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\begin{document}

\title{Upward leaders from instrumented lightning rods competing to connect a
downward leader during a lightning attachment process}



\author[1]{Marcelo Magalhães Fares Saba}%
\author[1]{Paola Beatriz Lauria}%
\author[2]{Carina Schumann}%
\author[3]{José Cláudio Oliveira Silva}%
\author[1]{Felipe de Lima Mantovani}%
\affil[1]{INPE - National Institute for Space Research}%
\affil[2]{The Johannesburg Lightning Research Laboratory}%
\affil[3]{APTEMC}%


\vspace{-1em}



  
  \date{May 17, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
In this paper we analyze electric-field and current measurements of
competing upward leaders induced by a downward negative lightning flash
that struck a residential building. The attachment process was recorded
by two high-speed cameras running at 37,800 and 70,000 images per second
and the current measured in two lightning rods. Differently from
previous works, here we show, for the first time, the behavior of
multiple upward leaders that after initiation compete to connect the
negative downward moving leader. At the beginning of the propagation of
the leaders that initiate on the instrumented lightning rods, current
pulses appear superimposed to a steadily increasing DC current. The
upward leader current pulses increase with the approach of the downward
leader and are not synchronized but present an alternating pattern. All
leader speeds are constant. The upward leaders are slower than the
downward leader speed. The average time interval between current pulses
in upward leaders is close to the interstep time interval found by
optical or electric field sensors for negative cloud-to-ground stepped
leaders. The upward leaders respond to different downward propagating
branches and, as the branches alternate in propagation and intensity, so
do the leaders accordingly. Right before the attachment process the
alternating pattern of the leaders ceases, all downward leader branches
intensify, and consequently upward leaders synchronize and pulse
together. The average linear densities for upward leaders (49 and 82
\selectlanguage{greek}µ\selectlanguage{english}C/m) were obtained for the first time for natural lightning.%
\end{abstract}%



\sloppy


Upward leaders from instrumented lightning rods competing to connect a
downward leader during a lightning attachment process

Marcelo M. F. Saba\textsuperscript{1}, Paola B.
Lauria\textsuperscript{1}, Carina Schumann\textsuperscript{2}, Jos\selectlanguage{ngerman}é
Claudio de O. Silva\textsuperscript{3}, Felipe de L.
Mantovani\textsuperscript{1}

\textsuperscript{1}INPE -- National Institute for Space Research - São
José dos Campos, Brazil.

\textsuperscript{2}JLRL University of the Witwatersrand -- Johannesburg,
South Africa.

\textsuperscript{3}APTEMC - São José dos Campos, Brazil.

Corresponding author: Marcelo M. F. Saba (\emph{marcelo.saba@inpe.br)}

Key Points:

\begin{itemize}
\tightlist
\item
  Parameters of upward leaders from images, electric-field and current
  measurements
\item
  Competing upward leaders alternate their progression during initial
  propagation
\item
  Current pulses of upward leaders increase intensity and synchronize
  right before attachment
\end{itemize}

Abstract

In this paper we analyze electric-field and current measurements of
competing upward leaders induced by a downward negative lightning flash
that struck a residential building. The attachment process was recorded
by two high-speed cameras running at 37,800 and 70,000 images per second
and the current measured in two lightning rods. Differently from
previous works, here we show, for the first time, the behavior of
multiple upward leaders that after initiation compete to connect the
negative downward moving leader. At the beginning of the propagation of
the leaders that initiate on the instrumented lightning rods, current
pulses appear superimposed to a steadily increasing DC current. The
upward leader current pulses increase with the approach of the downward
leader and are not synchronized but present an alternating pattern. All
leader speeds are constant. The upward leaders are slower than the
downward leader speed. The average time interval between current pulses
in upward leaders is close to the interstep time interval found by
optical or electric field sensors for negative cloud-to-ground stepped
leaders. The upward leaders respond to different downward propagating
branches and, as the branches alternate in propagation and intensity, so
do the leaders accordingly. Right before the attachment process the
alternating pattern of the leaders ceases, all downward leader branches
intensify, and consequently upward leaders synchronize and pulse
together. The average linear densities for upward leaders (49 and 82
\selectlanguage{greek}µ\selectlanguage{english}C/m) were obtained for the first time for natural lightning.

