Recently, the MMARIA (Multi-static, Multi-frequency Agile Radar for Investigations of the Atmosphere) concept of a multi-static VHF meteor radar network to derive horizontally resolved wind fields in the mesosphere–lower thermosphere was introduced. Here we present preliminary results of the MMARIA network above Eastern Germany using two transmitters located at Juliusruh and Collm, and five receiving links: two monostatic and three multi-static. The observations are complemented during a one-week campaign, with a couple of addition continuous-wave coded transmitters, making a total of seven multi-static links. In order to access the kinematic properties of non-homogenous wind fields, we developed a wind retrieval algorithm that applies regularization to determine the non-linear wind field in the altitude range of 82–98 km. The potential of such observations and the new retrieval to investigate gravity waves with horizontal scales between 50–200 km is presented and discussed. In particular, it is demonstrated that horizonal wavelength spectra of gravity waves can be obtained from the new data set.

The upper mesosphere–lower thermosphere (MLT) is a highly dynamic region
dominated by a variety of waves (gravity waves, tides, planetary waves)
covering different spatial and temporal scales. To characterize this
variability, it is desirable to develop remote sensing techniques to retrieve
horizontally resolved structures from continuous observations. A particular
challenge is the determination of horizontally resolved wind fields at
mesospheric altitudes, needed to access small scale variations associated to
gravity waves (GWs). GWs are considered to be a major driver of MLT dynamics
as they carry energy and momentum from other (mainly lower) atmospheric
layers into the mesosphere

Over the past few decades specular meteor radars (SMRs) have become a reliable
and widespread tool to investigate mesospheric mean winds

The spatial and temporal intermittency of GWs are hardly accessible from
point measurements. Airglow imagers

Recently,

Schematic of a multi-static meteor radar network. The grey shaded areas stand for the typical field of views for each systems. Within the network all system should at least overlap to one of the other network members.

The paper is structured as follows. In Sect. 2 we present a summary of the normal meteor radar wind retrieval. This method is going to be expanded in Sect. 3 to horizontally resolved winds in a full Earth geometry. In Sect. 4 we perform an initial validation and consistency check. The potential use of the new horizontally resolved wind retrieval is given in Sect. 5 presenting first horizontal wavelength spectra. Our main conclusions are presented in the last section. The appendix contains all equations required for the WGS84 coordinate transformations.

Meteors entering the Earth's atmosphere form an ambipolar plasma trail, if
they are fast and heavy enough. The trail is drifted by the ambient neutral
winds at the altitude of its deposition. Combining the radial Doppler
measurement with radar interferometry

To increase the robustness of the standard wind fit estimation, e.g., better
temporal resolution and altitude coverage, it is possible to use
regularization by adding constraints based on a priori information. Recently,
we have implemented a routine to derive mesospheric winds using full
non-linear error propagation, an additional weighting to account for sampling
effects, and a smoothness regularization. The error propagation is
straightforward as most of the available systems provide errors for the
radial velocity measurements. The angular uncertainties are estimated to be
in the order of 2

The temporal and vertical total shear amplitude

The smoothness regularization scheme consists of the vertical and temporal
derivative for each wind component taken as constant within each bin. The
initial guess is given by a standard least squares solution without any
regularization constraint, but already contains the Gaussian weighting with

A bit more sophisticated than the “all-sky” fit is the so called volume
velocity processing (VVP)

Here

Such an analysis does not only provide mean winds for each time and altitude
bin, but also access higher order kinematic processes as horizontal
divergence, relative vorticity as well as stretching and shearing
deformation. In order to unambiguously obtain the relative vorticity
multi-static measurements are required

Illustration on how local coordinates (zonal, meridional) change with geographic position with respect to a radar location.

