RESEARCH ARTICLE
10.1029/2023JD038715
Key Points:• A machine-learning classifier for
negative return strokes (RSs) isbuilt using a large data set with 3-D
location information• Both an accuracy and an efficiency
of about 98.8% are achieved and theaccuracy-efficiency tradeoff can beeasily controlled• Some RSs and intracloud discharges
produce special waveforms that are
fundamentally difficult to classify
without 3-D location results
Supporting Information:

Supporting Information may be found in
the online version of this article.
Correspondence to:T. Wu,
wu.ting.x4@f.gifu-u.ac.jp
Citation:

Wu, T., Wang, D., & Takagi, N. (2023).
High-accuracy classification of radiation
waveforms of lightning return strokes.
Journal of Geophysical Research:
Atmospheres, 128, e2023JD038715.
https://doi.org/10.1029/2023JD038715
Received 16 FEB 2023
Accepted 12 JUL 2023

High-Accuracy Classification of Radiation Waveforms ofLightning Return Strokes
Ting Wu1, Daohong Wang1, and Nobuyuki Takagi1

Department of Electrical, Electronic and Computer Engineering, Gifu University, Gifu, Japan

1

Abstract A machine-learning classifier for radiation waveforms of negative return strokes (RSs) is built
and tested based on the Random Forest classifier using a large data set consisting of 14,898 negative RSs
and 159,277 intracloud (IC) pulses with 3-D location information. Eleven simple parameters including threeparameters related with pulse characteristics and eight parameters related with the relative strength of pulses
are defined to build the classifier. Two parameters for the evaluation of the classifier performance are also
defined, including the classification accuracy, which is the percentage of true RSs in all classified RSs, andthe identification efficiency, which is the percentage of correctly classified RSs in all true RSs. The tradeoff
between the accuracy and the efficiency is examined and simple methods to tune the tradeoff are developed.
The classifier achieved the best overall performance with an accuracy of 98.84% and an efficiency of 98.81%.
With the same technique, the classifier for positive RSs is also built and tested using a data set consistingof 8,700 positive RSs. The classifier has an accuracy of 99.04% and an efficiency of 98.37%. By examining
misclassified waveforms, we show evidence that some RSs and IC discharges produce special radiation
waveforms that are almost impossible to correctly classify without 3-D location information, resulting in afundamental difficulty to achieve very high accuracy and efficiency in the classification of lightning radiation
waveforms.
Plain Language Summary Lightning location systems are required to classify return strokes (RSs)from intracloud (IC) discharges accurately and efficiently because the RS is the main discharge component thatposes direct threats to the human society. In this paper, we report a machine-learning classifier for negative RSs
built using a large data set with accurate 3-D location information. The classifier has an accuracy of 98.84%(98.84% of classified RSs are correct classifications) and an efficiency of 98.81% (98.81% of RSs can becorrectly classified). With the same technique, we also built a classifier for positive RSs with similarly highaccuracy and efficiency. Our classifiers only require some simple waveform parameters so the same technique
can be used by various lightning location systems relatively easily. A sample Python script to use the classifieris provided and readers are encouraged to test the classifier using their own data set. We also demonstrate thatsome RSs and IC discharges produce abnormal waveforms, so 100% accuracy or efficiency is fundamentallydifficult to realize using only waveform information.
1. Introduction
Ground-based lightning location systems (LLSs) are widely used to monitor lightning activities. A prominent
feature of ground-based LLSs is that lightning activities in a wide area can be monitored in real time with only alimited number of sensors. Some famous national and continental LLSs include the National Lightning Detection
Network (NLDN) covering the continental United States (e.g., Cummins & Murphy, 2009), the European Cooperation for Lightning Detection network (EUCLID) covering the European continent (e.g., Schulz et al., 2016),
and the Earth Networks Total Lightning Network (ENTLN) (e.g., Zhu et al., 2022) with the aim of a global
coverage.

© 2023. American Geophysical Union.
All Rights Reserved.

WU ET AL.

It is a basic requirement for LLSs to automatically and efficiently classify cloud-to-ground (CG) lightning flashes
from intracloud (IC) flashes as the former consist of discharges with direct connections to the ground and thus
pose a much larger threat to the human society. The fundamental difference between a CG flash and an IC flash isthat a CG flash contains one or more return strokes (RSs), so the classification of CG flashes is basically realized
by classifying RSs. Further, it is well known that RSs produce characteristic electric field radiation waveforms
that are largely different from those of IC discharges (e.g., Lin et al., 1979), so most LLSs classify RSs based on
their waveform characteristics.

