Passive over-the-horizon radar with WWV and the …lwa/pubs/wwv_radar.pdfHELMBOLDT ET. AL: PASSIVE OTH RADAR WITH WWV AND LWA1 3 The transmitters for both WWV and WWVH are relatively

Radio Science, Volume ???, Number , Pages 1–12,

Passive over-the-horizon radar with WWV and the first

station of the Long Wavelength Array

J. F. Helmboldt,1 T. E. Clarke,1 J. Craig,2 S. W. Ellingson,3 J. M. Hartman,4,5 B.

C. Hicks,1 N. E. Kassim,1 G. B. Taylor,2,6 & C. N. Wolfe3

We present a new passive, over-the-horizon (OTH) radar system consisting of thetransmitters for the HF radio station WWV and the dipole-antenna array that comprisesthe first station of the Long Wavelength Array (LWA), or “LWA1.” We demonstrate thatthese two existing facilities, which are operated for separate purposes, can be usedtogether as a relatively powerful bistatic, HF radar, capable of monitoring the entirevisible sky. In this paper, we describe in detail the techniques used to develop all-sky,OTH radar capability at 10, 15, and 20 MHz. We show that this radar system can be apowerful tool for probing ionospheric structure by quantifying the degree of “tilt” effectedby ionospheric density gradients along the ray paths, including the effect this has on OTHgeolocation. The LWA1+WWV radar system appears to be especially adept at detectingand characterizing structures associated with sporadic-E. In addition, we alsodemonstrate how this system may be used for long-distance, OTH mapping ofterrain/ocean HF reflectivity.

1. Introduction

High-frequency (HF; 3–30 MHz) radars have beenused for decades for several applications. Operat-ing as both monostatic and bistatic radar systems,ionosondes have been and continue to be used tosound the ionosphere, probing the evolution of theionospheric electron density profile. They remainvaluable assets for both basic ionospheric researchand as support systems for operational radars. So-called over-the-horizon (OTH) radars were devel-oped after World War II to exploit the ionosphereas a “virtual mirror” that could reflect both outgo-ing and returning HF signals to track OTH targets.

1US Naval Research Laboratory, Code 7213,Washington, DC 20375, USA.

2Department of Physics and Astronomy, Universityof New Mexico, Albuquerque NM, 87131, USA.

3Bradley Dept. of Electrical & ComputerEngineering, Virginia Tech, Blacksburg, VA 24061.

4Jet Propulsion Laboratory, California Institute ofTechnology, Pasadena, CA, USA.

5NASA Postdoctoral Program Fellow6Greg Taylor is also an Adjunct Astronomer at the

National Radio Astronomy Observatory.

Copyright 2013 by the American Geophysical Union.0048-6604/13/$11.00

OTH radars remain a valuable long-distance surveil-lance tool used, for example, to monitor illegal nar-cotics trafficking in the Caribbean [see Headrick andThomason, 1998, for a more thorough discussion].

As detailed by Headrick and Thomason [1998],the transmitter portion of operational OTH radarsare particularly cumbersome and difficult to developgiven the large size required for high-power HF trans-mitting antennas. This paper details efforts to de-velop a so-called “passive” radar capability in the HFregime that uses existing transmitters, whose opera-tion is independent from that of the radar system it-self. This concept was successfully employed to studyhigh-latitude ionospheric scattering events by Meyerand Sahr [2004] using FM stations at ∼100 MHz.

Here, the transmitters used are those of the Na-tional Institute of Standards and Technology (NIST)radio station located near Ft. Collins, Colorado, call-sign WWV. WWV broadcasts the current time atfive different HF frequencies. Relatively nearby, butover the horizon is the newly operational first sta-tion of the Long Wavelength Array (LWA), referredto as LWA1 [Taylor et al., 2012; Ellingson et al.,2012]. The full LWA will consist of 52 stationsspread throughout the state of New Mexico designedto work as a large HF/VHF interferometer/telescopefor imaging cosmic sources [Taylor et al., 2006]. Eachstation will be a roughly 100-m wide phased array of

1

2 HELMBOLDT ET. AL: PASSIVE OTH RADAR WITH WWV AND LWA1

256 crossed-dipole antennas. The unique capabilityof LWA1 to image the entire sky rather than point atone particular location makes it a particularly flexi-ble radar receiving system. We will demonstrate thatwhen used together, LWA1 and WWV constitute apowerful OTH radar system that could potentiallyoperate continuously and relatively cheaply. We de-scribe the techniques involved (Sec. 2–3) as well asexamples of possible applications of the system (Sec.4) and future capabilities as more LWA stations areadded (Sec. 5).

2. LWA1 and WWV2.1. LWA1

LWA1 is the first station of the planned LWAwhich will consist of more than 50 similar stations,acting together as an HF/VHF, interferometric tele-scope. Like LWA1, each station will consist of 256cross-dipole antennas capable of operating between10 and 88 MHz arranged in a quasi-random pat-tern spanning roughly 100 m designed to minimizesidelobes. Each dipole antenna consists of a wire-grid “bow-tie” mounted to a central mast with armsangled downward at a roughly 45◦ angle. This de-sign maximizes sensitivity/throughput over the en-tire observable sky. For a detailed discussion ofthe antenna design, see Hicks et al. [2012]. LWA1is currently being operated as an independent tele-scope/observatory located at 34.070◦N, 107.628◦Wand is described in detail by Taylor et al. [2012]and Ellingson et al. [2012], including a descriptionof the calibration of the array using bright cosmicsources and an additional “outrigger” antenna lo-cated roughly 300 m east of the array center.

The antennas can be operated as a single phasedarray with up to four simultaneous beams. Eachbeam can use up to two tunings, each with a pass-band having up to 16 MHz of usable bandwidth. In-dependent from the beam-forming mode, LWA1 alsohas a transient buffer (TB) mode that records theindividual output from each antenna, allowing oneto beam-form to any point on the sky after the factand making all-sky imaging possible.

The TB can be operated in one of two modes. Thefirst is a wide-band mode (TBW) which captures 61.2ms of the raw signal from each antenna at a samplingrate of 196 Msps with 12 bits per sample. With thisdata, one has access to the full bandwidth accessibleby the antennas. However, since the data volume is

so large (>9 GB per capture), it takes more thanfive minutes to write each capture to disk and thuscannot be run in a continuous way. Conversely, thenarrow-band mode (TBN) tunes each antenna signalto a specified central frequency with a sampling rateof up to 100 ksps with up to 67 kHz of usable band-width. The data rate for this mode is small enoughthat it can be run continuously for up to roughly20 hours before filling the available disk space. Ex-amples of all-sky images of cosmic sources madeusing TBN data and the LWA1 Prototype All-SkyImager [PASI; Ellingson et al., 2012] can be foundat http://www.phys.unm.edu/∼lwa/lwatv.html,which is updated in near real time as data are taken.An example of an image of the entire visible sky con-structed from TBN data was also presented by Dow-ell et al. [2012].

