Meteor radar observations of polar mesospheric summer echoes over Svalbard

A 31 MHz meteor radar located in Svalbard has been used to obse rve polar mesospheric echoes (PMSE) during summer 2020. Data from 19 July was selected for detailed anal ysis, with a focus on extracting additional information to characterize the atmosphere in the PMSE region. The use of an all-sky meteor radar adds an additional use to data collecte d for meteor observations and enables the detection of PMSE layer s cross a wide field of view. Comparison with data from a 53.5 MHz narrow-beam MST radar shows good agreement in the morpho logy of the layer as detected between the two systems. 5 Doppler spectra of PMSE layers reveal fine structure, includ ing regions of enhanced return that move across the radar’s fi eld of view. The relationship between range and Doppler shift of of f-zenith portions of the layer enable the estimation of wind speeds with high temporal resolution during PMSE conditions. Tria ls demonstrate good agreement between wind speeds obtained from PMSE Doppler spectra and those calculated from specula r meteor trail radial velocities. Combined with the antenna polar diagram of the radar, this same relationship was used to infe r the aspect sensitivity of observed PMSE backscatter, yiel ding a 10 mean backscatter angular width of 6.6± 2.8◦. A comparison of underdense meteor radar echo decay times du ring and outside of PMSE conditions did not demonstrate a strong correlation between the presence of PMSE and shortened underdense meteo r radar echo durations.

. NSMR all-sky received power (incoherently averaged across all five antennas) for 19 July, 2020. 30 second averages in 1.8 km range bins. Plot intensity has been capped at 8 dB to enhance the visibility of weak features. The bright vertical segments above 85 km are meteor echoes.

Comparison of all-sky and narrow beam observations
The observations of PMSE by SSR's narrow vertical beam seen in Fig. 2 strongly correlate with the observations by NSMR. 85 SSR detected the 0500-0530 PMSE-like feature more strongly than NSMR and displayed split layer behavior that was not seen in NSMR data. SSR's detection of the 0647-0738 layer was also much stronger than what was seen by NSMR, with two layers clearly visible on the range-time intensity plot. The main PMSE detection by SSR shares a similar time evolution to that seen by NSMR, with transient layer splitting detected between 83-88 km. SSR observations do however exhibit a more gradual decrease from 1100-1200, as opposed to the decrease to a low SNR plateau seen by NSMR. 90 SSR has the advantage of having a 0.5 km range resolution, as opposed to 1.8 km for NSMR. Combined with the focusing of power into a narrower beam, this allows finer details in the PMSE layer to be seen, including split layers and dynamic upper and lower edges. One key difference to NSMR observations is the lack of vertical smearing above the layer, which supports the interpretation that the vertical smearing in NSMR's range-time intensity plot is due to off-zenith detection of a thin layer.
The split layers seen by SSR are consistent with higher resolution measurements produced by the MAARSY narrow beam 95 VHF radar (Czechowsky et al., 1989) and the EISCAT VHF incoherent scatter radar . The observations of Cho and Röttger (1997) in particular also show periods of split layer PMSE, in addition to periods of continuous return across the entire PMSE region. The presence of split PMSE/PMC layers may be further evidence of complex mesopause structures, with multiple distinct local temperature minima (She and Von Zahn, 1998;Thulasiraman and Nee, 2002) allowing for the formation of PMC at multiple heights.

