Distinguishing features of high altitude negative leaders as observed with LOFAR

We present high resolution observations of negative leaders at high altitude using the LOFAR radio telescope. We show that the structure of negative leaders at high altitude (altitudes larger than 7 km) differs in several respects from that of negative leaders at lower altitudes. In particular, the High Altitude Negative Leaders (HANLs) show very distinct steps of a few hundred meters, stepping times of the order of a few milliseconds and a filamentary structure that extends outward over several hundreds of meters; as opposed to lower altitude ( ≲ 5 km) leaders, which have stepping times and distances around 0.01 ms and 10 m. Similar to lower altitude leaders, high altitude leaders emit copious VHF radiation from their propagating tip and have propagation velocities of the order of 10 5 m/s. Corona-flash like bursts can be distinguished when zooming in to meter and nanosecond scales.


Introduction
Lightning is a well known process that, however, harbors much poorly understood physics. Being an electric phenomenon, a lightning discharge proceeds with positively and negatively charged channels in the atmosphere, called leaders, that are rather hot and reasonably conducting (Dwyer and Uman, 2014;da Silva et al., 2019). It is well known from early streak camera observations that positive leaders propagate (or grow) in a rather continuous fashion while the negative leaders, which are the prime subject of this work, usually propagate in discrete jumps, called steps (Dwyer and Uman, 2014). The physics picture behind this observed stepping process in lightning is still not clear because detailed in-situ observations are difficult.
It has been observed that the structure of lightning stepping depends on the altitude, and thus on air pressure. (Wu et al., 2015) reported that the stepped leaders propagate faster at lower altitudes. At lower altitudes (Lyu et al., 2016) finds a stepping length that seems much larger than what has been found in (Hare et al., 2019). This may be related to the better resolving power of the observations presented in (Hare et al., 2019). In addition (Lyu et al., 2016) as well as (Wu et al., 2015) focussed their work on the initial part of the leaders in contrast to (Hare et al., 2019) where the leaders after the initial stage were considered.
Using the Dutch stations of LOFAR, it has become possible to make high resolution (in space and time) images of lightning flashes using radio waves (in the 30-80 MHz band) for which clouds are transparent. In this work we report on observations of High Altitude Negative Leaders (HANL) that show a structure that is markedly different from negative leaders at lower altitudes. We present an initial survey of the structure of the HANL, which we recognize in all negative leaders at altitudes in excess of 7 km. They distinguish themselves from normal, lower altitude, negative leaders by a very dense envelope of a long (sometimes 300 m) filamentary structure. In addition, probably related to the lengths of the filaments, we observe a stepping length that is an order of magnitude longer than that for lower altitude negative leaders. Since the stepping time is an order of magnitude larger too, the propagation speed is very similar to that of negative leaders at lower altitudes (which we label as 'normal'). The long stepping length combined with the resolution that can be achieved with LOFAR allows us to resolve the fine detailed dynamics of this stepping process in natural lightning. It is Interesting to note that (Lyu et al., 2016) observed similar stepping lengths and times for higher altitude leaders as are found in this work.
Long streamer structures on negative leaders have been observed before. In  photographic images are shown of such a high altitude negative leader as it exits a cloud. These observation show rather long and dense clusters of streamers that appear to be very similar to what we have observed in radio.
Most of the flashes we have observed with LOFAR ( (Hare et al., 2019;Scholten et al., 2021a;Hare et al., 2020;Scholten et al., 2021b)) show initiation at a height of 4-5 km with positive leaders at higher altitudes (up to about 8 km) and negative leaders below. In three flashes (out of over 20 that were analyzed) we observe negative leaders at altitudes above 7 km and all (six in total) show very similar features.

Methods
Our Lightning imaging procedure uses the time-traces recorded with LOFAR (van Haarlem et al., 2013), a radio telescope primarily used for astronomy, that combines the signals in the frequency range from 10 to 240 MHz from thousands of antennas distributed over a large part of Europe. For this work we limit ourselves to the Dutch portion of this telescope that contains the core and remote stations up to 70 km from the core, see Appendix A and use the 30-80 MHz band.
A lightning flash is imaged by locating the sources that emit VHFpulses. From the (interferometric) cross-correlations between small sections of the time-traces for different antennas with that for a reference antenna, we obtain arrival time differences for a pulse from the same VHF-source. From these arrival time differences for 100-400 antennas we 'locate' the position and time of the impulsive point source by triangulation. The total of all these sources make the 4D (space & time) image of the flash (see (Scholten et al., 2021a) for a more in-depth discussion of the procedure). Since we search for the maxima in the cross correlations between the signals in antenna pairs one may also regard our procedure for locating the sources as finding the most likely position (in 3D) of the interferometric maximum for a short (100 ns long) section of the time trace containing impulsive emission from a VHF-source.
The basic technique of determining arrival time differences from the cross correlation of signals in different antennas is used rather broadly for systems with a small (less than 10) number of antennas and baselines of the order of hundreds of meters, see (Rhodes et al., 1994;Shao et al., 1995;Kawasaki et al., 2000;Dong et al., 2001;Qiu et al., 2009;Yoshida et al., 2010;Akita et al., 2010;Sun et al., 2013;Akita et al., 2014;Stock et al., 2014;Liu et al., 2018). With LOFAR, we typically use a few hundreds of antennas and baselines of up to 100 km. This allows us to reach the unprecedented accuracy of a few meters in VHF imaging Scholten et al., 2021a).