It is the two TB modes that are particularly use-ful for passive radar applications. Because they allowfor all-sky imaging, any terrestrial transmitter whosedirect signal, ground wave, or sky wave (ionosphericreflection) is observable from LWA1 can be detectedand located with either TBW or TBN data. In caseswhere both the direct signal and the ground waveand/or sky wave are simultaneously detected (e.g., alocal FM station), the transmitter signal can be ob-tained by beam-forming toward the transmitter andthis can be used as a matched filter for obtainingranges for the ground and/or sky wave detectionsaccording to Meyer and Sahr [2004]. Alternatively,because LWA1 uses its own GPS clock to time-stampeach TB sample, a transmitter with a known pulse-like signal structure like WWV (see Sec. 2.3) can alsobe used for passive radar with good time-of-arrivalaccuracy (rms variation of about 20 ns ' 6 m).

2.2. WWV

WWV is an HF radio station that broadcasts thetime from the Ft. Collins, Colorado area (40.7◦N,105.0◦W; 770 km to the northeast of LWA1) at 2.5,5, 10, 15, and 20 MHz. It has a “sister” station inHawaii (22.0◦N, 159.8◦W), call-sign WWVH, whichbroadcasts the time at the same frequencies except20 MHz. These stations and their signal patternsare described in great detail by Nelson et al. [2005].In general, amplitude modulation of each signal isused to convey various types of information aboutthe current universal time (UT). Here, we briefly de-scribe those aspects of the WWV signals that arerelevant to passive radar.

HELMBOLDT ET. AL: PASSIVE OTH RADAR WITH WWV AND LWA1 3

The transmitters for both WWV and WWVH arerelatively powerful monopole antennas, each with anERP of 10 kW for 5, 10, and 15 MHz and 2.5 kWfor 2.5 and 20 MHz. The WWVH transmitters aredirectional with most of the power directed westwardto minimize interference with WWV. Both broadcastvoice announcements of the time at each frequency,modulated at either 500 or 600 Hz. They also broad-cast a coded signal, modulated at 100 Hz, that trans-mits the UT of the current minute. There are also oc-casionally alarm signals transmitted, which are mod-ulated at 2000 Hz.

We have found that the amplitude modulationschemes used for the main portions of the WWV sig-nals described above make for rather poor matchedfilters. Using LWA1 observations of WWV echoes(see 2.3), we have attempted to apply the WWVsignal as a matched filter to itself and found thatit produces multiple peaks at different lags, makingif difficult, if not impossible, to use the same tech-niques employed by Meyer and Sahr [2004] with FMstations for ranging. This is basically the result ofthe relatively slowly changing amplitudes of the pri-mary constituents of the continuous WWV signal,namely the main carrier, the 100-Hz time code, andthe 500/600-Hz voice announcements. For instance,within the 100-Hz time code, date bits of zero or oneare indicated using constant amplitudes over inter-vals of 200 or 500 ms, respectively. The main car-rier and voice announcements have amplitudes thatare similarly temporally stable as indicated by theirspectral profiles which are just as narrow as that ofthe 100 MHz time code (see Sec. 2.3 and Fig. 1–2).

The most useful part of both the WWV andWWVH signals for passive radar are the 5-ms pulsesemitted at the beginning of each second (except onthe 29th and 59th second of each minute). All othersignals are suppressed 10 ms before the beginning ofeach pulse to 25 ms after the end of the pulse tohelp them stand out more. WWV pulses are modu-lated at 1000 Hz, and the WWVH pulses are mod-ulated at 1200 Hz, making them distinct from oneanother. Thus, by applying the appropriate filter-ing techniques, one may isolate these pulses withinsignals received by the LWA1 antennas for differentarrival times, corresponding to different ranges.

The main drawback of using the 5-ms WWV pulsefor ranging is that it provides little practical capabil-ity for determining Doppler speeds. Normally with apulsed transmitter, one can use the pulses that have

a common time of flight as a time series that canbe Fourier transformed to map the amount of poweras a function of Doppler frequency. However, theone-second cadence of the WWV pulses implies aNyquist limit of 0.5 Hz. At 10, 15, and 20 MHz,this maximum Doppler shift corresponds to speeds of7.5, 5, and 3.75 m s−1. While there may be OTH tar-gets and ionospheric structures with Doppler speedsthis low, there will likely be many more with higherspeeds that will be aliased to lower Doppler frequen-cies by the coarse, one-second sampling, and it wouldnot be possible to distinguish between these two sce-narios. Therefore, in practice, obtaining Dopplerspeeds with the WWV pulse it not feasible.

2.3. Imaging WWV Echoes with LWA1

Since the LWA1 antennas have little if any sen-sitivity below 10 MHz, the bands where LWA1 andWWV overlap are 10, 15, and 20 MHz. Given thedistance between WWV and LWA1, 770.0 km, the di-rect signal and ground wave are not detectable fromLWA1. However, conditions in the ionosphere arenearly always such that a reflection of the 10 MHzsignal is visible, and reflections at 15 and 20 MHz aresometimes detected. In addition, ionospheric echoesof the 10 and 15 MHz WWVH signals are often vis-ible. Given the large distance to WWVH (5236.0km), these reflections are almost certainly “multi-hop” reflections, that is, they have bounced betweenthe ionosphere and the ocean/terrain several timesbefore arriving at LWA1. Relatively speaking, theWWVH signal is typically more prominent at 15MHz.

Examples of ionospheric echoes of both the WWVand WWVH signals are illustrated in Fig. 1 and 2.Fig. 1 shows an all-sky image made via total-powerbeam forming at 10 MHz with 12.0 kHz of bandwidthfrom a single TBW capture. For such images, com-plex voltages were made using an FFT of the raw sig-nals and each antenna’s voltage was multiplied by atwo-dimensional array of phasers before adding themtogether to compute the total beam-formed powerover the whole observable sky. These phasers includecorrections for cable losses, unequal cable delays, andother amplitude and phase errors measured for eachantenna using observations of bright cosmic sourcesusing the outrigger antenna mentioned in Sec. 2.1.These corrections are described in more detail byEllingson et al. [2012] and are included within theLWA Software Library [LSL; Dowell et al., 2012].


The image displayed in Fig. 1 is a combinationof the total power from the north-south and east-west dipoles, yielding the total, Stokes-I power. Forthese images, the ordinate and abscissa are the so-called l and m direction cosines, defined in this caseto be l = cos e cos a and m = cos e sin a, where e isthe elevation above the horizon and a is the azimuthmeasured clockwise from north. This projection waschosen because the LWA1 beam changes very littlewithin the l,m-plane. One should note that in thisprojection, elevation does not vary linearly with ra-dius and that a source appearing extremely close tothe horizon (i.e.,

√l2 +m2 = 1) may in fact be at a

deceptively high elevation. For instance, the strong10 MHz echo seen in the upper left of Fig. 1 is at anelevation of 27◦.

Fig. 1 also shows a time series of the amplitudeof the signal beam-formed toward the approximatecenter of the 10 MHz echo seen in the all-sky image(marked with an ×). One can clearly see the 5-msWWV pulse modulated at 100 Hz with an arrivaltime of 2.97 ms after the beginning of the second, cor-responding to a distance traveled of 890 km. Becauseeach TBW capture is set up to start at the beginningof each UT second, the 61.2 ms duration of each cap-ture is more than enough time to detect such echoesfrom either WWV or WWVH. The power spectrumof this beam-formed signal is also shown in Fig. 1.The strongest part of the signal is the main carrierat 10 MHz. One can also pick out features mentionedin the description above (labeled in red) such as the100-Hz time code, the 600-Hz voice announcement,the 1000-Hz pulse, and the 2000-Hz alarm code. Alsoshown is a shaded region one might use as a side-bandfilter to isolate the 5-ms pulse while avoiding thevoice announcement and alarm codes, which is wideenough to achieve a temporal resolution of roughly 1ms.