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However, RSs actually can produce radiation waveforms with a variety of special features under some special
conditions. For example, some RSs in winter thunderstorms are known to produce abnormal radiation waveforms, some of which could not be correctly classified by LLSs (Wu, Wang, Huang, & Takagi, 2021; Wu, Wang,& Takagi, 2021). It is also well known that RSs striking tall objects produce much narrower radiation waveforms(Pavanello et al., 2007; Zhu et al., 2018). On the other hand, IC discharges include various discharge processes
such as narrow bipolar events and recoil leaders, some of which may produce radiation waveforms with certain
similar features as RS waveforms. As a result, for most LLSs, it is basically very difficult to achieve a very highclassification accuracy of RSs. For example, Zhu et al. (2016) reported that out of 339 RSs in Florida in 2014
that were also recorded by the NLDN, 312 (92%) were correctly classified as RSs by the NLDN. Kohlmann
et al. (2017) reported that the classification accuracy of EUCLID for RSs were generally around 90% basedon ground-truth data in various regions of Europe. For some particular thunderstorms or some special types ofdischarges, misclassifications by LLSs can be more common. For example, Fleenor et al. (2009) found that 204
out of 376 (54%) of RSs reported by the NLDN during a field campaign in 2005 were actually IC discharges.
Leal et al. (2019) found that compact intracloud discharges with estimated peak currents larger than 50 kA were
all falsely classified as RSs by both NLDN and ENTLN. Paul et al. (2020) reported that out of 40 RSs detected
at the Peissenberg Tower, 12 (30%) were falsely classified as IC discharges.
In order to overcome the uncertainties in classifications based only on radiation waveforms, Betz et al. (2004)
proposed a pseudo 3-D technique to assist the discrimination of RSs and IC discharges based on the fact that theelevation of IC discharges would have some contributions to the time delay. However, this technique also hassome limitations. For example, IC discharges need to have significant elevations, the baseline of the LLS cannot
be too long, and lightning discharges first need to be located accurately in 2-D. These limitations prevented thewide implementation of this technique.
In recent years, machine-learning techniques have been developing rapidly, and these techniques seem to be promising in significantly increasing the classification accuracy of lightning radiation waveforms. Wang et al. (2020)
developed a convolutional neural network to classify radiation waveforms of lightning discharges recorded by
the Advanced Direction-time Lightning Detection System in China. They reported an accuracy of over 99%.
However, they apparently did not have the height information of lightning discharges and thus could not unambiguously differentiate RSs and IC discharges, so the accuracy remains questionable. Zhu et al. (2021) used theSupport Vector Machines (SVM) model to classify CG and IC flashes recorded by the Cordoba Marx Meter
Array. The lightning data were in 3-D, so they could employ the discharge height information to build a data
set with accurate discharge types. They reported an overall accuracy of 97%. However, their proposed method
requires full waveform information, while most LLSs only retrieve a few parameters of electric field waveformsof lightning discharges. Apart from classifying RS waveforms, machine-learning techniques have also been used
to classify characteristic waveforms related with terrestrial gamma-ray flashes (Pu et al., 2023).
In this paper, we report a simple yet high-accuracy machine-learning technique based on the Random Forestclassifier to classify RSs. We will use a large data set containing about 15,000 negative RSs and many more IC
discharges with accurate 3-D location information to train and test the classifier. As will be described in thispaper, many of the recorded RSs and IC discharges produced atypical radiation waveforms that were challenging
to be correctly classified. However, the accuracy of our classifier is close to 99% demonstrated by evaluations invarious respects. Our classifier requires only some simple parameters of lightning radiation waveforms, so thesame technique can be adopted by most LLSs relatively easily.

2. Observation and Data
During the summer of 2017, we set up a low-frequency lightning mapping system called Fast Antenna Lightning Mapping Array (FALMA) in central Japan. The FALMA consisted of 12 sites covering an area of about
80 × 80 km 2. Locations of these 12 sites are shown as red squares in Figure 1a. At every site, a fast antenna working in the frequency band of 500 Hz to 500 kHz was used to receive radiation signals from lightning discharges.
The signals were recorded with a sampling rate of 25 MS/s. As described by Wu et al. (2018a), thanks to improvements made in both the hardware and the software, we realized high-quality 3-D lightning mapping with the
FALMA. As can be seen from examples of lightning flashes in Wu et al. (2018a, 2019), 3-D mapping resultsof FALMA have similar quality to those of very-high-frequency (VHF) systems such as the Lightning Mapping
Array (Rison et al., 1999).
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Journal of Geophysical Research: Atmospheres10.1029/2023JD038715

Figure 1. (a) Negative return strokes (RSs) (black dots) observed from 19 July to 26 August 2017. (b) Positive RSs observed from 26 September 2021 to 3 September
2022. Red squares represent observation sites of Fast Antenna Lightning Mapping Array.

