26 Feb 2021
26 Feb 2021
Fourdimensional mesospheric and lower thermospheric wind ﬁelds using Gaussian process regression on multistatic specular meteor radar observations
 ^{1}Haystack Observatory, Massachusetts Institute of Technology, USA
 ^{2}Leibniz Institute of Atmospheric Physics at the University of Rostock, Germany
 ^{3}UiT Arctic University of Norway, Norway
 ^{1}Haystack Observatory, Massachusetts Institute of Technology, USA
 ^{2}Leibniz Institute of Atmospheric Physics at the University of Rostock, Germany
 ^{3}UiT Arctic University of Norway, Norway
Abstract. Mesoscale dynamics in the mesosphere and lower thermosphere (MLT) region have been difficult to study from either ground or satellitebased observations. For understanding of atmospheric coupling processes, important spatial scales at these altitudes range between tens to hundreds of kilometers in the horizontal plane. To date, this scale size is challenging observationally, and so structures are usually parameterized in global circulation models. The advent of multistatic specular meteor radar networks allows exploration of MLT mesocale dynamics on these scales using an increased number of detections and a diversity of viewing angles inherent to multistatic networks. In this work, we introduce a four dimensional wind field inversion method that makes use of Gaussian process regression (GPR), a nonparametric and Bayesian approach. The method takes measured projected wind velocities and prior distributions of the wind velocity as a function of space and time, specified by the user or estimated from the data, and produces posterior distributions for the wind velocity. Computation of the predictive posterior distribution is performed on sampled points of interest and is not necessarily regularly sampled. The main benefits of the GPR method include this nongridded sampling, the builtin statistical uncertainty estimates, and the ability to horizontallyresolve winds on relatively small scales. The performance of the GPR implementation has been evaluated on Monte Carlo simulations with known distributions using the same spatial and temporal sampling as one day of real meteor measurements. Based on the simulation results we find that the GPR implementation is robust, providing wind fields that are statistically unbiased and with statistical variances that depend on the geometry and are proportional to the prior velocity variances. A conservative and fast approach can be straightforwardly implemented by employing overestimated prior variances and distances, while a more robust but computationally intensive approach can be implemented by employing training and fitting of model parameters. The latter GPR approach has been applied to a 24hour data set and shown to compare well to previously used homogeneous and gradient methods. Small scale features have reasonably low statistical uncertainties, implying geophysical wind field horizontal structures as low as 20–50 km. We suggest that this GPR approach forms a suitable method for MLT regional and weather studies.
 Preprint
(19718 KB) 
Supplement
(9531 KB)  BibTeX
 EndNote
Ryan Volz et al.
Status: open (extended)

