General Comments:

Dear Authors,

This is a very interesting paper on the topic of assessing bias-adjustment techniques, where I am also doing work in. It is relevant to the scope of the journal and could be a useful resource for the community for comparing the performance of univariate bias-adjustment methods vs. multivariate methods in the context of multivariate climate indices. However, there are a number of points that should be further discussed before publication is recommended:

Please provide a comment or two to describe to readers as to why SPEI and the Upper Jhelum Basin are appropriate for testing univariate and multivariate bias-adjustment approaches. Based on the results of the bias analysis and the Taylor diagrams, even though biases are reduced via the various methods it does not appear that SPEI is resolved well over all. Is the 50km resolution sufficient in resolving the topography of the region?

Please justify more explicitly/clearly that these findings (that both univariate and multivariate methods for SPEI perform similarly/well) is applicable to different regions in the world, input variables, and/or multivariate indices.

Specific Comments:

Page 4, line 5: I was not familiar with SPEI, so it was not immediately apparent how the Ra parameter was derived in the simplified Hargreaves-Samani equation. It would be useful for readers who aren't familiar with SPEI to indicate that the radiation parameter is derived using the latitude of the site/grid.

Page 4, line 16: Extremes events are defined as SPEI values ≥ +1 and ≤-1in this paper. Please comment on why these values were chosen – were there any past studies that also defined extreme events using these thresholds?

Page 4, line 31: Why were only 20 years (1986-2005) used as the historical and not a slightly longer 30 year period? I believe W5E5v1.0 was available from 1979-2016.

Page 8, section 2.6: When applying these methods, did you aggregate/pool the daily data into month-of-year/seasonal windows before bias-adjustment to account for precipitation biases in the seasonal cycle? Likewise, for MBCn, how many iterations were used? Could you describe in more depth how you applied these quantile mapping algorithms?

Page 8, line 46-48: Could you justify why nearest neighbor interpolation was chosen over other methods such as bilinear/cubic? Can you verify whether the “added value of the higher resolution WAS-22” is still present after remapping to the coarse resolution?

Page 9, line 1: Were the issues of temperature reversals (i.e., Tmin>Tmax) considered, and/or how did you resolve this? Based on Thrasher et al. (2012), temperature reversals may be encountered post bias-adjustment, while Cannon et al. (2021) multivariate bias-adjusted the daily diurnal cycle and Tmean before deriving Tmax & Tmin to ensure reversals are avoided.

Page 13, line 2-3: Is there a reason why the mean biases are expressed as a ratio and not as a delta?

Page 13, line 22: It is unclear what “partially elevated” means in this context, please clarify.

Page 15, line 7: “[…] but still shorter events than in the reference dataset are found after the corrections.” Awkward way of phrasing, or possibly a strange placement for the word “still”.

Page 18-20, Figures 6 & 7: The study area spans over 30 grid cells at a 50km resolution – are these large enough of a sample size to use for spatial analysis via Taylor diagrams?

Technical corrections:

Page 3, line 30+31: Section numbering should be 2 and 2.1

Page9, line 12: Heading should be spaced after text

Page 20: Legend for model names is a bit fuzzy when zoomed in – would it be possible to have this at a higher resolution?

Figures 3, 4, S1, S2, S3: Lower (left) bound value of the colour bar is not equal in increment to the others

Throughout the paper (e.g., Page 4 line 11; Page 22 line 9): citation formatting, i.e., brackets should just be around the publication year, like other examples throughout the manuscript when authors are directly addressed in the sentence.

I would be more than happy to review again once these comments have been answered and/or addressed.

In their study, the authors of "Climate change projections of wet and dry extreme events in the Upper Jhelum Basin using a multivariate drought index: Evaluation of bias correction" assess the performances of several univariate (2) and multivariate (8) bias correction methods applied to climate models outputs for impact studies. The multivariate drought index SPEI is considered to evaluate the adjustments of wet and dry extreme events over the Upper Jhelum Basin, in the Western Himalaya region. Two experiments of bias correction are performed in this study: 1) the component-wise approach that consists in applying bias correction (BC) methods prior to the computation of the SPEI index, and 2) the direct approach that consists in calculating the multivariate SPEI index first, and then adjusting it using univariate BC methods.  Corrections are performed to adjust daily maximum temperature, minimum temperature and precipitation from several CMIP6 GCMs, CORDEX and CORDEX-CORE RCMs with different spatial resolutions over the historical period (1986-2005). Corrections are evaluated in terms of inter-variable relationships and SPEI characteristics on the same historical period with respect to W5E5 reanalysis dataset. The authors find that the multivariate BC methods have some added value over univariate BC methods concerning the adjustment of inter-variable properties. However, both univariate and multivariate methods present similar performances for the correction of SPEI indices. The direct approach shows slightly better results than the component approach and no added value was obtained when considering high resolution products.

The article is scientifically interesting, its structure is clear and easy to follow, the results are well explained and summarized. I think this study certainly falls within the scope of the journal.  However, I think there are a few minor issues that should be considered to improve the study before publication.

General comments:

1. SPEI has been chosen to evaluate univariate and multivariate bias correction methods. In this study, the index is computed in several steps involving precipitation, Tmax and Tmin time series at different time scales. Thus, not only a good representation of the values (marginal properties) and dependence (inter-variable properties) of the variables is important for the SPEI index, but also the temporal properties. None of the multivariate BC methods used in this study are designed to adjust temporal properties.  Moreover, multivariate BC methods can also deteriorate temporal properties (e.g., François et al., 2020). Consequently, it is not clear in this study whether the comparable performances of multivariate BCs with respect to univariate BCs are due to compensating effects between improvement of inter-variable properties with multivariate BC and deterioration of temporal properties at the same time. Would the same conclusions be obtained by considering other multivariate indices than SPEI, e.g., indices for which inter-variable properties are important, but not temporal ones? I think that these points (1. importance of temporal properties for SPEI, 2. inability of the implemented BC methods to adjust temporal properties and 3. potential deterioration of temporal properties by multivariate BCs) should at least be mentioned in the discussions to provide some nuances to the conclusions of this study as explained above.

2. I really like the title which is clear but I find the term “climate change projections” a bit misleading. The historical period 1986-2005 is only considered in the study, and thus authors are not looking into climate projections, i.e.,  simulations of future evolutions of the climate system. The notion of “climate change” is also misleading as the changes of the climate system are not particularly investigated in this study, not even those that could have occurred during the 1986-2005 period. I would propose to find another title for the study avoiding the words "climate change projections".

3. In Section 4 - Discussion and conclusion: I really like the way results are summarized and discussed. However, I think it would be interesting to detail a bit more about future research by adding a few sentences. Besides investigating the robustness of results under climate change as already mentioned at the very end of the study, what are the next steps of this work? I think it would be helpful to mention a few avenues of research, as it would help to better connect this work to the research community. 

Specific comments:

• Page 2, L21: “The use of raw GCM and RCM output for subsequent impact studies without any post processing could lead to ill-informed adaptation decisions for the foreseeable future.”. Do you have any examples/references to support this sentence?
• Page 4, L20: “above/below 1”. I assume you meant “above 1 and below -1”?
• Page5, Table 1 and 2, and Section 2.4: I don’t understand why you detail the scenarios for the different models. As your study is focused on the 1986-2005 period, it seems that there is no particular reason to provide such details. It might be preferable to remove some parts of the text and tables mentioning information on scenarios.
• Page 5, Table 1: It might be preferable to round resolution numbers in the table.

If needed, I would be happy to review the revised manuscript.