This paper assesses the ability of a recently installed 55 MHz multistatic
meteor radar to measure gravity-wave-driven momentum fluxes around the
mesopause and applies it in a case study of measuring gravity wave forcing on the diurnal tide during a period following the autumnal equinox of 2018. The radar considered is in the vicinity of Adelaide, South Australia
(34.9

The assessment shows that the inclusion of the bistatic receiver reduces the relative uncertainty of the momentum flux estimate from about 75 % to 65 % (for a flux magnitude of

The case study reveals large modulations in the diurnal tidal amplitudes, with a maximum tidal amplitude of

It has been known for over three decades that the momentum deposition arising from the dissipation of atmospheric gravity waves (herein GW forcing) has a major influence on the background wind and thermal structure of the mesosphere–lower-thermosphere/ionosphere (MLT/I;

In recent years, monostatic meteor radars have been the most widely deployed of those ground-based instruments (e.g.

Like all other ground-based radar observations of momentum fluxes (see e.g. the discussions in

Given the demonstrated sensitivities of momentum flux estimation uncertainties, it is important that all users of meteor radars appreciate the uncertainties specific to their radar configuration (the count rates and count distribution, the radar location, the time of year, and the likely GW field) prior to interpretation of their measurements. This study considers such a simulation of momentum flux measurement uncertainties from a 55 MHz meteor radar in a mid-latitude Southern Hemisphere (SH) site in Australia and bears those uncertainties in mind in the interpretation of a case study of GW forcing on the diurnal tide. The aspects of this study that are unique can be summarized as follows:

we consider a multistatic meteor radar configuration consisting of a monostatic radar and a bistatic receiver separated by

we propagate realistic levels of receiver noise and mean phase bias to the angle-of-arrival (AOA) and radial velocity estimates that are used in the subsequent momentum flux estimation;

a realistic GW spectral model is used to synthesize the wind field from which the momentum fluxes arise.

Section 2 briefly overviews the radar configuration, the count rates obtained, and the phase calibration offsets applied. Section 3 gives a detailed description of the simulation that estimates the momentum flux measurement uncertainties and its results. Section 4 presents a case study of momentum fluxes estimated using the radar during the austral winter and attempts to validate them by looking at the interaction between the measured fluxes and the tidal winds. Discussion and conclusions follow.

The multistatic meteor radar considered in this study consists of a
stratosphere–troposphere (ST)/meteor radar located at the Buckland
Park (BP) field site (34.6

In meteor mode on the BP system, a single crossed, folded dipole is used for transmission and a five-element interferometer arranged in a configuration identical to that of

The remote receiver system consists of a six-receive-channel digital transceiver identical to the transceiver system of the BP ST/meteor radar. In the current configuration, only five of those receive channels are used. The same five receiver antenna arrangement is used at the remote site. To permit accurate range and Doppler estimates at the remote site, the system timing, frequency, and clocks at both sites are synchronized with GPS-disciplined oscillators (GPSDOs).

The techniques used to estimate various data products from the received meteor echoes, including radial velocity, meteor position, signal-to-noise ratio (SNR), and decay time, follow those outlined in

The dataset considered spans 17 March to 9 September 2018, with few interruptions (the number of meteors detected per day on both receivers for this interval are shown in Fig.

Experiment parameters used for the BP meteor radar transmitter, for all data presented in this paper.

Compensating for any systematic receiver channel phase offsets plays an important role in ensuring the accuracy of the position and height estimates of the detected meteors. To calibrate the phases of the receive channels for both of the meteor receiver interferometers used in this study, we have followed the approach suggested in

Phase offsets applied to Mylor meteor radar antennas as a function of time

The

The phase offsets applied to the Mylor system and the variability of the
offsets for the BP system (for which a fixed calibration was used) are shown in Fig.

The aim in developing this simulation has been to quantify the uncertainties
in the

Produce a sample of meteors in space and time for each site under consideration, by sampling from realistic spatio-temporal meteor detections corresponding to each site.

Specify a wind field based on the superposition of monochromatic gravity waves derived from a realistic GW spectrum and compute the wind velocities at each of the simulated meteors.

Compute the radial wind velocity measured at the receiver associated with each meteor detection.

For each meteor–site combination, synthesize in-phase and quadrature (IP and Q) time series for each receiver at the site, based on the radial velocity and AOA of the meteor.

