General Comments:

This is an interesting, comprehensive, and useful paper on runoff from land to the Arctic Ocean. The Arctic hydrological cycle is uncertain and changing, so the paper should be of interest to a large community of climate dynamicists working on the Arctic. The use of multiple reanalysis data products and observational products is an advantage and the paper is a state-of-the-science summary of the best existing runoff and river discharge data products.

The main results in the Conclusions are important and appear to be robust. The results on runoff and discharge seasonality (Figures 2, 4, 5) are useful. The corresponding trend results over the last 40 years (Figure 3, 6) are also useful. It’s interesting and surprising that the ERA5 and related products show runoff decreases, contradicting the observations from gauged rivers. There are several other valuable lessons for individual reanalysis/assimilation data products. The revised mean Arctic hydrological cycle (Figure 12) is useful too and improves earlier estimates because it uses better data products and treats the uncertainties carefully (to construct a balanced water budget within errors). The uncertainties in the revised hydrological cycle are improved over earlier estimates too.

A couple of general/overarching comments:

1. Although river discharge data and land/ocean water storage data are used carefully, the paper doesn’t use oceanographic data to estimate the marine water fluxes (it only uses reanalysis data). This isn’t a major problem because the paper focuses on runoff and river discharge, but it should be mentioned and discussed somewhere (Conclusions?). 
2. Related to point 1: What’s the scope/opportunity for future improvements on the the Arctic water budget analysis?  What model and data assimilation improvements would help?  What data are needed to refine the budget estimates?  Again, this isn’t a major omission, but it will help set the context for future work if this point is discussed somewhere (Conclusions?).

I think the paper needs a major revision although all the comments are straightforward.

Specific Comments:

1. Line 50: Cite where it says the ERA5 runoff features spurious trends.
2. Figures 1 and 2: What is the source of catchment data in Figures 1 and 2?
3. Section 2: Add a table containing information on the runoff and discharge sources (ERA5, ERA5-Land, GloFAS…, GREP etc.)
4. Line 70: “river discharge” includes both liquid water and ice (presumably)?
5. Line 73: For clarity, say that “associated domain” means the catchment area.
6. Line 104: It talks about “different bulk formulas and differences in the data assimilation…”  Different to what?  Be specific.
7. Line 105: The sentence starting “We also look into….ORCA025” appears out of place. Move up to line 72?
8. Line 130: “additional area” needs to be clarified. Is this a catchment area?
9. Section 3: Many math terms aren’t defined clearly. E.g., S_A, S_L, S_O, F. \sigma^2_k. Make sure all terms are carefully defined.
10. Line 142: Justify the neglect of atmospheric liquid water and ice.
11. Line 151: What does A_total represent?  The Arctic Ocean?  The Arctic Ocean plus terrestrial catchments?
12. Line 158: What about groundwater contributions to the land water budget?  (And their changes in time).
13. Line 178: It says “we assume sea-ice to be transported by the ocean currents…” but sea ice moves (somewhat) independently from the surface ocean current. More explanation/justification is needed.
14. Line 219: Equation (10) and the text about it are unclear.
15. Line 257: The sentence starting “Cuchi et al. (2020) run the hydrological model….” is out of place. Cut?
16. Line 259: It says “Model runs with ERA5 forcing show similar river discharge seasonalities at the Lena catchment as GloFASERA5new.” This isn’t what I see in Figure 2 for the Lena. Check and cut or clarify.
17. Line 278: “Again this could be caused by delayed river ice breakup and backwater that is considered in GRACE, but not in ERA5” is a bit misleading. GRACE observes the natural system, which includes delayed river ice breakup. The ERA5 model excludes does not represent these processes. Instead, maybe end the sentence with “that is observed by GRACE, but not considered in ERA5”.
18. Line 309: Say that the “hydrological analogy” means extrapolation to the un-gauged rivers and streams.
19. Figure 3: The legend identifies “GloFAS_{ERA5}” and similar, but the legends in Figure 2 call it “Glo_{E5}” (also Table 3). Use consistent notation throughout.
20. Line 341: The sentence “Additionally Greenland features a storage decline of -134 km3 per year, accounting for roughly 50% of the total storage change” is unclear. Clarify and cite.
21. Figure 5: Remind the reader that the dashed lines sum to the brown line.
22. Table 4: Add a column with units (applies to other tables too, trends in particular have an unclear unit). The “m3 s−1 ∗ 10−3” unit contradicts Table 3. 
23. Section 4.2.3: The discussion on the ERA5 runoff glitches is useful. Speculate on how they could be fixed?
24. Figure 9: Explain what the different lines in the right panel mean.
25. Line 512: It says “both F and runoff R feature adjustments beyond their a priori spreads, demonstrating that the a priori uncertainties are larger than indicated as systematic biases are not incorporated”. What are the likely systematic biases?
26. Line 535: State briefly the origin of the ERA5-Land runoff declines of 5-6% and comment on their realism.
27. Line 552: It says “With oceanic and land storage declining…”, yet many papers exist on the accumulation of freshwater in the western Arctic Ocean (e.g., see Proshutinsky et al., 2019, 10.1029/2019JC015281). Mention and comment on this issue.

