We thank Jorge L. Chau for his public comment on the 3DVAR retrieval.

Vertical velocities are an important physical quantity to measure and often part of scientific disputes. In the case of meteor radar observations, it was known since the first systems were deployed that the wide field of view and least square fitting techniques won’t provide reliable results for various reasons. For the analysis of reliable vertical winds, there is nothing unimportant e.g., phase calibration, antenna positions, surface motions (frost), mutual antenna coupling, etc. they all play a role and are nearly impossible to handle. Retrievals that offer a mathematically elegant way involving a priori knowledge to reduce the impact of all these quantities by giving preference to solutions that are physical more likely, which also provides an opportunity to reduce biases that are intrinsic to the least square fitting for certain mathematical problems. 

The results presented herein are obtained by applying advanced mathematics with non-linear error propagation, a spatio-temporal Laplace filter, and WGS84 geometry. All three elements provide key contributions to the presented results. The geometry is important for the non-linear error propagation, which defines weights for the spatio-temporal filter between the iterations (max 8). Thus, we use complicated cost functions with several different weights and only the WGS84 geometry is always the same. Removing the WGS84 geometry certainly degrades the solutions, which is demonstrated in Figure 2 (Stober et al., 2018, AMT).  Due to the radial nature of the observations any change of the horizontal winds also impacts the vertical wind solution (eq. 1, this paper). However, we did not explicitly evaluate how much each part contributes to the final solution for the meteor radar, but we did perform such a comparison for the Middle Atmosphere Alomar System in Gudadze et al., 2019 and there it turned out that the vertical velocities become even smaller when considering a WGS84 geometry compared to the case without.

There is no doubt that the WGS84 geometry is important in retrievals to obtain the results, but it is certainly not the only factor. However, we are confused about the statement in the public comment that Chau et al. 2021, and Conte et al, 2021 include the WGS84 geometry. We carefully read the papers and found no statement or reference or citation that suggests that such an important aspect is included. Neither is a WGS84 geometry presented in Chau et al., 2017, which uses spherical coordinates for the volume velocity processing (VVP, Waldteufel and Corbin, 1979). We also found no statement in Egito et al., 2016 about the implemented geometry for the fitting. Due to the missing information about the geometry, we assumed that this is the likely cause for the substantial deviations.

The second aspect in regards to the comment  “without including additional damping terms or regularization constraints” which presumably refers to previous retrievals (Stober et al., 2017, Wilhelm et al., 2017), which included a strong damping of the solution towards w=0 m/s, which is comparable to a damped least square. However, this part was removed from the retrievals in this work. There is also no regularization included to cure a potential rank deficiency for the monostatic case. Nethertheless, it is true that our cost function tends to have a preference to smaller norms (giving preference to smaller errors for the vertical velocity), which appears to be related to small values of w, although a small value of w is not required and large values that are statistically significant should be still retrievable. The Sodankyla meteor radar indicates a certain skewness towards larger positive values, which are 3 times larger compared to Kiruna.  This approach is also described for the 3DVAR retrieval, but with a different implementation. Currently, we are working on new retrievals with even more complicated cost functions to further improve this aspect and to perform certain benchmark tests.

Furthermore, we have to note that we were not able to retrieve vertical velocities with a smaller statistical uncertainty compared to its absolute value, which suggests that the effective measurement response for an instantaneous vertical measurement is negligible and no statistically significant values can be obtained. This led us to the conclusion to refer to these values as residual bias.  

More importantly, we tested whether the retrievals are meaningful concerning existing model physics. Therefore, we performed an initial comparison of the meteor radar data using the UA-ICON model and simulated a meteor radar beam to extract vertical velocities. A comparison of the horizontal winds is presented in Stober et al., 2021 (https://acp.copernicus.org/preprints/acp-2021-142/). The UA-ICON run is published in Borchert et al., 2019 (https://gmd.copernicus.org/articles/12/3541/2019/). The histograms presented in the supplement Figure below are obtained using all available data from the meteor radars at Sodankylä and Kiruna and the complete UA-ICON run to ensure a sufficient statistics.

Although the agreement is impressively good, we don’t want to claim that our retrievals are representing ‘true’ vertical velocities. Our retrievals appear to provide statistically sound solutions to the meteor radar data, but certainly if one of the mathematical aspects turns out to be not applicable or not generally true, this might change. However, we are glad that our paper triggered such a good discussion and brought that much attention to the topic.

References:

Wilhelm, S., Stober, G., and Chau, J. L.: A comparison of 11-year mesospheric and lower thermospheric winds determined by meteor and MF radar at 69 ° N, Ann. Geophys., 35, 893–906, https://doi.org/10.5194/angeo-35-893-2017, 2017.

Stober, G., Matthias, V., Jacobi, C., Wilhelm, S., Höffner, J., and Chau, J. L.: Exceptionally strong summer-like zonal wind reversal in the upper mesosphere during winter 2015/16, Ann. Geophys., 35, 711–720, https://doi.org/10.5194/angeo-35-711-2017, 2017.

Stober, G., Chau, J. L., Vierinen, J., Jacobi, C., and Wilhelm, S.: Retrieving horizontally resolved wind fields using multi-static meteor radar observations, Atmos. Meas. Tech., 11, 4891–4907, https://doi.org/10.5194/amt-11-4891-2018, 2018.

