At the heart of this program are six observing runs conducted in summer 2013 with the first station of the Long Wavelength Array, LWA1. A 100 m diameter array of 256 bent-dipole antennas, LWA1 is the first station within what is intended to be a larger array of more than 50 similar stations spread throughout New Mexico for high-angular-resolution imaging of cosmic sources in the HF/VHF (high-frequency–very high-frequency) regime. While the future of the full LWA is uncertain, LWA1 is currently run as a stand-alone observatory (at ϕ= 34.070∘ N, λ= 107.628∘ W), capable of operating within the 10–88 MHz range in one of three modes. These include a relatively wide-band (16 MHz) beam-forming mode and two transient buffer (TB) modes that each capture the signals from individual antennas, allowing for all-sky imaging after the fact. For more details of the LWA1 radio telescope, see , , and .

It is the all-sky TB modes that have the greatest potential for passive radar, the exploitation of transmitters of opportunity to illuminate a given target. In this case, the “targets” are Es layers and meteor trails. Specifically, showed that the HF transmitters of the NIST radio station WWV near Ft. Collins, Colorado (see Fig. ), could be used with LWA1's TB modes to probe the ionosphere. WWV broadcasts the time at 2.5, 5, 10, 15, and 20 MHz, including a 5 ms pulse at the beginning of each UT second that can be used for ranging. The frequency overlap between LWA1 and WWV is thus at 10, 15, and 20 MHz. Sky waves from WWV are often observed at 10 MHz, either from the lower F region or from Es. The geometry is such that 15 and 20 MHz sky waves can only originate from dense, low-altitude (∼ 100 km) plasma, i.e., Es.

The LWA1+WWV passive radar works with both the wide-band and narrow-band TB modes (TBW and TBN, respectively). The TBW mode produces a 61 ms capture of the raw signal from each antenna, allowing access to the full band (10–88 MHz) for all-sky imaging. Unfortunately, the time it takes to write this data to disk (nearly 10 GB for one capture) is so long (∼ 5 min) that the duty cycle is rather low. With the TBN mode, each antenna's signal is tuned to a selected frequency with 100 kHz of bandwidth (∼ 70 kHz is actually usable) that can be run continuously for up to 20 h (when the available disks fill up).

Using either mode, the antenna outputs are processed to isolate the WWV pulse at different group paths and are then used to generate image cubes that show the received pulse power over the entire visible sky at each group path. From these, one can measure the altitude, azimuth, and group path of any detected sky wave. Consequently, with TBW captures, one can simultaneously measure sky wave properties at 10, 15, and 20 MHz, but only every 5–6 min. Conversely, TBN data allows one to do the same with 1 s sampling, but only at a single frequency. In either case, the combined radar is quite useful for observing Es, especially at 15 and 20 MHz. In particular, the all-sky imaging capability and bistatic nature of the LWA1+WWV system manifest a probe of Es structures that can pinpoint their horizontal positions to a precision as good as 1 km over a relatively large area (∼100 km wide and several hundred kilometers long). This is discussed at greater length by .

All-sky imaging with LWA1 can similarly be used to detect, locate, and characterize VHF transmissions backscattered by field-aligned irregularities (FAIs) and/or meteor trails. For the right bistatic configuration, ionospheric structures with small-scale irregularities (half the observing wavelength) aligned along magnetic field lines will Bragg scatter signals to the receiver array. In addition to FAIs, meteor trails collectively act as a persistent source of VHF backscatter. As meteors ablate in the lower ionosphere (∼ 80–100 km), they produce dense, transient structures that are nearly linear and can produce specular reflections of VHF radiation.

For LWA1, there is a relatively nearby and powerful analog TV transmitter located in Ciudad Juárez, Mexico, roughly 280 km south-southeast of LWA1. According to the Federal Communications Commission (FCC), the effective radiative power (ERP) of this nondirectional, horizontally polarized transmitter (call sign XEPM) is 9.5 kW. It broadcasts on “Channel 2” with a very narrow-band, amplitude-modulated video carrier at 55.25 MHz. demonstrated that using this video carrier, ≳ 9000 meteor trails can be detected and located on the sky per hour using LWA1 TBN data. This is well over an order of magnitude larger that the count rates achieved with more commonly utilized dipole-based, all-sky meteor radars such as the Canadian Meteor Orbit Radar (CMOR) arrays and All-Sky Interferometric Meteor Radar (SKiYMET) systems ∼ 100–300 h-1 near local midnight;. The data processing and imaging pipeline developed by can also be used to identify and track FAIs along arcs in the sky north of the array where backscattering is possible. At 55.25 MHz, LWA1 has an angular resolution on the sky of about 3.1∘. This is comparable to the azimuthal resolution (∼4∘) of the 30 MHz imaging radar deployed in St Croix (US Virgin Islands) in 2002 and used to study backscatter from Es irregularities over Puerto Rico, i.e., at a latitude not dissimilar to LWA1 see, e.g.,.