Add a realistically sized phase bias and noise floor to each receiver channel.

Estimate the radial velocity and AOA of the meteor from the simulated time series.

Estimate the wave field covariances using the meteors retrieved from different combinations of sites.

Return to step (1) and repeat for the number of realizations required to produce covariance error distributions (in the next step) of the desired statistical significance and resolution.

Compare the estimated covariances with those computed directly from the 3-D wind velocities at the meteors and those calculated at 2 min resolution at the origin of the coordinate system.

To incorporate the dependence of the

The sampling from these probability distributions at the beginning of each realization was done according the following process:

Prescribe a number of meteor detections for the day of measurements and altitude in question (e.g. 1340 d

Use rejection sampling to distribute those meteors across the day, according to the relative number of meteors in each hour in the input probability distribution.

Distribute the meteors prescribed in each hour of measurements according to the spatial probability distribution for that hour, again using rejection sampling.

Return to step (1) and repeat for the number of days prescribed in this realization (for results presented in this paper, 1 or 10).

The horizontal position coordinates assigned to each meteor in the probability distribution (and subsequently the model) are based on the distances from the receiver site in Transverse Mercator coordinates, calculated using the method of

To clarify the effect of a variable number of meteor radial-velocity–AOA pairs on the covariance error distribution, a variety of meteor detection rates have been simulated. We have endeavoured to make the detection rates used resemble the number of meteors detected across a range of heights by the combined BP–Mylor radar link (we note again though that the simulation itself is performed around a single altitude). The detection rates we have used for different heights, listed in Table

Meteor detection rates used for the simulations in this paper. The rates shown are per day, in 2 km wide bins centred at the altitude specified.

The wind field in the simulation is comprised of tidal components and a
superposition of monochromatic GWs whose amplitudes have a vertical
wavenumber and frequency dependence. Diurnal and semidiurnal tidal components are assumed, with amplitudes of 25 and 10 m s

As per Sect.

To ensure that the correlations between the horizontal and vertical winds take on physically reasonable values, we have allowed the component fluctuation amplitudes to be related by the linear GW polarization relation

In order to give the wind field a level of spatially correlated randomness akin to what is seen in mesospheric wind fields when no predominant wave scales are present, we have opted to let

The 2-D spectrum we used for results presented in this paper consisted
of 80 different vertical wavelengths and wave periods, spanning the ranges
0.5–20 km and 5–240 min (uniformly sampled in vertical wavenumber and frequency), respectively. These limits largely encompass the waves responsible for the majority of the momentum deposition in the mesosphere–lower-thermosphere (MLT) region (see e.g.

The wave propagation azimuths were sampled from a uniform random distribution spanning

The absolute values taken by

A diagram summarizing the bistatic reception geometry is shown in Fig.

Bistatic meteor reception geometry. Using similar terminology to that in

To ensure that realistic radial velocity and position estimation errors are
propagated to the covariance estimation, we have opted to generate synthetic
receiver time series based on the observables discussed in the previous
sections and to then attempt to re-estimate the observables from the time
series. The complex time series for the

The background noise function consists of values derived from a Gaussian distribution, with a root-mean-square (rms) value derived from a probability distribution of meteor echo SNRs from the monostatic 55 MHz meteor radar at BP. The values used for

Probability distributions of SNR and decay time used in producing the receiver time series discussed in Sect.

The phase calibration offsets

Radial velocities and meteor positions are estimated from the noise and phase-offset time series following the procedures outlined in

It should be noted that in rare (

The way we have estimated mean horizontal winds in this simulation is similar to that typically applied to meteor radars in the literature (e.g.

In order to remove outliers from the input radial velocity distribution, we follow the iterative scheme proposed by

To remove the previously estimated mean winds and tides from the time series, we have calculated a low-pass-filtered version of the hourly averaged horizontal wind time series using an inverse wavelet transform with a Morlet wavelet basis, linearly interpolated a wind estimate at the time of each meteor, and subtracted the radial projection of the wind from the radial velocity time series. This is in principle similar to the approach of

To ensure that the filtered time series pertain to tidal-like (or longer) wind oscillations (and not short-period GWs), we select a minimum scale size in the reconstruction of 6 h and a total number of scales of 250. The reconstructed time series is then interpolated to the times of each of the meteors in question, and the radial component of this wind at each of the meteor positions is subtracted from the measured radial velocity.

