the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Jan 2026
Brief Communication: Inferring Glacier Equilibrium Line Altitudes in Central Europe with FROST
Abstract. Glaciers in Central Europe are projected to almost disappear by 2100. To improve projections, glacier models must be calibrated to match observations. Using the open-source Framework for assimilating Remote-sensing Observations for Surface mass balance Tuning (FROST), we infer equilibrium-line altitudes and surface mass balance parameters for all Alpine glaciers during 2000–2019 through an Ensemble Kalman Filter. The method combines an elevation-dependent surface mass balance model with ice dynamics from Instructed Glacier Model (IGM). Validation against in-situ mass balance and end-of-summer snowline data (correlations of 0.76 and 0.62) shows that FROST enables satellite-based regional estimates of glacier equilibrium conditions.
Competing interests: Johannes J. Fürst is a member of the editorial board of TC.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 06 Mar 2026)
- RC1: 'Comment on egusphere-2025-5486', Anonymous Referee #1, 12 Feb 2026 reply
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RC2: 'Comment on egusphere-2025-5486', Codruț-Andrei Diaconu, 22 Feb 2026
reply
The paper applies FROST (Herrmann et al., 2025), which combines an ensemble Kalman filter with IGM, to infer SMB/ELA-related parameters from elevation change data. Compared to the original FROST study on a single glacier, the current study extends the framework to a regional Alpine application. A useful additional contribution is the snowline altitude (SLA) product derived from satellite optical imagery, which should be stated more clearly in the abstract as part of the paper’s contributions. Overall, the manuscript presents a relevant regional-scale demonstration of the framework. I do not have major concerns, only a couple of minor-to-moderate comments and questions that would help clarify a few points and limitations.
General comments1. Uncertainties in the evaluation against GLAMOS:
- "We select glaciers with more than five years": is this enough to neglect ELA / MB-gradient variability over time? I would look (maybe in the supplement) at the variability of the average ELA over a certain window (>5 years) relative to the 20-year average, using glaciers that have full temporal coverage (assuming there are some).
- Second, regarding the MB gradients, are the actual profiles piecewise linear (with only two segments)?
2. Uncertainties in the SLA: was the methodology evaluated in a prior work? How accurate should the estimated SLAs be? And the temporal-coverage concern I raised in the previous point could also be mentioned here. I think I would at least look at how well the SLAs align with GLAMOS ELAs for glaciers with a good temporal overlap.
3. In the FROST paper I see that there is a bin-size parameter: how was it chosen here (per glacier?), and how does it influence the precision of the inverted ELA?
4. Since it's a Brief Communication, I would add a few more "so what" statements (including in the abstract). Otherwise, it sounds mainly like an application paper where FROST is further validated.Line-by-line comments
- 19: Surface Mass Balance (SMB) is first used here
- 23: I would cite also OGGM v1.6 (https://doi.org/10.5281/zenodo.7718476), since only starting from 1.6 the geodetic MBs are used, as far as I know. Since you rely on OGGM for data processing as well, it's good to refer to a specific version.
- 32: See AGILE v0.1 (Schmitt et al. 2026) --- very recently published but fits quite well to this discussion
- 42: I would briefly justify the 1 km^2 choice.
- 47: "more robust" compared to what?
- 49: I would also add the GLAMOS citation here.
- 58: Also for the accumulation area?
- 75-77: Was the method applied on both bands separately, or on some index?
- 77-79: How exactly was the SLA estimated from the snow masked DEM?
- 80-81: Does this mean that if >3 images are present, the estimated SLA is always retained for that particular year & glacier?
- 87: Maybe define mean absolute error (MAE) here and use MAE everywhere else.
- Fig 1:
- It is quite difficult to see any correlation. I would be tempted to discard the glacier-area encoding to reduce overlap (or try another visualization). Otherwise, I am not sure the climatic gradients mentioned in the text can actually be observed. On top of this, I see in Fig. S1 that there is no significant correlation between area and ELA.
