the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Jan 2026
Combining geodetic data and summer MODIS albedo anomalies for annual glacier mass balance estimation
Abstract. Annual glacier mass balance time series are essential for understanding the impacts of climate change on glacierized regions. Satellite-based observations enable consistent and regionally comprehensive monitoring of glacier mass balance. While geodetic methods provide reliable estimates over decadal timescales, deriving accurate annual glacier mass balance estimates remains challenging. In this study, we propose a new approach that combines 20 years geodetic mass balance data with glacier-wide average summer albedo anomalies from MODIS to produce reliable annual glacier mass balance estimates for land-terminating glaciers. We generated time series from 2000 to 2024 for 2748 glaciers across three regions: the European Alps, Scandinavia, and Svalbard. Validation against 1108 available in-situ mass balance measurements yielded root mean square errors (RMSE) of 0.45, 0.79, and 0.42 m w.e. and coefficients of determination (R²) of 0.60, 0.44, and 0.35 for the European Alps, Scandinavia, and Svalbard, respectively. These results demonstrate the method’s effectiveness and its potential for application in other glacierized regions.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-5779', Argha Banerjee, 02 Mar 2026
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RC2: 'Comment on egusphere-2025-5779', Anonymous Referee #2, 13 Mar 2026
Review of Callegari et al,
Callegari and co-authors describe a study where they combine long-term geodetic data and annual, mean summer albedo measurements to estimate annual surface mass balance for glaciers in Europe, Scandinavia and Svalbard. The authors suggest their approach provides an effective technique to estimate glacier mass balance, both for these three regions, but also perhaps for other glacierized regions. The relation between albedo and surface mass balance is not a new technique and variants of this relation have been explored in a number of previous studies. That is not to say that this study lack merit. In many ways it helps to chart new ways to estimate mass change from unmonitored glaciers. While I think this approach has some merit and deserves to be further explored, I have a number of questions about the methodology and overall performance of their model. Below, I expand on my major concerns of the submitted paper and provide some suggestions on which the authors may choose to improve their study.
- Methodology needs clarification and justification. I found myself asking many questions about the reported methods which made it difficult for me to assess the reliability and validity of the approach. The essential ingredient of the proposed method hinges on the use of equation (1) which defines mass balance for year (i) to be a product of the long-term (2000-2019) geodetic balance, mass-balance/albedo gradient (regional or global) and glacier wide summer albedo anomaly. Two things strike me. First, how does the use of the long-term geodetic balance which ends in 2019 affect this approach for albedo measurements following 2019? Second, what happens for a glacier where the long-term geodetic balance is zero? It would suggest that each year’s mass balance (2020-2024) is zero which clearly would be unusual. I think the authors need to spend more time explaining why and how they decided on their approach and provide some additional justification for the physical reasons that such as relation might be expected to work. I would also suggest the authors add additional details about the methodology (e.g. why did they choose mean summer albedo when many previous studies use end of summer minima, what is the rationale for a threshold of 70% for retained days and gap filling, what is the effect (and need?) of interpolation on the summer albedo?). I think that some of these thresholds could easily be addressed within supplementary materials which might help to justify their values.
- Uncertainty estimates and degrees of freedom – An important aspect to this work, both in the way it is presented and in the presented analysis, is the nature of the spatial correlation and degrees of freedom. Most of the goodness-of-fit statistics rely on an estimate of n which, in many cases can be thought of as the degrees of freedom (number of observations). Many studies demonstrate glacier mass change (and albedo variations ) strongly covary in space since they are affected by synoptic-scale meteorological conditions. This spatial covariance affects the overall significance of performance statistics by reducing the number of independent observations. There does not seem to be any attempt to correct for this known effect. At the very least, I think the authors need to acknowledge that this affect likely reduces the degrees of freedom of these tests in the methods, results and/or discussion. Further, the authors need to be careful evaluating their results to other studies that use similar data. While Figure 9 shows some similarity to their time series, I’m not overly surprised since both approaches uses geodetic data from the same study (even use of long term data will affect the apparent fit). Additionally, I think the authors could spend a bit more time thinking about the actual uncertainties of their method. For example, the long-term geodetic mass balance from Hugonnet comes with an error term, and the mass balance/albedo gradients are based on regression with error. Would it not be reasonable to produce an error term for each derived mass balance estimate?