Following the removal of the mean and tidal components of the horizontal wind from the radial velocities, covariances that pertain predominantly to gravity-wave-driven wind perturbations are estimated. The approach we apply is based on those presented by

It is noted that, as per the wind estimation case, the

A two-step radial velocity outlier rejection procedure is utilized to remove meteors with dubious square radial-velocity–AOA pairs from the input distribution in an attempt to reduce the bias in the resulting covariance estimates. The first step is to discard all radial-velocity–AOA pairs that have a projected horizontal velocity of

The performance of the second outlier rejection criterion on simulated data is briefly summarized in Sect.

To evaluate the truth value of the simulated covariances – i.e. that used to estimate the accuracy and precision of the covariances derived through inversion of Eq. (

In the case of using wave fields generated from the previously discussed gravity wave spectral model, we found that the covariances estimated by inverting Eq. (

This section considers the covariance bias distributions associated with a wind field generated using the GW spectral model discussed in Sect.

The biases for 15 000 realizations of 1 d integrated covariance estimations are shown in Fig.

Simulated wind covariance bias distributions for 1 d of integration

The width of the bias distributions for

It should be noted that

It also appears that there is no clear dependence of covariance uncertainty
on the use of a monostatic or multistatic configuration, for a fixed detection rate. This is evidenced by the uncertainties at 84 km for the multistatic configuration (1460 detections) being 14.4 and 14.5 m

Figure

As per Fig.

As per the 1 d integration case,

Figure

Once again, a systematic underestimation of

The previous section considered a wind field containing a multitude of waves whose spatial/temporal scales spanned a large part of the spectrum atmospheric gravity waves are expected to occupy. This section briefly addresses the other limiting case, which is that of a wind field consisting of a single monochromatic wave.

In all simulation realizations for this case, we have set the single monochromatic wave's propagation direction to 45

The bias distributions for 15 000 realizations are shown in Fig.

As per Fig.

Means and standard deviations of the simulated

Similarly to the spectral wave field case, both covariance terms are systematically underestimated (ranging from about 2 % to 26 % for

This section shows the effect of the application of the outlier rejection criterion of Eq. (

To emulate a radial velocity time series partially corrupted with outliers in this section, Gaussian-distributed noise with a standard deviation of 50 m s

Figure

Covariance bias distributions for different combinations of outlier contamination and outlier rejection. Black is no rejection or outliers, red is rejection with no outliers, blue is outliers without rejection, and green is outliers with rejection.

The application of the criterion is clearly beneficial in the presence of
outliers, resulting in a reduction in relative uncertainty of the

Despite the fact that it appears to introduce a small measurement bias, we still apply the criterion in the subsequent analysis of BP–Mylor data, so that we can be assured that anomalous radial velocities do not contribute to the covariance measurement errors.

This section uses the methodology described in the previous section to estimate covariances from the BP–Mylor meteor radar link from 17 March 2018 through to 9 September 2018. The aim of this analysis was originally to verify that the estimated covariances and flow acceleration derived from them were physically reasonable; however, in observing an apparent tidal modulation of the covariances, we realized that the results themselves may be of more general interest.

Plots of the mean horizontal winds and the

Mean horizontal winds

As is expected for this time of year at a mid-latitude SH site (see e.g.

The level of (anti)correlation between the covariance terms and the winds is
highly variable. The

The feature we focus the remainder of this discussion on concerns the coincident enhancement in the

Figure

As per Fig.

This figure shows evidence of a pronounced periodicity around 10 d in the zonal wind, which attains its highest amplitude at approximately day 110 around 85 km. At this time and in the same altitude region, the mean meridional winds abruptly (over a period of a few days) switch from northward to southward. All of this variability is likely attributable to a superposition of planetary waves. Albeit noisy (owing to the relatively short integration time), the

We have also noted that this interval is associated with an abrupt enhancement of the amplitudes of the diurnal and semidiurnal tides. Figure

Amplitude of the diurnal

The large tidal amplitudes during this period lead us to expect the propagation directions of the GWs removed from the wave spectrum by the winds to exhibit a diurnal variation. A complicating factor is that these waves may also amplify, dampen, or shift the phase of the tide, depending on the waves retained in the spectrum at the wave breaking height; the large variability in the tidal amplitudes during this period indicates that this may have indeed occurred. To provide some clarity on the extent to which the GWs have been modulated by the tide and vice versa, in the next section we examine a composite day of the tidal winds, covariances, and the implied flow accelerations over a 20 d interval spanning the interval in which the diurnal tide has a reasonably consistent phase and an enhanced amplitude.