- I would move the text labels so they do not overlap with the points.
- Fig. 2:
- I am not sure what “Mean error” means here, but I would report the MAE before and after bias correction. From the text, I understand that “Mean error” = MAE.
- Is the comparison between the modeled dh/dt and the observed one telling us anything critical, since the observations themselves were used to calibrate the model? Perhaps this is better suited for the supplement, and the space could be used for something more interesting. For instance, it would be interesting to see a comparison between the calculated SLAs and GLAMOS ELAs, or another type of validation for the SLAs, to help interpret the metrics from panel (b).
- Maybe add the sample sizes in both panels.
- I would force integer tick labels for panel (a).
- The title of panel (b) is confusing.
- Fig 3:
- What do the ellipses represent?
- I see that Aletsch is an outlier also in (g) & (h). Any idea why? The ice thickness looks better (this is the one I expected to be an outlier following the discussion from lines 128–130).Citations
Schmitt, P., Maussion, F., Goldberg, D.N., Gregor, P., 2026. AGILE v0.1: The Open Global Glacier Data Assimilation Framework. Geoscientific Model Development 19, 1301–1319. https://doi.org/10.5194/gmd-19-1301-2026
Citation: https://doi.org/10.5194/egusphere-2025-5486-RC2
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- 1
The manuscript ‘Inferring Glacier Equilibrium Line Altitudes in Central Europe with FROST’ by Herrmann and co-authors presents an application of the newly developed IGM assimilation framework FROST to all glaciers in the European Alps. The framework assimilates surface velocity, ice thickness and elevation change data to calibrate a simple mass balance model, returning ELAs and altitudinal gradients of ablation and accumulation. The authors validate these results against satellite derived end-of-season snowlines and in-situ measurements, showing generally good agreement.
I enjoyed reading this paper and seeing a concrete regional application of the FROST framework. It shows promising results and definitely represents a new stepping stone for data assimilation in glacier models. There were several instances where I would have liked more details on the method and its underlying limitations although I also appreciate that the short format makes it difficult to expand on these – potentially merging the result/discussion or discussion/conclusion may help remove repetitions and gain space to expand on some of the discussion of the limitations? Beyond this, I still had a number of concerns that I believe should be considered.
General Comments
Description of the model and its limitations: There are a number of limitations/assumptions to the approach/model used that are barely mentioned and that end up being listed in the discussion but with very little explanation of their effects on the results. A few examples:
Furthermore, I find the half-results, half-discussion paragraph (L114-123) not well structured and hard to follow.
Manual tuning of the IGM optimization parameters: this part is very vague but actually quite crucial for the application of the method and potentially strongly influences the results. More details are needed on how this was actually done and based on what criteria. It’s also unclear whether GlaThiDa was used in the optimization or just the validation. Presumably the wealth of thickness data in the Alps (or at least in Switzerland, cf. Grab et al. (2021)) would allow for a cross-validation experiment.
Limitation to GLAMOS: While GLAMOS is an exemplary dataset, I find it disappointing that measurements from Austria, Italy or France were not included.
Snow line mapping: I find the definition of snowlines using a simple Otsu threshold overly simplistic. One simple Otsu threshold is likely to get the snowline wrong in the presence of debris. Even without debris, if the snowline goes beyond the firn transition, how can one be sure that the depicted snowline doesn’t correspond to the ice-firn transition, while the snowline would be higher? This makes me wonder if that could not explain the ELA bias obtained from the EoS SLAs. There are a number of significantly more robust approaches to map snowlines out there (Loibl et al., 2025; Roussel et al., 2025; Kim et al., 2025 to name but a few recent ones), including some actual EoS SLA datasets for the Alps if I recall. I therefore wonder why go with such a simplistic approach.