For FAI and meteor trail observing alone, the complementary TBW mode offers no apparent advantages over the TBN mode. However, for the purpose of examining how meteor activity impacts Es while also detecting and characterizing FAIs associated with Es, the extremely wide bandwidth of the TBW mode offers a singularly useful kind of data set. With a series of TBW captures, one can simultaneously observe specular meteor trail reflections, Es reflections of WWV pulses at 10, 15, and 20 MHz, and VHF backscatter from Es FAIs. With this motivation, time was obtained with LWA1 for six observing runs in 2013 during summer nighttime when Es is most prevalent. Specifically, each run consisted of a series of 80 TBW captures spaced by 6 min from 03:00 to 11:00 UT (roughly 19:50 to 03:50 local time). The observations were conducted on 23 June; 21 July; 4, 13, and 21 August; and 1 September (or, as days of the year, on DOY 174, 202, 216, 225, 233, and 244).

The data were processed with python-based software, including the LWA Software Library LSL;, to produce all-sky or group path image cubes using WWV pulses at 10, 15, and 20 MHz. These cubes were analyzed according to to measure the sky location and group path of each WWV reflection. To monitor for FAIs and meteor trails, all-sky images were also produced within 45 frequency channels, centered at 55.25 MHz and spaced by 16.33 Hz, covering a range in Doppler speed of about ±1000 m s-1 with a resolution of roughly 90 m s-1. To convert these spectral images into all-sky maps of backscattered signals, the image for each channel was normalized by its noise level, estimated with the median absolute deviation (MAD). These signal-to-noise (S/N) all-sky maps were then converted to a single peak S/N map for each TBW capture by simply computing the maximum S/N over all channels at each all-sky pixel. This was done to mitigate the effect of very bright meteor trails which artificially increase the noise within an image because of the sidelobes associated with the LWA1 beam. Because the video carrier signal is inherently quite narrow (∼ 20–30 Hz), this typically only affects 1–3 channels near the Doppler frequency of a bright trail. Thus, this S/N-based approach allows fainter sources at significantly different Doppler frequencies to still be detected. A similar technique used to maximize meteor trail detections with TBN data is detailed in the Appendix of .

Supplementing the LWA1 observations and data products are two additional remote sensing assets. The first is the digital ionosonde, or “digisonde”, near Boulder, Colorado (station ID BC840). The location of BC840 relative to LWA1 and WWV is shown in Fig. . Ionogram data (frequencies, ranges, and amplitudes) were obtained for BC840 for the times during the LWA1 observations from the Digital Ionogram Database DIDBase;, except for 23 June (DOY: 174) when no BC840 data were available. From these, mean ionograms were produced within half-hour intervals during all but the first observing run. Visual inspection of these revealed the signature of Es during many of the observations below virtual heights of 122 km.

The second asset is an array of continuously operating GPS receivers. These were chosen from the publicly accessible Continuously Operating Reference Station (CORS) (ftp://www.ngs.noaa.gov/cors/rinex/) and UNAVCO (ftp://data-out.unavco.org/pub/rinex/) databases. All stations from these repositories that were within 400 km of the midpoint between LWA1 and WWV were chosen so that they would cover roughly the same area as the LWA1+WWV radar (the separation between LWA1 and WWV is 770 km) and BC840. The 61 stations that meet this criterion are almost exclusively in Colorado and northern New Mexico; their exact locations are shown in Fig. .

Data for the GPS array were obtained in Receiver Independent Exchange (RINEX) format for the dates of the LWA1 observing run. These were processed with software available within the GPS Toolkit GPSTk; to generate relative slant TEC (STEC) time series for each receiver–satellite pair. To remove instrumental biasses and to focus on TEC fluctuations, these STEC time series were de-trended according to . Within this de-trending scheme, at each time step, the average between the time steps that are τ seconds before and after the time step is subtracted, where τ is a flexible timescale. This finite differencing method has the drawbacks of increasing the noise somewhat (by a factor of about 1.5=1.22) and rendering the first and last τ seconds of each time series useless. However, the chief advantage is that it produces a predictable temporal frequency response: 2sin⁡2(πτν), where ν is the temporal frequency. In other words, a TEC fluctuation with a period of ν-1 and amplitude A will have a modified amplitude A′=2Asin⁡2(πτν) after de-trending is applied. Thus, the choice of τ allows one to tune the GPS data to a particular range of fluctuation periods or frequencies. This is especially important for the spectral analysis that will be used to characterize TIDs.

