Dear authors,

Many thanks for providing us with the revised version of your manuscript. Given that one referee suggested a rejection of the paper, 3 referees a major revisions and that the changes to your document are substantial, I decided to send out your work for further evaluation by the referees.

Sincerely,

Bert Wouters - TC Editor

Dear authors,

As mentioned in my previous evaluation, the changes in the manuscript are substantial and it will therefore be send out for review by the referees again. After their feedback I will re-evaluate the manuscript.

Sincerely,
Bert Wouters

Dear authors,

Many thanks for uploading the manuscript and my apologies for the delay caused.

sincerely,
Bert Wouters

Dear authors,

Thank you for uploading the revision and replies to the referee comments. I think the manuscript has much improved, but at this stage there are still some issues that prevent your work to be published in The Cryosphere. I have copied the referee comments below for your convenience.

Referee #2 suggest to look into ERA5 for the precipitation analysis. I support this, but it is not a necessary requirement for publication, as long as you can provide convincing arguments why results are not expected from ERA5 are not expected to be significantly different.

Referee #3 has more substantial and major comments. He/She is correct in saying that EOF modes are always orthogonal and therefore the orthogonality test has little added value. This and the other major comments of R3 need to be addressed.

Furthermore, I have attached a pdf with my own comments. One major shortcoming is that leakage of hydrological signals outside the region of interest seems not to be accounted for. I realize that this will require effort, but at least a quantification of the effect and related uncertainties on the annual mass change should be included. Additionally, it is not always clear which mode is used for the results in section 5. Please clarify where possible. Finally, as you probably are aware, EOF analysis struggles in separating trends between different modes in physically meaningful way. When discussing the long-term trends, please include a side note discussing the glacier mass change recovered by your inversion for mode 1 and the full set of modes (i.e., the original GRACE fields).

Sincerely,
Bert Wouters


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Referee #2
The authors have demonstrated ability to differentiate seasonal signal from a complex
topographic region in the High Mountain Asia. It is true that the South Eastern Tibetan plateau,
known as the Hengduan Shan or Eastern Himalayas experience high intensity of monsoonal
precipitation (Spring and Summer), which complicates the separation of hydrological and gravity
signal from GRACE satellites. General comment regarding the use of gridded precipitation
products to understand the total precipitation. I feel that the authors have used less reliable
precipitation data products that does not work well in the Himalayas. I would encourage the
authors to use ERA5 or better products that will work for this region.
Minor comments.
1. Line 89, the authors mention the use of scale factor to compute the total meltwater
contribution from river Brahmaputra. Can you explain the significance of the values used
in the scale factor.
2. Line 155: The author has mentioned ‘The gridded data is compared with station
observations and the correlation index ranges from 0.69 to 0.82 in the interannual
variation (Figure S6), indicating a good consistency. The figure S6 indicates the recovered
mass changes from the second EOF for different dataset. Can you include the
corresponding figure as in the statement.
3. Line 163: Can you indicate where the localized spring precipitation is studied. Please can
you remove the word ‘shown later’ and include the reference to a figure.
4. Line 200: Instead of the text ‘demonstrate it later’, can you include a reference to the
section or figure where the peaks in three-month window offset has been noticed in the
annual oscillations.
5. Figure 3. Title of the figure. The white dots represent the glaciers. I assume that they are
not dots, it is shaded region. The authors are requested to refer glaciers (white) as shaded
regions in the rest of the figures.
6. Supplement Fig S3: Instead of the word ‘blue dots’, can you use the words ‘blue shaded
region’ for glaciers.
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Referee #3
Some of my major concerns are not addressed. I elaborate them as follows.

R0: My initial concern was not that “a sinusoidal function is unsuitable for glacier and snow mass change.” I was questioning the logic of testing the orthogonality of the EOFs (Section 4.4). Please see my comments below.

R1: The analysis starts with an EOF decomposition of the GRACE data (section 4.1); two EOFs are obtained. The authors point out the hypothesis: The two EOFs separate the hydrological and glacier/snow components.

To test this hypothesis, the key is to use independent evidence to address the physical meaning of the two EOFs. An analysis of the orthogonality of the EOFs does not help (Lines 255-260 in the manuscript along with Section 3 in the supplement). The orthogonality is automatically ensured by the algebra of an EOF decomposition. The authors can always apply an EOF decomposition to the GRACE data, and the resulting basis functions will always be orthogonal, but they do not necessarily represent the hydrological and glacier/snow components. I hope this clarifies my concerns and I believe the orthogonality test should be excluded from the manuscript.

R2: The response is a bit confusing. The soil moisture (SM) data employed in the manuscript are not actual observations. Is SM better represented in the model than the other water storage components (so these other components are excluded from the analysis)? I think this should be clarified.

Fig. 3b and Fig. 5c show a clear difference in terms of spatial pattern, not just in magnitude. As I pointed out in the initial comment, Fig. 3b might be influenced by a combination of water demand from irrigation and a decrease in precipitation. These factors can affect both the magnitude and the spatial pattern, and it is likely that these factors are embedded in the trends. For this reason, I think it would be of interest to perform the EOF analysis on the de-trended data and check if there is any improvement of agreement in the spatial pattern.

R6: Different colors in the plot represent different precipitation estimates (station, HAR, TRMM), correct? There is a big spread among these different precipitation estimates. How consistent are the EOFs from these different precipitation products?

R7: Please clarify how sensitive your results are to the choice of masks.

R17: Please clarify the physical basis of this weighting procedure.

Dear authors,

I'm generally pleased with the changes you made to the manuscript and believe the manuscript is nearly ready for acceptance. I understand your point of view on my comments and those of the referees, but ask you to make the following changes to the manuscript:


1. Most of the hydrological signal will indeed by captured by mode 1, but leakage can still occur in the higher EOF modes, especially since you are working with global spherical harmonics. This also shows in figure S7. Although the effect may be small, change lines 110-113 from:
"The leakage error is determined by how effectively the hydrological and GS signals are separated by the EOF technique. Based on the modelled and recovered glacier mass changes, their residuals are estimated to have a seasonal variation of up to 11% of the modelled glacier mass change (refer to section 3.2 in the supporting materials), which is used to calculate the seasonal leakage error."

to:

"We assume that the majority of the hydrological signal is captured by the first EOF mode. The leakage error is then determined by how effectively the hydrological and GS signals are separated by the EOF technique. Based on the modelled and recovered glacier mass changes, their residuals are estimated to have a seasonal variation of up to 11% of the modelled glacier mass change (refer to section 3.2 in the supporting materials), which is used to calculate the seasonal leakage error. We do not quantify or account for potential hydrological (non-GS) signals in EOF mode 2."

2. Figure R2 adds a lot to the credibility of your method. Include this in the SI and add a reference to the figure in the main text.

3. change line 257-259 from "Two conclusions are obtained: only when the GS mass change peaks in May (3 months before the peak month of the hydrological signal) can our simulated result agree with the GRACE observation; the EOF decomposition can well restore both seasonal variation and the trend of the GS signal if the orthogonality is satisfied."

to

"Only when the GS mass change peaks in May (3 months before the peak
month of the hydrological signal), our simulated result show similiarities to the GRACE observation."

Sincerely,
Bert Wouters

Dear authors,

Many thanks for incorporating my suggestions. It is my pleasure to let you know that your manuscript has been accepted for publication in The Cryosphere. Congratulations, and thank you for contributing to our journal!

Sincerely,
Bert Wouters