A new aspect of the MMARIA concept is the necessity to consider the geometry
of the Earth. At present our domain area in Germany has a horizontal
extension of approximately

In the following we outline the procedure how to compute new local
coordinates (ENU: east–north–up) for each meteor to reduce potential errors
in the wind field estimation due to projection issues. Considering that the
Earth is not a perfect sphere, we have to deal with two different coordinates,
the geodetic coordinates (longitude and latitude) and the Earth-Centered,
Earth-Fixed (ECEF) coordinates, also called geocentric coordinates. The
geodetic coordinates are determined by the normal to the ellipsoid, whereas
the ECEF coordinates are defined by the Earth center using a (

We need to transform the observed meteor positions relative to the radar into
a local coordinate frame (ENU) by determining the geodetic longitude,
latitude and height of the meteor itself. The corresponding transformations
are listed in the appendix. The procedure contains four steps: firstly the
geodetic coordinates of the radar (longitude-

In summary we perform the following steps:

conversion of the geodetic coordinates of the radar

transformation of meteor coordinates into ECEF

conversion of ECEF frame meteor position into geodetic coordinates

determination of local ENU using the geodetic position of each meteor in ECEF coordinates

Figure

The retrieval of arbitrary and non-homogenous wind fields is mathematically
more demanding as the number of unknowns exceeds the number of measurements,
which does not allow to directly solve the equations applying standard least
squares or singular value decomposition algorithms. However, it is possible
to constrain the problem by additional assumptions or a priori knowledge.
Very often the smoothness is used to regularize the problem so that it can be
solved by applying statistical inversion algorithms

At first we define a spatial grid and a domain area. In the case of the
German MMARIA network we use a

Schematic of 3-D gridding to compute horizontally resolved wind fields including the Earth surface.

A first step of the wind field inversion procedure is to assign each observed
meteor to a grid cell

The weight

We can relate the measured radial velocity of each meteor to the three
dimensional wind velocity by using local ENU coordinates for each measurement

The radial wind equation for arbitrary measurements and grid cells can be
expressed as a linear matrix equation. The mapping from the zonal,
meridional, and vertical components to observed radial velocities is given by
a geometry matrix

The geometry matrix

Ill-posed problems can be solved by adding additional constrains. Very often
the smoothness of the unknown provides a reasonable way to regularize an
ill-posed problem

The matrix

Schematic of

Finally, we have to deal with grid cells in the domain area where no
measurement is available for a given time–altitude bin. This issue is solved
by introducing a mesoscale wind field solution to these grid cells. We tested
three possible mesoscale solutions and checked how much the final solution
depends on this mesoscale boundary condition. The most trivial way is zero
padding or simply not using an explicit a priori for these grid cells, the
second one is estimating a mean wind using all radial velocity measurements
with the “all-sky” fit and the third possibility is to derive a mesoscale
wind field solution by computing local mean winds for each multi-static
geometry and to estimate a distance weighted background wind field for each
grid cell. A similar result is achieved by applying volume velocity
processing (VVP)

Comparison of 2-D wind fields for three different

Combining all the information and the smoothness constraints into a set of
equations allows solving the ill-posed problem. We obtain an estimate for
the 3-D wind components

In the inversion process the weight

In the following we are going to demonstrate the robustness of our algorithm,
independent of the choice of regularization parameter

Solving Eq. (

Comparison of wind field solution in dependence of the background
mesoscale solution.

In Fig.

We tested different possibilities to define an optimal regularization
strength

As already mentioned above, there are grid cells where we have no direct
measurements from one of the systems. We suggested using a mesoscale
solution for these points. Now there is the question whether our solution
depends on this pre-described mesoscale wind field. Therefore, we prepared two
test cases. In the first test, all grid cells with no direct measurements are
zero padded. For the second test, we use a computed mesoscale wind field
estimated from VVP. Figure

Comparison of wind retrievals. Panel

Further, we investigated the differences between the full wind retrieval and
the packed wind retrieval. Therefore, we kept the regularization strength
fixed for both retrievals. The packed retrieval makes use of the total wind
variances for each grid cell and a mesoscale regularization, whereas the full
wind retrieval uses each individual radial velocity uncertainty and no
explicit mesoscale regularization. The other weights and the error treatment
is the same. Figure

Comparison of zonal and meridional winds as derived from the full wind retrieval algorithm and the packed wind retrieval.

The above described algorithm is applicable to all types of multi-static
observations. In 2014 we started to build the MMARIA network in Germany. At
present the network consists of 2 monostatic SMRs (located at Juliusruh
54.6

Technical specifications of the two active meteor radars.