Plain Language Summary

The effectiveness of a lightning protection system depends on its
efficiency to intercept the down coming leader of a cloud-to-ground
lightning flash. The interception is usually done by an upward
connecting leader that initiates from grounded structures, humans, or
living beings that protrude from nearby ground. The understanding of the
upward connecting leader and of the attachment process with the downward
leader plays an important role in the determination of the zone of
protection and therefore in the improvement of a lightning protection
system. Unconnected upward leaders, i.e., upward leaders that fail to
connect the downward leader, are also of great importance in lightning
protection. They can be large enough to cause damage to equipment
vulnerable to sparks or induced currents, and enough to injure people
from who it initiates. In this paper we analyze electric-field and
current measurements of competing upward leaders induced by a downward
negative lightning flash that struck a residential building. The
attachment process was simultaneously recorded by two high-speed
cameras, an electric-field sensor, and current sensors installed on two
lightning rods. Differently from previous works, here we show, for the
first time, the behavior of multiple upward leaders that compete to
connect the negative downward moving leader.

1 Introduction

Previously, we have reported high-speed video images of attachment
process of three negative downward cloud-to-ground flashes to an
ordinary residential building (Saba et al., 2017). As mentioned in the
cited paper, the effectiveness of a lightning protection system (LPS)
depends on its efficiency to intercept the down coming lightning leader
which is related to its efficiency to emit upward connecting leaders
(UCL). The understanding of the characteristics of an UCL and of the
attachment process with the downward leader plays an important role in
the determination of the volume or zone of protection of a LPS and in
the improvement of LPS designs. Unconnected upward leaders (UUL), i.e.,
those events that initiate an upward leader but fail to make contact
with the downward leader, are also of great importance in lightning
protection. They can be large enough to cause damage to equipment
vulnerable to sparks or induced currents, and enough to injure people.

Although a few current measurements of upward leaders have been reported
from tall towers higher than 60 m (e.g. Saba et al., 2015; Visacro et
al., 2017; Arcanjo et al., 2019; Nag et al., 2021 for towers over
mountains), from buildings (Saba et al., 2017), and from small
structures (Schoene et al., 2008, vertical conductor of 7 m height), no
current measurements of upward connecting leaders from common
residential buildings have been reported in the literature. Moreover, no
study has ever been done on upward leaders competing to connect a
downward leader. Besides, some of these past studies do not have
electric-field and current measurements together with high-speed video
observations which is crucial to visualize what is happening with the
upward and downward leaders involved in the attachment process.

This study presents observational data of several positive upward
leaders competing to connect a negative leader of a downward
cloud-to-ground flash that strikes an instrumented lightning rod of a
residential building. It is the first to report current measurements of
two upward leaders induced by the same downward leader. The use of
high-speed video images and electric field measurements reveal the
nature of the physical process that is generating the currents measured
on the vertical lightning rods on the top of buildings.

2 Instrumentation

The lightning attachment to the building was observed by two high-speed
video cameras Vision Research Phantom v12 and v711 operating at 70,000
and 37,800 frames per second with exposure times of 13.55 \selectlanguage{greek}µ\selectlanguage{english}s and 25.85
\selectlanguage{greek}µ\selectlanguage{english}s and time intervals of 14.29 \selectlanguage{greek}µ\selectlanguage{english}s and 26.46 \selectlanguage{greek}µ\selectlanguage{english}s respectively (videos
available in Supplementary Information). Image spatial resolution used
for the flashes herein was 128 \selectlanguage{ngerman}× 360 pixels and 368 × 416 pixels,
respectively. They were positioned at 220 m from a pair of identical
14-story apartment buildings, named P1 and P2, located in São Paulo City
(23.483°S, 46.728°W), Brazil (Figure 1a). Their steel reinforced
concrete structures are used as natural LPS. Each building has a
vertical lightning rod, and their tips are at a height of 52 m
respective to ground level. All reported distances and speeds given by
the analysis of the images from the high-speed videos were measured in
2D and therefore underestimated.