For each satellite, a three-dimensional Fourier analysis was performed over the array, with one temporal dimension and two spatial ones. For this, each de-trended STEC time series was broken into 30 min segments, overlapping with the mean ionograms produced with the BC840 data. Each segment was then analyzed according to . This starts with a straightforward temporal discrete Fourier transform, followed by a specialized spatial Fourier analysis meant to deal with the consequences of the sparse and irregular nature of the GPS array that was used. This includes the incorporation of deconvolution techniques developed and thoroughly tested within the field of radio astronomy for the similar problem of generating synthesis images of cosmic sources with radio-frequency interferometers. These techniques mitigate the impact of high-frequency structures caused by the array geometry (i.e., sidelobes) as well as phase errors caused mainly by wavefront distortions and/or point-of-view effects that vary in magnitude over the array. See for a much more detailed description. The end product of this analysis is a power spectrum cube (again, one temporal frequency axis and two spatial frequency axes) of TEC fluctuations within each 30 min segment.

During the application of this process, different values for the de-trending timescale, τ, were tried. In the end, τ=600 s was adopted as it appeared to provide the optimum temporal frequency response for MSTIDs during the LWA1 observations, similar to what was found by in the same geographic region. The analysis was also limited to times when the observed satellites were above 30∘ elevation to avoid biases resulting from extreme line-of-sight effects and to ensure that the area of the ionosphere being probed was reasonably similar to that observed with LWA1+WWV and BC840.

For the LWA1+WWV observations, Es detections and non-detections were assessed based on the group path measured for the 10 MHz sky waves. The distributions of returned power within bins of group path for 10, 15, and 20 MHz are shown in Fig. . The 20 MHz distribution was scaled by a factor of 4 because the 20 MHz transmitter has an ERP 4 times lower than the other two (2.5 vs. 10 kW). One can see that virtually all the returned power at 15 and 20 MHz, reflections of which are (nearly) always from Es, is at group paths below 840 km. There is a small amount of power from “two-hop” signals – those that reflect off the ionosphere, then off the ground, then off the ionosphere again – but generally, the 840 km group path provides a good cutoff to distinguish between Es and F-region reflections at 10 MHz. Note that the linear distance between LWA1 and WWV is 770 km, implying that a group path of 840 km corresponds to a virtual height of about 170 km. This is a bit high for Es, but one should note that this empirical limit essentially takes into account uncertainties within the group path measurements and the fact that a virtual mirror approximation is a poor representation of the often complex signal path associated with propagation through intricate Es structures.

For the BC840 data, the 30 min average ionograms were used to determine during which time periods Es was and was not present. Average TEC fluctuation spectral cubes were made for the four groups (two with Es and two without), and a map of the peak spectral power over all temporal frequencies is shown for each in Fig. . These maps show the maximum spectral power as functions of east–west and north–south spatial frequencies (ξEW and ξNS). Polar grids are shown for reference at radial steps of 0.002 km-1. For reference, the spectral resolution within these maps is roughly 0.0015 km-1 (full width at half maximum).

The two non-Es spectra show relatively weak signatures (amplitudes ≲ 0.08 TECU) of waves moving in several directions. These include MSTIDs (wavelengths ∼ 250–350 km) moving westward, northwestward, northward, and northeastward and larger TIDs (∼ 1000 km wavelength) moving due south. There is also a relatively weak signature of ∼ 1000 km wavelength TIDs moving toward the southwest seen only within the LWA1+WWV non-Es spectral map. The fact that it is only seen within this map may be related to contamination from two-hop Es reflections that were incorrectly flagged as F-region sky waves due to their larger group paths (see above and Fig. ).

The two Es maps are markedly different from their non-Es counterparts. They both exhibit quite prominent features associated with southwestward-directed MSTIDs. Save a single, relatively weak, southward-directed, large TID feature seen in the LWA1+WWV map, these are essentially the only significant features apparent within the two maps. The main differences in these features between the two maps is that the TID feature is stronger within the BC840 map (amplitude ∼ 0.22 TECU; note, the figures display fluctuation power as amplitude2) and peaked near a single wavelength (∼ 350 km). In contrast, the southwest feature in the LWA1+WWV map is distributed among a somewhat larger range of wavelengths (∼ 250–500 km), with peak power corresponding to amplitudes of about 0.15 TECU. Despite these differences, the occurrences of dominant southwest-directed features within spectra corresponding to Es detections and the virtual absence of such features within the non-Es spectra together confirm earlier, similar results that are consistent with the existence of some form of E–F coupling.