Analysis
We observed that negative leaders at high altitudes have a structure that differs considerably from that of normal negative leaders observed at low altitude . Scanning through all our fully imaged flashes we found such a structure in only three from a total of more than twenty imaged flashes, and these negative leaders all occurred an altitudes higher than 7 km. No normal negative leaders have been observed at these altitudes. We therefore name them High Altitude Negative Leaders (HANLs), although it should be noted that the compelling evidence is not a proof that the observed features are indeed directly linked to the altitude of the leaders. The three flashes were recorded on September 21, 2018 at 19:42:59 UTC (Flash A, showing 1 HANL) and two on August 14, 2020, Flash B at 14:14:58 UTC (showing 3 HANLs) and Flash C at 14:32:41 UTC (also showing 3 HANLs). In this work we focus on flashes A and B. Flash C shows similar features. The complete images for each of these three flashes is given in Appendix A. The weather map for flash A can be seen at (KNMI, 2018) and that for the 2020 flashes at (KNMI, 2020).
A typical example of such a HANL is shown in Fig. 1, where it is compared to a negative leader seen in the same flash (Flash B) at a lower altitude. It is immediately clear that they are rather different. Compared to normal negative leaders we observe at lower altitudes, typically below 6 km, HANLs.
• have a much larger lateral spread, of the order of 100 m or more while normal negative leaders show a lateral spread of the order of 10 m. The sub-structure seen in a HANL is elaborated upon in the following section while in Section 3.2 the transition from a normal negative leader to a HANL is discussed.
HANLs have some properties that are very similar to those of normal negative leaders that distinguishes them from positive leaders or dart leaders such as: • impulsive activity at the propagating tip only, as opposed to positive leaders that show impulsive VHF emission in twinkles along most of their length (Hare et al., 2019). • propagate at typical speeds of order 10 5 m/s as opposed to recoil leaders that propagate one order of magnitude faster. • have a conductive core that is (sometimes) made visible by recoil leaders.
Most of these properties are immediately clear from Fig. 1. The HANL covers a distance of 3 km in 60 ms and thus propagates with 0.5 × 10 5 m/s while the right shows a recoil leader propagating with 0.6 × 10 6 m/ s followed at t = 220 ms by a negative leader propagating at 0.7 × 10 5 m/s. This speed is typical for all HANLs we have observed. The recoil leader passed through a channel that supported earlier recoil leaders at t = 70 ms and at t = 150 ms as seen in Fig. A.7, left.
We observe recoil leaders passing through a HANL, sometimes more than once, often about 100 ms after the HANL was formed. The large HANL seen in Flash C continues to propagate at the tip after a quiet period at about t = 100 ms, see right side of Fig. A.7. These properties are not unlike one may find in normal negative leaders. Fig. 1 one may distinguish that the 'fuzzy' structure of a HANL is in fact formed by a filamentary structure pointing outward at an angle of approximately 45 ∘ with respect to the main backbone structure. A zoom-in on this structure is presented on the left of Fig. 2 showing several filaments fanning out from a common origin, in sharp contrast with the structure of a normal negative leader shown on the right. The filaments may be streamers or leaders or something in between, but since we cannot distinguish them at this stage we prefer the more neutral label of filaments. A HANL appears to consist of a core surrounded by a rather dense filamentary structure, where each filament may reach a length of 300 m, although for Flash A these filaments are shorter and   reach 100 m at most. Our VHF mapping does not reveal the core of the structure, and so its location can only be derived from later recoil leaders.