The electric field changes caused by the attachment process was measured
by a flat plate antenna with an integrator and amplifier. The antenna
was located on top of building P2 only 4 m away from the lightning rod
that was struck by a cloud-to-ground lightning flash (see Figure 1a). A
fiber-optic link was used to transmit the signal from the
integrator/amplifier to the digitizer. The bandwidth of the system
ranged from 306 Hz to 1.5 MHz. The physics sign convention is used when
referring to the electric field and its change. The approach of a nearby
negative leader produces positive electric field change, and a negative
CG return stroke produces a negative field change.

One current transformer sensor (Pearson model 301-X) was installed on
the lightning rod of each building. This current sensor is capable of
recoding current up to 50,000 A with a useable rise time of 200
nanoseconds, a low frequency 3 dB cut-off of approximately 5 Hz and a
high frequency 3 dB cut-off of approximately 2 MHz. The output of the
sensor is split in two channels (20 dB and 50 dB attenuation over 50 \selectlanguage{english})
and sent to a data acquisition system through a pair of fiber optic
links. Before installation, both sensors were tested and calibrated in a
high voltage facility. The electric field and current were continuously
recorded at a sampling rate of 5 MS/s. GPS antennas were used to
synchronize all measurements and video images.

Data from lightning location systems (LLS) were used to obtain the
polarity, the time, and an estimate of the peak current of the return
stroke. A complete study on the accuracy of peak current estimation
given by the LLS has not been performed yet. However, for one recent
event of a cloud-to-ground flash that struck one of the buildings, the
error was within 20\% for the strokes that were correctly classified as
cloud-to-ground. In that event, four strokes were detected by the LLS
and they were directly measured by the current sensor installed in the
vertical lightning rod to where the attachment occurred. Further
information about these systems and their performance are given in
Naccarato et al. (2012 and 2017).

More information about the cameras, the locations of the two buildings
and the topography of the terrain can be found in the previous work
(Saba et al., 2017).

3 Data

On 1 February 2017 a single-stroke negative cloud-to-ground lightning
discharge struck the tip of the lightning rod B on building P2.
According to the LLS, its peak return stroke current was -73 kA and
occurred at 19:01:10.689307 (UT). During the approach of the stepped
leader, a positive UCL was launched from the tip of the lightning rod B
on building P2 together with five positive UULs from the vertical
air-termination rod A of the other building (P1) and other nearby
structures and corners (named C, D, E, F), as shown in Fig. 1. The first
upward leader to start a continuous propagation was the UCL leader. It
started propagation when the downward leader closest tip was 102 m away
from the tip of the P2 lightning rod where it started. The leaders had
their origin at different distances from the electric field sensor and
at different times (t = 0 s correspond to the attachment and beginning
of return stroke in all tables and graphs). The leader types, 2D lengths
(measured one frame before the occurrence of the return stroke), their
horizontal distances from the electric field sensor, and inception times
are shown in Table 1.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

(a) (b) (c)

\textbf{Figure 1.} a) structures A to F, where the leaders (also named A
to F) are initiated. A and B indicate the tips of the instrumented
lightning rods of buildings P1 and P2 respectively; b) downward negative
leader and positive competing leaders launched from the tip of the
lightning rods and other nearby structures; c) geometry of the return
stroke channel.

\textbf{Table 1 -} Structures that initiated upward leaders, leader
type, length, distance from the electric field sensor and time of leader
inception.

