The manuscript “Mispointing correction methods for the conically scanning WIVERN Doppler radar” analyzes different methods for the correction of azimuthal and elevation mispointing for the Earth Explorer Candidate WIVERN. The authors nicely describe the respective methods and derive the respective precisions and temporal / spatial scales.

The paper is well structured, easy to read and the analysis is profound and well described. Nevertheless, it could benefit from some minor revisions.

1 Introduction

L 16: Abbreviation ALADIN not introduced.

Please revise the citations for the Aeolus mission. E.g. Lux et al., 2021, is a paper on a very specific topic on laser frequency stability and probably not a good reference for the whole Aeolus mission. A good overview of the Aeolus mission is given e.g. by ESA (2008).

In line 24f, you motivate the WIVERN radar as a complementation of current global wind measurements in cloudy conditions. However, you do not clearly state the limitations of the other observation techniques, especially Aeolus, before. This could be added e.g. in line 21.

2 Mispointing errors

Your whole paper is based on equation (1). Could you please add a proper derivation of this very important equation?

3 Doppler correction methods

Eq (2): The variable H_S/C is not introduced.

L 79: Why “therefore”? Maybe better “unfortunately”?

L 87: blue -> orange dashed

L 88: How is the noise subtracted? Does this noise subtraction method have an impact on the precision of your correction method(s)?

L 140: Why 0.4 m/s? In the introduction you state that it should be below 0.3 m/s.

L 151f: Why do you choose these box sizes?

Figure 7: What is the difference between dashed and solid lines? Description is missing.

L265: The method is in detail described by Weiler et al. 2021. So maybe this is a better reference here.

Figure 13: Is this Figure really necessary?

L 182: Why only between -65° and 65° latitude?

Figure 14: Difficult to see the difference between solid and dotted lines. Please adapt line style.

4 Summary and conclusion

L 332: And on which time scales can such models be considered unbiased? What about the wish to have model-independent measurements?

In the introduction you motivate your study with phase 0 industry studies showing mispointing errors above 0.3 m/s particularly for slow varying components. Are the time scales of your methods sufficiently fast to correct for these? So, what exactly are “slow varying components”? This should be addressed either here or in the introduction.

References

European Space Agency (ESA): “ADM-Aeolus Science Report,” ESA SP-1311, 121 pp., available at: https://earth.esa.int/documents/10174/1590943/AEOL002.pdf, 2008. 

Weiler, F., Rennie, M., Kanitz, T., Isaksen, L., Checa, E., de Kloe, J., Okunde, N., and Reitebuch, O.: Correction of wind bias for the lidar on board Aeolus using telescope temperatures, Atmos. Meas. Tech., 14, 7167–7185, https://doi.org/10.5194/amt-14-7167-2021, 2021.

This paper examines four methods for diagnosing pointing errors for the proposed WIVERN mission, which would use a Doppler radar performing a conical scan for wind measurements in cloudy areas.  I think the title and introduction give the impression that errors are being corrected.  However, I found the focus of the paper to be a little different, namely focusing on the errors in estimating the mispointing but not necessarily addressing the problem of correcting the pointing and the associated velocity.  I think evaluation of the mispointing is definitely worthwhile, but the authors may want to consider adjusting the title and introduction.  My other concern is that the nature of the pointing errors doesn’t seem completely general.   From Figure 1, it looks like the rotation axis is assumed vertical so that the only errors are a deviation from the elevation angle theta and a deviation of the azimuth angle from that estimated.   This means that that the azimuth and elevation angles appear to be considered independently here.  Should errors in which azimuth and elevation are coupled also be considered?  Could such errors occur, as with a scan-axis mounting offset?  Perhaps this is already included but it wasn't clear to me.  Lastly, I think adding some additional math to describe each method may make the work considerably clearer.

Equation (1): Please include a reference for this equation or a derivation, either in the text here or as an appendix. This would help with the concern about coupling between azimuth and elevation errors.

Line 65: I would expand the phrase in parentheses for better clarity, for example changing i.e., to "is". Even more clear would be "forward direction is phi=0; backward is phi=pi"

Line 91: insert ",it " after “threshold”

Line 100: For this technique, the delta-z is translated to a delta-theta via (2).  The delta-z error comes from mis-estimation of the peak of the surface return, as shown in Figure 2.  Are there additional uncertainties in apply (2) that would increase the delta-theta error, e.g., timing jitter?

Line 125: I suggest expanding a bit on the need for flatness.  While directly affecting the range to the surface, for method I, its effect on Doppler is not obvious.  How would a surface with non-moving topography affect the measured Doppler?   How much of the Earth’s land would qualify as flat?

