Review of the manuscript:

Reanalysis of the longest mass balance series in Himalaya using nonlinear model: Chhota Shigri Glacier (India)

Authors: Mohd. Farooq Azam, Christian Vincent, Smriti Srivastava, Etienne Berthier, Patrick Wagnon, Himanshu Kaushik, Arif Hussain, Manoj Kumar Munda, Arindan Mandal, and Alagappan Ramanathan

Submitted to The Cryosphere, spring 2024

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General

The authors continue their earlier work on the mass balance (MB) of the Chhota Sigri glacier in the Lahaul-Spiti valley of Western Himalaya, India, within a tributary basin to the Indus river basin. Both existing MB results from field measurements (glaciological method) carried out during the period 2002–2023, and geodetic MB results from satellite imagery (ASTER and Pleiades) collected in 2003, 2014 and 2020, are used in the study.

Geodetic MB is generally considered more accurate since the data cover the entire glacier surface. In contrast, stake locations where annual accumulation or ablation is recorded may not yield data that are  fully representative for the glacier-wide MB. Identifying and correcting for biases in field-based MB data thus forms an important component of ongoing evaluations of glacier mass balance data from many glaciated regions of the world.

In their reanalysis, the authors employ a nonlinear model yielding MB as a function of elevation originally devised by Lliboutry (1974) and later employed by e.g. Vincent and others (2018). A linearly changing hypsometry of the glacier from year to year, based on the remote sensing data, is also employed. Comparison of results produced by the nonlinear model with traditional MB results (glaciological MB, profile method), shows that use of the model leads to a reduced bias in the field-based MB data, as demonstrated by comparing glacier-wide results with the geodetic results. 

The authors obtain the convincing figure of –0.47 ± 0.19 m w.e. a−1 for the average annual MB of Chhota Shigri during the period 2002–2023, corresponding to a cumulative mass loss of 9.81 mw.e. As noted by the authors, the results are typical for this particular region of the Himalaya. The authors also devise a way of using the nonlinear model to estimate glacier-wide MB if only very few field measurements are available from a particular year. Moreover, the nonlinear model can be used to correct or remove suspicious point MB data resulting from mistakes in observations or other factors.

Overall, this manuscript presents carefully worked-out and bias-corrected MB results from one of the most important benchmark glaciers in the Himalaya, produced by an Indian-French research group that has been actively studying this glacier for more than 2 decades.

This reviewer does not have specific criticisms of the data or methodology, except to mention that it would be valuable to include a discussion of the likely reasons for the bias in the glaciological measurements (w.r.t. geodetic) and why it switches sign between the two periods considered (Table 2, p. 18), from a negative bias of –0.11 m/a in 2002–2014 to a positive bias of +0.33 m/a in 2014–2020.

Suggestions for English language improvement on the manuscript are included below.

Title

using nonlinear model

-->

using a nonlinear model

L15

from traditional glaciological method 

--> 

obtained with the traditional glaciological method

L20

Further, nonlinear model is also used...

-->

Further, the nonlinear model is also used....

L23-24

The nonlinear model outperforms the traditional glaciological method...

Is this appropriate wording? The nonlinear model uses data collected with the traditional method and improves on the results, so these are not two independent methods.

L37-43

Drop "the" in:  "to understand the possible glacial hazards"

L41

or measured using field-based glaciological method

-->

or measured using the field-based glaciological method

L47

cannot be used to understand…

-->

cannot be used to study…

L48-49

Conversely, field-based traditional MBs —estimated at annual/seasonal scale—directly respond to local meteorological conditions.

--> (suggestion)

Conversely, field measurements using standard methods (ref) yield data on the seasonal/annual response of glacier mass balance to local meteorological conditions.

L53-54

For annual glacier‒wide MB estimation, traditional field-based glaciological method

has been used in the Himalaya (Azam et al., 2018).

-->

Maybe "field-based" can be dropped in this sentence - it is already mentioned in L48

L59

representative of surrounding areas

-->

representative of the surrounding areas

L60-61

thus, the snow avalanche inputs are not included,

-->

thus, snow avalanche inputs onto valley glaciers are not included

L62-63

controls snow blowing/deposition

-->

controls snow drift and deposition

L68

due to accessibility  due to accessibility issues (might be better)

L80

hence ignoring --> but ignored

L102-103

Not clear here what:  "over medial and lateral moraines from 4100 to ~4900 m"  means - obviously there is debris on those moraines, otherwise they would not be moraines.

L134

inserted up to 10 m inside the glacier  inserted up to 10 m into the glacier

L156

some years were undersampled

-->

the mass balance was undersampled in some years.

Or:

a limited number of MB measurements could be carried out in some years.

L156-157

“when” instead of “where” – twice

L158

before the storm. --> before the September storm.

L166

spatial effect term --> a spatial effect term

temporal term --> a temporal term

L168

Parentheses missing around equation number (2)

L169

the spatial effects --> the spatial effect

L172

by the maximum --> and the maximum        

L175

each location --> should this rather be “all point locations”  ?

L182

over minimum ten years --> over a minimum of ten years       : probably better

L210-211

hence, the nonlinear model cannot be run.