Figure

A composite day of the horizontal winds

The flow accelerations (e.g. in the case of the zonal direction) have been evaluated using the expression (e.g.

As expected from the amplitudes in Fig.

In contrast, the

Between about 88 and 92 km, the zonal flow acceleration shows a pronounced minimum between 04:00 and 06:00 UT, a maximum around 13:00 UT at about 88 km, and a weaker minimum around 19:00 UT. The maximum occurs at a similar time to the corresponding zonal wind minimum, whereas the first minimum lags the zonal wind maximum by about 5 h, and the second minimum precedes it by about 5 h. Conversely, there is little flow acceleration structure below 87 km, other than a broad maximum at about 85 km around 01:00 UT. These observations are difficult to reconcile for three reasons: (1) the wave forcing is consistent with a rapid deceleration of the zonal wind from 04:00 to 06:00 UT at around 90 km, but there appears to be no positive forcing around 20:00 UT to accelerate the wind; (2) the strong positive forcing which does occur around 13:00 UT appears to result in little wind variability; and (3) the positive forcing around 85 km between 23:00 and 04:00 UT is associated with an acceleration of the zonal wind, but this acceleration is much smaller than that around 90 km.

From 88 to 92 km, the meridional flow acceleration shows a small maximum around 04:00 UT, a minimum at about 10:00 UT, and a large maximum around 20:00 UT. As per the zonal case, this leads to a peculiar relationship with the meridional wind; the forcing's large maximum occurs at a similar time to the wind minimum, the minimum corresponds roughly with a rapid wind deceleration, and the smaller maximum corresponds with a rapid wind acceleration. As for the zonal component, there is little meridional flow acceleration structure below around 86 km.

In the simulations section of this paper, we have tried to conclusively define estimates for the absolute and relative uncertainties of the

As shown by

As evidenced by the differences in the distribution widths of Figs.

The spectral components of the wave field may vary during the integration period. This is particularly problematic for the 10 d window; for example, during a period of intense but short-lived monochromatic wave events followed by more complex wave activity, increasing the integration time may actually increase the uncertainty in the covariance estimate of the monochromatic wave activity – not only because of the likely change in the mean covariance, but also because of the noise added to the radial velocity time series by the more complex activity.

Despite these caveats, we can broadly conclude that the 10-day integrated covariances (Fig.

The 1 d integrated covariances (Fig.

The 20 d composite covariances (Fig.

Unfortunately, it is impossible to know (using the meteor observations alone) if the discrepancies between the 1 and 10 d integration (for example, the absolute values of the covariances during the enhancement between days 105 and 110) are a result of statistical noise in the 1 d estimate or a precise estimate of a strong, transient monochromatic wave event using the 1 d integration. The observation of waves in the MLT airglow may aid in the interpretation of how monochromatic the background wave field is; in the future, we intend to complement these meteor radar case studies with images of the sodium and hydroxyl airglow taken nearby the BP site. This, in conjunction with the random resampling method employed by

In the 10 d integrated results, the small difference in measurement error at the peak and lower edge of the height distribution (around 20 %, for an order of magnitude increase in detections) places an important question on the usefulness of further increasing the integration times/detection rates. On this point,

All of our simulations have shown that a systematic underestimation of
non-zero covariances arises when an attempt is made to remove tidal effects.
This clearly becomes more of a problem in the presence of large-amplitude GWs
with ground-based periods close to those of the tides. A number of questions
about the process of tidal removal could be raised:

What is the importance of incorporating the momentum fluxes of gravity waves with ground-based periods close to the tides in climate models?

If those longer-period waves are unimportant, what is an appropriate frequency cut-off for covariance measurements?

If those waves are important, what is the optimal way to remove the tides?

With regard to 3, it may be that a wavelet/S transform has insufficient
frequency resolution to define solely tidal features; a long-windowed harmonic fitting (as used by e.g.