Alternative metrics of glacier state: There is a focus on ELA in this study, but I believe that this is sometimes not the most telling metric when it comes to characterizing glacier health. For this I would suggest using the Accumulation Area Ratio, which may lead to stronger correlations in Supplementary figure 1.
Line-by-line comments
L1: I find this first two sentences strange and not very convincing as a justification.
L5: the Instructed Glacier Model
L6: ‘correlations’ is vague, be more specific about the actual metric used
L7: The term ‘glacier equilibrium conditions’ is not standard and slightly confusing. Maybe rather mention how this information could be used?
L12: or have already disappeared…
L13-14: ‘these glaciers are vital … for hazard management’? Doesn’t really make sense (one would argue that there’d be no glacier-hazard management without glaciers), should be reformulated
L16: Not convinced that the Birchgletscher collapse is a result of glacier retreat.
L17: Syntax error with the sentence split in 2
L20-23: it is apparent here that you’re referring to regional-scale models which up to now have basically only used Hugonnet for calibration (although this is changing – see Cremona et al. (2025) with snowlines). The reference to these types of models should be made clearer, because at the smaller glacier/catchment scale, Hugonnet is only one of the many options to calibrate an energy-balance model.
L23: reduces -> reduce
L24: more correct to specify that these are spatially distributed datasets
L30: I see what is meant but have to disagree here. IGM does invert for a so-called ‘sliding’ term, but this is just a black box with many hidden processes. In no way does it say anything realistic about the actual internal glacier structure/basal conditions.
L36: Space to be removed after ‘model internals’
L41: ‘building on… Hermann et al. (2025), we apply it…’ Something wrong with the syntax here.
L42: So here you refer to 2000 as the year of RGI 6.0 for the European Alps, but this is an approximation, right? Would be better to specify the year range.
L57: I can’t help wondering why is a Kalman filter actually needed here. There are only 2 observations, so a more basic Monte Carlo approach would do just as well?
L57: What was the range of parameters used?
L61: specify that you’re using RGI 7. This makes me wonder how you recalculated the geodetic mass balance with these outlines since Hugonnet et al. (2021) use RGI 6.
L67: In principle yes although I see some strong limitations there, the main one being the relative simplicity of the mass balance model. One particular issue comes with the presence of debris, which strongly affects the mass balance gradient in the ablation zone. Even in the Alps there are extensively debris-covered glaciers (Unteraar, Zmutt, Glacier Noir…) and it would have been interesting to know how these affect the ELA patterns.
L71: 5 years sounds small, especially if these are the most recent years, overall much warmer, making their representativity questionable.
L73: I don’t think that the acronym EoS has been defined
L76: (Otsu, 1979)
L80-81: Not sure what is meant here
L88: Pearson’s correlation is standard and I do not see the need to include the formula here.
L96: ‘of from’ – one of these can be removed
L100: The other figures of the SI are not referenced in the main text.
Figure 1: Indicate what the numbers in parenthesis mean
L115: extent
L114: I understand what is meant, but the sentence is unclear and would deserve to be expanded upon.
L119-120: I do not understand where this affects the results.
L123: I disagree, ice thicknesses are quite extensive in the Alps.
Figure 2: Specify ‘glacier-wide’ mean elevation change, and ‘EoS’ Snow Line Altitude
L127-129: This should be explained in detail in the methods – how was this done exactly? Was this validated?
L136: Unclear to me what is meant by ‘regional biases’. Is this a reference to the product uncertainties?
L143: More details would be welcome here. Has this effect been investigated to explain the poor results obtained for Aletsch?
L151: What do you have in mind more specifically? This is the first mention of transient data assimilation, why is this coming up only here? More generally, it’s frustrating to see the application of this mass balance model without any explanations on how this can be used for future model improvement. This is barely mentioned at the end of the conclusion.
L163: I would have been interested to see more discussions on these velocity artefacts, especially where they come from.
L175: Missing references to the velocity & ice thickness datasets