-->

hence, the nonlinear model cannot be run for this mass-balance year.

L215

on 6 September 2021 Sentinel image --> on a 6 September 2021 Sentinel image

L216-217

It is to be noted --> It should be noted

L218

using nonlinear model --> using the nonlinear model

L222

conducted hence --> conducted; hence

L222-223

The two grid cells selected are 200x200 m and the zero values picked for them should thus not be referred to as “point MBs”

L224

on delineated --> on the delineated

The background is Sentinel image --> The background is the Sentinel image

L227-228

The calculation of glacier‒wide MB needs to get a spatial distribution of 𝛼𝑖 over the whole surface area of the glacier.

-->

For the calculation of glacier-wide MB a spatial distribution of 𝛼𝑖 over the whole surface area of the glacier is needed.

L241-242

“As expected, the residuals followed a normal distribution with a standard deviation (STD) of 0.35 m w.e. a‒1 (Fig. 4B).”

-    This sounds like the STD value of 0.35 had been estimated beforehand, which is unlikely to be the case.

L248

wrong and discarded --> erroneous and were discarded        : probably better

L248-249

The wrong field measurements come from different years

-->

The erroneous data were collected in different years

L251

reduced --> was reduced

L255

from glacier snout --> from the glacier snout

L287-290

This sentence is a bit unclear, suggest rewording to:

“Further, the geodetic MBs of the western tributary of Chhota Shigri (the WT glacier, see Fig. 1), which fragmented sometime around 2012, were estimated from area-weighted comparison with Chhota Shigri, for direct comparison with traditional and nonlinear MBs.“

That is, if this reviewer understands the meaning of the sentence correctly, which is not certain.

L320

two periods when the geodetic MBs were calculated

-->

two periods for which the geodetic MBs were calculated

L350

Reference to Table 3 before Tables 1 and 2 have been mentioned.

L370

September 2020 year  September 2020 each year (?)

L463

observed --> collected

L489-490

or observers not experienced enough.

-->

or observers not being sufficiently experienced.

L509-511

“The outperformance of the nonlinear model suggests that the extrapolation of point accumulations (in case of missing point measurements) in estimating the glacier‒wide MB using the traditional method is risky.”

This could be understood as meaning that the nonlinear model is outperformed by the traditional model, whereas the intended meaning is opposite. Suggest to change to:

The better performance of the nonlinear model...

L536

(2023/23_2020) --> (2022/23_2020)

L583

hence. --> hence,

General comments

This study revisits the glacier mass measurements conducted on Chhota Shigri Glacier since 2002 and homogenizes the glacier-wide mass balance time series by combining the use of a non-linear statistical model and geodetic estimates of glacier mass changes. The authors obtain that the mean glacier-wide MB over 2002-2023 was -0.47 +/- 0.19 m w.e. a-1, with slightly higher mass losses in the 2014-2020 period (-0.51 +/- 0.06 m w.e. a-1). They indicate that the nonlinear model outperforms the traditional glaciological method when compared with geodetic estimates and can be used to detect erroneous measurements.  

The methods are sound and the topic is very relevant, but several issues need to be addressed, notably regarding the novelty of the study, the structure of the paper, and the presentation of the results. I recommend having the text further proofread, especially for the lack of usage of ’the’ and ’a/an’.

Novelty

The study is based on a nonlinear statistical model that was first proposed by Vincent et al. (2018) and applied to four glaciers, including Chhota Shigri Glacier using the glacier mass balance measurements available at that time (2002-2016). In the study of Vincent et al. (2018), the time series of glacier-wide mass balances was generated with their nonlinear model and adjusted for systemic biases using geodetic mass balances estimated over the period 2005-2014. The methods presented here are very similar, the main differences lie in the addition of the mass balance data collected until 2023, the use of a second period of geodetic mass balances (2014-2020) for the time-series homogenization and the estimation of glacier and debris area changes. In their introduction, the authors should better state how their study represents a scientific advance compared to what has been done before, and what has been learned from the additional in-situ mass balance data. 

Paper structure

I believe the structure of the manuscript would need to be slightly revised and be further consistent with the aims of the paper given at the end of the introduction. The comparison of the nonlinear model against the traditional method takes a substantial place in the manuscript, but it is not announced in the description of the paper structure (l. 85-96). The result section starts with observed glacier area changes and geodetic mass balances, while these were not mentioned as objectives of the study. Similarly, the discussion section covers the limitations of the nonlinear model-SLA method and mostly focuses on the methodological aspects, but does not put into context the obtained annual MB time series nor mention the broader relevance of the findings of this study. 

Presentation of the results



The performance of the nonlinear model is assessed against the traditional mass balance method and shown to be superior. However the comparison is shown at the glacier-wide mass balance level, it would be worthwhile to show the reader this non-linearity present in the in-situ mass balance data (perhaps showing the mass balance measurements against their elevation for individual years) and also to show the outputs of the nonlinear model either in a distributed manner (as it is applied over a 200m by 200m grid) or aggregated per elevation band. The authors mentioned (l. 509-511) that the extrapolation of point accumulations in estimating the glacier‒wide MB using the traditional method is risky, but this important point could be further strengthened by disentangling how the nonlinear model performs against the traditional method for a specific year. 