Meteor radar PMSE Doppler profiles
The observation of PMSE layers by a wide field-of-view radar has the advantage that different portions of the horizontal extent of the layer may be detected at differing ranges and Doppler shifts. The curvature of the range-Doppler profile of PMSE detection is related to the speed of the background wind with which the layer is moving. For each Doppler frequency component the minimum detected range corresponds to return from along the zenith-wind vector plane. Figure 3 shows several examples 105 of Doppler profiles associated with PMSE layers. PMSE mostly presents in the Doppler profiles as arcs curving upward from the 0-Doppler detection of the layer, the point which corresponds to return from around zenith.
The first two profiles from 0506 and 0514 are from the weak transient PMSE layer detected by NSMR and SSR. These two profiles differ from the profiles seen for the main detection period in that they exhibit a pronounced asymmetry and an almost linear range-Doppler relation. This may indicate that the scattering geometry for the early transient PMSE detection may differ 110 from that of the main PMSE detection. The 0943 profile displays an asymmetric Doppler profile at the onset of strong PMSE return. This is indicative of an anisotropic wind field, as the layer is seen as a region of slow winds (more vertical, negative portion of the profile) which is being replaced as wind speed increases above the radar. At 1023 there is strong detection during the main PMSE layer period, with fine structure apparent including layer splitting visible near the edges and multiple small, persistent features. The is consistent with the scattering layer leaving the radar's field of view. At 1147, PMSE SNR is decreasing towards the end of the detection period and significant SNR is limited to around 0-Doppler.

Estimating wind speed from range-Doppler profiles
If it is assumed that PMSE occurs in a thin layer of approximately constant height, then range-Doppler profiles can be used to 120 estimate the wind speed in the PMSE region.
The range R to a point at zenith angle θ and height h above the approximately spherical surface of Earth is given by where R ⊕ is Earth's local radius. Here, the oblateness of Earth is neglected, which is justified on the ground that PMSE is detected primarily at zenith angles within ±30 • at around 86.4 km. This means that the horizontal extent of PMSE detected by 125 meteor radar is not more than 100 km, so there will not be variation in R ⊕ sufficient to significantly affect equation 1.
The basic radar Doppler equation for a radar transmitting at frequency f 0 and wind speed V with radial component v r can be rearranged, assuming a horizontal wind, to infer the zenith angle of a component of the spectrum with Doppler shift ∆f , as where c is the speed of light.
Considering the return from the zenith-wind vector plane, it will form a distinct bottom edge to the range-Doppler profile of PMSE return. Therefore, the angular dependence of equation 3 can be used to describe the relationship between zenith angle and Doppler shift in the zenith-wind vector plane. Inserting then equation 3 into equation 1, we have a function R(∆f, h, V ), 135 that specifies the curve of the range-Doppler profile of a scattering layer moving horizontally at height h with speed V , resulting in Doppler shifts of ∆f .
For NSMR range-Doppler profiles, a least squares fit was applied to determine the wind speed parameter of R(∆f, h, V ) for observation periods where the peak PMSE layer SNR was at least 6 dB. Overall, PMSE-based estimates of wind speed, assuming V is purely horizontal, were mostly in keeping with estimates obtained from the more conventional meteor trail 140 radial velocity technique. This comparison is discussed in further detail in section 4.2.

PMSE Doppler profile sub-structures
Beyond the range-Doppler relationship due to background winds, the spectra in Fig. 3 also display smaller scale return that are indicative of scattering from sub-structures within the PMSE layer. In some cases, it can also be seen that the background wind moves regions of enhanced scatter through the field of view of the radar.   from meteor detections and fits to the range-Doppler profile. This demonstrates that the PMSE layer is not homogeneous, but contains moving regions of enhanced reflectivity that alter the shape of the spectral power distribution over time.

Comparison with meteor detections
The use of a meteor radar to observe PMSE also presents the opportunity to use conventional meteor radar detections to provide additional information about the state of the atmosphere during and around PMSE detection periods. Meteor radar detections are commonly used to estimate winds in the 80-100 km height range. PMSE derived wind speeds provide an opportunity to verify the accuracy of meteor derived wind estimates. Furthermore, PMSE has been implicated in the anomalously short 155 decay times of underdense meteor echoes below 90 km. The direct detection of PMSE by meteor radar simplifies the process of assessing the effect of PMSE on meteor echo decay times, which also relates to the broader study of middle atmosphere plasma chemistry (see e.g. Rapp and Lübken (2001), Murray and Plane (2003), Murray and Plane (2005), Friedrich et al. (2011)).