RC1: 'Comment on amt202140', Anonymous Referee #1, 15 Mar 2021
reply
This is an important, clearlywritten article which describes the
application of Gaussian process regression (GPR) to MLT meteor radar
winds data acquired with multistatic MIMO meteor networks which
produce angle of departure and angle of arrival observables in
addition to Doppler shifts. Thanks to wavevector diversity, data from
the network can be used to characterize the threedimensional wind
field without the ambiguity inherent in individual monostatic systems
which provide no information about horizontal vorticity. The GPR
method is tested here as a framework for resolving finescale
structure in the flow field and for performing error propagation. The
GPR formalism is developed and tested using synthetic and actual
data. The results are compared with those from the more conventional
homogeneous and gradient methods.Ovearll, the significance of the paper is excellent in view of the
importance of the MLT winds (which are crucial for understanding
ionosphere/atmosphere coupling) but difficult to measure using other
groundbased methods. Also noteworthy is the novelty of the
multistatic method which is revitalizing the meteorradar field. The
potential of the method can be realized through incisive analysis such
as is provided by GPR. The scientific method is also excellent in view
of the appropriateness of the methodology and the clarity of the
fomalism and explanations. The presentation quality is good and could
be improved by clarifying the meaning of some of the figures.The paper is acceptible for publication but could benefit from
addressing a few minor questions:1. Throughout the paper, the GPR method is described as being
nonparametric. However, the prior model for the winds is necessarily
parametrized by the means and variances of the wind components
(theta). In what sense is this method nonparametric?2. The paper distinguishes the GPR method from Tikhonov regularization
which is viewed as a competing method. However, 2nd order Tikhonov
regularization can be interpreted as the adoption of a Gaussian prior
for the state vector. How is this fundamentally different from the
method presented here?3. The paper describes the assumption of a Gaussian random process for
the winds as "convenient" because of the tractable computations that
result. Could not the authors provide a more satisfying rationale by
considering whether the central limit theorem applies to the MLT wind
components?4. The authors of the paper note the absence of other kinds of MLT
wind measurements that could be used to validate the wind estimates
produced by the GPR method. Have the authors considered the use of
generalized cross validation?5. The authors note that the region of validity and the spatial
resolution of their method depends on the geometrical configuration of
the multistatic meteor array. Have they considered developing a
geometrical dilution of precision (GDOP) estimator?6. Finally, interpreting figures 24 and 7 is very difficult in view
of the fact that color gradations are being used to represent multiple
quantities simultaneously (i.e. horizontal winds, vertical winds, and
data quality). The authors should attempt to clarify these figures.
AC1: 'Reply on RC1', Ryan Volz, 30 Apr 2021
reply
Thanks for your thoughtful comments. We will address each of them in our formal reply and revised version, but for now we would like to comment on the following selected points:
1. (GPR as "nonparametric") We describe GPR as nonparametric in the same sense as it is used in the referenced Rasmussen and Williams (2006) book: an estimation method which does not compress the training data into a finitedimensional parameter vector, in contrast to parametric methods like linear regression. The mean and covariance function parameters are usually called hyperparameters to emphasize that they are parameters of a nonparametric model. We also find this terminology confusing, so we will seek to clarify it in the next revision.
2. (Comparison to Tikhonov regularization) The methods are indeed related, and there is a good discussion of this topic throughout Rasmussen and Williams (2006), particularly in Chapter 6. The most direct difference is that Tikhonov regularization would best relate to GPR with a squared exponential covariance, whereas we have employed a Matern5/2 covariance. That detail strikes at the heart of the difference between the two methods: it can often be more natural to express prior knowledge in terms of a GPR covariance than as a likelihood penalization. Practically, the difference also comes down to how it is more natural to perform nongridded estimation and analyze uncertainty with GPR compared to regularization approaches. In many respects, the approaches are two sides of the same coin, which is why we see value in future intercomparison that can help refine both approaches.
5. (Geometrical dilution of precision estimator) Perhaps it is clearer to say that the measurement geometry controls the wind estimate uncertainty, which we can calculate through the posterior covariance, and naturally there are (location, wind direction) pairs that have higher uncertainty. As far as we understand it, we can quantify the GDOP as a function of location in this case by taking the root mean square of the wind component uncertainties. If this doesn't describe what you were pointing toward, then we'd love to hear more details!
6. (Figure clarity) We very much would like these figures to be both expressive and interpretable, and we recognize that this is a difficult task given the amount of information that they attempt to include. We strived to use color scales for the different elements that are distinct enough to be identifiably separate and thought we had achieved a good balance. Given that, we're uncertain about how exactly to make satisfying improvements, although we can try. Do you have specific detailed critiques that we could implement (e.g. the vertical wind colors on the streamlines are too hard to distinguish from the background colors, or the information conveyed with them is not worth the visual clutter)?

AC1: 'Reply on RC1', Ryan Volz, 30 Apr 2021
reply

CC1: 'Comment on amt202140', Chris Meek, 27 Mar 2021
reply
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt202140/amt202140CC1supplement.pdf

AC2: 'Reply on CC1', Ryan Volz, 01 May 2021
reply
We appreciate your concern. We believe there is a misunderstanding, since our Dopplerderived lineofsight velocity measurements are no different than what have been used for decades to estimate winds from specular meteor scatter, including the Hocking et al. (2001) and Holdsworth et al. (2004) papers cited in the first paragraph of section 2. At least for an ideal meteor trail, we agree with the motion and measurement depicted in your figure. The trail moves from (A) to (B) with a given velocity, and we measure the projection of this velocity onto the line of sight which moves the reflection point from (A) to (C). Where we disagree is that this "creat[es] an apparent vertical motion" in the first case or "horizontal motion" in the second case. Yes, the projection has a vertical (horizontal) component, but that does not mean that we conclude from those measurements that the wind velocity has a vertical (horizontal) component. From a single measurement, we can't know what the full velocity vector is. But by combining nearby measurements with assumptions about the smoothness of the wind field and quantification of the measurement uncertainty, we can estimate the complete wind velocity vector. The measurement geometries provided by the multistatic configuration allow for such "overlapping" measurements of different meteors with a diversity of projection directions, so this works well in many cases. More importantly, we also know when we don't have sufficient information to resolve the full wind vector, and the estimate uncertainties reflect that. Indeed, the uncertainties for the vertical wind component are generally higher than the horizontal components relative to the mean because we observe relatively few meteor trails with a large vertical line of sight projection (trails close to horizontal). We hope this addresses your concern and clarifies the technique.

