My comments include an equation and a figure, so also see the attached PDF.

This paper presents interesting results that offer both hope and caution for L-band InSAR and InSAR generally. The quality and extent of the field validation data are impressive, perhaps the best I’ve seen from a field snow experiment.

Three suggestions to improve the analysis and the presentation:

1. My major critique is that the target audience has to know a lot about radar and radar remote sensing of snow properties to understand the paper’s implications. Craig Bohren has a pointed phrase about a subject being “well known to those that know it well,” and this paper unfortunately hits that spot especially in the Introduction. Some colleagues tell me that the coded vocabulary makes the radar remote sensing literature hard to penetrate.
2. The approach for all the methods for SWE retrieval seems to combine a measurement of depth by some remotely sensed method, and then to multiply those depths by estimates of density. With snow depths retrieved from lidar or photogrammetry, this is the viable approach, but from InSAR data it’s feasible (and probably better) to directly retrieve SWE without estimating depth or density.
3. The explanations for getting SWE from InSAR are scattered throughout: in the Introduction, Section 3 (Methods), or the Appendix. Perhaps consolidating might be the answer, or advise some readers to read the Appendix first.

Some line-by-line comments, but consider in the context of the three points above.

Line 30: maybe insert a short parenthetical definition of L-band (frequency 1-2 GHz).

Line 35: I tend to avoid adjectives (“high” here) to describe statistical measures like correlation. In some spectroscopic retrievals I work on, r<0.9 is awful. Present the values themselves.

Line 34: Is “coherence” the same as “correlation”? Without knowing that, some of the rest of the Abstract is hard to interpret. In general, this issue pervades the paper. Coherence is shown to be important but isn’t defined.

Line 36: poor in one year, good the next. Any explanation? I see on Line 420 that this may be an artifact of mis-registration between airborne and in situ data.

Line 37: The sentence “We found that …” seems incongruous with RMSE between 19-22 mm. It would also be useful to specify the ranges of SWE (total) and ΔSWE (between passes) in the experiment. This information does show up later in the paper.

Line 47: The Wrzesien 2018 paper covered North America but the sentence is global. Maybe cite the 2019 paper instead (DO10.1029/2019WR025350I) or clarify that the sentence applies to North America in the 2018 paper.

Line 54: SNOTEL stations are all on nearly flat terrain, hence interpolating between them misses effects of slope and orientation. This sampling bias, combined with the spatial and elevational extent of the snow pillow network, subjects interpolation to artifacts.

Line 56, let’s correct a misunderstanding: National Academies of Sciences, Engineering and Medicine are NOT a “government agency.”

Line 60: I don’t think SnowEx was a “mission.” The Durand et al. 2018 reference uses “campaign.”

Line 65: “is” not “are”.

Line 72: Need a short tutorial here explaining what backscatter, time-of-flight, and co-polar phase difference are. And then a sentence about why the paper focuses on InSAR (which indeed is defensible). The reference to Borah et al. 2023 perhaps distracts. If indeed we can measure SWE up to 800 mm based on backscattering at X- and Ku-band, why go to interferometry? Earlier work by Jiancheng Shi also got impressive results based on multifrequency multipolarization backscatter, albeit with validation by a only few snow pits.

Consider this comment in the context of data processing. Then the details of how you measure coherence, time delay, phase angle, etc. (now Lines 85-107) can be covered in Section 3 or in the Appendix (but make the forward reference).

Line 74 et seq. At the first introduction of “frequency,” it would be useful to include a short table that translates between “Q”-band, frequency, and wavelength. I hope that this paper will be read by people who have no idea what X-band is, or whether X-band’s frequency is greater than or less than P-band’s.

Line 85: Maybe a sketch here to explain what a phase change and a coherent reflection are, or cite where one can find an explanation, or refer to Section 3 or the Appendix. In the current version, it’s difficult to figure out how one goes from measurement to estimate of phase change.

Line 86: “The technique was first established at C-band . . .” First established to do what? Does this remark refer especially to snow, or to interferometric retrievals of elevation?

Line 88: “interferogram” indeed well known to a small community, possibly obtuse to other readers.

Line 98: Not sure what “only two of these studies have not considered atmospheric signal delays” means. Does it imply that signal delays are important, but seemingly well covered?

Line 100-108: This paragraph has information, but not enough to know how one gets a measurement of phase difference between an interferometric pair. Also, is coherence the same as a product-moment correlation? Or something related but different?

Line 170: I suggest expanding section 3.1 with material from the Introduction (line 85-107) For the less informed reader, the relationship between coherence and phase is arcane. In particular, the snow properties that degrade coherence are important and affect the need for frequent image acquisition. How is the interferometric phase angle determined from the correlated (cohered?) pairs?