To further explore how this correlation between the appearance of Es and F-region MSTIDs relates to the properties of the Es layers, weighted mean spectra, similar to those shown in Fig. , were made using the signal amplitude at different frequencies. For the LWA1+WWV data, different mean spectra were made using the 10, 15, and 20 MHz sky wave amplitudes as weights. For the 10 MHz sky waves, only those with group paths < 840 km were used (see above). The resulting spectra are shown in the left panels of Fig. . From these, one can see that the TID amplitude increases with the reflection frequency and, implicitly, with Es density. At higher frequency or density, it also appears that the MSTIDs are skewed more toward somewhat smaller wavelengths (∼250 km). Separate mean fluctuation spectra were made using Es signal amplitudes from the BC840 ionograms, averaged within five different frequency bins. Four evenly spaced bins were used between 1 and 6.6 MHz with the fifth bin including all Es signals for f>6.6 MHz. The first three frequency bins roughly correspond to the inferred plasma frequencies for the LWA1+WWV system at 10, 15, and 20 MHz assuming an Es height of 110 km and a simple virtual mirror approximation. These first three bins show a similar, but more pronounced trend of increasing fluctuation power with increasing Es frequency as is apparent from the LWA1+WWV weighted spectra. However, no comparable change in dominant wavelength is evident. Within the mean spectrum for the next highest frequency bin, 5.2–6.6 MHz, the wave amplitudes are significantly weaker, and for the largest frequency bin, the southwestward-directed MSTIDs are virtually nonexistent. This is similar to the results presented by , which showed a decrease in MSTID activity for foEs > 3 MHz.

An analysis similar to that presented in Sect. 3.1 for the GPS-based TEC fluctuation spectra was performed on the all-sky 55.25 MHz S/N maps described in Sect. 2.1. Figure  shows mean S/N maps for the same Es and non-Es groups that are represented in Fig. . The region to the north where backscattering by Es FAIs is expected to be prevalent is marked in each panel with a black dotted line. This was computed using the location for XEPM obtained from the FCC (at ϕ=31.706∘ N, λ=106.478∘ W), an assumed height range of 90–130 km, and using the international geomagnetic reference field (IRGF) parameters for the 2013 epoch. While there are certainly meteor trails detected within this region on the sky, sources within this area are excluded from meteor trail analysis due to the higher likelihood that they corresponds to FAIs.

Within the panels of Fig. , the circle corresponding to an elevation of 30∘ is marked with a black dashed line. Above this elevation, found that >85 % of detected point-like sources at 55.25 MHz are true meteor trails, based on high-resolution time series (5.12 ms sampling) of signal amplitudes. Below this elevation limit, other transmitters and reflections off aircraft constitute a significant fraction of sources. An ongoing survey for meteor streams with LWA1 at 55.25 MHz has found that more than 90 % of sources above this limit have time series best explained by meteor trail reflections. Furthermore, this survey found a preponderance of sources within the likely FAI region in the summer of 2014 that are much longer-lived than typical meteors, consistent with Es FAIs.

For both the LWA1- and BC840-based groups, meteor trail activity and likely FAIs were significantly more prominent when Es was present. Like the results for MSTIDs shown in Fig. , this is much more pronounced within the BC840-based groups. In this case, there are few if any sources above 30∘ elevation (i.e., likely meteor trails) and the arcs likely associated with FAIs are not discernible at all in the mean S/N map for the non-Es group. Specifically, the mean S/N within the FAI and meteor trail regions are 30 and 10 % larger, respectively, within the Es map versus the non-Es map when using BC840 data, but only 10 and 5 % higher when using LWA1 data. Again, this may point to contamination within the LWA1 non-Es group by two-hop Es reflections. The FAIs that appear within these all-sky maps sometimes appear in resolved groups with elongated, wavefront-like structures. These appear to have no single dominant orientation and are generally consistent with similar observations of Es backscatter at 30 MHz over Puerto Rico .

Averaged 55.25 MHz S/N maps are also shown in Fig. , weighted by sky wave amplitudes at different frequencies. These are counterparts to the averaged TEC fluctuation spectral maps shown in Fig. . Here, it is evident that for both LWA1+WWV- and BC840-based averaging, both meteor trail activity and the incidence of FAIs correlate with Es density to some degree. Specifically, the mean S/N within the meteor trail region increases by a few percent from 1.5 to 4.5 MHz. The FAI region average S/N increases by more than 10 % from 1.5 to 6 MHz. The exact dependences on fp will be discussed more in Sect. 4.