Fig. 2 shows the same thing as Fig. 1, but at15 MHz, highlighting a detection of an echo fromWWVH. The all-sky image shows some contributionfrom “second-hop” signals from WWV, those that re-flected off the ionosphere, then off the ocean/terrain,then back off the ionosphere to LWA1, which aredistributed around the horizon. Because of thesesecond-hop signals, the beam-formed signal shown inthe upper right panel is not as clean as that shown inFig. 1 for WWV at 10 MHz, but the 5-ms pulse is stillclearly visible. In this case, the arrival time is signifi-cantly larger, 19.8 ms (or, 5952 km), indicative of the

more distant origin in Hawaii. In addition, the pulsehas more cycles than the 10 MHz signal (six versusfive), consistent with WWVH’s pulse modulation of1200 Hz. This can be seen more clearly in the powerspectrum where the peaks from the 5-ms pulse arecentered at ±1200 Hz instead of ±1000 Hz.

3. LWA1+WWV Bistatic Radar

The examples shown in Fig. 1–2 demonstrate thepotential for using WWV and LWA1 as a relativelypowerful bistatic HF radar, capable of probing theionosphere and OTH targets using the ionosphere asa virtual mirror. Here, we describe the methods wehave developed to do just that using both TBW andTBN data.

3.1. TBW and Multi-frequency Radar

As described above, the LWA1 TBW mode offersa unique capability to make total power images fromsignals spanning the entire available frequency range,10–88 MHz, all observed simultaneously. The sacri-fice one makes for this wide-band coverage is thatone can only get 61.2 ms of data every five minutesor more. Fortunately, each TBW capture is timedto start at the beginning of each UT second, makingit possible to detect reflections from the WWV 5-mspulse within this short 61.2 ms window.

To isolate echoes of the 5-ms WWV pulse withinTBW data, we have used the following multi-stepapproach. First, the format of the data dictates thatone read in almost the entire 61.2-ms capture as partof any post-processing effort. A TBW binary datafile is broken up into frames, each consisting of 400samples from a single antenna. The frames are notorganized by antenna ID or time; they are writtenout on a kind of “first-come-first-serve” basis. Be-cause of that, all of the data for a particular antennamight be contained within the first few percent ofthe file, while for another, one may have to parse theentire file to retrieve all of its data. In addition, thispattern is different for each file [see Ellingson, 2007,for a more detailed description of the TBW system].

Because of this file structure, it is more efficient touse an FFT to filter the data for each antenna as itis read in, yielding a time series of complex voltagesfor each antenna once the whole file has been read.In practice, for each antenna, an FFT is applied ev-ery 1024 samples, and the resulting voltages for thefrequencies closest to 10, 15, and 20 MHz (9.953,


14.93, and 19.91 MHz) are saved, giving a time se-ries of 11,718 voltages for each band, each with abandwidth of 4.98 MHz.

Following this, an FFT is applied to each of thesetime series and the resulting complex spectrum is fil-tered with two side-band filters illustrated in Fig. 1.An inverse FFT is then applied to each side band toyield a new complex voltage time series with a tem-poral sampling of 1.004 ms within which the 5-mspulse appears as a square pulse rather than a sinu-soid. For each point in this time series, a total-powerbeam-formed image is made over the whole sky (seeSec. 2.3), separately for each side-band and each po-larization. These four images are then combined toform a single image cube that gives the total poweras a function of azimuth, elevation, and time of ar-rival/range.

We have used three sequences of TBW capturesto help illustrate the typical output of this com-bined radar system. These were conducted between00:05 and 13:25 UT, May 6, 2012; between 05:05 and14:05, May 7, 2012; and between 19:55 and 15:05 UT,September 30–31, 2012 as part of telescope commis-sioning efforts. Within each sequence, the captureswere spaced 10 minutes apart. Fig. 3–5 show exam-ple image cubes for 10, 15, and 20 MHz, which are thefirst frames of three electronically available moviesmade from these TBW sequences. Each frame showsthe total-power, all-sky map of the 5-ms pulse at dif-ferent times of arrival, converted to distance traveledfrom 153 to 7374 km with the horizon marked witha white circle. We note again that due to the pro-jection used to display these images (see Sec. 2.3),nearly all of the detected echoes appear as if theyare at or just above the horizon, even though thetypically elevation is actually about 10◦ and variesfrom a few degrees to as high as 40◦. We also notethat the times of flight for the detected echoes aretoo large for them to be ground waves from WWV.

The relatively poor range resolution afforded bythe width of the 5-ms pulse is evident within theseimage cubes. However, one can see that the all-skyapproach, when combined with range information,allows one to readily distinguish among the first-hop WWV signal (16◦ east of north), second-hopWWV signals at various azimuths, and the echo ofthe WWVH pulse (almost exactly due west). Onecan also see that while 10 MHz echoes are almostalways visible from both WWV and WWVH, onlyWWVH is consistently visible at 15 MHz. Echoes of

the WWV pulse are only detected some of the timeat 15 and 20 MHz. This is not entirely unexpectedgiven the large plasma frequencies and/or low anglesof incidence needed to reflect 15 and 20 MHz trans-missions between WWV and LWA1. The instanceswhere the WWV signal is seen at 15 and 20 MHzare likely related to sporadic-E (Es), which will bediscussed further below.

3.2. TBN and Continuous Radar

While the multi-frequency data available withTBW captures offers a method for sounding the iono-sphere, TBN observations allow one to monitor aparticular ionospheric region/layer (or, OTH target)at one frequency with much better temporal cov-erage (i.e., one sample per second versus one ev-ery 5 minutes or more). For those readers famil-iar with digisonde dipole arrays, in this context, theTBW and TBN modes are analogous to the digisonde“sounding” and “sky map” modes.

In principle, one may analyze TBN observationsusing the same procedure described for the TBWdata in Sec. 3.1. However, the differences in filestructures between TBW and TBN data make itmore practical to use a different but related approachwith TBN data. Since the data are already filteredin TBN mode before they are written out, what isrecorded are complex voltages rather than raw sig-nals. Typically, these are written out with a sam-pling rate of 100 ksps (16 bits per sample), but lowersampling rates are possible. TBN binary files arebroken up into frames, similar to TBW files. How-ever, within a TBN file, a frame consists of 512 sam-ples from a single antenna and the data for all an-tennas are written out together for each time stamp(although, not necessarily ordered by antenna ID).This makes it faster to read in just the time stampof each frame until the first frame closest to the nextUT second is identified. After this, due to the lowersampling rate, one can easily read all of the data forall antennas covering the next several tens of mil-liseconds into RAM, even with a modestly equippeddesktop computer (e.g., 40 ms amounts to roughly 4MB).