Data obtained from 19 July to 26 August are used in this study for building and testing the classifier for negative RSs. All data are reprocessed for this study. As a negative RS produces a positive radiation pulse (as in
the atmospheric electricity sign convention), in order to classify negative RSs, we need to examine all positive
pulses. A positive pulse here simply means a positive electric field change whose amplitude exceeds a pre-defined
threshold, and we do not set any restrictions on other characteristics of the pulse to ensure the simplicity of thismethod and thus its easy implementation in real observations. The largest positive pulse in each 20-ms window
is located in 3-D, and discharges located in the region shown in Figure 1a, a 90 × 90 km 2 area over the FALMA
network, are used in order to ensure reliable 3-D locating. Pulses with source heights lower than 500 m are treatedas candidates of RSs. Their waveforms are then confirmed manually, and for some ambiguous pulses, they arefurther manually located to determine their source heights. In this way, we can unambiguously determine thatthe selected pulses are truly RSs. The number of IC discharges are much larger than that of RSs, so we cannot
manually confirm waveforms of all IC discharges, and we only use pulses with source heights larger than 3000 m
as IC pulses. There are 14,898 pulses confirmed as negative RSs and 159,277 pulses as IC discharges. Although
the height thresholds of 500 m for RSs and 3000 m for IC discharges are somewhat arbitrary, only 1064 (0.6%)
pulses are located between 500 and 3000 m, so neglecting these pulses will have little influence on the resultsof this study. Locations of all negative RSs are shown as black dots in Figure 1a. It should be noted that we willbuild a classifier for negative RSs rather than negative CG flashes; a CG flash consists of at least one RS and also
many IC discharges, both of which need to be correctly classified.
Using the high-quality data set of 2017 summer, we will establish the technique for building the classifier as will
be described in Sections 3.1–3.5. Further, using the same technique, we will also build a classifier for positive
RSs as will be described in Section 3.6. However, positive RSs in central Japan in summer are quite rare (Wuet al., 2018b). In order to accumulate a large number of positive RSs, we will use the data collected during a long
period, from 26 September 2021 to 3 September 2022. During this period, we set up a FALMA network coveringa large area for 2-D locating of both summer and winter lightning. Observation sites are shown as red squares in
Figure 1b. A total of 8700 positive RSs observed in an area with a radius of 300 km are identified and will be used
for building and testing the classifier for positive RSs. Locations of these positive RSs are shown as black dots
in Figure 1b. The procedure for the identification of these positive RSs will be further described in Section 3.6.
Our classifiers will be built and tested mainly based on the Random Forest classifier, which is one of the mostwidely used machine-learning models for classification tasks. The random forest classifier is an ensemble
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Journal of Geophysical Research: Atmospheres10.1029/2023JD038715

classifier consisting of multiple decision trees, with each decision tree being built on a subset of training samples,
and the final classification result is based on predictions made by the ensemble of decision trees. It has been shownthat ensemble classifiers are more likely to achieve higher accuracy and robustness (e.g., DeFries, 2000; Miaoet al., 2011). Moreover, the random forest classifier is well known for its computational efficiency and simple
parameter setting as compared with other ensemble classifiers (e.g., Belgiu & Drăguţ, 2016). In Section 3.5, we
will also make a brief comparison with the SVM classifier, another popular machine-learning model.

3. Methods and Results
3.1. Method to Evaluate the Performance of a Classifier
Before building the classifier, first we need to define some parameters as indicators of the performance of a classifier. One obvious parameter to evaluate the performance is the classification accuracy, or simply accuracy, thatis, the percentage of true RSs in the waveforms classified as RSs. However, only this parameter is apparently notenough, as it is always possible to build a classifier with very strict criteria so that it only identifies very typical
RS waveforms. Another important parameter is the identification efficiency, or simply efficiency, that is, thepercentage of correctly classified RSs in all RSs.
Suppose the number of RSs is NR, and the number of IC discharges is NI. Of the NR RSs, NRc are correctly classified (the subscript c stands for “correct”), and the remaining NR − NRc are misclassified as IC discharges. Of the
NI IC discharges, NIc are correctly classified, and the remaining NI − NIc are misclassified as RSs. The accuracy
and the efficiency can be calculated as follows.
𝑁𝑁𝑅𝑅𝑅𝑅𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 =(1)𝑁𝑁𝑅𝑅𝑅𝑅 + (𝑁𝑁𝐼𝐼 − 𝑁𝑁𝐼𝐼𝐼𝐼 )𝑁𝑁
𝐸𝐸𝐸𝐸 𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 𝑅𝑅𝑅𝑅
(2)
𝑁𝑁𝑅𝑅