In Sect.

A complication arises from the fact that the criterion results in a more precise (albeit less accurate) covariance estimate in the absence of outliers. This also illustrates an important point about the sensitivity of the Eq. (

A subject we have not addressed in this paper is the application of weights to the meteors in the inversion of Eqs. (

Our aim in analysing the GW-induced flow accelerations in Sect.

Simulated errors in flow acceleration estimates, using the bias mean
and standard deviations in the Fig.

The results are complex, illustrating tidal enhancement at some times of day, dampening at others, and that there are also times in which a forcing is present but no apparent effect on the tide is clear. A broad observation is that the forcing components have a more pronounced diurnal variability between about 86 and 92 km, with the result that the forcing dampens the tide at the tide's minimum (i.e. westward and southward phase) and shifts its phase at its maximum. Of course, our interpretation is complicated by the fact that we have no knowledge of what the tidal features may have looked like without any GW forcing.

It is widely accepted in modelling studies that GW forcing plays a role in the observed seasonal variation of the migrating diurnal tide (DW1) amplitudes (i.e. equinoctial maxima and solstitial minima) and that whether amplification or dampening of the amplitude occurs depends on the GW source spectrum (e.g.

The small number of recent observational studies that have sought to quantify
the effect of GW forcing on the DW1 amplitude and phase have also yielded
contradictory results. For example, using TIMED satellite data

Tides may also interact with GWs through the diurnal variations in atmospheric stability they induce (i.e. making conditions more favourable for GW breaking and hence GW forcing at particular times of day). For example,

This study has defined limits on the expected uncertainties in estimates of the

Our simulations showed that 10 d integrated covariance estimates could broadly be considered reliable for our 55 MHz multistatic radar configuration; shorter integration times may of course be possible for lower-frequency radars with higher meteor detection rates. However, we did note that the uncertainty appears to asymptote towards a minimum value after about 10 d of integration; this value is clearly governed by the wave field characteristics. We also suggest that the accuracy and precision of the covariance estimates may be able to be improved slightly by using a more rigorous radial velocity outlier rejection scheme than applied here.

The simulation code developed in this study is available on request from Andrew J. Spargo, as are the data from the BP and Mylor meteor radars.

To embody the ellipticity of the Earth's surface in the estimation of meteor altitudes, Bragg vector orientations, and wind field components (for both bistatic and monostatic receiver cases), we followed the coordinate system conversion algorithms outlined by

Furthermore, in the interests of reducing computational overhead we applied
the

The time series reconstructed from the wavelet transform can be expressed as (

To create a climatology of the diurnal variability in density from SABER instrument data that was representative of conditions around Adelaide during the autumnal equinox, we acquired densities from individual limb scans with tangent point latitudes spanning 28–42

A spatial sampling region and measurement time-of-year span of this size was necessary to fill all time-of-day bins with measurements. An average over 11 years of data was performed to reduce the level of aliasing arising from GW-induced perturbations occurring in individual scans.

The climatology produced using this method had features that were qualitatively consistent with the same time averaging on NRLMSISE-00 model output from Adelaide's location. However, we did note that given density surfaces from SABER were, on average, 2 km lower than NRLMSISE-00's predictions between about 80 and 95 km. Nevertheless, the use of the SABER-derived density climatology in the production of Fig.

AJS carried out the model development and data analysis and wrote the paper. IMR contributed to the Instrumentation section and made other minor revisions to initial drafts of the paper. IMR is the principal supervisor of AJS's postgraduate candidature, and ADMK is the co-supervisor.

The meteor radars used in this study were designed and manufactured by ATRAD Pty. Ltd., and Iain Reid is the executive director of this group of companies.

Andrew Spargo would like to thank Jorge Chau, Chris Adami, Bob Vincent, David Holdsworth, Gunter Stober, Joel Younger, Richard Mayo, Andrew Heitmann, Yi Wen, Tom Chambers, and Baden Gilbert for useful discussions regarding this work.

Andrew Spargo is supported by an Australian Government Research Training Program Scholarship. The BP ST/meteor radar is supported by ATRAD Pty. Ltd. and the University of Adelaide. The Mylor receiving site and equipment is supported solely by ATRAD Pty. Ltd.

This paper was edited by William Ward and reviewed by Chris Meek and one anonymous referee.