We found that rather than using the FFT/filter/inverse-FFT approach employed with the TBW data, it wasfaster/more efficient to apply a sliding window filterto these data as they were read in. Specifically, asthe data are read in, they are up/down converted by±1000 Hz, after which a 5-ms wide Hamming windowis applied and the data within this window are aver-


aged. The Hamming window was chosen to suppresscontributions from higher frequencies and is steppedat 1-ms intervals to give comparable temporal sam-pling to the TBW approach. This is done for thefirst 40 ms of each UT second, yielding 40 up- anddown-converted complex voltages (i.e., at the carrierfrequency ±1000 Hz) for each antenna correspondingto 40 different times of arrival for the WWV pulse.Similar to the TBW approach, the up- and down-converted voltages are imaged separately and thencombined for each time of arrival. In applying thisanalysis to actual TBN data (see below), we foundthat the time stamps in the TBN files were off by10.24 ms, a result of the time stamps being assignedafter the data had been passed through the hardwarefilters, which have a length of 1024 samples. All timesof arrival within the TBN analysis are corrected forthis effect.

As a demonstration of this method, we have used a15-minute TBN observation at 15 MHz that startedat 00 UT on September 25, 2012. This time waschosen based on the results from the TBW captures,which indicated that this is a time when 15 MHzechoes from WWV are common. The analysis de-scribed above was applied to this data-set, and wehave made a movie of the resulting image cubes avail-able electronically. Note that, as mentioned in Sec.2.2, the WWV pulse is not broadcast on the 29th and59th second of each minute, which causes a “blink-ing” effect within this movie with a cadence of about30 seconds. At these times, only the main 15 MHzcarrier and/or the voice announcements are broad-cast, so that even though echoes are detected, thearrival times are relatively meaningless without the1000-Hz-modulated pulse.

The movie shows that the first-hop signals fromWWV often have observed structure beyond a simpleunresolved, point-like source. This additional struc-ture commonly lasts for only one to a few seconds.However, there is a strong secondary echo to thesouthwest of the main echo that appears at 565 s andremains present to varying degrees for about 110 s. Aframe from the movie that prominently features thisstructure is shown in Fig. 6. This highlights the ben-efits of using the TBN mode for probing ionosphericstructure on smaller temporal scales. With TBWcaptures being spaced by a minimum of five min-utes, a sequence of TBW captures could easily missthe formation and evolution of such structures. Thesame is true for most ionosonde systems, which typ-

ically use integration times on the order of a minuteor more to boost signal-to-noise. As with the TBWcaptures, second-hop echoes are seen throughout theobservation, which vary noticeably in both strengthand location due to significantly ionospheric variabil-ity.

4. Applications

While the fixed broadcast frequencies used byWWV limit flexibility, the combination of continu-ously broadcasting, relatively high-power transmit-ters with the all-sky capability of LWA1 make thecombined passive radar system a potentially power-ful tool for exploring both ionospheric structure anda variety of OTH targets. Here, we describe exam-ples of the possible applications of the LWA1+WWVradar system.

4.1. Ionospheric Structure and its Impact onGeolocation

The movies of the image cubes made with boththe TBW and TBN data illustrate the significantamount of variability within the ionosphere as onecan see the first-hop WWV signal move noticeablyin the sky. This is likely due to density gradientsat the altitude/layer where the signals are reflected,which is one of the know limitations to geolocationprecision for operational OTH radar systems [e.g.,Headrick and Thomason, 1998].

To illustrate this, we have used the TBW data at10, 15, and 20 MHz to geolocate the WWV trans-mitters. To do this, we used a kind of center-of-masscomputation using the total power as a weight to es-timate the observed elevation, azimuth, and range ofeach TBW capture and frequency when the first-hopecho was detected (detection limits were deduced em-pirically by eye). Using this type of center-of-masscalculation also allows us to compute estimates forthe uncertainties in the sky position and range us-ing estimates of the 1σ error in the measured powerfor all the images in the cube. We did this by mea-suring the standard deviation in the center of eachimage within the cube where there are essentially noWWV or WWVH echoes. These errors were thenpropagated through the full geolocation calculationdescribed below. In each case, the computation waslimited to a rectangular region on the sky (deter-mined by eye) and ranges between 454 and 1658 km.


We then geolocated the signal assuming a virtualmirror approximation [see Headrick and Thomason,1998, and references therein]. In other words, we ap-proximated the ionosphere with a flat mirror, usingthe determined sky position and range with the lawsof cosines and sines to determine the angular sep-aration between LWA1 and the transmitter on thesurface of the Earth. While some of the final ge-olocations have relatively large errors, the typical 1σuncertainties for significant first-hop detections were0.007◦ and 0.01◦, or 0.8 and 1 km for the latitudesand longitudes, respectively.

The geolocation results are plotted in Fig. 7. Fromthese, one can immediately see that the measuredpositions contain a significant amount of scatter andare systematically off from the expected position tothe northeast (left panel). The latter is a mani-festation of a known pointing error associated withLWA1. While the source of this pointing offset iscurrently unknown, it fortunately appears to be sta-ble with time and has been well constrained usingbright cosmic sources with well-known sky coordi-nates [see Dowell and Grimes, 2012]. After apply-ing the pointing correction described by Dowell andGrimes [2012], the mean geolocated position agreesvery well with the known WWV location, within0.03◦, or 3.2 km (right panel of Fig. 7).

There is a significant amount of scatter amongthese positions with an RMS deviation from the ex-pected WWV position of about 0.13◦ or 14.6 km,more than an order of magnitude larger than thetypical measured uncertainty based on the noise inthe all-sky images. As noted above, this scatter islikely from density gradients within the ionospherethat work to invalidate the virtual mirror approxima-tion and is consistent with previous measurementsof HF bearing errors at midlatitudes [Tedd et al.,1985]. In total, there were 237 separate geolocationmeasurements, but the error in the mean position,0.03◦, is more than an order of magnitude largerthan RMS/

√N , the result one would expect if the

ionospheric errors in the positions were uncorrelated.This suggests that a significant portion of the struc-tures responsible for these position offsets span thetypical temporal/spatial scales probed by these ob-servations.

To explore these structures further, we have useda “tilted mirror” approximation, allowing for den-sity gradients in the ionosphere to act as distortionsin what would otherwise behave as a flat mirror.

We have done this by using the known positions ofLWA1 and WWV with the sky position (corrected forthe pointing error) and range of each measurementto compute the three dimensional vectors pointingfrom LWA1 to the virtual point of reflection withinthe ionosphere, ~rr, and from this point to WWV, ~rt(see Fig. 8 for a schematic representation). Specifi-cally, ~rr = rr(li+mj +

√1− l2 −m2k) where l and

m are the direction cosines described Sec. 2.3 (i.e.,the sky position measured from the image cube) andrr is simply the length of ~rr. If we define a vec-tor, ~d, that points from LWA1 to WWV such that~d = dxi+ dy j + dz k, and note that the length of thepath traveled by the signal measured from the imagecubes is given by R = rr+rt, the law of cosines yieldsthe following

rr =1

2

R2 − d2

R− (dxl + dym+ dz√

1− l2 −m2)(1)

where d2 = d2x + d2y + d2z and rt is the length of ~rt.Following this, one can compute ~rt by noting that~d = ~rr + ~rt.

After solving for both ~rr and ~rt, one can computethe virtual height, hv, of the ionospheric reflection,i.e., the height above the Earth’s surface where ~rrand ~rt intersect. The plasma frequency, fp at this lo-cation can also be estimated as fp = f cos θ/2, wheref is the observing frequency and θ is the angle be-tween ~rr and ~rt computed via the dot product oftheir associated unit vectors, rr and rt.

