This paper presents some procedures that help in making vertical land displacements useful as complementary data to GRACE for inverting hydrological loads, including noise analysis, using discrepancies between GPS and GRACE to detect missed GPS offsets, and an improvement of the CMC Imaging method of Kreemer and Blewitt (2021). The data produced is ultimately very useful for researchers interested in hydrologic loading. Where will the VLD time-series be available?

Possible issue with Correlation presentation:

The calculation of correlation between GPS and GRACE (per watershed) is not clear to me, given that you have X GPS time-series and Y GRACE mascon time-series. I suspect there is a missing step, that doesn’t seem to be explained: how GRACE data is translated to VLD at the station level. Please explain that. Furthermore, I don’t see how a poor correlation can be attributed to a single station (as the case for St. Lawrence) ; this is assuming that the authors didn’t mean to say that there was a missed GPS offset in all of the time-series, which seems unlikely.

Minor points:

Line 85. Kreemer and Blewitt did not introduce the term CMN, but rather used the term CMC (common mode components), which was first introcuded by Tian and Shen (2016)

Line 118. Originally is not used properly in this contextLine 118. “layout” should read “lay out”

line 126-127: “We overcome CMC’s limitation of include spatially correlated hydrology signals...”. This sentence is grammatically not correct, nor is the context clear: which limitation? That includes both noise and unmodeled signal?

Line 192: I think P_lm is missing in front of “are the associated Legendre polynomials”

Line 220: “𝐴 and 𝐵 being the amplitude and phase”. That is not how formula 2 is written, which is erroneous, should be A*cos(2*pi*t+B)

Line 302-303: “We identified the need for antenna offset corrections (in the case of Great Lakes)”. Before the St. Lawrence watershed was named in this context, now Great Lakes. Later (line 458) Lake Michigan is mentioned. Which is it?

The article is a valuable compilation of methods and approaches used in the geodetic literature to analyze time series. However, it contains several shortcomings that limit its understanding or use of the dataset. The main limitation is that the authors do not make the created dataset and its uncertainties available (as they promised in the abstract and introduction), which greatly prevents me from assessing its potential. Some of the results are presented laconically (as the uncertainties; I presume these are the uncertainties of trend, or…?), and others lack adequate explanations (where is the RW in the data coming from? Perhaps it is the result of inadequate series length? or other effects?). The authors are keen to streamline the procedure for qualifying the data for further analysis, but sometimes speeding up preprocessing or classification can lead to erroneous conclusions.

Major shortcomings include:

1. I believe that a key requirement for publishing an article in ESSD is that the proposed dataset be available. Unfortunately, I found nothing about this either in the article or in the supplementary materials. Do the authors plan to make available GPS VLDs that can be taken directly for comparison? Their uncertainties were also described, but are not available. Will these be the uncertainties of individual observations or the uncertainties of trends?
2. It would also be useful to make available a list of stations that the authors considered being those responding elastically to the applied load, their coordinates, and a list of stations excluded from comparisons as those responding poroelastically.
3. The authors do not explain all the abbreviations used in the article.
4. Please show some of the GRACE and GLDAS time series against the GPS time series so that readers can get a general idea of how the time series agree with each other. Not all users of the dataset need to be geodesists.
5. It is not clear how the authors converted the TWS available for JPL mascons to displacements. Equation 1 does not describe the entire procedure.
6. It is also unclear how the authors interpolated the gap between GRACE and GRACE-FO. This is because they present trend estimates for the period 2018-2021.5, which includes a gap of more than a year in GRACE observations.
7. Equation 2 lacks time dependency y(t).
8. It is not clear what “ccs” means in the CMN algorithm.
9. It is not clear with which noise model the authors perform the analysis for CMC and CMCHF.
10. Table 1: What μ means here? Why the authors do not compare the amplitudes of noise or the percentage contribution of different noises to the analyzed combinations? This might be interpretable.
11. Figure 6: Is this the uncertainty of trend, or…?
12. The authors mentioned a case of unlogged offset. It is presented in the supplementary materials, but only for one case. I think the authors should approach the topic more descriptively and present other cases in which unlogged offsets were also corrected manually.
13. Lines 229-230: The authors mention describing interesting cases in Supplements, but they are missing there.
14. Several sentences in the text are missing a noun or verb, the authors should carefully review the entire text.