CC2: 'Reply on AC2', Chris Meek, 03 May 2021
reply
Thank you; that was a good response to my comment and recognizes the problem,
but doesn't solve it. Meteor wind papers all seem to accept the handeddown wisdom
that the "echo" motion is equal to the lineofsight (LOS) component of
the wind. But based on this assumption, and that all echoes are seen above the
horizon, then a vertical wind must automatically exist, no matter what the trail
orientation (rotation around the LOS). The early papers were analysing for horizontal
wind, so the actual scatter mechanics were not as important.
Because I only have experience with a monostatic system some of my followjng comments
probably apply only approximately to a bistatic system. But hope that
these considerations are completely mitgated by it is not enough to convince.Because the actual expected wind vertical component are in cm/s rather
than m/s, 2D wind (horizontal) values are reasonable and agree well
with other measurements, and are correct under the assumption of
zero vertical velocity. If 3D fits are done, extreme vertical
wind values are often found  I have found nonspurious 2030 m/s. At the
time I had no explanation.
If meteor echo distribution were uniform in azimuth, the problem of vertical
wind artifacts could be mitigated to some extentf  but it is not
uniform. Statistically the azimuthal direction rotates during the day
(at least at Eureka). So a multistatic system unless maybe very large spacing
doesn't change this[ I tried once to fix this lopsided echo distribution by dividing into
octants and equalizing the weight given to each in the wind fit  but there were always
one or two octants with very few, or no, meteors ]
Another related comment (while I have the podium) is about component wind errors/perturbations.
I don't know if this applies to the current paper.
A standard least squares fit allows the formal calculation of component errors. But constant
wind models with uniform echo distribution and an artficial perturbation/error added
in one component show that the variation "bleeds" into the other component. That's because of the
radial nature of the sampling. A perturbation in zonal wind, say, causes a perturbation in
radial speed component, which appears as a perturbation in the meridional component.
I don't see a solution for these problems, and they must have some effect on results.
particularly as more detailed and complicated analyses are used. Caveats should be stated
(or assumptions, like zero vertical velocity  which I think is the hidden, but understood,
assumption in horizontal wind analysis).
Trail orientation can potentially be estimated from echo polarization  but I don't
think this helps here  though might be interesting for meteor studies.
Finally, I think confirmation of the results requires a realistic model, including a variety of
trail orientations and a sporadic meteor model (e.g. Margaret CamplbellBrown's)
 Unfortunately this is not a simple process for bistatic.
cem