Fig. 9 shows what is essentially a comprehensiveionogram for all three sequences of TBW capturescolor-coded by frequency with different point stylesfor different sequences. We have also included resultscomputed using image cubes from the 15-minuteTBN observation at 15 MHz. The left panel showsvirtual height versus fp if only the secant law is used,that is, if we assume hv = (R/2) cos (90◦ − e) andfp = f cos (90◦ − e), where e is the elevation of thedetected echo. One can see that the linear featuresin this plot do not at all resemble typical ionograms.However, the right panel shows results using the fullgeometric computation detailed above, which resem-ble what one might expect for an ionogram when Esis present.

The 10 MHz data show a mixture of echoes thatprobe the general density profile during these obser-vations and those that reflected off Es layers. Thetwo are identifiable by eye in the plot and we haveseparated them empirically with a dashed line. The20 MHz data seem to consist of reflections off the


same Es layers as the 10 MHz data given that theyhave similar virtual heights (∼95 km). However, fpis higher for these echoes (5.5 versus 3 MHz), im-plying that the 10 MHz data yield something akinto fbEs (the Es “blanketing” frequency) and the20 MHz data foEs (the Es maximum reflected fre-quency), to use ionogram terminology. The 15 MHzTBW data show reflections from a somewhat higherEs layer (hv'115 km) with fp somewhat lower (∼5MHz) than what was seen at 20 MHz. The 15 MHzTBN data show evidence for an even higher Es layer(hv'125 km) with fp comparable with the 20 MHzTBW observations.

The computed vectors ~rr and ~rt also allow fora characterization of the ionospheric structure byquantifying both the magnitude and direction of theeffective tilt. Following the law of reflection, the nor-mal vector, n, the vector perpendicular to the re-flecting surface, is simply the (normalized) differencebetween rr and rt. However, this difference givesthe normal vector in a coordinate system centeredon LWA1 rather than the location of the ionosphericreflection. To remedy this, the n vector is rotatedinto a coordinate system with the latitude and lon-gitude of the virtual reflection point as the origin. Inthis coordinate system, the angle between the verti-cal axis and n and the azimuthal coordinate of n givethe magnitude and direction of the tilt, respectively.We therefore use these two quantities, tilt and tilt az-imuth (measured clockwise from north), to quantifythe observed density structures.

Fig. 10 shows the virtual height, plasma frequency,tilt, and tilt azimuth derived from the TBW data asfunctions of local time, separately for those detec-tions classified as reflecting off Es layers and thosethat did not. These use the same color-coding andpoint styles as Fig. 9. One can see that for theseTBW sequences, the 10 MHz signals are only able topenetrate above 150 km in the afternoon/evening, atabout 13:00 and between 17:00 and 21:00, local time.The 10 MHz data only seem to be affected by Es inthe late evening between 20:00 and midnight. Re-flections from Es at 15 and 20 MHz were prominentbetween 16:00 and 23:00. While the Es heights tendto be relatively stable, fp seems to increase some-what between 19:00 and 23:00. During this time pe-riod, the tilts for the Es layers become more erratic,reaching nearly 25◦, and are directed mostly to thesouth. This is comparable to the properties of denseEs “clouds,” which are known to have tilts up to 30◦

[e.g. Paul , 1990]. In general, the observed Es layersshow a larger degree of structure with tilts from afew degrees up to about 15◦ or more while the tiltsmeasured from non-Es echoes are a few degrees orless. This is consistent with tilts measured for themidlatitude ionosphere [Tedd et al., 1985] and for Es[Paul , 1990]. This is also reflected in the geolocationresults presented above; for Es echoes, the RMS de-viation from the expected WWV position is 0.24◦,or 26.5 km; for non-Es echoes, the RMS geolocationerror is 0.076◦, or 8.5 km.

For the 15-minute TBN observation at 15 MHz,we have made the same plots as in Fig. 10, but at amuch higher temporal resolution, i.e., 1-s versus 10-minutes (see Fig. 11). These show evidence of smalltime-scale variations in all four quantities. The mea-sured value for hv seem to suggest the presence oftwo main Es layers at heights of roughly 115 and135 km with plasma frequencies of about 6.2 and 5.5MHz, respectively. The higher layer has a roughly 5◦

tilt that gradually evolves from being directed east-ward at the start of the observation to northward atthe end. The lower layer seems to have a roughlynorthward-directed tilt of about 12◦ throughout theobservation. The effect of the strong secondary echoshown in Fig. 6 and discussed in Sec. 3.2 can be seennear 17:00 local time as several echoes from lower,denser Es structures appear with large (∼ 20◦) tiltsdirected toward the southwest.

4.2. OTH Terrain Mapping

As noted in Sec. 3.1 and 3.2, there are second-hopsignals observable at all three frequencies and withinboth the TBW and TBN data. Given some simpli-fying assumptions, these can potentially be used toproduce maps of HF reflectivity for the distant ter-rain and/or ocean. In order to locate the point on theterrain/ocean where the second-hop signals reflected,we are forced to make the assumption that both iono-spheric hops occurred at the same altitude. This as-sumption allows us to compute the distance traveledby the WWV signal from the reflection point on theterrain/ocean to LWA1 by simply dividing the totaltime/distance of flight in half. Then, using the im-age cubes described in Sec. 3.1 and 3.2, one can mapthe reflected HF power using a simple virtual mirrorapproximation (i.e., without tilts). The results pre-sented in Sec. 4.1 suggest that ionospheric structureand variability will introduce geolocation errors ofabout 0.13◦. We can assume that this is increased by


roughly a factor of√

2 to 0.18◦ for second-hop datasince these signals have reflected off the ionospheretwice. However, for this type of mapping exercise,this is an acceptable level of uncertainty given thatthe LWA1 beam is much larger. Specifically, the fullwidth at half maximum of the LWA1 beam at 10, 15,and 20 MHz is 15.8◦, 10.5◦, and 7.9◦, respectively.

Something that is a concern for terrain mappingand not the analysis presented in Sec. 4.1 is the effectof sidelobes associated with the LWA1 beam. Theseare apparent in all of the images presented in Fig. 1–6. Since the analysis in the previous section focussedon finding the centroid of the brightest first-hop sig-nal on the sky, these sidelobes were of little concern.However, as we attempt to map the HF reflectanceusing the detected power from several different di-rections at once, confusion from sidelobes will havea significant impact.

Within the field of radio astronomy, an effective it-erative approach has been developed to mitigate theconsequences of such sidelobes that combines decon-volution and self-calibration. However, these tech-niques have been designed to work with data from a“multiplying” rather than “adding” interferometer.In other words, they work on images made with vis-ibilities, which are correlations between all possiblepairs of antennas, or “baselines.” For a baseline withantennas i and j, Vi,j =

⟨εiε

∗j

⟩, where V is the vis-

ibility, ε is the complex voltage, and the average isperformed over a fixed time interval. Images madewith such visibilities are equivalent to total-powerbeam-formed images, but with a constant “DC” termsubtracted.

Specifically, the intensity on the sky is related tothe visibilities by the following

I(l,m) =

∫∫∫V (u, v, w)e2πi(ul+vm+nw)du dv dw

(2)

where l and m are direction cosines for a particularpart of the sky (i.e., not necessarily the zenith as wehave used here), n =

√1− l2 −m2, and the baseline

coordinates, u, v, and w are the differences betweenthe positions of the two antennas of the baseline in acoordinate system such that w points toward the ob-servation field center, u points eastward, and v pointsnorthward.