\textbf{Structure}

\textbf{Structure type}

\textbf{Leader (type)}

\textbf{Leader}

maximum length (m)

\textbf{Distance (m)}

\selectlanguage{greek}\textbf{Time of leader inception (µs)}\selectlanguage{english}

A

P1 lightning rod

A (UUL)

40.2

22.5

- 314

B

P2 lightning rod

B (UCL)

50.4

4.0

- 342

C

Building P2 corner

C (UUL)

15.0

14

- 212

D

Construction elevator

D (UUL)

7.7

63

- 106

E

Construction elevator

E (UUL)

7.2

105

- 79

F

Construction corner

F (UUL)

4.7

141

- 71

A sequence of images that shows the initiation and propagation of each
upward leader is presented in Figure 2. The last image (number 24, t = 0
\selectlanguage{greek}µ\selectlanguage{english}s) shows the connection of the upward leader B with the downward
leader.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2.} High-speed video image sequence of the upward leaders
obtained at 70,000 frames per second. Each image contains the relative
time to the image number 24 which shows the connection between the
downward leader and upward leader B.

Figure 3 presents the electric field measured during approximately 9
milliseconds before the occurrence of the return stroke. As mentioned
before, in this work the electric field change is positive when negative
charge over the sensor moves downward. Therefore, the electric field is
intensified with the approach of the negative downward leader. However,
as the positive leaders initiate and move upward, positive charges are
positioned between the electric field sensor and the negative charge of
the downward leader. Thus, the field is reversed with the initiation of
the upward positive leaders and the occurrence of the return stroke.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3.} Electric field change caused by the approach of the
negative downward leader, the initiation of the positive upward leaders,
and the return stroke (t = 0 ms).

Leaders A (UUL) and B (UCL) had their current measured by the current
sensors installed on structures A and B in Figure 1a (lightning rod
masts of buildings P1 and P2 respectively). Figure 4 shows the current
measurements of upward connecting leaders and the electric field during
550~\selectlanguage{greek}µ\selectlanguage{english}s before the return stroke. In the plot, the numbers 1 to 24
indicate the correspondent video images (shown in Figure 2) associated
with the current pulses. 18 unipolar current pulses of some tens of amps
(10's A) from both vertical masts are observed during this interval. The
positive polarity of the pulses indicates an upward-directed transfer of
positive charge. The highest current pulse (413 A; t = -180 \selectlanguage{greek}μ\selectlanguage{english}s) appears
in leader B. Close to the occurrence of the return stroke, the pulses
are superimposed on a DC current that was not considered when measuring
the pulse current peak. The blue curve in Figure 4 traces the electric
field changes during this time interval. The field starts saturated
before pulse number 3 and saturates again with the occurrence of the
return stroke.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4.} Measured current profile of an UCL from B and an UUL
from A, and the electric field acquired during the event. The electric
field was saturated before time -400 \selectlanguage{greek}µ\selectlanguage{english}s.

4. Analysis and discussion

4.1 Leader speed

Based on the video images of both high-speed cameras it was possible to
measure the 2D speed of leaders A and B, but also of other four UULs
that are described in Table 1. The fastest upward leaders were the UCL
(leader B) and leader A, the closest UUL to the attachment point. All
upward leaders propagated in a constant speed (Figure 5). The downward
leader that connected to leader B had also a constant speed but 2.0
times higher (V\textsubscript{d} = 28.5 \selectlanguage{ngerman}× 10\textsuperscript{4} m/s)
than the speed of leader B. This confirms what was found for other cases
of attachment process in the same buildings by Saba et al. (2017), i.e.,
that contrary to what is observed in taller structures (Lu et al., 2013
and 2015) and assumed in some leader propagation models (Rizk, 1990 and
1994), speeds are approximately constant, and the speed of the downward
leader is higher than the speed of the upward leaders (speed ratio
between 2.0 and 5.5). Table S1 in Supplementary Information compares the
speeds, speed ratios and other important characteristics for the case
analyzed in this work with three other attachment processes in the same
building as reported by Saba et al. (2017). We haven't found any
published report of these characteristics for common structures (height
under 60 m).

There is a significant increase in the speed of leader B (UCL)
immediately before connection that suggests the final jump condition of
the attachment process (also observed by Saba et al., 2017). Leader B
(UCL) propagated at a constant speed of 14.3 × 10\textsuperscript{4} m/s
and, during the last frame before connection, the speed increased to
51.4 × 10\textsuperscript{4} m/s, 3.3 times higher than the previous
average speed. Combining the time and length information given in the
images from both cameras, the final jump speed (a combination of the
downward and upward leader propagation, see e.g. discussion done by Saba
et al. 2017) was estimated to be higher than 640 ×
10\textsuperscript{4}m/s, that is, at least 45 times faster than the
average speed of the upward leader.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5.} Leader propagation 2D speeds.

