times are given a label, say GE-pres for Glads-ensemble present day, RF-mean calibrated on the mean of Glads. A table could help too.
Line by line comments
Title: What is the difference between "parametrisation", "surrogate model" and "emulation"? The authors have another paper with a statistical model where they call it "emulation", why now "parametrisation"?
L2: "in response" could refer to both frictional changes or eff.-pressure
L13: always use "perfect ocean connectivity" (likely an issue in other places)
L24: Cite https://doi.org/10.5194/tc-12-3931-2018 instead of Fischler
L25: Also cite Hewitt 2013
L43: needs context of emulation based subglacial drainage work. Brinkerhoff & al, Verjans&Robel, other?
L53: state clearly that it is a one-way coupling only
L54: here could be a good location to give a bit more an overview over the many methods used in this paper
L68: a bit more context on what E_creep does would be good. Just one sentence.
L75: "Present day ice sheet geometry and meshing"
L107: "perturbed-parameter ensemble" is never defined. I find it helpful when papers define concepts like this clearly, name them and then strictly stick to the defined name. This could be done for this phrase but there are other concepts/phrases in this MS too.
L109: "numerical stability limit"
L111: "five-year epochs" not defined.
Figure 1: How is the median simulation picked? What median? This needs to be in the Methods. Note that using "Glads simulation" to refer to a simulation output is confusing, in particular in the context of many ensemble runs. This is often encountered throughout the MS.
Figure 1: "cross-validation" is never defined. Note that it features both as "cross-validation evualuation" and "cross-validation prediction", unclear how those are related. There are a number of ways cross-validation is done in statistics, so this needs clarification. In fact, I think there are two types of cross validations done in the MS.
Figure 1: never defined what errors, absolute, relative?
L135: "full-factorial sampling" is (maybe?) too much stats jargon for TC journal?
L135: "Samples are drawn from the logarithm of the parameter values" this is not clear. Maybe "Parameter values are log-uniformly sampled."
L136: "and" -> "using"
L143: briefly state what l_c does
L155: 100 samples again? What is the melt water input?
Section 2.3: this needs to be much more careful.
L160: specify that it is a "spatial pointwise" mapping
L162: as far as I can tell, the RF trained on nine ice-sheet variables and the full ensemble is never used.
L163: "forcing fields" undefined
L166: "... importance values for the final parametrisation." but come up with a better name for the "final" parametrisation.
L175: Brinkerhoff & al 2021 needs to be discussed here
L176: Not sure a neural net is harder to integrate into ISSM. It would be, for instance, differentiable and thus better for control-method inversions.
L178: This is a separate drainage model and warrants a separate section
L180: "physics-based model" What is this? Is it Glads or POC? Just say it.
L204: There are 700 scenarios here for both Glads-runs and RF-runs, which one?
L205: "friction coefficient fields"
L215: state briefly why also log-misfit is used
L215: Eq B2 states abs-squared misfit
Section 3.1: here "ensemble" is used both in plural and singular. The authors need to come clear on how they want to name it and then be consistent throughout. (could be an ensemble for each catchment or just one ensemble)
Figure 2: I don't understand how flotation fraction is capped at 1 but eff.-pressure can go negative (most obvious in panel c vs f)
Figure 2: delete "language=en"
Section 3.2: a new model run setup is presented here ad-hoc (typically that is done in the methods). This would not be the end of the world but is really symptomatic of this MS: almost every section in the results introduces some new model setups and runs. I found this really hard to ingest.
L242: "mean" is never defined
L243: according to a later section (3.6), the training of the RF is quick, so this argument does not hold.
L255: this 1.8 and 18 must be a factor? If so state. But as R2 can go negative, an absolute change would be better to state. Same for Fig 3
L258: odd indeed that the Shreve potential, which is the sum of bed and thickness, is also needed. Have the authors tried to use effective pressure in units of meter H2O instead of Pa? This would "scale" the quantity better, or does RF not care about scaling?
L262: "... retrained reduced model compared to the previous model (Fig 3a versus 3b)"
L267: "repeat", as far as I can tell no previous cross-validation exercise was done (apart form a mention if Fig 1)
L269: "each" -> "one"
L275: state what "quantity", is it the number of catchments?
Table 3: the "u" column is not described/used in the text, I think
Table 4: Not clear how the comparison is really done. Is RF run for all parameter combos for which Glads was run?
L298-308: isn't this one of the key results of the paper? Should this not be given more room? Would it not fit better into the previous section?
L306: here "perturbed geometetry" term is defined. But instead it should be defined in section 2.2.2
L311: delete "."
L321: not clear what is done here. I think that this is already described in the methods, but as so many extra model runs & setups are described ad-hoc in the results, I am not sure. Is this using the mean?
L344: not clear what effective pressure fields are used. Mean, ensemble?
L344: "using the corresponding friction coefficient inferred from present-day conditions and surface velocity observations" is a repetition of the previous sentence.
L363: "unconstrained friction coefficient", what is this?
L366: state what C is used
L366: "grounding line speed" is unclear. ice speed at the grounding line? Also L431
L381: Do the Glads simulations run in parallel on the 32 cores of this CPU or single core?
L382: Assuming Glads runs on a single core, the runtimes to steady state and number of runs suggests that this CPU would have needed to run for almost half a year to complete the Glads runs (11 ensembles x 100 samples x ~100h runtime / 32 cores ~ 140 days). Is this correct? Elsewhere 16days are stated.
L388" "ice dynamics"
Figure 6: for SSA "depth averaged" and surface flow speed are the same. I suggest to only use the latter as that is what is also measured.
Figure 7: not clear what "sensitivity" means. This should be defined somewhere
Figure 7: not sure what the bands refer to. Ensemble, something else?
Figure 7: is there a difference between "perturbed-parameters samples" used here and "perturbed-parameters" used elsewhere?
L395: I suggest to use "momentum balance" everywhere
L433: how can a glacier accelerate by 25 years?
L441: also cite https://doi.org/10.1017/jog.2020.116 and https://doi.org/10.1029/2018JF004921
Section 4.2: discuss Brinkerhoff & al here. In particular, they fit scalar parameters and not fields like C here, which would be interesting to contrast.
L481: fast to train once the Glads simulations are run
L590: what about the outlook of doing combined ice-flow-drainage inversions? Would this be feasible with RF+ice-flow?
Table A1: The caption does not define the shown quantities well enough
Table A1: https://doi.org/10.1016/j.scitotenv.2024.172144 gives 51m3/s for PIG
Figure A1: "Histograms of ..." from what ensemble is this? Present day?
L615: not clear what Glads parameters or if for ensemble
Figure C1: caption suggests that column C should have 8 lines in each plot
Citation: https://doi.org/10.5194/egusphere-2026-343-RC2
Model code and software
timghill/antarctic-glads Tim Hill, Matthew J. Hoffman, Gwenn E. Flowers, Derek Bingham https://doi.org/10.5281/zenodo.18381581
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 349 | 217 | 30 | 596 | 24 | 55 |
- HTML: 349
- PDF: 217
- XML: 30
- Total: 596
- BibTeX: 24
- EndNote: 55
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
See attachment