Typically, visibilities are “fringe-stopped” by mul-tiplying them by exp(−2πiw), so that for a small fieldof view (i.e., n≈ 1), the w term can be ignored be-

cause n− 1'0. In this case, the image can be madeby gridding the visibilities in the u,v-plane and per-forming a two-dimensional FFT. For our LWA1 ob-servations, the field of view is far from small. How-ever, because the LWA1 antennas lie nearly withina plane and we have defined the field center of ourimages at zenith, the w term is still small in our case(i.e., w ' 0). In addition, as one can see from Fig.1–6, all of the detected WWV echoes are near thehorizon where n ' 0. Thus, by not fringe-stoppingour computed visibilities, we effectively make the nwterm in equation (2) negligible and can used a stan-dard FFT-based imager with our LWA1+WWV vis-ibilities.

The scheme used to reduce sidelobe confusionwithin FFT-based visibility imaging is as follows.After the data are initially calibrated, an image ismade and a deconvolution algorithm is applied. Themost commonly used algorithm is clean [see Cornwellet al., 1999], which models the image with a seriesof delta functions, called “clean components,” con-volved with the impulse response of the interferome-ter, or “dirty beam.” The locations of the clean com-ponents are determined iteratively by placing one atthe location of the pixel with the largest absolutevalue and subtracting a scaled version of the dirtybeam at that location at each iteration. This pro-cess is usually terminated at the first iteration whenthe pixel with the largest absolute value is actuallynegative. After this, the clean components are con-volved with a Gaussian beam with a width similarto the main lobe of the dirty beam and added backto the residual image.

Following the application of the clean algorithm,the clean components are used as a model of theintensity on the sky to refine the visibility calibra-tion. Within this self-calibration process, antenna-based phase corrections are solved for using a non-linear fit (usually, a gradient search). Because anarray with N elements has N(N − 1)/2 unique base-lines, this is generally an overly constrained problem,e.g., for LWA1, one has to solve for 256 phase cor-rections using 32,640 baselines. Amplitude correc-tions can also be solved for within this process, butit is usually safer to use phase-only self-calibrationto avoid biasing the calibration toward the loca-tions of the clean components. After applying theresulting calibration, the visibilities are re-imagedand clean is run again. Because of improvements inimage fidelity made possible by the self-calibration-determined phase corrections, subsequent applica-


tions of clean are able to mitigate the effect of side-lobes to a greater degree. After cleaning, one can re-peat self-calibration with the new clean-componentmodel and continue to iterate until the process con-verges.

To apply these techniques to the TBW and TBNdata, visibilities were computed by correlating thecomplex voltages for each time of arrival over theentire observing period. Visibilities for both polar-izations and both side-bands (i.e., carrier frequency±1000 Hz) were averaged together. For the TBWdata, the correlations were computed using all TBWcaptures and for the TBN data, the entire 15-minuteobservation was used. This was done separately foreach frequency. For each time of arrival and fre-quency, the visibilities were imaged with three itera-tions of clean and self-calibration. Additional itera-tions did not significantly change the appearance ofthe images produced.

The final cleaned images from the TBW data ateach frequency and time of arrival are displayed inFig. 12. For the purposes of terrain mapping, onlytimes of arrival corresponding to travel distances be-tween 1958 and 4666 km were used to minimize con-tamination by first-hop WWV signals and echoes ofWWVH. Similar images were made from the TBNdata, but are not shown here. In Fig. 12, the horizonis indicated in each panel with a grey circle. Onecan see that sidelobes have been effectively elimi-nated, particularly around bright echoes. It is alsoapparent that despite the narrow range in time ofarrival used, contamination from WWVH and first-hop WWV echoes is still an issue. For the analysisto follow, polygon regions were drawn by eye aroundthe first-hop WWV echoes at 10, 15, and 20 MHzand around the WWVH echoes at 10 and 15 MHz(recall, WWVH does not broadcast at 20 MHz) toexclude those regions from the terrain mapping pro-cess; they are shown in white in Fig. 12. The originof the strong source significantly beyond the horizonto the east in the 15 MHz is not entirely clear. How-ever, it seems likely that since its strength roughlycorrelates with the WWVH echo that it is an aliasedversion of WWVH introduced by our FFT-based im-ager.

Within each truncated image cube (i.e., onlyranges between 1958 and 4666 km), the sky posi-tion and range of each cubic pixel was used to com-pute a latitude and longitude, using the assumptionsdetailed above. The pixels where then binned into

a latitude and longitude grid, and the mean powerwithin each grid cell was computed to produce powermaps for each frequency. These are shown in Fig. 13for the TBW data and in Fig. 14 for the TBN data.For all maps, the regions excluded due to contami-nation by first-hop WWV echoes are shaded in greyas are the WWVH-excluded regions for the 10 and15 MHz maps.

One can see that while the 5-ms width of theWWV pulse limits the resolution in the directionradially away from LWA1, there are many distinctfeatures visible. One of the most striking is a strongsignal originating from the Gulf of Mexico which isapparent in the 10 and 20 MHz TBW maps, butnot in either 15 MHz map. This could be indicativeof Bragg scattering from waves in that region withspacings of about 7.5 m. Such waves would produceBragg scattering at wavelengths of 15 and 30 m (20and 10 MHz), but not at 20 m (15 MHz).

There is a strong feature originating from the Pa-cific Ocean to the southwest of the Baja Peninsulawithin all of the TBW-based maps. The superior az-imuthal resolution of the 20 MHz map shows thatthis feature may consist of two or more Bragg lines.What is likely a similarly strong Bragg line is seennear the Oregon coast in all the TBW maps. Theseare not seen in the 15 MHz TBN map. The 20 MHzmap also shows evidence of substantial reflectionsfrom the Pacific Ocean west of California that werenot observable at 10 and 15 MHz because of contam-ination from WWVH echoes.

Both 15 MHz maps as well as the 20 MHzTBW map show strong reflections from the mid-western and plains states, stretching from Min-nesota/Wisconsin to eastern Texas. This is likelydue to the general lack of rough or mountainous ter-rain in these regions that would tend to scatter anyincident HF signals.

5. Discussion and Conclusions

We have demonstrated that using existing tech-nologies, developed and operated for other purposes,it is possible to construct a relatively powerful, pas-sive OTH radar system. Using the first of many sta-tions of the LWA to observe echoes from the NISTstation WWV, we have shown that one can probeand monitor ionospheric structure, map HF reflec-tivity of land and sea over a large area, and poten-tially track OTH targets. The all-sky capability ofLWA1 allows us to locate and track both single-hop


and multi-hop echoes from WWV in any directionduring a variety of ionospheric conditions.

