General comments

The study described by the manuscript is an interesting and well-designed test of the potential of radio occultation (RO) data for wind field monitoring across the equator where the geostrophic balance breaks down. Two types of bias are investigated: a) biases from the equatorial-balance approximation (referred to as "equatorial-balance bias") by comparing actual and equatorial-balanced wind fields from ERA5 reanalysis data, and b) biases from using RO data (referred to as "systematic data bias") by comparing wind fields from RO and ERA5 obtained by the balance approximation. Key questions addressed are how well the equatorial-balanced winds bridge the geostrophic winds across the equator, and which roles the horizontal wind components, as well as the resulting wind speed, play in the break-down of the geostrophic approximation.

Scientifically, the study presented is perhaps not a major leap forward, but it is a well-designed study, it fills a gap in the literature, it is well-written and easy to follow and it provides practically useful information. For anyone interested in generating atmospheric wind fields from RO data, this paper will provide highly valuable information.  

The manuscript is well worth to be published. However, before accepting the manuscript for publication, I would like to see some questions clarified. See the specific comments and questions below. Addressing these questions is essential to fully understand some of the issues discussed in the manuscript, and addressing them will certainly improve the manuscript. 

Specific comments and questions

1) Equations 1 and 2: what, precisely, are the variables x and y? I would like to see a level of detail here corresponding to that provided for Equations 3 and 4. Also, latitude is used in Equations 1 and 2 before it is introduced in association with Equations 3 and 4.

 

2) RO data retrievals: The key variable used in the study is geopotential height as a function of pressure (or pressure as a function of geopotential height). How is pressure retrieved?  It is mentioned that the RO geopotential climatologies are available from 1000 hPa to 5 hPa. That covers atmospheric regions where the "dry" approximation is applicable as well as regions where it is certainly not applicable. Some explanations of how that is handled is needed. 

3) You mention that the monthly-mean RO data at the 2.5x2.5 degree grid points are computed by "Gaussian latitude-longitude weighting" within a radius of 600 km. What is the width of the Gaussian? Is it 600 km? Or is 600 km the distance from the grid point within which the profiles contributes to the grid point mean?

4) You mention the need to further average to a 5x5 degree grid for the equatorial-balance calculation. Did you try other differencing techniques than forward finite-differences? It may be to simplistic, and other differencing schemes may be more suitable. 

5) In Section 4, the analyses and discussions related to the RO data are focused on three atmospheric layers: 10 hPa, 50 hPa, and 200 hPa. However in Figures 5 and 6, RO data down to 1000 hPa is shown. Whether it makes sense to show RO data in the lower troposphere depends on how the RO data were retrieved. Depending on the answers to comment 2 above, you should consider not to show the full vertical span down to 1000 hPa.

6) Related to comment 5, there is a sentence in Section 4.3 which I don't know how to interpret (lines 259-260): "the larger influence of moisture leads to a higher need of background information in the RO retrieval chain, and as a consequence to an increase in the bias". Is this an indication that you use the "dry" solution all the way down to 1000 hPa?

Conclusions:

Based on the limited innovations of this paper, some potential flaws in the methodology, and very limited discussion, I suggest a major revision of the paper. In the revised version, the authors should properly address the below mentioned issues. The extra analysis can be added in the supplement or appendix in order not to lengthen the paper. In the current form, the study raises more questions than it undoubtedly answers. Without performing a much more detailed analysis, I find the paper unsuitable for publication in EGU AMT. I am mostly concerned about the innovations of this paper – it seems we have not learned much, or that the authors have only confirmed what is known already. But I still do think the outcomes of the study could be useful for the scientific community.

Major comments:

In the introduction, the authors state “In this study [you] aim to close the gap in RO wind field computation across the equator”. However, I am not able to easily identify this gap based on the introduction you provided. Therefore, I suggest that the authors clearly and directly identify this gap. What are the innovations that this study addresses, how do you aim to expand the present knowledge, why is the potential new knowledge important, can we use it in NWP or climate science, etc.? What new can we learn from this study in comparison to other studies? Please, elaborate in more details in the revised manuscript.