4.2 DC background current

Some distinct patterns were observed in the current plots of leaders A
and B. Some preliminary luminosity and current pulses at the tip of the
lightning rods were observed (the first four current pulses appearing in
images 1 to 4 in Figure 2) a few tens of microseconds before the upward
leaders start. Once the leaders start a continuous propagation (images 5
to 23 in Figure 2 after t~=~-350~\selectlanguage{greek}µ\selectlanguage{english}s), several current pulses occur
superimposed on a constant DC current. The DC current of leader B (UCL)
is much higher than the DC current of leader A (UUL) and both increase
exponentially (Figure 6). A similar growth in current was modelled by
Becerra and Cooray (2009), however no current pulses were present in
their simulation and there was no statement about the exponential
character of the current growth. A similar pattern was also observed by
Visacro et al. (2017), although it was not reported to have an
exponential increase.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Figure 6.} Exponential growth of the DC current measured for
leader B (UCL, upper plot) and leader A (UUL, bottom).

4.3 Leader pulses alternation and synchronism

One interesting feature that can be observed in Figures 2 and 4 is that
although leaders A and B have their luminosity and current pulses
increasing in time as the downward stepped leader approaches, they are
not synchronized at the beginning (up to image 18 in Figure 2 and up to
t~=~-114 \selectlanguage{greek}µ\selectlanguage{english}s in Figure 4).

It is also possible to observe from the high-speed video (in
Supplementary Information -- videos 1 and 2) that the downward leader is
highly branched (Figure 1b) and the branches alternate luminosity during
their downward propagation. The upward leaders A and B respond to
different downward propagating branches and, as the branches alternate
in propagation and intensity, so do leaders A and B accordingly.
However, during the last 100 \selectlanguage{greek}µ\selectlanguage{english}s, the alternation ceases, all downward
leader branches intensify and consequently leaders A and B synchronize
and pulse together. This period coincides with the rapid exponential
growth of the DC base current (Figure~6, upper plot). It seems that the
proximity of the downward leader branches is such that differences in
leader branches propagation and intensities are not driving the upward
leaders differently anymore.

4.4 Leader charge density and charge transfer

From the current and 2D leader length measurements it was possible to
estimate how the transferred charge and the linear charge density of the
leaders vary with time. In Figure 7 the continuous lines show the charge
transferred by the upward leaders A and B and the triangles their linear
charge density during propagation. The charge and the charge density
during the return stroke is not plotted for the UCL leader but its
effects are seen in the charge and charge density plots of the UUL
leader and will be addressed in the next section.

The charge densities of the leaders do not stay constant but increase
rapidly with time during the propagation of the upward leaders (a
similar result was obtained by Chen et al. 2013 for triggered
lightning). This means that for both UUL and UCL the charge in the
leader increases much faster than the length of the leader, which has a
constant speed as shown in Figure 5. Note also that the step like
character of the charge variation is due to the current pulses during
the leader propagation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Figure 7.} Charge density and charge transferred by leaders A
(UUL) and B (UCL).

4.5 Backflow current

Approximately 500 \selectlanguage{greek}µ\selectlanguage{english}s after the attachment of the downward negative
leader with leader B (UCL), when the intense luminosity of the return
stroke subsides, no upward leaders are visible, meaning that they have
all collapsed. The electric field that was driving the propagation of
the UULs from several nearby structures collapses with the occurrence of
the return stroke in B. Therefore, the charges contained in these
leaders flow back to their origin in a very short time, creating an
intense current in the opposite direction.