Using preliminary commissioning data, we havebeen able to demonstrate the impact ionosphericphenomena such as sporadic-E may have on OTH ge-olocation precision. We have shown that that struc-tures associated with the detected Es layers persistin time and space such that averaging over many,relatively closely spaced observations does not im-prove geolocation accuracy as much as one may ex-pect (i.e., by a factor of

√N). As more LWA stations

are added, continued observations of WWV will al-low us to establish a kind of coherence scale length,the separation beyond which ionospheric structuresof a given type are uncorrelated. Beyond this scale,the geolocation errors added by different parts of theionosphere will likewise be uncorrelated such thatone may achieve a

√N improvement in accuracy

by averaging the results from N stations indepen-dently observing the same OTH signal and spaceda minimum of the coherence length apart from oneanother. For example, by using 10 stations spacedin this manner, the RMS geolocation error reportedhere of 14.6 km would be reduced to 4.6 km andwould be achieved in real-time (i.e., by averaging overspace rather than time).

In light of the results presented here, having manyLWA stations observing WWV would also be a pow-erful probe of ionospheric structure, especially withinEs layers. The techniques described here and else-where [e.g. Paul , 1990] allow one to estimate theionospheric tilt at a particular location within theionosphere. Having multiple stations with indepen-dent lines of sight capable of observing simultane-ously at 10, 15, and 20 MHz will allow for detailedthree-dimensional maps of Es layer structure, whichcan be monitored as a function of time.

The ocean/terrain mapping capability of this sys-tem will also be enhanced with multiple stations byimproving sensitivity and location accuracy. Thismay be important for possible real-time applicationssuch as monitoring wave activity and currents si-multaneously in the Gulf of Mexico and the PacificOcean via Bragg scatter of the HF signals.

Acknowledgments. The authors would like tothank F. Schinzel and T. Pedersen for useful commentsand suggestions. Basic research in astronomy at theNaval Research Laboratory is supported by 6.1 base fund-ing. Construction of the LWA has been supported bythe Office of Naval Research under Contract N00014-07-C=0147. Support for operations and continuing develop-ment of the LWA1 is provided by the National Science

Foundation under grand AST-1139974 of the UniversityRadio Observatory program. Part of this research wascarried out at the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, under a contract with the Na-tional Aeronautics and Space Administration.

References

Cornwell, T., R. Braun, and D. S. Briggs (1999), Decon-volution, in Synthesis Imaging in Radio Astronomy II,ASP Conference Ser., vol. 180, edited by G. B. Taylor,C. L. Carilli, and R. A. Perley, pp. 151–170, ASP, SanFrancisco, Calif.

Cornwell, T. and E. B. Fomalont (1999), Self-Calibration,in Synthesis Imaging in Radio Astronomy II, ASPConference Ser., vol. 180, edited by G. B. Taylor, C.L. Carilli, and R. A. Perley, pp. 187–199, ASP, SanFrancisco, Calif.

Dowell, J., D. Wood, K. Stovall, P. S. Ray, T. Clarke,G. Taylor (2012), The Long Wavelength Array Soft-ware Library, J. Astro. Inst., 1, id. 1250006, doi:10.1142/S2251171712500067

Dowell, J. and C. Grimes (2012), LWA1 Pointing Errorand Correction, Long Wavelength Array Memo 194,Oct. 2, 2012 http://www.ece.vt.edu/swe/lwa/

Ellingson, S. W. (2007), Transient Buffer -Wideband (TBW) Preliminary Design, LongWavelength Array Memo 109, Nov. 11, 2007http://www.ece.vt.edu/swe/lwa/

Ellingson, S. W., et al. (2012), The LWA1 Ra-dio Telescope, IEEE Trans. Ant. Prop., submitted,Long Wavelength Array Memo 186, Aug. 22, 2012http://www.ece.vt.edu/swe/lwa/

Headrick, J. M., and J. F. Thomason (1998), Applica-tions of high-frequency radar, Rad. Sci., 33, 1405–1054

Hicks, B. C., et al. (2012), A Wide-Band, Active AntennaSystem for Long Wavelength Radio Astronomy, Pub.Ast. Soc. Pac., 124, 1090–1104

Meyer, M. G. and J. D. Sahr (2004), Rad. Sci., 39, 39,RS3008, doi:10.1029/2003RS002985

Nelson, G. K., M. A. Lombardi, and D. T. Okayama(2005), NIST Time and Frequency Radio Stations:WWV, WWVH, and WWVB, National Institute ofStandards and Technology Special Publication 250-67

Paul, A. K. (1990), On the variability of sporadic E, Rad.Sci., 25, 49–60

Taylor, G. B., et al. (2012), First Light for the First Sta-tion of the Long Wavelength Array, J. Astro. Inst., 1,id. 1250004, doi: 10.1142/S2251171712500043

Taylor, G. B., et al. (2006), LWA Overview,Long Wavelength Array Memo 194, Oct. 2, 2012http://www.ece.vt.edu/swe/lwa/

Tedd, B. L., H. J. Strangeways, and T. B. Jones (1985),Systematic ionospheric electron density tilts (SITs) atmid-latitudes and their associated HF bearing errors,J. Atmos. Terr. Phys., 47, 1085–1097

J. F. Helmboldt, US Naval Research Laboratory, Code7213, 4555 Overlook Ave. SW, Washington, DC 20375([email protected])

(Received .)



1.0 0.5 0.0 0.5 1.0

direction cosine (radians) EAST →

1.0

0.5

0.0

0.5

1.0

dir

ect

ion c

osi

ne (

radia

ns)

Nort

h →

WWV at 10 MHz

0.0 0.2 0.4 0.6 0.8 1.0power / max. power

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20

time past nearest UT second (ms)

5

10

15

20

25

30

35

40

beam

-form

ed s

ignal am

plit

ude (

arb

. unit

s) R=890 km

3000 2000 1000 0 1000 2000 3000frequency - 10 MHz (Hz)

40

30

20

10

0

10

20

30

spect

ral pow

er

(dB

; arb

. unit

s)

time code

voice announcement

5-ms pulse

alarm

Figure 1. An all-sky image made at 10 MHz from asingle TBW capture (see Sec. 2) showing the ionosphericecho of WWV (upper left), the amplitude of the beam-formed signal toward the center of the echo marked withan × in the image to the left (upper right), and the powerspectrum of the beam-formed signal (lower) with greyshaded regions representing the filter used to isolate the5-ms, on-the-second pulse.


1.0 0.5 0.0 0.5 1.0

direction cosine (radians) EAST →

1.0

0.5

0.0

0.5

1.0

dir

ect

ion c

osi

ne (

radia

ns)

Nort

h →

WWVH at 15 MHz

0.0 0.2 0.4 0.6 0.8 1.0power / max. power

0.0

0.2

0.4

0.6

0.8

1.0

15 20 25 30 35

time past nearest UT second (ms)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

beam

-form

ed s

ignal am

plit

ude (

arb

. unit

s)

R=5952 km

3000 2000 1000 0 1000 2000 3000frequency - 15 MHz (Hz)

60

50

40

30

20

10

0

spect

ral pow

er

(dB

; arb

. unit

s)

time codevoice announcement

5-ms pulse

Figure 2. The same as Fig. 1, but at 15 MHz, showingthe detection of an echo from WWVH using the sameTBW capture.


Figure 3. An example of an all-sky/range image cubefrom the 10 MHz WWV signal with a single TBW cap-ture. The white circle indicates the horizon/field of re-gard. This is the first frame of a movie of three separatesequences of such captures, which is available electroni-cally.


Figure 4. The same as Fig. 3, but using the 15 MHzsignal from the same TBW capture. This is also thefirst frame of a movie of three separate sequences of suchcaptures, which is available electronically.