Figure 7: what are the dashed curves?

Line 167: In receiver mode, I assume that the ARC does not return a signal to the radar.  If so, then this analysis uses the data recorded by the ARC.  Further, my understanding is that the ARC will get scanned only once, so the example in Fig 9b is the data that would be recorded by the ARC on a single sweep by the radar antenna.  Hence, the ARC essentially records a cut through the 3D pattern.  Due to the circular shape, the cut is slightly bent, as noted in the text.   Is this a correct description of the ARC measurement? Assuming so, my further understanding is that for an azimuth error, there is a resulting time offset.  Are there other, non-pointing, factors that could also cause errors, e.g. timing?  What about ARC geolocation accuracy?  Are there other error factors in the elevation measurement? 

Line 249: By “identical”, do the authors mean equal magnitudes but opposite signs?

Line 259: My understanding is that this paragraph means that the A and D pdfs will converge to one if there is no azimuth error.  However, if the two pdfs differ due to the azimuth error, the difference would continue with more data.  is this correct - if not, please clarify. I think some minor editing to improve the clarity would be good.  Also, I think the frequency of the error needs more explanation.  If the frequency is much higher (faster) than the orbital frequency, then presumably both A and D pdfs are smeared; clarification would help.  Instead of varying quickly, what if the bias is constant?  I think showing equations for the winds and biases would make this much clearer.

Line 294: Please better define "all-sky" - is this all directions, instead of just sidelooking?

Line 305: The results of Figure 15 look promising.  However, I'm not clear on how the statistics here translate to an uncertainty in the azimuth offset.  An uncertainty of 200 urad is provided in the conclusions, but it's not clear where that came from.  Please add a short discussion on how the 200 urad can be derived from Figure 15.

The study titled “Mispointing correction methods for the conically scanning WIVERN Doppler radar” by F. Scarsi et al. presents four different Doppler velocity correction methods induced by potential satellite antenna mispointing that are applicable to the proposed ESA Earth Explorer WIVERN mission. Each technique is described in detail and with the help for several figures. Sensitivity tests have also been performed. The study closes with a short summary on the findings and conclusions.  

Recommendation:

I suggest the manuscript to be published after minor revisions. The authors should address the following points:

General comments:

I recommend to add “velocity” after each occurrence of “Doppler” to increase readability of the text. Also make sure that whenever you draw a conclusion that is based on Eq. 1, state that in the appropriate spot of the description of Doppler velocity correction method 1-4.

Also, in terms of structure of manuscript, consider removing the numbering of subsubsections 3.1.1. and 3.2.1 as there are no further subsections (3.1.2 and 3.2.2).

Minor comments:

Line 2: congratulations to making it to the next phase – replace “four” by “two” candidates for ESA’s Earth Explorer 11 mission

Line 4: add “Doppler” in front of “velocities”

Line 19: define acronym ALADIN

Line 20: define acronym NWP

Line 26 – 27: Rephrase this convoluted sentence, e.g. as “With clouds covering roughly 30% of the tropospheric volume, Doppler cloud radars have the potential to complement wind observations by Doppler lidar in clear-sky and thin cloud conditions”.

Line 32: be more precise about the “large spacecraft velocity”: add velocity range in brackets

Line 42: “sources” (not source)

Line 59: after “Doppler mispointing error” add “ in Doppler velocity deltav_mis”

Line 67 – 69: Expand this short paragraph by stating which technique is applicable to azimuth- or elevation mispointing or both or alternatively mention this fact at the subheadings of each technique (e.g. in line 70: …”elevation mispointing correction of Doppler velocities”)

Line 75: define acronym AOCS

Line 103-104: Add “According to Eq. 1” in front of “the last three solutions…”

Line 127 – 128: Clarify what you mean by “surface Doppler at all heights”.

Line 138: Do you mean “corrected” instead of “achieved”?

Line 163: Replace “looks” with “views”

Line 223: To increase readability, rephrase to “…the closer the overpass is to ARC, the lower is the uncertainty in the azimuthal mispointing determination”

Line 259: Add “this” in front of “case”

Comments on Figures: 

Fig 5:  Where are the thin dotted black lines?

Fig 7: What do solid and dashed lines refer to?

Fig 10 + 11: increase font size of axes and labels

Fig 11: right panel: captions says theta = 560 microrad, legend (and text) state theta = 480 microrad à correct.

Fig. 12 and Table 2: replace “passes” with “overpasses”