The authors recommend using the nonlinear model on all traditional glaciological mass balance series worldwide but there could be some discussions on what data amount can be considered as sufficient for this method to be applied.



Specific comments

p1. l.1 (title): Consider using “a” in front of “nonlinear model”.

p1. l.15: This is a rather vague statement to start the abstract, especially since the cause of these biases is not given explicitly (in the abstract), nor which one of them will be addressed in this study.



p1. l.31: This recommendation could be strengthened by a discussion, at a later stage in the manuscript, of what quantity of data can be seen as sufficient for the nonlinear model to be applied.



p3. l.73: Which point MB-elevation relationship is referred to here, a linear regression of MB against elevation? Is the nonlinear model able to account for variability in point MB within a given elevation band (due to differences in slope and aspect for example) ? 

p.3 l.86: A key asset of this study is that it reanalyses what they state is the longest annual glacier-wide mass-balance series in the Himalayas. While this is surely the case, it could be worthwhile to review which other annual glacier-wide MB time-series exist (e.g. Sunako et al. 2019) and add a bit more context to the time series presented in this study. 

p5. l.146: Please provide a source or an explanation for the values of these fixed densities.



p.6 l.163: It would be very worthwhile to also provide the values of point MBs for each individual year.



p.7 l. 226-227: Please consider providing (later in the manuscript or in the SI) a visualization of distributed model outputs corresponding to the 200m x 200m spatial resolution to help the reader understand how the model outputs look before their aggregation to the glacier-wide scale. 

p.9 l. 226-227: Please consider summarizing how many values of αi, γi, and βt are provided by the nonlinear model. The values obtained for βt could also be reported somewhere in the manuscript or SI. Additionally, a visual representation of the spatial distribution of these obtained values could help the reader understand how this model takes into account the spatiotemporal variability of MBs.



p.9 l.233: Consider adding the percentage of the total glacier area that these values represent (0.15 km2 and 0.68 km2).

p. 11, l. 282. Please consider describing briefly the patch method here, as the quantification of geodetic uncertainties is an important step in deriving geodetic mass balances.



p. 14 l.343-347: Are the two steps (5 and 6) necessary to compute the adjusted altitudinal mean MB and couldn’t they be combined into one step (be,t,cal = be,t + Ba,cal - Ba) ? Didn’t I understand correctly that the same deviation was applied to all elevation bands? If so please state it clearly and simplify this sub-section. There are numerous variables in this sub-section, which doesn’t make it easy to follow.



p. 14 l. 359. Is σε constant for each 50-m elevation band? If so, could the sum in equation (7) be written in a simpler form?



p. 15 l. 378-379: the geodetic mass balances and their uncertainty are an important component of this study as they are used to assess the performance of the nonlinear and traditional methods, as well as to calibrate the annual MB time series. The uncertainty bounds given in geodetic glacier-wide MB are quite small (e.g. ‒0.51 ± 0.06 m w.e. a−1 during 2014‒2020), which is ideal for using this estimate to then homogenize the MB time series, but please consider providing additional material (in Figure 7 and/or in the SI) attesting the quality of the co-registration (for example a histogram of elevation change on stable terrain). This would help the reader gain confidence in these geodetic estimates and uncertainties, knowing that uncertainty in DEMs and therefore glacier volumes are often underestimated in the literature (Hugonnet et al. 2022). 

p.20 l. 472-475:  The traditional method seems to perform rather poorly for the period 2014-2020 (bias of 0.33m w.e. a-1) compared to the nonlinear model. Please clarify your explanation of this poor performance due to the missing measurements, and consider adding a figure displaying how the nonlinear model performs against the traditional method for a specific year where important mass balance measurements were missing. 

p. 22 l. 503-511: This is a very interesting point of the paper which could be, cf. my comment above, strengthened by additional visual material representing the problems caused by the extrapolation of ablation/accumulation points in the traditional method which was avoided in the nonlinear model.

p. 23 l. 530-532: The mention that βt is several affected by the years with little measurements dilutes the message given after about the ability of the nonlinear model to give a reasonable glacier-wide MB estimate for a year having a limited number of measurements. Consider restructuring this sentence such that the message of this sub-section stands out more clearly.



Technical corrections

p. 20 l. 444: add uncertainty bounds to the cumulative loss.

References not included in the manuscript

Hugonnet, R., Brun, F., Berthier, E., Dehecq, A., Mannerfelt, E. S., Eckert, N., & Farinotti, D. (2022). Uncertainty Analysis of Digital Elevation Models by Spatial Inference From Stable Terrain. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 15, 6456–6472. https://doi.org/10.1109/JSTARS.2022.3188922

SUNAKO, S., FUJITA, K., SAKAI, A., & KAYASTHA, R. B. (2019). Mass balance of Trambau Glacier, Rolwaling region, Nepal Himalaya: in-situ observations, long-term reconstruction and mass-balance sensitivity. Journal of Glaciology, 65(252), 605–616. https://doi.org/10.1017/JOG.2019.37