Throughout the paper, the WMO thresholds for data quality of winds (+- 2 m/s and +- 5m/s) are mentioned. It would be nice to elaborate to which of the following data do the thresholds apply:

• Instantaneous winds
• Instantaneous zonal-mean winds
• Monthly-mean winds (applied in Nimac et al., 2023)
• Monthly-mean zonal-mean winds (e.g., Fig. 2)
• Monthly-mean zonal-mean latitudional-band-mean winds (e.g Fig. 3)
• something else?

In the paper, you are mentioning the threshold for different of these options, but the thresholds are not equivalent for e.g., monthly-mean winds and monthly-mean zonal-mean winds, they are certainly more strict for the latter.

Furthermore, there are inaccurate claims at different instances in the introduction, which need to be revised, in relation to the references pointing to not yet revised studies.

For example, the study Nimac et al. (2023), in revision at the same journal, does reproduce ERA5 monthly and zonal-mean geostrophic winds rather well (their Fig. 6). It is very important to state it precisely, as suggested by the underlined text above.

On the other hand, Fig. 7 in Nimac et al. demonstrates that the monthly mean ROg-ERAg winds (without zonal averaging) often exceed +- 2 m/s bias threshold. Comparing their Figs. 6 and 7, it is also clear that +- 2 m/s threshold is often only achieved in the zonal-mean monthly-mean winds due to compensating biases along the latitude circle.

The computation of the geostrophic winds is very sensitive to the applied resolution of the input data, as you have shown in Figure 1. To avoid the zig-zag pattern at high-resolution, the authors should either use higher-order symmetric approximation of the derivatives (instead of first order forward) or compute the derivatives exactly using a spectral method. At least, the authors should prove that the choice of numerical approximation don’t play a major role in the zig-zag pattern. Furthermore, I would be curious to see, how the choice of averaging period affects the “optimal” resolution (only briefly mentioned in line 165). I guess 0.5-degree resolution would not be an issue, if the data averaging was 3 months instead of a single month, but I am eager to see your results. On the other hand, I ask what the reason is for testing equatorial balance in higher-resolution reanalysis data, if the RO data are only available at 2.5-degree resolution.

The equatorial balance equation for the zonal wind works reasonably well in the stratosphere in the equatorial area, but we know this already from other studies, e.g., Healy et al., 2020. The meridional wind deduced from equatorial balance equation does not seem to reproduce the original winds, as shown in Fig. 2d,e and Fig. 7b,h,e. The explanation why it fails is speculative and unconvincing (“This could be because the v component contains a derivation with respect to latitude as well as longitude which is computationally not as robust as the second derivative with respect to latitude.”). Apparently, the balance is not satisfied in the deep tropics.

Another possible reason is that the steady-state assumption (neglecting temporal derivatives of meridional wind) might not be valid for meridional wind component. As this is one of the key results of this study, the authors should do more effort to analyse and explain it. You could do this by inspecting the magnitude of the terms in the meridional derivative of full Euler equation for meridional wind.

Is the inability of equatorial balance equation to reproduce meridional winds also the reason why other authors opted not to use it? I also find it rather disturbing that the analysis of meridional wind was only performed for a certain longitudinal band, - 10 to 10 degrees longitude? Why not performing similar analysis also for other bands?

I like the results presented in Section 4.3. These are very interesting, and the revised paper should build on that, while presenting a detailed analysis why the geostrophic approximation provides an even better reconstruction.

Descriptions in the figure captions should be more accurate, and English should also be improved at many places.

Specific comments (ordered by line number):

It should be stated somewhere in the Abstract that the authors are using monthly ERA5 and RO data.

1: vertically

2-3: Without “availability”. Consider the following reformulation:

Greater availability of wind data is particularly needed, especially in tropical regions and the southern hemisphere.

7-8: sentence “We analyze the equatorial balance equation within this latitude band.” Is redundant in my opinion.

9-10:  what do you mean by “volatile in derivation”? Please, express it more clearly.

20: Bauer et al. is not a good reference in this context, as it only briefly mentions what is missing in the observing system, but does not actually provide any content. Instead, I suggest citing Baker et al., 2014.

30: several heights but mostly upper troposphere

31: I would exclude AMVs here as they are almost global

33: ADM Aeolus does not really perform 3D wind profiling as it only measures a profile of a projection of the wind perpendicular to the satellite track, which is quite similar to the zonal wind component.