Meteor winds
Winds were estimated in a conventional manner using meteor detection radial velocities to produce wind profiles with 30 160 minute and 2 km vertical resolutions. Meteor-based winds were calculated (assuming the vertical wind w = 0) using a least squares fit to the relation where v r is the radial velocity of the meteor trail, u and v are the zonal and meridional components, and l and m are the direction cosines (see e.g. Holdsworth et al. (2004)). Prior to wind estimation, the observed zenith angles θ of meteor detections were 165 converted to local zenith θ loc angles using the relation R ⊕ was calculated at NSMR's latitude using the WGS84 ellipsoid (Decker, 1986).
Outlier rejection was implemented by checking the predicted v r for each meteor and rejecting any detections differing by more than 30 m s −1 . Wind components were then recalculated with the remaining meteors and the process was repeated until 170 all predicted v r were within tolerance. If less than 6 meteors were present in the height/time bin or were left after outlier rejection, it was considered an empty bin.
Seen in Fig. 5, the meteor wind profiles show that the main PMSE detection from 0901-1220 coincides with the semi-diurnal tide maximizing the eastward wind just above the layer height and the northward meridional wind maximizing around the layer height.

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Vertical wind shear was also calculated as the magnitude of the vector difference between winds in adjacent height bins.
The main PMSE detection period at 0901-1220 occurred during moderate vertical shear, but an examination of the relationship between shear conditions and the occurrence of earlier transient PMSE layers was inconclusive.

Comparison of meteor and PMSE Doppler winds
In order to compare the observed Doppler profiles of PMSE detections with local wind conditions, winds were estimated using 180 meteor detections for each range-Doppler profile. The wind in the layer region was estimated for each PMSE profile using meteors detected within ±15 minutes of the profile time and within ±1 km height of the layer's 0-Doppler maximum intensity range.
Seen as dashed lines in Fig. 3, the meteor wind estimates closely match the peak power of the range-Doppler profiles of PMSE return. This is consistent with the interpretation that observed scatter from PMSE seen by NSMR is from a thin layer 185 as seen across a wide field-of-view. The asymmetric range-Doppler profile for 0943 shows good agreement for the negative Doppler portion of the spectrum, but not the positive Doppler, which is again consistent with a changing wind field in the radar's field of view.
When wind speed estimates from PMSE Doppler and meteor trail radial velocities are directly compared, as shown in Fig.   6, it is seen that the range-Doppler estimates of horizontal wind at the height of maximum PMSE return power are mostly in A similar reversed situation, albeit with a smaller effect, is seen in the 1112 example, where the high speed region of the 200 wind field is departing with the incident positive Doppler component displaying a noticeably smaller Doppler. It is also possible that the negative excursion around 0925 in the meteor wind estimate is due to the same causal factor as the similar negative excursion in the range-Doppler wind speed estimate approximately ten minutes later. In this case, it is useful to point out that meteor detections occur across a substantially larger field of view than PMSE, encompassing a radius of approximately 300 km, as opposed to an approximately 50 km maximum radius for the detected horizontal extent of PMSE.

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As wind speed estimates based on meteor trail radial velocities are dependent on the distribution of meteors within the radar's field of view, there can be times when meteor detections are concentrated more in some parts of the field of view than others. In an anisotropic wind field, this may lead to excess weight being placed on regions of the sky where meteors happen to be detected for a particular observation period. When comparing wind estimates made from the range-Doppler profiles of a thin PMSE scattering layer in a smaller region of the sky with wind estimates made from meteor detections scattered across 210 a larger area, it may be that wind speed estimate perturbations seen by the different methods may be the result of sampling different regions of a divergent wind field.
The disagreement between meteor and range Doppler wind speed estimates at the end of the primary PMSE detection period is due to a different mechanism. From about 1140-1200, the significant PMSE SNR in the range-Doppler profile is limited to a narrow spectral region around the 0-Doppler component. Under this condition, the applied fit does not produce an accurate 215 range-Doppler curve. The result is an erroneously flat fit, which corresponds to an overestimate of wind speed. It should be noted that the narrow, flat return at 0-Doppler is also indicative of a more aspect sensitive scatter mechanism, wherein detected backscatter is only visible near zenith.

