Mesospheric gravity wave (GW) momentum flux estimates
using data from multibeam Buckland Park MF radar (34.6

There has recently been particular interest in the use of specular returns
from all-sky interferometric meteor radar to measure the gravity wave
(GW)-driven vertical fluxes of horizontal momentum (herein momentum fluxes)
in the mesosphere–lower thermosphere/ionosphere (MLT/I;

Direct measurements of momentum fluxes in the MLT/I were pioneered by

The assumption of statistical stationarity of the wind and wave field over the volume spanned by the scatterers. As discussed by

This is clearly more problematic for meteor observations, where angle-of-arrival (i.e. the “effective receive beams” of the radar) distributions
peak at large off-zenith angles (typically 40–50

The required integration time for statistical significance of the estimates.

A contrary argument was put forward by

Additionally,

The contamination of momentum flux estimates by temporal wind shear (leading to overestimation of the true fluxes). Some authors (e.g.

This paper presents the application of hybrid Doppler interferometry (HDI)

Section

The Buckland Park MF radar, located about 36 km NNW of Adelaide, South
Australia, operates at a frequency of 1.98 MHz. It consists of 89 crossed
half-wave dipole antennas, each aligned

The HDI experiments presented here were conducted across four multi-day
campaigns during July, September, and October 1997 and June 1998 (see
Fig.

Antenna configuration used in the June 1998 HDI experiments. Each thin vertical line denotes an approximately north–south-oriented antenna. For ease of viewing, antenna elements have not been drawn to scale. Each bold triangle indicates a group of antennas that were connected to a given transmit or receive channel: “TR” denotes both transmit and receive, and “T” transmit only.

Modelled far-field transmit and receive polar diagrams for the
Fig.

Error codes for the HDI analysis.

Modelled transmit (left) and receive (right) polar diagrams for the
antenna configurations in Fig.

Normalized 2-D histograms of the EBPs estimated by HDI at selected
range gates for the June 1998 experiment. The thin black circles
approximately denote the half-power half-width contours of the transmitted
beams (5.7

The sampled range gates encompassed the height range 50–102 km (daytime)
and 74–102 km (overnight), in 2 km bins. The transmit pulse's half-power
half-width (HPHW) was 2 km. The pulse repetition frequency was fixed at
100 Hz for daytime observations, and 20 Hz for night time, with 20 and 4
software coherent integrations applied, respectively. The time series
recorded for each beam contained 560 points (i.e. a record length of 112 s), and the beam direction was changed every 2 min. The beam sequence
was [vertical, north, east, south, west], with an off-zenith angle of
12

HDI was applied to analyse each 112 s raw data record. Briefly, this
involved the synthesis of beams in software (using the post-statistics
steering method;

Acceptance rate profiles for the four HDI experiments.

An example of the EBPs determined with HDI is shown in Fig.

The scenarios under which the analysis failed on any given data record are
summarized in Table

A simple computer model has been created to obtain a qualitative assessment
of the accuracy and precision of the momentum flux estimates from the five-beam
Doppler, vertical beam HDI, and meteor radar techniques. The model propagates
monochromatic gravity and tidal waves over the field of view of a “radar”,
which samples radial wind velocities at positions and times corresponding to
real records of the respective radar techniques. The approach used has
parallels to those used in the following previous works:

The model is based around the following workflow (where necessary, the
individual steps are described in more detail in subsequent subsections):

Specify a wind field analytically.

Acquire an ensemble of scattering positions and times (and add Gaussian-distributed uncertainties to a copy of the positions).

Evaluate radial projections of the wind velocity at the “correct” positions/times (measurement noise is effectively added to the radial velocities due to uncertainty in the scattering position).

Evaluate the momentum flux components by inverting the fluctuating radial velocity components at the noise-influenced positions/times.

Evaluate the momentum flux components by computing the covariances of the wind field at a fixed position directly above the simulated radar.

Loop back to 1, and repeat for a different realization of the wind field/different uncertainties in the scattering positions.

Investigate the mean and standard deviation of the differences between the results of 4 and 5 (herein referred to in the text and in Figs.

The wind field in the model is comprised of a fixed “mean flow” background
velocity (with speed

Prior to a simulation, the background wind vector, the number of waves to
include, and the horizontal perturbation amplitude

A 48 h sample of scattering position data used in the model (black: 5BD; red: VBD; blue: meteor.) See text for details.

A summary of the gravity wave parameters used in the different test
wind field cases. (The subscript

Summary of different Doppler techniques referred to in this paper.
See Sect.

The basis of all the scattering positions used in the model is shown in
Fig.

Only data with zero error code (see Table

A configuration utilizing solely vertical beam data from the 5BD experiment (herein V5BD) was also considered in the model. This resembles an analysis that could be applied on systems with no (practical or otherwise) capability for beam steering on transmission. Vertical transmission in that experimental case was only applied for 2 min per 10 min steering cycle, and so a 10 min analysis interval has been used to represent it here.