32-34: This needs to be reworded. Not only that Aeolus “has potential”, but it has also demonstrated its usefulness, which has been described in several studies, such as Rennie et al., 2021, Pourret et al., 2022

30-35: I think it is important to mention that much of the wind information is nowadays obtained also implicitly in NWP to initialise the forecast, i.e. through 4D-Var humidity and/or ozone tracing (Geer et al., 2018 ; Zaplotnik et al., 2023), as well as through the geostrophic adjustment, and directly through the background-error covariances, especially where the geostrophic balance applies. The microwave humidity sounders are now the most important observation system in ECMWF IFS, in large part due to aforementioned tracing effect.

47-52: It would be informative to mention the horizontal resolution as well, not just the vertical resolution. It could also give reasoning for my further comment line 78.

50-51: the so-called sweet spot for GPSRO is 10-32 km, see Semane et al., 2022, their Fig. 1.

61: no comma before “isobaric levels”.

63: between 15N in 10 S.

64-65: It is important to mention that Healy et al. (2020) applied equatorial balance equation only in the stratosphere, using zonally and monthly averaged data (for apparent reasons). It is not clear, whether such balance holds also instantaneously at particular location and time instance.

65: analyzed instead of “started to analyze”

66: to reproduce ERA5 geostrophic winds (“original winds” sound like total winds). You properly introduce “original” only later in the text, in line 115, leaving the reader confused at this stage.

68: I am not sure whether “Anthes” region is an established geographical term. Did you perhaps mean Andes?

70: equatorial band

70: “approaches” instead of “converges”

70: I would exclude “going further towards equator than other studies”, as this might not be entirely justified by results in their Figs 6 and 7.

71: Reformulate sentence “Interesting was also to see…”

78: what is the reasoning for the choice of 2.5deg x 2.5 deg grid for the assessment of the quality of the approximation? Is it done to follow Nimac et al., 2023, or is there any physical reasoning, e.g. the horizontal resolution of the RO data? If so, it has to be explicitly written to avoid speculation. Note that by increasing the resolution, the greater portion of the total wind is represented by ageostrophic motions, which are unbalanced.

79: latitude-longitude

86: The magnitude of ageostrophic contributions are vastly influenced by the resolution at which one performs the analysis. See for example the study of Bonavita (2023), their Fig. 5.

97-104: it is necessary to mention, that Coriolis parameter is now approximated using equatorial beta-plane approximation.

100-110: It appears a bit strange, that you use derivative over (x,y) in equatorial balance equation and (lambda,phi) in geostrophic balance equation. Choose one set of variables for both.

106: remove “still”

125: do the WMO-OSCAR, 2023 requirements apply to instantaneous winds, monthly means or monthly and zonal-means? This is very important.

131: “to limit the length of the paper” is a rather strange argument. You can always provide a supplementary file in the EGU Journals.

135: “includes”/”provides” instead of “combines”

135 and 137: sometimes you use “data” as singular noun and sometimes as plural, e.g. “The ERA5 reanalysis data combines…” vs. “The data are available…”

138: no comma before “to find”, no comma before “for the equatorial balance…” Revise misuse of comma at the other places of the text as well.

142: I do not agree with that statement, as mentioned in the General comments.

Figure 1: are the zig-zag features similar at other latitudes?

Figure 1: it should be mentioned in the figure caption what the dashed lines represent

154: does it mean that no correction due to latitudinally varying centrifugal force is applied?

161-162: is 600 km the halfwidth of the Gaussian or is this the localisation threshold? If so, what is the halfwidth of the Gaussian smoother?

163: the smoothing procedure is rather strange – first you do a Gaussian smoother, then you further perform binning. Can you provide an example in the supplementary, how the raw fields evolve in your preprocessing routine.

178: no comma

193: I would not say “it is not that well reproduced”, I would say it is not reproduced at all (Fig 2. d,e). Given the large relative differences between v_o and v_eb, I would suggest to add a new figure of relative differences. Based on Fig 2d,e, I also find it very unconvincing to use equatorial balance for meridional wind component at all.