Already in
Propagation of the HANL is by a sequence of steps where each step consists of a large number of filaments fanning-out from a common center. At the end of the reach of these filaments the process may repeat itself. Each step may cover a distance of a few 100 m with several milliseconds between steps. This can be seen from the plan view presented in Fig. 2. Since the steps are this large and clearly visible in the images, there was no need to perform a statistical analysis of the stepping length like what was done in .
To investigate the dynamics of one such a step and its filamentary nature we show in Fig. 3 a further zoom in on the HANL-section displayed in Fig. 2. To show the dynamics of this structure we show a sequence of frames covering small (but unequal) time-steps. Frame 3; 281.5-282.0 ms The burst from the first frame keeps on expanding. Again a filamentary structure can be seen, although we reach the limit of our imaging capability.
Frame 4; 282-284 ms The last frame shows two more bursts starting at t = 283.1 ms, almost simultaneously some 100 m apart, and a third one at t = 283.6 ms (all three indicated by red circles in the plan view). The height v.s. Northing suggest that the burst of frame two did not (yet) pass through this area, and thus they seem all three to be triggered by the burst from the first frame, 1-2 ms after the ionization front passed through this area. The features seen here are typical for all HANLs.
Optical observations of lightning (Dwyer and Uman, 2014, Fig. 4.1) show that during the step formation, the leader brightens and extends in length while producing a burst of streamers at its tip, called a corona flash. Because optical measurements are sensitive to hot channels, the corona flash, composed of cold streamer filaments, is usually poorly resolved in optical. In electric field change observations of negative leader stepping (Krider et al., 1977), where one is sensitive to the electric currents, the intensity is maximal at the time and position of the flash, then rapidly decreasing, followed by a quiet period until the next flash. Even though in VHF observations are less sensitive to currents along the channel but very sensitive to streamers activity the picture is completely consistent with our earlier VHF observations of negative leaders . Also in Fig. 3 the intensity (as can be read from the density of sources) is strongly increasing at the time of the flash followed by a near exponential decrease with a quiet period before the next flash. A possible interpretation might be thus be that the bursts we see in Fig. 3 are corona flashes with outgoing streamers which we see as filaments. Even though this picture may be tempting, it is surprising to observe such a small number of streamers that even extend as far as a few 100 m from their starting point. From the images shown in Fig. 3 it can be seen that these filaments tend to branch. The filaments do emit VHF pulses which are a signature of currents that vary at nanosecond scales (Shi et al., 2016). Thus observing VHF emission can be the indication that we are dealing with branching negative streamers.
If these filaments are instead gradually growing streamers it is not understood what causes the emission of short (~50 ns long) VHF-pulses. This thus might indicate that the streamers do not grow gradually but more in an erratic pattern, even though generally in the direction of the ambient field.
An open issue is what the physics is that determines the position of the next corona flash. Since they appear to occur at the outer reach of the filaments from the previous flash it seems unlikely that this is position is determined by the crossing of multiple streamers Dwyer and Uman, 2014). It seems more likely that at this site there happened to be a larger size hydrometeor or that this is the tip of a filament when it stopped propagating. Since we do not see any evidence of a growing space stem, neither of a space stem connecting to the old leader tip at the time of the next corona flash, it seems more likely that charge starts to accumulate through the (poorly conducting) streamer body until there is a sufficient amount to create a corona burst (Briels et al., 2008;Kochkin et al., 2014Kochkin et al., , 2015Celestin et al., 2015). The observed fact that this appears to happen at the outer reach of the filament structure could be explained by assuming that in the region covered by the filaments the conductivity is large enough that any point will not be able to accumulate charge, charge accumulation can only occur at the outer perimeter of the ionized region. While it is tempting to identify the present VHF observations of HANLs with negative leader stepping, we should be cautious because at present we do not have simultaneous optical and VHF measurements and it is not clear if HANLs are indeed just larger versions of normal leader steps.   It may also be that the filaments are small leaders. In this case the VHF sources probably mark the steps in these negative leaders. However in this case the long wait between the passing of the leader and the following corona flash is difficult to explain.

Abrupt change of leader structure
Most of the HANLs we observed started already at rather high altitude, since the earlier part of these flashes were not recorded, and show all properties of a HANL already from the onset. An exception is the upgoing negative leader seen in Flash A (see Fig. A.6 in Appendix A for an overview). This leader started at a mere 4 km height to propagate almost straight up to level off at an altitude of 8 km. This upward going negative leader in Flash A starts out as a rather typical normal negative leader with fast and short steps and a lateral spread of about 10 m but shows the properties of a HANL when propagating at 8 km height. Since the leader is propagating upward in a rather curvy path (see Appendix B) it is difficult to discern its properties in a usual image and instead we show in Fig. 4 the statistics of the spread of the VHF sources around the mean path.
To emphasize the change in structure of the leader while propagating upward, we show in Fig. 4 the distribution of the distances of the sources with respect to the leader-core, drawn in light-blue in Fig. B.9. The red part of Fig. 4 applies to the leader at 4.6-6.0 km altitude while blue refers to the leader when it has reached 6.6-7.8 km altitude. Unfortunately, there are two negative leaders propagating upward in close proximity between 6.0 and 6.6 km altitude, see Fig. B.8, making the assignment of VHF-sources to one or the other leader ambiguous and for this reason this section could not be displayed. The scatter plots show the distance of the VHF-source location to the head of the propagating leader as function of time while the leader is propagating mostly upward. The histogram shows the probability distribution for the source distance for the two leader sections separately; red (long dashed) for the lower and blue (short dashed) for the higher altitudes.
The statistics marked in red in Fig. 4 is typical for a normal negative leader. The lateral spread is of the order of 10 m and individual steps are too close to distinguish on this scale (as shown in  the stepping time for a normal negative leader is of the order of 0.1 ms) thus the points spread rather homogeneously in time. The right side shows a considerably larger spread in distance to the leader, however still much smaller than what the HANL depicted in Fig. 1 shows. Another typical feature of a HANL is that the sources come in millisecond bursts. This burst structure is also clearly visible in the scatter panel. The structure of the negative leader thus has changed considerably over 5 milliseconds after climbing only one kilometer. The fact that the signature of a HANL is not as outspoken as for the example shown in Fig. 1 is probably because the HANL structure is more strongly developed at larger heights.
The trend of increasing stepping time and increasing stepping length may already have been observed in (Lyu et al., 2016) where for altitudes in excess of 9 km, a stepping length of 300 m and stepping times of the order of 1.5 ms are reported, which is similar to what we observe for the HANLs.