Meteor echo decay times
Underdense meteor trails, with linear electron densities of less than 2.4 × 10 14 electrons m −1 (McKinley, 1961), produce radar 220 echoes that decay at an exponential rate governed by the local ambipolar diffusion coefficient D (Lovell et al., 1947). The time, τ , for an underdense meteor trail's radar echo to decay to a factor of e −1 of the initial maximum is given by where λ is the frequency of the radar. This relation is the basis of methods to estimate temperature in the meteor ablation region either by using the slope of log τ as a function of height (Hocking, 1999) or by supplying pressures to the relation where K 0 is the zero field mobility of the diffusing ions (Mason and McDaniel, 1988), and T , p, and ρ are the atmospheric temperature, pressure, and density, respectively (Cervera and Reid, 2000).
It should be noted that this relation only holds for the case where only ambipolar diffusion is responsible for the evolution of meteor trail plasma. It has been observed that meteors detected at lower altitudes, especially below 85 km, have significantly 230 shorter decay times than is predicted by diffusion alone (Kim et al., 2010). Lee et al. (2013) and Younger et al. (2014) showed that this is most likely due to the neutralization of meteoric plasma initiated by the attachment of free electrons to neutral O 2 and N 2 in a three-body process. It is possible that the ice crystals thought to be responsible for PMSE also affect the observed decay time of meteor trail echoes, as electrons can attach to ice crystals, leading to additional crystal growth and meteoric plasma neutralization. If this mechanism plays a significant role on meteor trail evolution, then meteor trail decay times should 235 differ in the presence of PMSE.
The meteor trail echo decay times seen in Fig. 7 show some correlation between anomalous decay times and PMSE occurrence as minor negative excursions to decay time. The lack of a more dramatic correlation could be due to the dominance of neutral three-body attachment removing free electrons from the trails, as compared to the removal rate due to aerosol at- showed that meteor decay times in lower height bins displayed more temporal stability than meteor detections in the 86-88 km height bin, which suggests that distortion of meteor decay times is not significant at the lower edge of the detected PMSE region. Furthermore, previous work has indicated that the presence of PMC may actually slow the neutralization of meteor trails by the depletion of mesospheric atomic oxygen (Murray and Plane, 2003). Whatever the precise details of the interaction between PMC particles and meteoric plasma, the presence of detected PMSE cannot conclusively be proven or ruled out as the 250 primary causal factor in reducing meteor radar echo decay times in this case. An examination of NSMR data across all seasons including a cross-comparison with PMSE detection and non-detection periods is required to definitively answer the question with appropriate statistical rigour.