Line 177: And then we have to worry about “phase unwrapping,” but this text doesn’t tell us what that is. Also, is phase unwrapping a problem generally with SAR at L-band and higher frequency? Perhaps interpret the equations in Leinss et al. 2015 to explain? (Later I see phase unwrapping at ~100 mm)

Figure 2 and Line 196: Calculations of Incidence Angles from the Copernicus DEM lead to an uncertainty in cosine(incidence) of ~0.1 (from my own work, DOI 10.1029/2022JG007147), but are you able to overcome this problem because repeated images get you the right incidence geometry? Otherwise this is a source of uncertainty, even with the best available global DEM.

Line 215: Can you include a equation that defines Coherence? Or is it just Pearson product-moment correlation?

Line 235: Maybe include a citation to Reflex W? I may not need to know what a “de-wow” filter is, but I’d like to know that I could find out.

Line 248: The title of Section 3.2.3 is “TLS” but the section also covers the UAV lidar.

Line 283: “phase cycle” appears here for the first time. The cognoscenti know what this is but some readers may not.

Line 424: “phase unwrapping” is mentioned here and elsewhere. In processing the interferometric phase values, how do you decide when you’ve gone through a phase cycle? Or more than one?

ESTIMATING SWE DIRECTLY FROM InSAR (instead of estimating depth and multiplying by density)

[Check the attached PDF, as this section includes an equation and a figure]

A compelling argument for InSAR is its lack of dependence on density, in contrast to lidar for example where the biggest uncertainty is that in density.

Review

General Comment

The article ‚Evaluating L-band InSAR Snow Water Equivalent Retrievals with Repeat Ground-Penetrating Radar and Terrestrial Lidar Surveys in Northern Colorado’ compares SWE change retrievals from airborne interferometric SAR data, ground penetrating radar, terrestrial lidar scans, automated measurement stations and in-situ measurements. The paper provides an extensive data analysis for two winters (2020 and 2021) over different test sites in Colorado. The authors also analyze the impact of low coherence on the SWE change retrieval, providing valuable insights for future space borne L-band SAR missions.

Specific Comments

Line 37: Maybe you can add half a sentence why the agreement was poor in 2020.

Line 98: The meaning of this sentence is hard to understand. Maybe you could rephrase it.

Line 100-108: You could think of adding this paragraph about the interferometric coherence to Appendix A.2., where you also describe the interferometric phase.

Line 124: Why have you used a different heading for the 27.01. /03.02. interferogram and not the 141° as well?

Line 177: Do you know why the coherence was low for that interferogram? Please elaborate briefly.

Line 183: Maybe you can point out that it is a SWE change retrieval, so you can just measure changes between the measurements, and not directly the total SWE.

Line 211: Were the 20% GPR SWE change retrievals used for estimating the absolute phase selected randomly? And why have you not used the In-Situ stations for absolute phase calibration?

Line 271: What is the resolution your 3x3 pixel grid?

Line 352: Why have you chosen HH and not VV? Since the RMSE is smaller for VV.

Line 492: In this paragraph you are discussing the influence of wet snow. Maybe you can also add that wet snow increases the absorption and decreases the penetration depth of the radar wave in the snow volume.

Line 520: In your Appendix A.1 you describe the L-Band transmissibility, which is very interesting, but you never refer to A.1. 

Line 538: (Referring to comment on line 100-108). Maybe you could also add here an equation for the interferometric coherence, so it is easier to understand what it means and how you can obtain the interferometric phase.

Line 548: In A.2.2 you are describing the atmospheric correction for UAVSAR. I am not an expert in this field, but I understood that you are estimating a phase ramp due to the atmosphere and then are checking if the atmospheric correction is improving your SWE change estimates. You stated that it does not improve your results. But where does your calculated phase ramp then come from? Maybe you could explain this more.

Line 595: In (Leinss et al., 2015) an approach was presented, where a linear function between the SWE change and interferometric phase was derived. This has the advantage that you can directly derive the SWE change from the phase without the need of additional in-situ density measurements, which is the main advantage of the DInSAR approach compared to the GPR or LIDAR retrieval. Maybe you can think about it, since you also stated in line 66 that the need of in-situ density measurements adds uncertainty. Or state why you have chosen to use the approach with Equation (A5) and (A6). 

Line 598: You maybe could point out that these are snow depth changes and SWE changes.

Technical Corrections

Line 53: Reference for the SNOTEL stations

Line 183: ...is outlined in Appendix A.2?

Line 236: The GPR Workflow in Figure 2 shows the Radargram processing and it has first the step (4) and then the step (3). Maybe you can make it more consistent.

Line 320, Line 333: It is hard to see the points in Figure 5 (i) and Figure 6 (i).

Line 352: Space after Figure missing.

Line 352: Parenthesis after HH.

Line 353: In the Table S4 the RMSE is 21mm and not 22mm.

Line 375, Line 378, Line 382: There is no Figure 8 (a-i).

Supplementary Material:

Line 62:  There is only Figure 8 (a-b).