AC3: 'Reply on CC2', Ryan Volz, 06 May 2021
reply
There is a lot we agree about regarding the difficulties and pitfalls of the meteor wind measurement, but perhaps we're not quite speaking the same language. We'll try to clarify a few relevant points:
a) It is suitable to apply intuition from the monostatic case to the bistatic case, with minor adjustment to a notional equivalent monostatic system. For each meteor scattering, the bistatic scattering is equivalent to a monostatic geometry where the middle point of the bistatic link gives the virtual monostatic radar location, and the loci of zero velocity is an ellipse with foci at the tx and rx instead of a circle. The effective Bragg wavelength will depend on the geometry and will be greater than or equal to half the radar wavelength, and the "lineofsight" direction is given by the difference between the scattering and incident wave vectors. The particulars of the bistatic case are discussed in more detail in Stober and Chau (2015) and Chau et al. (2019).
Stober, G., & Chau, J. L. (2015). A multistatic and multifrequency novel approach for specular meteor radars to improve wind measurements in the MLT region. Radio Science, 50(5), 431–442. https://doi.org/10.1002/2014RS005591
Chau, J. L., Urco, J. M., Vierinen, J. P., Volz, R. A., Clahsen, M., Pfeffer, N., & Trautner, J. (2019). Novel specular meteor radar systems using coherent MIMO techniques to study the mesosphere and lower thermosphere. Atmospheric Measurement Techniques, 12(4), 2113–2127. https://doi.org/10.5194/amt1221132019
b) Accounting for Earth curvature is an important consideration when working with measurements over an area of this scale. This shows up in differences between what would be seen as "vertical" or "horizontal" motion in the EastNorthUp reference frame at the radar receiver versus the local vertical and horizontal directions in the ENU frame at the meteor location. There is a discussion of this and the coordinate conversion procedure that we use in Stober et al. (2018). Whenever we refer to vertical or horizontal winds, we mean with respect to the Earth's surface underneath that location taking into full account these coordinate conversions. Perhaps that addresses some of the concerns here.
Stober, G., Chau, J. L., Vierinen, J., Jacobi, C., & Wilhelm, S. (2018). Retrieving horizontally resolved wind fields using multistatic meteor radar observations. Atmospheric Measurement Techniques, 11(8), 4891–4907. https://doi.org/10.5194/amt1148912018
c) The LoS Doppler measurement indeed contains contributions of vertical velocity, and most works based on monostatic systems have ignored the vertical velocities because of sampling issues, inhomogeneous horizontal winds, etc. The assumption has been that horizontal winds are much larger than vertical winds, and the mean vertical wind is very small. The GPR technique is agnostic to the assumptions the user wants to impose about the horizontal winds, and one could force a zero vertical wind component or scale the variance of the vertical component relative to the horizontal to suitably affect the final estimated winds. There are important estimation decisions here that welcome further consideration, but we consider that to be beyond the scope for the introduction of the GPR technique as contained in this paper.
d) To that point, the Ph.D. student of one of the coauthors (JLC) is about to submit a paper dealing with the vertical velocity estimates using a virtual meteor radar system (i.e., geometry and realistic sampling) on a high resolution atmospheric model (Upper Atmosphere  ICON). Namely, the measured line of sight velocities are replaced by projected velocities using UAICON winds at each meteor detection point. One of the main conclusions is that a variability of ± 12 m/s is an apparent vertical wind variability due to horizontal wind inhomogeneities. So we agree, mean vertical wind estimates in monostatic and bistatic systems obtained over the whole area (a few hundred of kms diameter) present a large artificial variability.
e) In this work, our focus is in the wind estimates with much smaller horizontal scales than traditional meteor systems, taking advantage of more samples and different viewing angles (equivalent as having different monostatic systems with relatively close separations). That is contrary to previous works: we don’t do a global 3D wind fit on the illuminated area, but instead we effectively do it locally in smaller areas (controlled by the covariance length scale). We show that the reliable area of vertical velocities is narrower than the area for horizontal velocity estimates. These areas depend on the sampling geometry that in turns depend not only in the system geometry but also, as you mentioned, on the meteor population.
f) Although we don't highlight it, the GPR technique also provides the twocomponent covariance values as final estimation outputs in addition to the singlecomponent posterior variances. These covariance entries allow one to quantify exactly one of the issues you mention: how perturbation/error in one wind component bleeds into the estimate of another wind component. This doesn't solve the problem of correlated errors, but it does let us be aware of it, quantify it, and potentially optimize meteor radar network geometries to minimize it. This is an important topic that begs for further investigation, and we think that the GPR outputs/analysis can help with that.

AC3: 'Reply on CC2', Ryan Volz, 06 May 2021
reply

CC2: 'Reply on AC2', Chris Meek, 03 May 2021
reply

AC2: 'Reply on CC1', Ryan Volz, 01 May 2021
reply

CC3: 'Comment on amt202140', Gunter Stober, 18 Jun 2021
reply
This is an interesting approach for multistatic meteor radar networks. Some part of the retrievals might deserve some additional information about the inversion method:
1. How does the method differ from a classical 2DVAR data assimilation approach applying a standard cost function? The inversion is computed layerbylayer using a 'large vertical averaging'? However, the atmosphere shows very often strong vertical shears. Are these shears considered in the cost function or error estimates or both?
2. The algorithm makes use of the WGS84 geometry. It might be appropriate to cite the original paper and references of the implemented algorithms.
3. Retrieving vertical winds is usually challenging due to exponential instability growth for parameters with low measurement response. This often limits the vertical resolution for radiometers. Do they check the solutions for such instabilities? The values that can be found in the examples are rather high.