Aspect sensitivity
The detection of Doppler components of the PMSE layer away from zenith present an opportunity to estimate the angular 255 dependence of observed backscatter from PMSE. There are however some limitations that the large beamwidth of NSMR imposes on attempts to infer the aspect sensitivity of observed PMSE. The narrow beam expression for the aspect sensitivity parameter θ s as in Hocking et al. (1986) is not applicable in this case, as using equation 3 with range-Doppler profiles allows us to directly sample received power within the beam at different zenith angles, rather than tilting the beam. Similarly, the sparse, widely spaced interferometer array makes the use of the Capon method (Sommer et al., 2014)  To do this for each profile, the PMSE range-Doppler estimate of wind speed was applied to equation 3 to produce an estimate of zenith angle. The peak power in each zenith (frequency) bin was estimated from the amplitude of a Gaussian curve fitted to power in the bin as a function of range. A Gaussian distribution was then fit to the peak powers of PMSE Doppler as a function 275 of estimated zenith angle, corrected for antenna gain. The width of the fitted Gaussian curve is the PMSE aspect sensitivity parameter, θ s , and the center of the fitted curve is the offset from zenith or tilt angle.
In order to minimize contamination from meteor echoes, zenith-peak power profiles were limited those with maximum average power less than 600 (arbitrary hardware units). Profiles were also required to have successful Gaussian range/power fits with peak Doppler SNR between 3 and 30 dB in at least 40% of zenith (frequency) bins. Finally, only Doppler bins in the 280 frequency range of -2.5 to 2.5 Hz were used to exclude the majority of meteor detections that occur with higher Doppler values closer to the horizon.
Applying this process, θ s was successfully estimated for 76 of the one minute observation periods between 0900-1300. The fitting process additionally provided the offset from vertical, which gives some indication of the preferential scattering or tilt angle of the observed PMSE. Seen in Fig. 8, θ s = 6.6 ± 2.8 • . The estimated aspect sensitivity showed considerable variation 285 throughout the primary PMSE detection period. The offset of the zenith angle was close to zero with predominantly negative excursions, indicating that the observed PMSE scattered preferentially in the negative Doppler direction. The mean and range of estimated aspect sensitivity values seen in Fig. 8 are consistent with other studies (see e.g. Reid (1990)). For comparison, Czechowsky et al. (1988), exploiting the sidelobes of a radar with similar configuration to SSR at Andenes, found values of 2-10 • with typical values in the range of 5-6 • . Swarnalingam et al. (2011) found a median value 290 of 8-11 • using a 51.5 MHz MST radar, with significant dependence on the height of the scattering layer. Larger values were estimated at higher altitudes, which is indicative of increasing isotropy with height. Smirnova et al. (2012), using a 52 MHz MST radar, found two populations of scatterers with aspect sensitivities of 2.9-3.7 • and 9-11 • , also showing an increase with altitude. Both these studies yielded similar results to the earlier work by Huaman and Balsley (1998) that gave mean values of 10 • at 80 km and 14 • at 90 km, but with substantial differences between radars at Andenes (5-6 • ) and Poker Flat (12-13 • ).
This study did not show a clear correlation between layer height and aspect sensitivity. However, it should be noted that the method used is only applicable to the height of maximum scattering intensity, so does not capture the full behavior of aspect sensitivity in different parts of the PMSE layer.

Conclusions
This study demonstrates that all-sky radars provide a useful complement to the more common narrow-beam studies of PMSE.

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The key advantage of all-sky systems is that they are able to capture Doppler contributions from PMSE continuously across a wide range of zenith angles. This reveals fine structure in PMSE layers and provides an immediate opportunity to infer the motion of the scatterers. The use of a 31 MHz radar is also noteworthy, given that most previous radar observations of PMSE have been conducted with MST radars with transmission frequencies above 50 MHz. This indicates that the λ/2 scattering condition is also fulfilled at larger spatial scales than for the more common 50 MHz and above observations. Thus, it has also 305 been shown that the longer wavelength, which is optomized for meteor trail detection, is not a significant impediment to the detection of PMSE layers.
In particular, the range-Doppler profile of thin layer return obtained by wide field-of-view radars can be used to infer wind speed in the layer and the aspect sensitivity of the layer's scattering mechanism. A comparison of wind speeds obtained through this method and more conventional meteor echo based wind estimates shows good agreement for fully developed PMSE, an 310 assessment that is also supported by the apparent motion of density perturbations within the distribution of received power from the layer. Aspect sensitivity estimated using range-Doppler profiles is consistent with previous estimates made using 51-52 MHz narrow-beam MST radars.
While this study was necessarily limited in its scope, the methods presented should in future be applied to longer data sets.
Ideally, this will take the form of a campaign over summer at a polar location where frequent PMSE is observed. Additional 315 data, such as lidar temperatures could also facilitate a more thorough interpretation of the results of the methods described.
Data availability. NSMR meteor detection data is available from http://radars.uit.no/MWR/NTMR/yyyymmdd_met.met where yyyymmdd is the date. Processed data and NSMR Doppler profiles are included in the supplementary data. Raw time series data is available upon request from The Arctic University of Norway.
Author contributions. JY developed the methodology, performed the analysis, and prepared the manuscript. IR and CA assisted with the 320 investigation. CA advised on technical details of instrumentation. CH and MT manage NSMR. CH and CA manage SSR.
Competing interests. The authors declare that they have no conflict of interest.