Gudadze, N., Stober, G., and Chau, J. L.: Can VHF radars at polar latitudes measure mean vertical winds in the presence of PMSE?, Atmos. Chem. Phys., 19, 4485–4497, https://doi.org/10.5194/acp-19-4485-2019, 2019.

Borchert, S., Zhou, G., Baldauf, M., Schmidt, H., Zängl, G., and Reinert, D.: The upper-atmosphere extension of the ICON general circulation model (version: ua-icon-1.0), Geosci. Model Dev., 12, 3541–3569, https://doi.org/10.5194/gmd-12-3541-2019, 2019.

Stober, G., Kuchar, A., Pokhotelov, D., Liu, H., Liu, H.-L., Schmidt, H., Jacobi, C., Baumgarten, K., Brown, P., Janches, D., Murphy, D., Kozlovsky, A., Lester, M., Belova, E., and Kero, J.: Interhemispheric differences of mesosphere/lower thermosphere winds and tides investigated from three whole atmosphere models and meteor radar observations, Atmos. Chem. Phys. Discuss.

We thank the reviewer for assessing the submitted publication on the 3DVAR retrieval algorithm and the constructive suggestions to improve the manuscript. The final revision will include a point-by-point reply to each raised concern.

Data availability:

The 3DVAR retrievals are implemented to permit routine operation for both radar networks. The data shown in this paper is available upon request through Alexander Kozlovsky at SGO for the Nordic Meteor Radar Cluster and from Alan Liu for the CONDOR network. There was a plan to later upload these files to the ARISE database. However, current funding limitations have delayed this project.

Difference plots:

Difference plots between both retrieval grids shown in Figure 4 are doable. However, the interpolation to a common grid introduces additional errors. We will rerun both domains to ensure and diagnose whether different meteors enter the retrieval at the domain boundary (this is certainly the case at Sodankyla), which could introduce additional systematic offsets. The revised manuscript will include a figure illustrating these differences.

Reference suggestions:

We thank the reviewer for pointing at additional references, which are going to be included in the proposed paragraphs in the manuscript.

Other comments:

There are a couple of other suggestions mentioned by the reviewer, which we will consider as proposed in the revision. We are going to expand the discussions and add more details to explain the Figures. However, we have not yet performed a systematic seasonal analysis for all the different events. Our main intention of the submitted manuscript is the retrieve and demonstrate that various meteorological events can be found and analyzed from the data. We are also grateful for correcting typos and other mistakes in the figures and figure captions. 

We thank the reviewer for the valuable comments on our paper. The manuscript will be revised according to the suggestions. A more detailed point-by-point reply with all the changes is going to be prepared after the public discussion is closed.

Comment:

Line 38. The Na Doppler lidar has been an important ground-based instrument, and has many important contributions to the MLT dynamics, due to its capability of day and night-time simultaneous measurements of temperature and horizontal winds [Krueger et al., 2015]. Due to its horizontal wind capability, it can derive the intrinsic properties of GWs. It is unfortunate that the author misses this important instrument.

Reply:

Some Na - Doppler lidars are indeed capable of measuring horizontal winds but often assume w=0 m/s. We will expand this part of the introduction and add more specific information on different Na- lidars and include citations to the proposed publications. However, we have to note that due to the imaging capability of the 3DVAR algorithm there is no need to measure temperature to derive the intrinsic gravity wave properties. The intrinsic horizontal wavelength is directly assessable from the images and the phase velocities can be inferred from successive images (see also Stober et al., 2014, Stober at al., 2018).  Gravity wave properties from lidar observations are often analyzed applying a hodograph analysis, which requires temperature measurement to derive unambiguously the intrinsic gw properties.

Furthermore, NA-lidar winds could in principle be used and included similar to all other types of radial observations. The 3DVAR algorithm has a build-in tool to permit the usage of different data sets.

Comment:

Line 44-45. There are actually many of this collaborative investigations between the Na Doppler lidar and airglow instrument. So, I suggest the author replace “only a few” with many. The problem with such Na Doppler lidar – Airglow investigations is that they are mostly focusing on single case studies, such as Yuan et al. 2016, Cai et al., 2014, and, thus, cannot provide statically large numbers of cases to build robust database of these intrinsic properties of GWs.

Reply:

Thanks for the recommendation in rewording the issue. The revised manuscript is going to be changed and the suggested reference is going to be added. However, we have to point out that the 3DVAR retrievals are 24/7 observations. Case studies will be possible, but the scientific emphasis is certainly more towards statistical GW effects and their seasonality. We are going to rephrase this aspect and use more precise wording to express these differences.

We thank the reviewer also for all the technical corrections, which are going to be included in the revised manuscript.

References:

Stober, G., Sommer, S., Rapp, M., and Latteck, R.: Investigation of gravity waves using horizontally resolved radial velocity measurements, Atmospheric Measurement Techniques, 6, 2893 – 2905, https://doi.org/10.5194/amt-6-2893-2013, http://www.atmos-meas-tech.net/6/2893/2013/, 2013.

Stober, G., Sommer, S., Schult, C., Latteck, R., and Chau, J. L.: Observation of Kelvin–Helmholtz instabilities and gravity waves in the summer mesopause above Andenes in Northern Norway, Atmospheric Chemistry and Physics, 18, 6721–6732, https://doi.org/10.5194/acp-18-6721-2018, https://www.atmos-chem-phys.net/18/6721/2018/, 2018b