# Lightning Interferometry with the Long Wavelength Array
## 2 Methods  
### Data  
The LWA-SV consists of 255 dual horizontally polarized VHF antennas arranged in an array of roughly 100 m diameter, located at the Sevilleta National Wildlife Refuge in La Joya, New Mexico. In addition to the 255 primary antennas, there is a single out-trigger antenna (for 256 total antennas) located approximately 300 m west of the center of the array. Each antenna has an operating bandwidth of 3-88 MHz and a well-characterized gain pattern, which is maximum at the zenith and minimum at the horizon. The LWA-SV includes a number of transient buffer data collection modes. None of the collection modes are ideal for lightning studies, as the LWA is not capable of recording the raw time-domain signals from all antennas for the duration of a lightning flash. However, the transient buffer frequency domain (TBF), while imperfect, was designed with lightning observations in mind. In this mode, signals from both polarizations of all 256 antennas are continuously sampled at 204.8 MS/s and 8 bits. The data are then converted to the frequency domain with an 8192 sample (40 \(\upmu\)s) FFT on the acquisition board. Up to 1584 complex amplitudes (covering 39.6 MHz of bandwidth) can be transferred as 8-bit complex numbers in a 5 s circular buffer. The signals from a subset of the antennas are used to generate a trigger signal for the array. On triggering, an arbitrary pre- and post-triggerlength is then written to disk for later analysis. Although the TBF buffer is approximately 5 s in size, the system takes approximately 3 min to rearm for every 1 s of data recorded and is not capable of back-to-back triggers. The initial acquisitions presented herein were thus limited to \(\leq\)250 ms in duration to maximize the likelihood of a nearby lightning capture. Images can be formed directly from the frequency domain observations recorded in the transient buffer, but these images will be limited to the time resolution of the FFT (40 \(\upmu\)s). For lightning observations, a much higher time resolution is desired. To achieve this, the frequency domain observations for each 40 \(\upmu\)s window are converted back into the time domain using an inverse FFT for each antenna. After the entire time series record for an antenna is reconstructed, a filter is applied to correct the frequency-dependent and sub-sample portion of cable delay, as well as the variations in the stand heights of the antennas. The resulting time series are then stored to a file for later use and imaging, with the added benefit that the time series data can be partitioned into arbitrary integration periods. The integration periods used for imaging still need to meet the Nyquist criterion and so should be longer than 25 ns. An example time series from one antenna is shown in Figure 1c as a histogram, with the coloration showing the density of time-amplitude pairs. Depicting the time series in this way allows both the peak and the mean behavior to be seen. At the time of the flash, no other supporting observations were available at the site. Figure 1d shows the nearest available electric field change record, which was provided by the Earth Networks Total Lightning Network (ENTLN) sensor in Los Lunas, 50.9 km to the north. There is good correspondence between the pulses detected by the ENTLN sensor and the VHF data recorded by the LWA, consistent with the known time-keeping accuracy of the LWA-SV of 100 ns. Figure 1: (**a**) Interferometric map of the lightning flash shown on the image plane (direction cosines), colored by time. (**b**) Time–elevation angle plot of the interferometric map of the lightning flash, with the same coloring as panel (**a**). (**c**) VHF waveform recorded by one of the LWA antennas; color represents the density of time–amplitude pairs in the VHF data. (**d**) Electric field change signal recorded by an ENTLN sensor 50.9 km north of the Sevilleta site (timing corrected for propagation delay). Blue circle markers on panels (**a**,**d**) show direction to and time of ENTLN IC pulses located for the flash.