AC4: 'Reply on CC3', Ryan Volz, 24 Jun 2021
reply
Thanks for the comment!
1. (Comparison to classical 2DVAR data assimilation) Can you point to a reference to which we might compare? In general we expect similarities with many statistical estimation approaches, with the primary differences arising from the specific formalism used and how that allows one to express the prior knowledge and constraints on the estimate. We think the strengths of the GPR method are that specifying a covariance function allows one to easily apply physical intuition, that it works in 4 dimensions at once and does not impose a gridding of the measurements or estimates, and that it is natural to carry through and compute uncertainties on the estimates.
In particular concerning vertical averaging and accomodating strong vertical shears, the natural way to express that in the GPR framework is to enforce a small value for the covariance length scale in the vertical dimension. The examples in this paper use a fitted value for the vertical length scale of 3 km, which arises both from what the density of meteor measurements will support and also from the observed vertical correlations particular to the winds seen with these data. So we can say that the averaging is approximately over a vertical region of 3 km and that any sharper vertical shears will be smoothed over (i.e. the effective vertical resolution is 3 km). It is certainly possible to manually set the covariance parameters to better investigate vertical shears in particular if that is what the user sets out to do. The GPR framework provides great flexibility, and we certainly don't think that we have already arrived at a form for the covariance functions that achieves best case performance in general and especially for specific analysis objectives.
2. (WGS84 geometry) There are two relevant applications of applying WGS84 geometry related to this work: in geolocating the meteors and calculating the corresponding Bragg vector in the meteor local ENU coordinate system, and in estimating the winds from the meteor data. This paper only lightly touches on the first case in assuming that the meteor radar data has already been processed into meteor observations complete with a Doppler shift, geodetic latitude and longitude, and Bragg vector. The procedure to get to that point is exactly the same as in the works cited in Section 4, e.g. Chau and Clahsen (2019), although full detail can be found in Clahsen (2018) [full citation below], with the meteor geolocation procedure also described in Stober et al. (2018). We will clarify this in the next revision.
For the second case in applying WGS84 geometry within the wind estimation, we describe our procedure of using a local azimuthal equidistant projection in Section 2. This application is new to this work, although the azimuthal equidistant projection using the WGS84 sphereoid is wellknown. We use a projection only for computational efficiency, as it is much easier and faster to work in a Euclidean coordinate system when performing the estimation than to use the full geodetic computations, although it is possible to do the latter.
3. (Vertical winds) We agree on the challenges of estimating vertical winds and the care that must be taken in doing so. This procedure takes into account the projection effects that result in the vertical wind component usually not being as wellcharacterized as the horizontal components, and this relative uncertainty is quantified in the posterior estimated variances. This is best demonstrated in the simulation results and in particular Figure 4. In general, the user of this technique can impose their prior belief in generally small vertical wind values by appropriately setting a small value for the vertical wind covariance amplitude or by checking that fitted values correspond to that expectation.
There are a few locations in the examples where the estimated vertical wind exceeds a magnitude of 10 m/s. We don't make a note of it because the estimated confidence interval of the vertical wind at those points (and indeed, all over) is large enough to allow for a true value that is in line with what has been observed in the MLT region by different instruments and groups, e.g. Vierinen et al. (2013), Lu et al. (2017), Chau et al. (2020). These examples show MLT vertical winds on the scale of a few meters per second at minute to hour timescales.
Additional ReferencesChau, J. L., Urco, J. M., Avsarkisov, V., Vierinen, J. P., Latteck, R., Hall, C. M., & Tsutsumi, M. (2020). FourDimensional Quantification of KelvinHelmholtz Instabilities in the Polar Summer Mesosphere Using Volumetric Radar Imaging. Geophysical Research Letters, 47(1), e2019GL086081. https://doi.org/10.1029/2019GL086081
Clahsen, M. (2018, January 31). Error analysis of wind estimates in specular meteor radar system (M.S. Thesis). University of Rostock, Rostock, Germany.
Lu, X., Chu, X., Li, H., Chen, C., Smith, J. A., & Vadas, S. L. (2017). Statistical characterization of hightomedium frequency mesoscale gravity waves by lidarmeasured vertical winds and temperatures in the MLT. Journal of Atmospheric and SolarTerrestrial Physics, 162, 3–15. https://doi.org/10.1016/j.jastp.2016.10.009
Vierinen, J., Kero, A., & Rietveld, M. T. (2013). High latitude artificial periodic irregularity observations with the upgraded EISCAT heating facility. Journal of Atmospheric and SolarTerrestrial Physics, 105–106, 253–261. https://doi.org/10.1016/j.jastp.2013.08.012