Figure 5. The same as Fig. 3, but using the 20 MHzsignal from the same TBW capture. This is also thefirst frame of a movie of three separate sequences of suchcaptures, which is available electronically.


Figure 6. An all-sky/time-of-arrival image cube fromone second of a 15-minute TBN observation at 15 MHzstarting at 00 UT on 25 Sep. 2012. As in Fig. 3–5, thewhite circle indicates the horizon/field of regard. This isa frame from a movie (roughly 2/3 from the beginning)that covers the entire 15 minute TBN observation andwhich is available electronically.


106.0 105.5 105.0 104.5 104.0 103.5

longitude

39.6

39.8

40.0

40.2

40.4

40.6

40.8

41.0

lati

tude

no pointing correction; separation = 0.14◦, 15.9 km

10 MHz15 MHz20 MHzWWVweighted mean

106.0 105.5 105.0 104.5 104.0 103.5

longitude

39.6

39.8

40.0

40.2

40.4

40.6

40.8

41.0

lati

tude

with pointing correction; separation = 0.03◦, 3.2 km

10 MHz15 MHz20 MHzWWVweighted mean

Figure 7. Geolocation of the WWV transmitter(s) usingdetections of echoes at 10, 15, and 20 MHz from TBWcaptures using a standard virtual mirror approximation.The two panels show the results before (left) and after(right) the LWA1 pointing correction was applied (seeSec. 4.1).


LWA1 WWV

ionospheric layer

!rr!rt

!d

n

!"

hv

Figure 8. A schematic representation (not to scale)of the vector computations used to locate the point ofreflection in a tilted virtual mirror approximation. Thevector notations are described along with the calculationsin Sec. 4.1.


1 2 3 4 5 6 7 8inferred fp (MHz)

50

100

150

200

250

300

350

infe

rred v

irtu

al heig

ht

(km

)

06-MAY-2012, TBW07-MAY-2012, TBW30-JUL-2012, TBW25-SEP-2012, TBN

secant law

1 2 3 4 5 6 7 8inferred fp (MHz)

50

100

150

200

250

300

350 10 MHz15 MHz20 MHz

empirical ES limit

full geometry

Figure 9. Using all TBW and TBN observations, re-constructed ionograms, using a virtual mirror approxi-mation. The left panel shows the result when only thesecant law is assumed, and the right panel displays thecomputed parameters when the full geometry is takeninto account, allowing for tilts within the virtual mir-ror approximation. Point styles indicate which data weretaken from which dates/observing modes (see upper leftcorner of the left panel) and colors indicate observingfrequency (see upper left corner of the right panel). Theempirical separation between sporadic-E (Es) and thegeneral ionospheric density profile is shown with a dashedline in the right panel.


0 5 10 15 208090

100110120130140

vir

tual heig

ht

(km

) sporadic-E; TBW

0 5 10 15 20

100

150

200

250

300

350non-sporadic-E; TBW

0 5 10 15 202

3

4

5

6

7

f p (

MH

z)

0 5 10 15 202

3

4

5

6

7

0 5 10 15 200

5

10

15

20

25

tilt

(◦)

0 5 10 15 200

5

10

15

20

25

0 5 10 15 20local time (hours)

150100

500

50100150

tilt

azi

muth

(◦)

0 5 10 15 20local time (hours)

150100

500

50100150

Figure 10. From TBW observations, the derived virtualheight, plasma frequency, east-west tilt (derivative of alti-tude with respect to east-west distance), and north-southtilt (derivative of altitude with respect to north-southdistance) as functions of local time. Results for data des-ignated as Es (see Sec. 4.1 and Fig. 9) are shown on theleft; those resulting from the general ionospheric densityprofile (10 MHz only) are shown on the right. The pointstyles and color-coding are the same as were used in Fig.9.


16.85 16.90 16.95 17.00 17.05100105110115120125130135140145

vir

tual heig

ht

(km

) sporadic-E; TBN

16.85 16.90 16.95 17.00 17.055.0

5.5

6.0

6.5

7.0

f p (

MH

z)

16.85 16.90 16.95 17.00 17.050

5

10

15

20

25

tilt

(◦)

16.85 16.90 16.95 17.00 17.05local time (hours)

150100

500

50100150

tilt

azi

muth

(◦)

Figure 11. The same as Fig. 10, but for the 15-minute,15 MHz TBN observation conducted on 25 Sep. 2012.For this observation, all the reflections were from Es, aswas the case for the 15 MHz TBW observations. Thepoint style and color-coding is the same as was used inFig. 9.


1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4666 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4366 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4065 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=3764 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=3463 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0

dir

ect

ion c

osi

ne (

radia

ns)

Nort

h →

R=3162 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2861 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2560 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2259 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=1958 km

10 MHz

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4666 km

direction cosine (radians) East →

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4366 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4065 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=3764 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=3463 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=3162 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2861 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2560 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2259 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=1958 km

15 MHz

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4666 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4366 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=4065 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=3764 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=3463 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=3162 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2861 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2560 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=2259 km

1.0 0.5 0.0 0.5 1.0

1.0

0.5

0.0

0.5

1.0R=1958 km

20 MHz

0.00 0.01 0.02 0.03 0.04 0.05

amplitude / max. amplitude

0.0

0.2

0.4

0.6

0.8

1.0

0.000 0.002 0.004 0.006 0.008 0.010


0.0

0.2

0.4

0.6

0.8

1.0

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030


0.0

0.2

0.4

0.6

0.8

1.0

Figure 12. Average all-sky images from all TBW cap-tures at 10, 15, and 20 MHz for ranges consistent withsecond-hop signals from WWV, i.e., too large to be first-hop signals and too small to be from WWVH. Regionsused to exclude contamination by first-hop WWV sig-nals and echoes from WWVH from terrain mapping areshown with white polygons.


130 120 110 100 9015

20

25

30

35

40

45

50

lati

tude

10 MHz; TBW

0.000

0.006

0.012

0.018

0.024

0.030

0.036

0.042

0.048

am

plit

ude /

1st

-hop a

mplit

ude

130 120 110 100 9015

20

25

30

35

40

45

50

lati

tude

15 MHz; TBW

0.0000

0.0015

0.0030

0.0045

0.0060

0.0075

0.0090

0.0105

am

plit

ude /

1st

-hop a

mplit

ude

130 120 110 100 90longitude

15

20

25

30

35

40

45

50

lati

tude

20 MHz; TBW

0.0000

0.0004

0.0008

0.0012

0.0016

0.0020

0.0024

0.0028

0.0032

am

plit

ude /

1st

-hop a

mplit

ude

Figure 13. Terrain maps made from the TBW-basedimages shown in Fig. 12. Regions excluded to mini-mize contamination by first-hop WWV signals and echoesfrom WWVH are flagged in light grey.


130 120 110 100 90longitude

15

20

25

30

35

40

45

50

lati

tude

15 MHz; TBN

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

am

plit

ude /

1st

-hop a

mplit

ude

Figure 14. The same as Fig. 13, but for the 15-minute, 15 MHz TBN observation conducted on 25 Sep. 2012.

Documents

Passive over-the-horizon radar with WWV and the …lwa/pubs/wwv_radar.pdfHELMBOLDT ET. AL: PASSIVE OTH RADAR WITH WWV AND LWA1 3 The transmitters for both WWV and WWVH are relatively