Dear Authors,

I have sent your revised version of the manuscript for one more round of reviews (to the Referee #3 who proposed major revisions in the first round) to help me make my decision. I have received the review (see below). The reviewer recommends your paper for publication however had some minor criticism (regarding the sensitivity analysis and reference-surface mass balance) that should be addressed further.
Please submit through the online system your responses to the reviewer's comments and the revised manuscript.

Best Regards,
Valentina Radic

Reviewer#3:

In the revised version of their manuscript the authors addressed most of my previous comments. While I still believe that a more in depth discussion of the climatic drivers of mass-balance over the considered time period would have improved the scientific significance of the manuscript, I think that the manuscript can be published in TC after a few modifications.

Sensitivity analysis:

I can see from the correlation between winter and annual MB (Table 2) that accumulation drives MB variability at this glacier, but I still think that the extremely small influence of temperature shown in Fig. 3C could be a model misinterpretation. This small influence of temperature contradicts with results from studies in e.g. the sub-tropical Andes, where temperature does not necessarily directly drive melt but the phase of precipitation which in turn has a strong influence on MB (Gurgiser et al., 2013, Maussion et al, 2015). I wonder if the results presented here are only an effect of the glacier size or if they are representative for a larger region? The omission of liquid vs solid precipitation and albedo by the model should be discussed in this broader context.

Furthermore, I suggest to redesign the sensitivity experiment as such: when keeping precipitation or temperature fixed, the degree-day model should be recalibrated for alpha and mu. The model would represent a kind of "partial correlation" (in the very broad sense): how much modelled MB variability can be explained by the variability temperature or precipitation alone? With the current experiment design (where mu and alpha can compensate each other) it is possible (but not certain) that the importance of temp is under-estimated.

Reference-surface mass balance:

The discussion about glacier geometry has improved in the revised study. From LL 181-189, it is not clear to me what data is available from the WGMS at ECH? A quick look at the FoG database's documentation indicates that the "standard" in WGMS is to provide specific MB time-series. In practice, the timeseries are probably something in between, as the data providers won't update their outlines on a yearly basis. But are you suggesting that WGMS data at ECH *is* the reference MB or are you assuming that reference MB and specific MB are close enough to be assumed equivalent for that period?

Specific comments:

L311: a "by" is missing

L339 (and possibly elsewhere): add the uncertainty ranges to the estimations ("reached almost 10 m plusminus w.eq")

References

Gurgiser, W., Marzeion, B., Nicholson, L., Ortner, M., & Kaser, G. (2013). Modeling energy and mass balance of Shallap Glacier, Peru. The Cryosphere, 7(6), 1787–1802. http://doi.org/10.5194/tc-7-1787-2013

Maussion, F., Gurgiser, W., Großhauser, M., Kaser, G., & Marzeion, B. (2015). ENSO influence on surface energy and mass balance at Shallap Glacier, Cordillera Blanca, Peru. The Cryosphere, 9(4), 1663–1683. http://doi.org/10.5194/tc-9-1663-2015

Dear Authors,

I noticed that Equation (4) might not be correctly written (The current expression does not make much sense, though I think you calculated correctly in the results and plots).

If your cumulative sum is:
r(T) = sum from t=0 to t=T of r(t)
isn't it then that your commutative error should be:
error(T) = root (sum from t=0 to t=T of error(t) ^2)

Please recheck and correct accordingly.

Cheers,
Valentina