The results presented within the previous two subsections imply that up to plasma frequencies of about 5 MHz, Es layer density increases steadily with the level of meteor activity and that this increased density may enhance E–F coupling. However, above this level, other processes must influence the structure of the Es layers as the strength of detected MSTIDs wanes above 5 MHz and the trend between fp and meteor activity exhibits a similar turnover. Therefore, these relatively high Es densities cannot be explained by increased deposition of heavy ions via meteor ablation and are likely related to some process that may also disrupt E–F coupling.

To explore this further, the LWA1–WWV and BC840 data were combined to discover whether or not there is evidence for dense, isolated Es structures that could yield high-frequency reflections but would not constitute an overall increase in the total ion content of the Es layers. Following , we used the WWV sky waves imaged by LWA1 to localize the signals on the sky and infer the horizontal position of each Es reflection point. This was done using the 15 MHz data since 15 MHz WWV reflections are all from Es, which is not the case at 10 MHz, and the 15 MHz transmitter is 4 times more powerful than the one at 20 MHz. The positions were measured parallel and perpendicular to the great circle connecting the LWA1 and WWV positions at an altitude of 110 km and are plotted for each LWA1 observing run in Fig. , color-coded by signal amplitude. Upon visual inspection of these plots, it is clear that within a single observing run, the reflection points can be quite clustered, especially for the mid-August observing runs (DOY: 225, 233).

To quantify the level of clustering, the correlated power was computed among 15 MHz reflections within bins of horizontal separation for each observing run, then averaged into a single correlation function. This was done by multiplying the amplitude of each 15 MHz reflection by the amplitudes of all others within an observing run and then summing these products with bins of horizontal separation. This was repeated for all 15 MHz sky waves and for all observing runs and combined into a total correlation function. A normalized version of this (divided by the total over all bins) is shown in red in the panels of Fig. . The signals appear to be, on average, significantly correlated on horizontal scales up to about 250 km, which is not surprising given the results shown in Fig. . However, the correlation is significantly stronger for separations < 150 km, especially between 10 and 40 km.

To examine how this changes with Es layer density, the correlation function was recomputed, this time weighting the correlated power from each sky wave pair by the product of the Es signal amplitudes from the corresponding BC840 ionograms within different frequency bins. The ionogram frequency bins used were the same as those used for Figs.  and . The weighted and normalized correlation functions for these frequency bins are shown as black histograms in the panels of Fig. . One can see that correlation on 10–40 km scales (highlighted in grey) steadily increases with ionogram frequency up to 6.6 MHz. This is also where the backscatter S/N for FAIs peaks, implying that the 15 MHz echo clumps are associated with the same structures that host the meter-scale FAIs. Indeed, the typical distance to these FAIs from LWA1 is ∼ 200 km, implying that the groups of FAIs seen within the all-sky images shown in Figs. – are consistent with sizes of a few to a few tens of kilometers.

In addition, these same size scales are consistent with wavelengths of shear instabilities thought to be the driving formation mechanism for structures associated with QP echoes . They are also consistent with the observed wavelengths of frontal structures with Es echoes imaged at 30 MHz over Puerto Rico ∼30 km;. Moreover, it is known that QP echoes are much more prominent within Es layers that have substantial disparities between peak and mean densities as indicate by larger values of foEs-fbEs see, e.g.,. For the data set presented here, the values for fbEs were relatively tightly clustered with a mean of 2.1 MHz and standard deviation of 0.5 MHz. Thus, in this case, higher values of fp can be taken as indicators of larger peak rather than blanketing densities. This makes the proffered notion of QP predominance at higher fp all the more plausible. However, note that the temporal sampling of the LWA1 data, one 61 ms capture every 6 min, precludes classification of these structures as bona fide QP echoes. It should be stressed that it is the size, spacing, and density of these, along with their association with Es, that makes them similar to the known properties of structures associated with QP echoes, not their temporal variability.

The unprocessed GPS data used in this investigation are publicly available in compressed RINEX format via anonymous FTP from the two databases listed in Sect. 2.2. The digisonde data for BC840 was obtained from the DIDBase repository (DIDBase, available at: http://ulcar.uml.edu/DIDBase/; Reinisch et al., 2004). Processed data, including fluctuation spectra, are available upon request to the author. Raw LWA1 data are proprietary and are not publicly available. However, all-sky images and image cubes generated from these data for this manuscript can be made available upon request to the author.