193-194: I find the explanation for the mismatch between v_eb and v_o rather unconvincing. I would say that the derived physical balance does not apply for meridional wind. If you look at the derivation precisely, there is an important assumption of steady state flow. However, the tropical disturbances are not steady, especially the features involving meridional flow such as MRG waves.

195-196: this might be coincidental. What is the reason for better V_eb if it contains wrong v_eb? How can it be shown?

Figure 4 should include two more rows: 1) monthly-mean winds V_o and 2) monthly-mean winds V_eb. The caption should be: Temporal development of the wind-speed bias…

207: tropopause in the deep tropics is rather found between 100 hPa and 70 hPa, instead of 200 hPa

213- : It is important to note that the similarity between ERA5 v_eb and RO v_eb does not imply that the use of equatorial balance is meaningful due to large differences in ERA5 v_o and v_eb. It only suggests that the input geopotential data of ERA5 and RO for the computation of u_eb and v_eb are similar. This is not unexpected, as the same COSMIC data were assimilated (albeit in a somewhat different form) in the production of ERA5 reanalysis (Hersbach et al., 2020).

222: revise “high occultation statistics”

224: provide references to those missions.

231-233: The alignment of an increase of systematic bias with the drop in the number of RO profiles is a very interesting feature. However, my question is how you can be certain that only this factor explains the increase of bias. No proof is provided, so the statement should be milder and speculative. From the statistical perspective, a reduction of the number of profiles would only increase the random error.

237: “section”

237: no comma before “to complete”

244-245: “geostrophic break down”  the “the geostrophic approximation does not apply any more”

Figure 7 is another proof, that v_eb (as well as v_g) are likely unable to approximate v_o.

272: it is again unclear to the reader, what are the “winds calculated using ERA5 data and original winds”. Try forming the Conclusions in a way that is understood even to readers who did not read the whole methodology.

276: word order: “we could successfully apply”

276-277: as this is not some new conclusion, I would say “as in Healy et al. (2020)”.

277: what do you mean by “the resolution was possible to obtain” (I could not understand with going back to the results section). Please, express more clearly.

279: this reads as the zonal wind speeds are 1 m/s and meridional wind speeds are 15 m/s. Again, be more precise for which levels in the equatorial +-5 deg channel do this wind speeds apply.

287: first comma is excessive

References:

Baker, W. E., and Coauthors, 2014: Lidar-Measured Wind Profiles: The Missing Link in the Global Observing System. Bull. Amer. Meteor. Soc., 95, 543–564, https://doi.org/10.1175/BAMS-D-12-00164.1.

Bonavita, 2023: On the limitations of data-driven weather forecasting models. arXiv:2309.08473

Geer, AJ, Lonitz, K, Weston, P, et al. All-sky satellite data assimilation at operational weather forecasting centres. Q J R Meteorol Soc. 2018; 144: 1191–1217. https://doi.org/10.1002/qj.3202

Rennie, M.P., Isaksen, L., Weiler, F., de Kloe, J., Kanitz, T. & Reitebuch, O.(2021) The impact of Aeolus wind retrievals on ECMWF global weather forecasts. Q J R Meteorol Soc, 147(740, 3555–3586. Available from: https://doi.org/10.1002/qj.4142

Pourret, V., Šavli, M., Mahfouf, J.-F., Raspaud, D., Doerenbecher, A., Bénichou, H., et al. (2022) Operational assimilation of Aeolus winds in the Météo-France global NWP model ARPEGE. Quarterly Journal of the Royal Meteorological Society, 148(747), 2652–2671. Available from: https://doi.org/10.1002/qj.4329

Semane, N., R. Anthes, J. Sjoberg, S. Healy, and B. Ruston, 2022: Comparison of Desroziers and Three-Cornered Hat Methods for Estimating COSMIC-2 Bending Angle Uncertainties. J. Atmos. Oceanic Technol., 39, 929–939, https://doi.org/10.1175/JTECH-D-21-0175.1.

Zaplotnik, Ž., Žagar, N. & Semane, N.(2023) Flow-dependent wind extraction in strong-constraint 4D-Var. Quarterly Journal of the Royal Meteorological Society, 149(755, 2107–2124. Available from: https://doi.org/10.1002/qj.4497