Time resolved 3D interferometric imaging of a section of a negative leader with LOFAR

We have developed a three dimensional interferometric beamforming technique for imaging lightning flashes using very-high frequency (VHF) radio data recorded from several hundred antennas with baselines up to 100 km as offered by the Low Frequency Array. The long baselines allow us to distinguish fine structures on the scale of meters, while the large number of antennas allow us to observe processes that radiate at the same intensity as the background when using a time resolution that is close to the impulse-response time of the system, 100 ns. The new beamforming imaging technique is complementary to our existing impulsive imaging technique. We apply this new tool to the imaging of four stepped negative leaders in two flashes. For one flash, we observe the dynamics of corona bursts that are emitted in the stepping process. Additionally, we show that the intensity emitted in VHF during the stepping process follows a power law over 4 orders of magnitude in intensity for four leaders in two different lightning storms.

Figure 1

Layout of the Dutch LOFAR stations. The core of LOFAR is indicated by the red $⨁$ sign, while the yellow stars show the general location of flashes A and B that are discussed in this work. The black frame indicates the general area ($140\times 140{\mathrm{km}}^2$) where flashes can be mapped accurately and is centered at the LOFAR core. Stations marked in red are not included in TRI-D imaging (see text).

Figure 2

A typical interferometer image for flash B (for an integration time of $5\mu \mathrm{s}$). The axes show the grid in voxel number where (0, 0, 0) is the center voxel in the image cube. Both images are made for a thin (one voxel thick) section through the center voxel. To show the general features of the intensity plot, the hypercube is chosen such that the maximum intensity is at the center voxel, which generally is not the case. The typical length scale for $d\varphi$ and $d{\theta }_e$ is about 1 m. The intensity unit (gb) is explained in Sec. 2c.

Figure 3

A comparison of the images for section “NL-B1” from a negative leader of flash B (see Table 1) as obtained by the impulsive imager [panels (a)] and the TRI-D imager [panels (b)] using the X dipoles from LOFAR. The boxes on the right indicate the enlarged volume for Fig. 4.

Figure 4

Side a shows an enlargement on a section of the negative leader shown in Fig. 3. The sources found by the impulsive imager (44 sources) are indicated by black open circles and in color those from TRI-D with a $I>30\mathrm{gb}$ (99 sources). The arrow indicates the radial direction and points to the core of LOFAR. Side (b) shows an even further enlargement on one particular burst, corresponding to the rectangular boxes in (a), as imaged using TRI-D with an intensity threshold of $I>0.3\mathrm{gb}$ showing 153 sources. In light (darker) grey the more intense TRI-D sources are shown that fall after (before) the time frame of the plot. The area of the circles is proportional to the intensity for the colored strong sources.

Figure 5

Distribution of source intensities (see text for further explanation) for the four negative leaders sections given in Table 1. The analysis shown is using the Y dipoles only. A power-law dependence is shown to guide the eye.