CC4: 'Reply on AC4', Gunter Stober, 25 Jun 2021
reply
Dear Ryan,
thanks for clarifying the 2D nature of the presented retrievals. From the reply I take that the winds are computed within a 2D layer with an irregular horizontal grid using a 3 km vertical average. This setup sounds reasonable. The terms 2DVAR or 3DVAR or higher are typically used for data assimilation e.g., Gelaro et al., 2017 for MERRA2 (3DVAR) and Eckerman et al., 2019 for NAVGEMHA (4DVAR) and references therein. It might be worth describing the algorithm concerning this aspect with some more details.
WGS84 geometry implementation:
The reply about the WGS84 geometry implementation somehow confused me. Chau and Clahsen (2019) cite Stober et al., 2018 as a source of the WGS84 geometry. I am even more confused as one of the coauthors of this paper (Jorge L. Chau) confirmed this in a public comment a few weeks ago (see link: https://doi.org/10.5194/amt2021124CC2).
I might also want to recall that we had a good meeting in Kühlungsborn in March 2017. The attendees were Ryan Volz, Philip J. Erickson, Juha Vierinen, Jorge L. Chau and Gunter Stober. We discussed the multistatic projects and presented the status and help the MIT colleagues to catch up with the multistatic developments that were done so far until 2017. The patent is mainly based on the details presented in Stober et al., 2018 including the WGS84 geometry, which was already in parts implemented in Stober and Chau (2015) , but only to solve the forward scatter geometry and the altitude of the meteors without angular correction. Due to the embargo time between patent submission and the patent acceptance the submission to AMT had to be delayed. If the editor needs further evidence for the timeline, I can forward the documents in a private email to avoid public embarrassment.
I also tried to google the cited thesis of Clahsen (2018), but I received a match to another AMT paper, which cites Stober et al., 2018.
Vertical winds:
I am also confused about the reply on the vertical winds. They now justify the vertical winds as real by presenting additional citations. This is contradicting another time a public comment by Jorge L. Chau (see again link from above) related to the SIMONe systems. In the public comment, Jorge L. Chau clearly confirms that there is no claim that the winds are physically meaningful or presenting the geophysical truth. I suggest they add a paragraph discussing this obvious contradiction or they present a physical explanation within the laws of thermodynamics that these winds are realistic. Considering that the residual circulation causes a 100 K deviation from the thermal equilibrium at the mesosphere lower thermosphere (Becker, 2012, Smith, 2012) and is associated to mean vertical velocities of a few mm/s to cm/s. So it might be worth estimating the adiabatic cooling of the presented 10 m/s upwelling and estimating the cooling rate per day. If these winds are real, this will be a gamechanger of our understanding of the middle atmosphere dynamics at the MLT. Otherwise, they can also discuss the obvious controversy to other observations. I added some references, which show different vertical velocities. It would be good to discuss these things a bit more. It is the one point that doesn’t fit, that brings science forward.
I really enjoyed reading the paper and I am looking forward to future scientific results.
Gelaro, R., McCarty, W., Suárez, M. J., Todling, R., Molod, A., Takacs, L., Randles, C. A., Darmenov, A., Bosilovich, M. G., Reichle, R., Wargan, K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A. M., Gu, W., Kim, G., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J. E., Partyka, G., Pawson, S., Putman, W., Rienecker, M., Schubert, S. D., Sienkiewicz, M., & Zhao, B. (2017). The ModernEra Retrospective Analysis for Research and Applications, Version 2 (MERRA2), Journal of Climate, 30(14), 54195454.
Eckermann, S. D., Ma, J., Hoppel, K.W., Kuhl, D. D., Allen, D. R.,Doyle, J. A., Viner, K. C., Ruston, B. C., Baker, N. L., Swadley, D., Whitcomb, T. R., Reynolds, C. A., Xu, L., Kaifler, N., Kaifler,B., Reid, I. M., Murphy, D. J., and Love, P. T.: HighAltitude (0–100 km) Global Atmospheric Reanalysis System: Description and Application to the 2014 Austral Winter of the Deep Propagating Gravity Wave Experiment (DEEPWAVE), Mon. Weather Rev., 146, 2639–2666, https://doi.org/10.1175/MWRD170386.1, 2018.
Smith, A. K.: Global Dynamics of the MLT, Surv. Geophys., 33, 1177–1230, https://doi.org/10.1007/s1071201291969, 2012.
Becker, E.: Dynamical Control of the Middle Atmosphere, Space Sci. Rev., 168, 283–314, https://doi.org/10.1007/s1121401198415, 2012.
Vertical wind observations:
Most of them contradict the wind speeds cited in the manuscript (certainly not complete).
Chau, J. L., Stober, G., Hall, C. M., Tsutsumi, M., Laskar, F. I., and Hoffmann, P.: Polar mesospheric horizontal divergence and relative vorticity measurements using multiple specular meteor radars, Radio Science, 52, 811–828, ttps://doi.org/10.1002/2016RS006225, 2017.
Fritts, D., Hoppe, U.P., and Inhester, B.: A study of the vertical motion field near the highlatitude summer mesopause during MAC/SINE, J. Atmos. Terr. Phys., 52, 927–938, https://doi.org/10.1016/00219169(90)90025I, 1990.
Hoppe, U.P. and Fritts, D. C.: Highresolution measurements of vertical velocity with the European incoherent scatter VHF radar: 1. Motion field characteristics and measurement biases, J. Geophys. Res., 100, 16813–16825, https://doi.org/10.1029/95JD01466, 1995a.
Straub, C., Tschanz, B., Hocke, K., Kämpfer, N., and Smith, A. K.: Transport of mesospheric H_{2}O during and after the stratospheric sudden warming of January 2010: observation and simulation, Atmos. Chem. Phys., 12, 5413–5427, https://doi.org/10.5194/acp1254132012, 2012.
I. Laskar, J. L. Chau, J. P. StMaurice, G. Stober, C. M. Hall, M. Tsutsumi, J. Höffner und P. Hoffmann, Experimental evidence of Arctic summer mesospheric upwelling and its connection to cold summer mesopause, Geophys. Res. Lett., 44, 91519158, doi:10.1002/2017GL074759, 2017.
Gudadze, G. Stober und J. L. Chau, Can VHF radars at polar latitudes measure mean vertical winds in the presence of PMSE?, Atmos. Chem. Phys., 19, 44854497, doi:10.5194/acp1944852019, 2019.
Vincent, R. A., Kovalam, S., Murphy, D., J, Reid, I. M., & Younger, J. P. (2019). Trends and variability in vertical winds in the southern hemisphere summer polar mesosphere and lower thermosphere. Journal of Geophysical Research: Atmospheres, 124, 11070– 11085. https://doi.org/10.1029/2019JD030735
Zhang, W., Chen, G., Zhang, S., Gong, W., Chen, F., He, Z., et al. (2020). Statistical study of the midlatitude mesospheric vertical winds observed by the Wuhan and Beijing MST radars in China. Journal of Geophysical Research: Atmospheres, 125, 2020JD032776. https://doi.org/10.1029/2020JD032776