Summary and discussion
At high altitudes we observed that the structure of negative leaders is very different from that of negative leaders at lower altitudes. The structure changes at a rather well defined altitude (between 5.5 and 6.5 km). The most noteworthy distinctions are the dense filamentary structure of the HANL and the bunched structure, where the bunches are separated by about one filament length, that can be on the order of 300 m at the highest altitudes. Since these leaders propagate at about the same velocity as normal negative leaders, these bunches occur once every few millisecond. It is not certain if these filaments are in fact streamers or leaders or something in between. We find the HANL structure for all our negative leaders at an altitude above 7 km, with no exception, and thus we assume that the structure and the altitude are linked, although for a hard proof more statistics on HANLs would be required. The fact that long stepping time and distances were also observed in (Lyu et al., 2016) for negative leaders at the highest altitudes, we see as additional circumstantial evidence.
In general one expects that with increasing height and thus decreasing pressure the properties of a discharge gradually change. A dependence of leader properties on altitude was observed already in (Wu et al., 2015). The present observations suggest that there is a critical height at which the structure changes rather abruptly. At an altitude of 7 km, at a pressure of about 500 mbar, the length of streamers appears to vary strongly with pressure and one, in fact, reaches some kind of phase transition. It is not understood why very impulsive VHF emission occurs during the propagation of the filaments.
According to similarity laws for streamers, the streamer transverse size scales inversely proportional with gas density (Liu and Pasko, 2004;Nijdam et al., 2020). However, to form very long streamers that take a long time to grow, the three body attachment, which leads to a loss of electrons and decrease of conductivity in the channel, is important. Because three-body attachment scales are inversely proportional to the square of the density, this mechanism will become quickly less  4. Statistics for two section of Flash A, right before (red) and after (blue) from where a negative leader transitions from normal to a HANL. In red the distance of the VHF sources to the mean leader head position, δ, is shown for the part of the leader between 4.6 and 6.0 km altitude and in blue for the 6.6-7.8 km altitude range while the leader is mostly propagating upward. important with increasing density. This thus favors a more than proportional increase of streamer length with altitude. The size of the streamer corona, which is generally the size of the region over which the average field is equal to the streamer propagation threshold field, is by itself also inversely proportional to the air density. Combining these effects, the streamer corona length could thus increases very rapidly with altitude.
Following the above argumentation it may be that the structure of low and high altitude negative leaders is in fact not different at all and one is dealing only with a non linear rapid increase of the streamer length at a certain pressure. It might thus be that the physics of HANL stepping is the same as that of normal negative leader stepping, but only on a much expanded scale. If so, HANLs offer the unique possibility to observe for natural lightning, using the LOFAR imaging capability, the fine-structure of the negative leader stepping process.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.   Fig. 1. The weather map for the time of these flash can be retrieved from (KNMI, 2020).

Appendix B. Upward leader section in Flash A
The upward negative leader of Flash A is shown in Fig. B.8. This leader starts out as a normal negative leader at an altitude of 4.5 km and converts to a HANL on its way up. Two zoom-ins of the leader are shown in Fig. B.9, left when it is still a normal negative leader and right when it just was converted into a HANL. However, due to the upward propagation the HANL and the limited altitude of the leader, its properties do not show as prominently as for the HANL shown in Fig. 1. To emphasize the differences in structure the statistics of the distances of VHF sources to the mean leader position, indicated by the light-blue line in Fig. B.9, is shown in Fig. 4.
The processed data used for making Figs. 1-4 is available at (Scholten et al., 2021c). All figures in this work have been made using the Graphics Layout Engine (GLE) Pugmire et al. (2015) plotting package.