In fact, this can be observed in the current and charge transfer plots
of leader A (UUL) in Figure 4 and in Figure 7 respectively. Note that
once the return stroke starts, there is a current polarity reversal and
charge transfer decrease. The reversed current of leader A (UUL) reaches
a minimum of -701 A. This backflow current was modelled by Becerra and
Cooray (2009) and measured by Schoene et al. (2008), Visacro et al.
(2010), and Nag et al. (2021) for structures with different heights
(Table 2).

Table 2 also shows the height of the structure that starts the upward
leader, the leader length, the total charge transferred, and linear
charge density for leader A (UUL) and B (UCL). The length values of
leaders A and B were estimated through the analysis of the frames
acquired for the high-speed camera v12. Total charge was calculated
through the integration of the current measurements up to the moment
when the UUL starts to collapse (current reversion). In this table, we
compare our values of positive leader linear charge density with
estimated values by models or measured in some triggered lightning
flashes and in laboratory discharge studies (no values were found in
natural flashes studies).

\textbf{Table 2 -} Height of structure, leader length, total transferred
charge, and linear charge density of leaders A and B.

\textbf{Register}

\textbf{}

Structure

\textbf{Structure height (m)}

\textbf{Leader}

length (m)

\textbf{Total charge (mC)}

\selectlanguage{greek}\textbf{Average linear charge density (µC/m)}\selectlanguage{english}

\textbf{Back flow}

current

(A)

A (UUL)

Building

52

40.2

3.8

49

701

B (UCL)

Building

52

50.4

19.8\textsuperscript{*}

82

-

\emph{Nag et al. (2021)}

Tower

91.5

-

6.4\textsuperscript{**}

-

283\textsuperscript{**}

\emph{Visacro et al., 2010}

Tower

60\textsuperscript{***}

-

-

-

\textasciitilde{}400 and \textasciitilde{}800 A

\emph{Schoene et al. 2008}

Grounded conductor

7

-

-

-

\textasciitilde{}20 A

\emph{Chen et al. (2013)}

Triggered lightning

266 /159

387 / 549

-

155 / 62

-

\selectlanguage{ngerman}\emph{Les Renardières (1977)}

Laboratory discharges

-

-

-

20 - 50

-

\emph{Becerra and Cooray (2009)}

Model

1.9

5.5

1.64

298

1530

\emph{\textsuperscript{*} Does not include the charge transfer due to
the return stroke. \textsuperscript{**} Median value of 8
measurements.\textsuperscript{***} On top of a 280-m height mountain.}

4.5 Time interval and amplitude of electric field changes and current
pulses

The electric field measurements show abrupt negative changes that are
synchronized with the occurrence of current pulses in upward leaders.
The changes in the electric field produced by the positive upward
leaders have the same orientation of the change produced by the negative
return stroke. Positive charges are carried by the leaders over the
electric field antenna in both cases. However, between the abrupt
negative changes caused by the positive leaders, it is possible to see a
slower positive change in the electric field due to the approach of the
negative leader. As the positive charges displaced by the upward leaders
are much closer to the electric field sensor than the negative charges
of the downward leader, the overall change of the field prior to the
return stroke is negative. Also, due to the larger distance from leader
A to the field sensor, current pulses of leader A (red curve in Figure
4) produce smaller negative electric field changes than leader B pulses
(black curve in Figure 4).

The average values of time interval between current pulses present in
leader A and B are very similar, 24.2 and 22.8 \selectlanguage{greek}μ\selectlanguage{english}s respectively (see
Table 3). If all intervals are considered, the average time interval
between pulses is 23.4 \selectlanguage{greek}μ\selectlanguage{english}s with a standard deviation of 4.7 \selectlanguage{greek}μ\selectlanguage{english}s (see
histogram of the distribution in Figure 8a). The average time interval
between current pulses in leaders A and B (23.4 \selectlanguage{greek}μ\selectlanguage{english}s) is close to the
interstep time interval found by optical or electric field sensors for
negative cloud-to-ground stepped leaders (Hill et al., 2011; Krider et
al., 1977). This strongly suggests that the current pulses present in
upward leaders are induced by the electric field change produced by the
steps in the propagation of the negative downward leader. Similar time
intervals between the current pulses for UUL from a 91.5 m tall tower
(Nag et al., 2021) are also shown in Table 3 for comparison. The time
intervals between the current pulses from a 7 m tall structure observed
by Schoene et al. (2008) (12 to 21 \selectlanguage{greek}μ\selectlanguage{english}s), and from a 60 m tall tower on
top of a hill observed by Arcanjo et al. (2019) (30 to 50 \selectlanguage{greek}μ\selectlanguage{english}s) are also
close to the average interstep time found in this work.