CC5: 'Reply on CC4', Gunter Stober, 25 Jun 2021
reply
Dear Ryan,
to avoid misreading of my comment on the WGS84 geometry. We had a scientific presentation and agreed to share all the geometric aspects necessary for the retrievals. Please don’t consider it as an accusation. This was not intended. So my apologies if it is someone understood like that.
I suggest it is best to cite Clahsen (2018) and Stober et al., 2018.
Best regards,
Gunter

AC5: 'Reply on CC4', Ryan Volz, 25 Jun 2021
reply
1. (Comparison to classical 2DVAR data assimilation) Sorry for the confusion, but we don't mean to say that the estimates are inherently done through 2D slices. The Gaussian processes are 4D, and the estimates at any point rely on all of the measurements in the manner described by the 4D covariance functions. In stating a 3 km vertical resolution, we mean to say that the covariance function we have used has a vertical length scale of 3 km, so that for any given estimate the measurements that contribute most strongly are within that vertical window. In this sense, one can think of the covariance function as having the effect of a type of soft binning.
2. (WGS84 geometry) We will be adding the Clahsen (2018) and Stober et al. (2018) citations in reference to the meteor processing in the revised manuscript, because the WGS84 aspect of the processing detailed therein is important enough to call out explicitly and not just transitively through Chau and Clahsen (2019). We appreciate the clarification.
3. (Vertical winds) The validity of the shortterm vertical wind estimates is still an open issue; what we claim is that our method provides uncertainties on the estimates based on the geometry and error propagation. We appreciate the references provided, but all of them deal with climatological vertical velocity estimates. In any case, we will leave the validation of such vertical velocity estimates for a future effort.