A comparison of the biases in the model covariance terms extracted from the 5BD (black) and VHF meteor radar (red) techniques, averaged over a 48 h period, with individual bin widths (or integration times) of length 2 h, for the single wave case. The error bars show the standard deviation in the bias determined over 200 realizations of the initial gravity wave phase/scattering position errors.

A slight variation on the V5BD was also included, which was based on data
from experiments consisting of a solely vertical transmitted beam (herein
VBD). The HDI-derived EBPs in this case were obtained from experiments run
between 20 June 1997 and 15 July 1997, again from the range gate centred on
88 km and from a beam with a half-power half-width of 5.7

A fourth simulated technique based on MF radar Doppler returns was intended
to emulate that used in older (and the only yet reported in the literature)
MF Doppler experiments for momentum flux estimation, which did not
incorporate direct estimates of the EBP (instead they were calculated based
on aspect sensitivity estimates; see Sect.

Finally, a technique based on 55 MHz all-sky meteor radar data was included.
For this case, data from the Buckland Park meteor radar recorded during
May 2014 at heights between 88 and 90 km were used. The radar obtained a peak
count rate of around 60 h

Errors of the form

The spatial distribution of radial velocities at this point will contain
contributions from the gravity and tidal waves specified in
Eq. (

For the 5BD, V5BD, VBD, and meteor techniques, the wind field variance and
covariance components are then calculated from the residuals by the inversion
technique described in

To emulate the C5BD technique, momentum flux components are calculated using
the

Two different wind field “configurations” have been used in the model;
they are summarized in Table

With exception to the final case discussed (Fig.

In each realization, diurnal and semidiurnal tides with fixed amplitudes of
15 and 20 ms

The biases for the 5BD and meteor technique momentum fluxes for a wind field
with a single gravity wave (Case 1), plotted against the horizontal
wavelength of the wave (for a fixed phase speed of 50 ms

A comparison of the biases in the model momentum flux terms extracted from the 5BD technique for different integration times (1, 2, 3, 4, 6, 8, 12, 24, and 48 h, with colours as shown in the key), for a spectrum of waves propagating in the eastern sector (Case 2). Average biases are shown in the upper panels, and the standard deviations of the biases in the lower panels.

On the whole, it is clear for such a wave field that both techniques will statistically measure the sign of momentum flux components correctly, and to a similar level of accuracy. The 5BD generally obtains better precision, although it has a tendency to underestimate these components, especially at low and high horizontal wavelengths. This occurs as a result of a failure of the technique to sample full wave cycles. It indicates the requirement for continuous sampling windows (or “integration times”) much longer than the maximum gravity wave period under investigation, if unbiased estimates of the covariances at those periods are sought. The obvious downside to this approach is the required assumption for stationarity of the wave field for the duration of the sampling window (this is more likely to be satisfied for a shorter window).

The 5BD technique also appears to obtain very low accuracy and precision when
the horizontal wavelength considered is such that wave period does not
sufficiently exceed the time taken (10 min) for a full five-beam cycle (note
that

Figures

Results for the 5BD technique are shown in Fig.

As
per Fig.

In contrast, results for the meteor technique in Fig.

Clearly, the selected integration time in the analysis is a compromise between the desired accuracy and precision of the techniques. On the basis of our desire to obtain the most accurate possible results for the 5BD and other similar techniques, 48 h windows are adopted for the analysis presented herein.

Figure

Normalized histograms showing the biases in the wind field covariance components, evaluated using the 5BD (black), V5BD (grey), VBD (blue), meteor (orange), and C5BD (red) techniques. The biases' mean, standard deviation, and standard deviation evaluated from the samples' median absolute deviation (see text for details) are also indicated in sequential order in three-element arrays for each technique in the upper-right corner of the plots.

The results imply that it is possible to measure momentum flux terms of the
correct sign with the V5BD and VBD techniques (for a wave field with a
realistic non-zero momentum flux), albeit with less accuracy than both the
5BD and meteor techniques and less precision than the 5BD technique. Like
the 5BD technique, both of these techniques have also shown a tendency to
underestimate the non-zero

The C5BD results show poorer precision than the VBD (but greater than the
V5BD) and are also substantially biased. The technique overestimates the
non-zero

These modelling results have shown, at least qualitatively, the pleasing
result that the momentum flux estimation and tide removal procedures employed
work to a satisfactory level on all variations of the Doppler technique
tested. We particularly stress the finding that EBPs from the V5BD experiment
exhibit a spatial variability sufficient to estimate these terms reliably. We
also note again that this result incorporates a modelled EBP uncertainty that
is likely much larger than that in reality but that is ultimately extremely
difficult to quantify

The analysis performed here on HDI radial velocities follows the methodology applied to Doppler data in the previous section, making use of the 5BD, V5BD and C5BD techniques to estimate momentum fluxes.

The C5BD technique required that pattern scale data (derived from the full
correlation analysis (FCA)

Partition the 2 min resolution data from a given campaign, as well as the concurrent FCA, into non-oversampled 2 h blocks (steps 2 to 7 pertain to each separate 2 h block).