Table 3 also shows the current amplitude for leader pulses. In both
leaders the amplitude of the pulses gets higher during the approach of
the downward leader to the upward leaders (Figure 8b). The amplitude of
the pulses present in leader B (UCL) are much more intense than those in
leader A (UUL). The values obtained by Nag et al. (2021) for an
instrumented 91.5 m tower are also presented for comparison. Note that
the amplitudes observed by Nag et al. (2021) in seven UULs are lower
than the ones obtained in the present study. This can be explained by
the fact that in our study the downward leader that induced the upward
leaders occurred overhead the instrumented lightning rods and produced a
-73 kA peak current return stroke. In Nag et al. (2021), the downward
leaders produced return strokes with peak currents ranging from -13 to
-69.3 kA but at larger distances (185 to 783 m) from the instrumented
tower.

\textbf{Table 3 -} Characteristics of the interval between pulses and
current amplitude for leaders A (UUL) and B (UCL)*.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
Parameter & Event & N & Min & Max & AM & DP & GM & MED\tabularnewline
\midrule
\endhead
Interval between pulses (\selectlanguage{greek}µ\selectlanguage{english}s) & A (UUL) & 13 & 16 & 33 & 24.2 & 5.2 &
23.6 & 24.0\tabularnewline
& B (UCL) & 17 & 14 & 29 & 22.8 & 4.4 & 22.4 & 23.0\tabularnewline
& A and B & 30 & 14 & 33 & 23.4 & 4.7 & 22.9 & 23.0\tabularnewline
& \emph{Nag et al. (2021)} & \emph{216} & \emph{4.2} & \emph{132.8} &
\emph{20.9} & \emph{11.4} & \emph{19.1} & \emph{20.0}\tabularnewline
Current amplitude (A) & A (UUL) & 18 & 18 & 149 & 76.1 & 37 & 66.3 &
71.0\tabularnewline
& B (UCL) & 18 & 21 & 413 & 145.7 & 124 & 99.3 & 102.5\tabularnewline
& A and B & 36 & 18 & 413 & 110.9 & 97 & 81.1 & 84.5\tabularnewline
& \emph{Nag et al. (2021)} & \emph{223} & \emph{3.4} & \emph{289.2} &
\emph{49.6} & \emph{55.1} & \emph{31.1} & \emph{30.1}\tabularnewline
\bottomrule
\end{longtable}

\emph{\textsuperscript{*}N is sample size, AM means arithmetic mean, DP
is the standard deviation, GM is the geometric mean, and MED the
median.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

\textbf{Figure 8.} a) Distribution of time intervals between pulses in
leader A (UUL) and leader B (UCL); b) peak current of pulses occurring
during the initiation and progression of the leaders.

Summary and Conclusion

In this study, for the first time, the current was measured
simultaneously in two upward and competing leaders during the attachment
process of a downward negative leader. The connection took place with
the lightning rod of a residential building and was simultaneously
recorded with high-speed cameras, electric field sensor and current
sensors giving the opportunity to compare the time interval between
current pulses, the amplitude of the pulses and the behavior of the DC
currents of an UCL and an UUL leader.

The approach of the negative downward leader induced 6 upward leaders
prior to the return stroke. The brightest and longest ones were
initiated from instrumented lighting rods and had their current
intensities measured. One of them (from structure B, building P2)
connected to the downward leader.