CC6: 'Reply on AC5', Gunter Stober, 28 Jun 2021
reply
Dear Ryan,
thank you for the reply. The classification as 2DVAR refers here to the projection shown in equation 1. There is no explicit dependency in the vertical coordinate and as they mentioned in the first reply the retrieval doesn’t include vertical shears. For me, it appears that the presented retrieval could be used to obtain 3D winds in a 2D layer at a given time and altitude without knowledge of the layer below or above as well as the time step and before and after. That’s why I would classify it as 2DVAR. The covariance matrix is always 4D for such retrievals as we obtain solutions at the x,y,z spatial coordinates for different times. However, it is often more computationally efficient to solve blockdiagonal covariance matrices with just softwaredefined weighting. In so far, a 4D covariance does not present a unique token of the retrieval compared to retrievals for such applications.
Vertical winds are important. In particular, the magnitude of the winds is under debate. The references that were provided included climatological variability. In Figure 7. the manuscript presents winds with magnitudes of about +/ 510 m/s at scales of hundred kilometers for 15 minutes resolution using a 30 averaging windows (see covariance matrix). Such patches can be found in all panels. Considering the climatological knowledge and other observations that could be found in the references attached to the first comment, this discrepancy seems to be rather large and deserves some reflection in the discussion section. These winds seem to exceed by 200400% the magnitudes of other observations and model predictions.
It is also surprising that the paper references several times Vierinen et al. 2019. This paper basically contradicts the need for such more complicated retrievals. The basic claim in Vierinen et a., 2019 is that only radial correlations are needed to obtain Reynolds stresses without any inversion of the 3D winds on spatial grids. Vierinen et al., 2019 seem to be only applicable to the small subset of meteor detections, which are observed at the same spatial coordinates in x,y,z, and t in multiple links (at least 3). Such a discussion would strengthen the value of the presented manuscript and put more emphasis on why it is beneficial to apply more sophisticated mathematical approaches.
I am looking forward to the final published version.
Best regards,
Gunter

CC6: 'Reply on AC5', Gunter Stober, 28 Jun 2021
reply

CC5: 'Reply on CC4', Gunter Stober, 25 Jun 2021
reply

CC7: 'Reply on AC4', Aaron Smith, 29 Jun 2021
reply
There seem to be a controversy regarding the prior use of WGS84 geometry. The use of WGS84 ellipsoid geometry is clearly described in the Stober et al. 2018 manuscript: https://doi.org/10.5194/amt1148912018. However, the cited M.S. thesis from M. Clahsen does not have an ISBN/DOI code and thus is not available for readers. I found the website of LeibnizInstitute of Atmospheric Physics at Rostock University providing their thesis works:
https://www.iapkborn.de/en/research/publications/thesismasterdiplomaphd
Unfortunately, no M.S. thesis from M. Clahsen is listed. There is a bachelor thesis from M. Clahsen (in German), dating back to 2015, which does not mention the WGS84 geometry. It would be beneficial for readers to share the cited M.S. thesis, either through the Institute website, or, if not possible, in the discussion forum here.

CC4: 'Reply on AC4', Gunter Stober, 25 Jun 2021
reply

AC4: 'Reply on CC3', Ryan Volz, 24 Jun 2021
reply
Ryan Volz et al.
Ryan Volz et al.
Viewed
HTML  XML  Total  Supplement  BibTeX  EndNote  

478  145  31  654  29  5  4 
 HTML: 478
 PDF: 145
 XML: 31
 Total: 654
 Supplement: 29
 BibTeX: 5
 EndNote: 4
Viewed (geographical distribution)
Country  #  Views  % 

Total:  0 
HTML:  0 
PDF:  0 
XML:  0 
 1