PRF – pulse repetition frequency

In parallel, we also operated a newly developed continuous wave
(CW) coded system that complement our pulsed SMR network for one week. The CW-coded
prototype was tested from 10–12 June 2015

During the March campaign in 2016 the multistatic network consisted of two
monostatic and five multi-static links. Some technical specifications of the
experiment settings of the SMRs and the locations of the multi-static links
are summarized in Tables

Technical specification of the multi-static links used in the experiment campaign in March 2016.

Kborn – Kuehlungsborn

In Fig.

For the same period we generated three movie sequences at 82, 90, 96 km
altitude using the full wind retrieval. They show the 2-D wind fields and
their temporal evolution with 1 h time steps. The movies can be found in the
Supplement. The clockwise rotation of vector field is mainly due
to the semi-diurnal tide. However, the movies also show the temporal and
spatial variability due to GWs. The appearance and disappearance of the red
points indicates whether this viewing geometry was available during the
inversion or not. Note that arrows are scaled within each image. As a result
more distorted wind fields are often related to weak winds
(

Schematic of a typical forward scatter meteor radar. The position of
the Tx and Rx are known and all other parts are measured. The Bragg vector

Figure

We did also perform an initial validation of the derived wind field for the
complete campaign period through testing the consistency of the wind
observations compared to the “all-sky” fit and the VVP. A comparison of the
mean zonal and meridional winds obtained from the all-sky fit and the mean
wind velocities of the full wind retrieval over the domain area and for all
available altitudes between 82–98 km are shown in
Fig.

We also performed an initial comparison between the VVP derived wind
estimates for each grid point and the 2-D horizontally resolved wind fields,
which were again obtained from the full wind retrieval. We compared all wind
velocities at all grid cells between 82–98 km altitude. In
Fig.

Overview of zonal and meridional wind components applying the standard wind analysis to the MMARIA network during the March 2016 campaign.

The presented full and packed wind retrieval algorithms opens new
possibilities to investigate atmospheric dynamics. The spatial information
seems to be useful to study the horizontal wavelength/wavenumber power
spectra of kinetic energy. For the troposphere and lower stratosphere,

Due to the regular spatial grid horizontal wavelength spectra are easily
obtained from the derived horizontally resolved wind fields. The mean
spectrum is computed by adding all latitudinal cuts through the domain area
at a given altitude during one day. Considering that the coverage of our 2-D
wind fields is variable, we included only latitudinal cuts with more than 12
grid points constrained by measurements. The resultant spectra are shown in
Fig.

Two examples of obtained wind fields showing a small vortical structure above the Baltic coast and a potential body force of a breaking GW.

Scatter plots of mean zonal and meridional winds obtained from the full wind retrieval and VVP. The mean is computed as average over the domain area.

The spectra shown in Fig.

Retrieving horizontally resolved wind fields from multi-static SMR networks
at the MLT provides new possibilities to investigate the intermittency and
spatial characteristics of GWs and vortical modes, which are not yet
accessible by other remote sensing techniques for these spatial scales and
with that temporal resolution. In particular, the wind and its spatial
characteristics are required to understand wave breaking and the associated
momentum transfer to the background

A crucial part of the presented wind field analysis, independent of the
choice of the retrieval method, is the spatio-temporal sampling. Increasing
the spatial resolution is only meaningful if we also decrease the temporal
sampling window. However, with a decreasing number of detections per grid
cell within the domain area the more sparse our wind field is constrained.
This brings us to the question on how representative an observed radial
velocity of an individual meteor is for our selected time, altitude and spatial
resolution. If we want to resolve small scale structures with characteristic
life times of minutes and horizontal scales comparable to our grid
resolution, e.g., bore events or breaking GW (ripples)

Comparison of zonal and meridional winds as derived from the new retrieval algorithm and the estimates for each grid point applying VVP.

Horizontal wavelength spectra and estimated slopes to identify the transition from the mesoscale GW to the synoptic scale.