Technical Corrections:

1. Many places: Apostrophes are not used correctly and there are spelling and grammar errors.
2. Abstract, line 16: Reword “look into Greenlandic discharge”
3. Abstract, line 22: Which “data-sets”?  Be specific for clarity.
4. Line 169: “reference salinity” should read “reference density” I think.
5. Figure 2: What are R and \mu in Figure 2 legends?

This is an extensive study that compares observational river discharge data with global reanalysis data products from ERA5 and GloFAS for the assessment of Arctic rivers´ freshwater contribution to the Arctic Ocean. The study further estimates the freshwater budget of the Arctic Ocean through a combination of observational river discharge data and global reanalysis data products. Overall, the manuscript brings valuable results and contributes to the continuous estimates of the river input and freshwater budget of the Arctic Ocean. The inclusion and evaluation of reanalysis data products are also valuable for future assessments. See also my general and specific comments listed below.

General comments:

The manuscript is well organized, but there are some spelling and grammatical errors that needs to be considered, including the use of commas and apostrophes. I also suggest to avoid using words such as “spurious”, “huge”, “clearly” etc., especially for the results and conclusions sections (see also specific comments).

Considering that previous studies focusing on the Arctic drainage basin have used different approaches and motivations for its geographical domain, I am missing a motivation for the chosen boundary of the Arctic Ocean drainage basin in this study, and why e.g., Hudson Bay, and James Bay was not included? (e.g., L302-305). Clarify also in L313 that total drainage area refers to the area for this study.

How do these reanalysis products take frozen components of the freshwater system into consideration, e.g., glaciers and permafrost, considering that many of the river basins in the study are underlain by permafrost? For example, lines 497-498 includes an interesting aspect that I would like to see more elaboration on.

In the conclusions, I am missing a general discussion on implications for future studies and assessments of freshwater budgets of the Arctic Ocean.

Specific comments:

L12: I suggest to avoid the use of “spurious” and instead explain or reference to what you are referring to.

L37: consider removing “remarkably”

L41-43: Consider rephrasing for clarity and also specify the part on climatological conditions.

L45: avoid using “huge”

L47-48: Consider rephrasing for clarity.

L48-49: This is not very clear, please explain what you mean by “spurious” (see also previous comment related to this).

L92: Which 16 rivers were included in the study, and how was the shorter observational records treated for the analysis in comparison to the longer observational records?

L119-120: What about frozen storage components, such as glaciers?

L134: I suggest to add references to earlier studies, and revise “popular” to “common” – if this is what you are referring to?

I suggest to remove a, b, c in subheadings (e.g., L196, 205).

L244: consider removing “clearly”

Fig 4: Is this figure only considering the shorter time series of the 16 catchments, or for the full time period (1981-2019)? Same question for figure 6 and the observed Pan-Arctic river discharge data.

L497-498: This is an interesting aspect that I would like to see more elaboration on.

L527: I suggest to include references here, and do you mean “common” rather than “popular”?

L528: How does this result compare to other studies?

L529: Runoff from ERA5 is substantially “too low” – do you mean “underestimated compared to observed discharge” or similar?

L531: Please consider rephrasing and describe the “unrealistic” aspects.

L548: What is considered “trustworthy” here – please explain.

L555: What is considered “reliable” – please explain

L559: What would be a full success here, please elaborate.

L560: revise month to months

L571: Please specify what you refer to with “in most reanalyses”.

L572: Please specify what you refer to with “spurious signals”.