The downward leader and upward leaders A and B propagated at a constant
speed, being the downward leader 2.0 to 5.5 times faster than the upward
leaders and the UCL 17\% faster than the UUL. The final jump speed
(upward and downward leaders combined) is estimated to be at least 45
times faster than the average speed of the UCL prior to the jump.
Although the peak current of the return stroke in this case was much
higher than the previous ones analyzed by Saba et al. (2017) (Table S1
in Supplementary Information), the speed ratios
(V\textsubscript{d}/V\textsubscript{ucl} and
V\textsubscript{d}/V\textsubscript{uul}) were similar. However, the
charge of the downward leader, which is related to the intensity of the
return stroke, may have influenced the speed of the upward leaders (all
of them faster than previously reported cases). The faster speeds of the
downward leader and the upward connecting leader reduced the time
interval between the UCL leader inception and return stroke. The
distance between the down-coming negative leader tip and the tip of the
vertical rod at the inception of a stable upward positive leader (102 m)
was not significantly different from previous cases (82, 120 and 62 m).

DC currents were measured during the propagation of both leaders (A and
B). Both increased exponentially with a similar growth predicted by
Becerra and Cooray (2009). The DC current of leader B (UCL) was much
more intense than the DC current of leader A (UUL).

Pulses superimposed on the DC current of the upward leader were reported
before. Although the amplitudes of the pulses are different in the case
of taller structures (Visacro et al., 2010, tower height of 60 m over a
300 m tall mountain), the pattern of the pulses observed in this case is
very similar to current measurements of UUL reported from tall towers
(e.g. Figure 8 in Visacro et al., 2010), and from small structures
(Figure 6 in Schoene et al., 2008, grounded vertical conductor of 7 m
height over a flat terrain). Multiple current pulses occur from the
lightning rods during the approach of the negative downward leader and
the amplitude of the current pulses tend to increase with time; the
current peaks of the superimposed leader pulses range from 18 A to 413
A; the pulses superimposed on UCL leaders are larger than the pulses
superimposed on UUL leaders.

The average time interval between current pulses in upward leaders is
close to the interstep time interval found by optical or electric field
sensors for negative cloud-to-ground stepped leaders, which strongly
suggests that the current pulses present in upward leaders are induced
by the electric field change produced by the steps in the propagation of
the negative downward leader

The upward leaders A and B respond to different downward propagating
branches and, as the branches alternate in propagation and intensity, so
do leaders A and B accordingly. During the last 100 \selectlanguage{greek}µ\selectlanguage{english}s there is a rapid
exponential growth of the DC base current, the alternation of the
leaders ceases, all downward leader branches intensify and consequently
leaders A and B synchronize and pulse together.

Although the leaders have a constant speed, their linear charge density
increases rapidly during their propagation. The total charge of the UCL
is 5 times larger than the total charge of the UUL. The average linear
densities for upward leaders (49 and 82 \selectlanguage{greek}µ\selectlanguage{english}C/m) were obtained for the
first time for natural lightning. Previous measurements and estimations
(from triggered lightning, laboratory measurements and theoretical
studies) show values that range from half to 4 times higher.

The identification and characterization of the UCL and UUL reported here
can help not only the understanding of the attachment process when
several upward leaders are induced, but also the impact of these upward
leaders in vulnerable equipment, in the ignition of flammable vapors and
in injures caused to humans (Schoene et al., 2008; Becerra and Cooray,
2009).

Acknowledgements

The authors would like to thank Lie Bie (Benny), Raphael B. G. Silva,
Marco A. S. Ferro, Hugh Hunt, Guilherme Aminger, and Eliah Fernanda S.
Sabbas for all support in equipment installation and data acquisition.
We also thank Dr. Alexandre Piantini, Dr. Ac\selectlanguage{ngerman}ácio Silva Neto, Dr. Celso
Pereira Braz and staff from the high-voltage facility at the Institute
of Energy and Environment (IEE) at the University of S. Paulo, Brazil
for the calibration tests of the current transformer sensor. This work
was supported by research grants from FAPESP (Project 2012/15375-7);
CNPq (Projects 141450/2021-5, 153799/2022-6).

Data Availability Statement

The high-speed videos analyzed in this work are available at:
https://doi.org/10.5281/zenodo.7244891

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\textbf{Hosted file}

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