The obtained 2-D wind fields are also ideal to complement other mesospheric
measurements. The combination of the horizontally resolved wind fields with
other mesospheric observations like airglow imagers

During the past few years, there were also several attempts to retrieve
horizontally resolved wind fields using Fabry–Perot Interferometer (FPI) in
the thermosphere

After establishing the MMARIA-concept in

The introduced packed and full wind retrieval algorithms for arbitrary
non-homogeneous wind fields show the potential to investigate mesoscale
dynamics at the MLT by employing multi-static SMR networks. Horizontally
resolved winds open possibilities to study the MLT dynamics. We demonstrate
that our preliminary derived wind fields are suitable to obtain horizontal
wavelength spectra to access the transition scale between a

Horizontally resolved winds at the MLT open new ways to investigate dynamical processes on scales between hundreds down to a few kilometers. Based on these winds it is going to be possible to study the momentum transfer of breaking gravity wave in case studies in much more detail. The resolved winds are further suitable to obtain a spatially resolved momentum flux, or to measure propagation directions of GW directly as well as their intrinsic spatial characteristics. The retrieved winds are also usable to complement other measurements such as airglow observations combining both data sets to estimate the intrinsic wave parameters, which are often not accessible without the knowledge of the background winds. At present there is also no other measurement technique available to observe and study the relative importance of vortical compared to divergent atmospheric modes.

We performed an initial validation of our packed and full wind retrieval algorithms by comparing the mean winds to the standard SMR wind analysis, which shows remarkably good agreement. Further, we compared the wind fields obtained from VVP, using a gradient extrapolation of the winds to our grid points with our full wind retrieval solution. This comparison reveals that both methods provide a good approximation of the mesoscale wind field, but show larger discrepancies at the smaller scales, which is expected as the 2-D full wind retrieval of 3-D wind vectors is designed to infer such small scale features.

The presented algorithms demonstrate the potential of SMRs to be used as
networks. These systems are cheap enough and sufficiently automated to be
deployed at remote locations and to build rather large networks with several
hundred kilometers in diameter. Further, the derived packed and full wind
retrieval algorithms are applicable to existing data collected from closely
co-located SMRs like in Scandinavia

The data can be accessed upon request by the authors. Please contact Christoph Jacobi (jacobi@uni-leipzig.de) for the Collm meteor radar data. The cw-meteor radar data are available from Jorge L. Chau (chau@iap-kborn.org). The meteor radar data from Juliusruh and Kuehlungsborn can be requested from Gunter Stober (stober@iap-kborn.de).

In the following we present a short summary of all the coordinate transformations that we used in the presented analysis scheme. All relevant parameters are listed and the used transformation matrices are shown.

The first transformation that we used converts geodetic coordinates into the
ECEF. The geodetic coordinates from the radar are given in longitude
(

Based on the WGS84 ellipsoid geometry of the Earth any given geodetic
location defined by a longitude, latitude and a height (height above WGS84
surface) is given by the ECEF coordinates (

The backward transformation to transform a given coordinate in ECEF into a
geodetic longitude (

Typically, MR observe meteors at a given distance and direction relative to
its geodetic coordinates. The meteor is given in ENU coordinates with respect
to the radar location. The up direction is defined by the tangent plane to
the Earth's ellipsoid. The meteor position is defined by ENU coordinates
(

Finally, we want to express our line of sight vector from the radar towards
the meteor in the frame of the ENU coordinates at the geodetic location of
the meteor itself, e.g., the line of sight velocity vector is observed at a
certain azimuth (

Hence, we obtain a local azimuth

The supplement related to this article is available online at:

The manuscript was prepared from GS with contributions from all co-authors. The source codes of the presented wind retrievals are developed by GS. JV and JLC developed the CW-experiments and carried them out. CJ helped with the data interpretation and ensured the operation of the Collm meteor radar. SW contributed to the mean wind analysis for the shown wind comparisons.

The authors declare that they have no conflict of interest.

We acknowledge the technical support of our radar systems by Falk Kaiser, Dieter Keuer, Jörg Trautner, and Thomas Barth. We are grateful for the support provided by Sven Geese, Nico Pfeffer, and Matthias Claßen in developing, deploying, and operating the CW-coded radars. We thank both reviewers for their help improving our manuscript. Edited by: Markus Rapp Reviewed by: two anonymous referees