Using the pattern scale and axial ratio information derived from the FCA, calculate circularly averaged values of the aspect sensitivity parameter,

Calculate the altitude of each Doppler measurement (from the recorded line-of-sight ranges) using two different techniques:

Simply assume that the zenith angle of the return is equal to the HDI-derived EBP (

Interpolate a

Use the interpolant to calculate an FCA-derived

Use the acquired

Using the two sets of altitudes calculated in Step 3, partition each block into 2 km width bins, with the lowest bin starting at 70 km and the highest at 96 km. For brevity, call the set of bins pertaining
to those measurements with altitudes derived from the HDI-based

By applying the inversion of

where

Evaluate mean radial velocities for each nominal beam direction in

Estimate mean horizontal and vertical winds from

Re-partition the 2 min resolution Doppler and FCA data into 48 h blocks, with the centre of each block displaced by 6 h from the adjacent one (the remaining steps pertain to each separate 48 h block).

Perform a least-squares fit for (Cartesian) tidal/planetary wave components in

Subtract a radial projection of the fitted components from the individual radial velocity records in

Estimate the variance and covariance components from the residuals using the

Repeat steps 9 and 10 for the mean radial velocity time series

Simultaneously solve for

Unweighted average profiles of the momentum flux components for the four
campaigns and the three Doppler techniques are shown in Figs.

Vertical profiles of the momentum flux components obtained from the July 1997 (upper panels) and September 1997 (lower panels) campaigns. The error bars shown correspond to the standard error in the mean of the samples at each height.

In general, the 5BD and C5BD results show the best level of agreement, with
especially good agreement at heights where acceptance rates are high. A
noteworthy result is the very similar vertical structure from the three
techniques' measurements of

As an aside, the better agreement between the 5BD and C5BD techniques
(relative to those from the V5BD) also lends support to the simulation
results presented in Fig.

In an attempt to verify the validity of these experimental results, we
(following the approaches of, e.g.,

As per Fig.

The body force uncertainty

Vertical profiles of the zonal and meridional body forces (determined by three independent techniques) and corresponding accelerations due to Coriolis torques, obtained from the July 1997 (upper panels) and September 1997 (lower panels) campaigns.

The vertical structures of the mean inferred body forces and Coriolis torques
show few similarities, in both the zonal and meridional planes. Some of these
discrepancies may be explained by noting that the relation between the two
quantities is only valid for a zonal average. Additionally, the results
presented here are centred on the winter months; during this time, planetary
waves can propagate into the MLT/I, and may both contribute to the body force
and change the “local” mean wind in such a way as to filter gravity waves
from the wave spectrum

Nevertheless, the inferred body forces are generally large enough to balance the Coriolis torque due to the orthogonal wind. Their senses are also consistent with what is expected: for example, in the July 1997 and June 1998 cases, the body forces are predominantly westward in the heights of the highest acceptance rates. This is consistent with a deceleration of eastward MLT/I winds during winter.

As per Fig.

Other studies of the same intercomparisons have had mixed conclusions, which
is not surprising given that good local agreement between the quantities is
not necessarily expected.

This study has suggested, through the use of both synthesized and real
observations, that vertical beam MF radars can measure momentum fluxes in the
MLT/I to an acceptable degree of accuracy and precision. This implies that
the EBP distribution brought about by refractive index irregularities
propagating through a fixed vertical beam volume should contain a sufficient
spread of radial velocity–pointing direction pairs to solve for the wind
field covariances. In particular, we believe this sheds new light on the

We thus conclude that vertical beam interferometric MF radars are viable
candidates to use for testing momentum flux estimates from interferometric
meteor radars, over which there are well-known concerns regarding accuracy
and precision, as discussed in Sect.

This study did consider basic testing of the meteor technique as well in a
simulated setting, using a synthetic GW field consisting of a superposition
of monochromatic waves, in much the same way as in previous studies such as

A potential problem with all Doppler beam-steering measurements of momentum
fluxes in the presence of non-uniform volume scatter (and hence EBP
distributions that may deviate away from an idealized complementary beam
arrangement) concerns the extent to which accurate estimates of the vertical
wind velocity perturbation can be obtained. A good contemporary review of the
well-known biases inherent in volume-scatter-derived wind measurements in the
presence of correlations between refractive index fluctuations and the
underlying dynamics is provided by

The IDL source code used to produce all analyses and plots in this paper is available from the authors upon request, as are the raw and HDI-analysed Buckland Park MF radar data.

The authors declare that they have no conflict of interest.

Funding for this research was provided by the Australian Research Council
grants A69943065, DP0450787, DP0878144, and DP1096901 and by the Adelaide
University ARC Small Grants Scheme. Andrew J. Spargo would like to thank Bob Vincent
for numerous useful discussions regarding this work, and Chris Adami and
Jonathan Woithe for technical support. The C source code used in this work
for the NRLMSISE-00 model is maintained by Dominik Brodowski, and is
available at