- Clarity of results – I was confused by some of the results of this paper. In figure 7, for example, the authors compare WGMS mass balance data against geodetic data from Hugonnet and others (2021) and their approach (MODIS+DEMs). Are the authors plotting long-term geodetic averages against the WGMS annual data or mean data? It is not clear to me in neither the figure caption nor the text. I think the authors need to spend a bit of time ensuring that the visual presentation of their data is clearly described. I looked at Figure 10 for some time and trying to understand how differencing the mean from the observations to yield anomalies can collapse the variance as profoundly as Fig 10b shows. What happened, for example, to the positive outliers of MOD10A1 which appear on 10b and disappear altogether on 10a? Deriving anomalies should simply be a scale translation, no?
Minor comments
Abstract: remove subjective words such as ‘accurate’ , ‘reliable’ since the RMSE values don’t really support these strong qualifiers.
Lines 38-40: This section largely avoids other methods (laser and radar altimetry) which have been shown to be useful for estimates of volume change of mountain glaciers. Several studies have used cryostat, icesat-2, GEDI for example.
Lines 105-149: As specified above, I would recommend the authors redraft this section of their paper, detail important assumptions they are making, explain the physical reasons/processes (perhaps right before the paper’s objectives) which helped them to formulate their study.
Figure 2: Since you include the dates for the albedo anomalies and average geodetic balance, ensure your rightmost box (annual balance estimates) include the range. Right now several of your results seem to report mass balance estimates beyond 2019. Figure 4, for example. How does this affect your results? Would the results improve if you only calculated mass balance up to 2019? How does one use your approach if you only use albedo up to 2019?
Figure 4: It would be good once uncertainties are calculated from equation one to add these to the figure. As commented on in the major points, you’ll need to convey to the reader why average summertime albedo is better than minimum (the latter is a closer proxy to transient snow line at end of ablation period – and closely related to net balance for many glaciers).
Figure 5: The degree of scatter here is fairly large. As specified earlier, I think your results would be more robust if you propagate your errors by using the uncertainty of the gradient in equation 1.
Table 2: Explained variance exceeds 50% for the European alps whereas the other two regions have much lower explained variance. I think the authors need to consider how reliable their method is in terms of estimating surface mass balance in light of these numbers. As mentioned previously, I think the number of independent (validation samples) needs to be consider at least in the discussion in terms of spatial covariance.
Figure 7: As specified in the major comments, I don’t understand how this graphs on the left column (WGMS vs DEMs) were constructed. Are these mean values for both?
Figure 8: It would be more informative to have the shading represent uncertainties derived from errors in equation 1. That would allow us to know, for example, the true ability of this annually-resolved approach to detect true changes in surface mass balance.
Figure 9: How are values post-2019 calculated in light of figure 2? It appear the this albedo approach always underpredicts extremes. Why? I presume this is due to the use geodetic mean and albedo mean values? What would happen if albedo minima were used? Would the results improve?
Lines 310-330: I’m not certain I agree with some of the discussion here and some of my points here pertain to clearly laying out the physics/background on why this approach should work at all. Surface mass change of these glaciers is due to any process changing mass. End of summer minimum surface albedo is correlated to net mass balance partly because it is recording glacier-wide changes in snow cover (any remaining snow is a positive). But the albedo is also driving surface energy melt. Impurity deposition due to wildfire or dust events (e.g. Europe) can lower albedo and help ablate surface mass. Harmonized Landsat Sentinel (HLS) data yields frequent (5-day) repeats which could be used with broadband albedo methods described elsewhere. I’m not proposing that the authors complete/test these methods, but it would be good re-structure their discussion to better reference these other methods, re-iterate the physical processes which they capture in their approach.
Citation: https://doi.org/10.5194/egusphere-2025-5779-RC2
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