During the process to build the classifier, we will experiment and tune various parameters of the classifier tomake the accuracy and the efficiency as high as possible.
Normally a data set is split into a larger training set and a smaller test set, with the training set used to train a classifier and the test set used to test or evaluate the performance of the classifier. In this study, we use an improved
approach. All RS and IC data are combined, shuffled and then divided into five equal parts. Each part is in turnused as the test set and the remaining four parts combined are used as the training set. In this way, a classifier isbuilt and tested for five times and five results of accuracy and efficiency are calculated. The average values offive tests will be used as the final results. In this way, we can avoid any random biases in the test set. Moreover,as will be described in Section 4, in this way all data can be tested and we can find as many atypical waveforms
as possible that are difficult to be correctly classified.
3.2. Waveform Parameterization
We will define some waveform parameters to be used for building the classifier. First we describe the procedure
to calculate waveform parameters based on multiple-site records. As waveforms recorded at a close distancecontain the electrostatic and induction field components (e.g., Thottappillil et al., 1997) that may significantly
distort the waveforms, observation sites within 40 km from a discharge are first excluded. Waveforms recordedby the remaining sites are used to calculate the parameters, and for each parameter, the median value of theresults calculated based on these sites are used as the final result of the parameter for the discharge. The medianvalue is used because different sites have different noises which may have some influences to the calculation ofparameters, and we believe using the median value is the simplest method to reduce the influences. Figure S1
in Supporting Information S1 also shows the distributions of median distances with observation sites more than
40 km away for all negative RSs and IC discharges used for building the classifier.
3.2.1. Parameters Related With Pulse Characteristics
First we define three basic parameters related with pulse characteristics. Definitions of these parameters areillustrated using an RS pulse (a first RS) in Figure 2a and an IC pulse (preliminary breakdown) in Figure 2b (blueparameters).
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Figure 2. Illustration of waveform parameters using (a) a return stroke pulse and (b) an intracloud pulse.

1. Trise: The rise time of a pulse (10% to peak).
2. Tfall: The fall time of a pulse (peak to zero).
3. Thalf: The pulse width at the half maximum.
With only these three basic parameters, we trained and tested the Random Forest classifier using the negative RS
and IC data set obtained in 2017 summer. As described in Section 3.1, the data set is divided into five parts andeach part in turn is used as the test set, so the classifier is trained and tested for five times. The accuracy ranges
from 72.25% to 73.57% with an average of 72.82%, and the efficiency ranges from 70.80% to 72.81% with anaverage of 71.59%. We also tried to add two related parameters, including the pulse width, which is the sum of
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the rise time and fall time, and the ratio of fall time to rise time, but the result has little difference (the average
accuracy is 72.17% and the average efficiency is 70.86%).
Indeed, with only these basic pulse parameters, it is difficult to accurately classify RSs.
3.2.2. Parameters Related With Relative Strength
An important feature of the RS waveform is that pulses right before and after an RS pulse is usually much weaker.
The following parameters are defined to employ this feature. These parameters are also illustrated in Figures 2aand 2b.
1. Rbp1: The ratio of A0 to Abp1, in which A0 is the peak amplitude of the target pulse, and Abp1 is the maximum
amplitude of pulses right before the target pulse (from −100 μs to 10% peak) as illustrated in Figure 2. The
subscript b stands for “before,” and the subscript p stands for “positive.”
2. Rbn1, Rbp2, Rbn2, Rap1, Ran1, Rap2, Ran2: These parameters are defined in the same way as Rbp1, also illustrated in
Figure 2. Note that the subscript a stands for “after,” and the subscript n stands for “negative.”
As can be seen in Figure 2, 300-μs waveform before and 400-μs waveform after the target pulse are used for
calculating these ratios. It should be noted that the lengths are to some extent arbitrary; the point here is that theselengths should be long enough to contain enough information about the strength of discharges both before andafter, but at the same time it should not be too long because the recording length, especially the pre-trigger length,
for one trigger may be quite short in some systems. Waveforms too long may also contain information that is notconsistently related with the target pulse and thus introduce noises.
The three parameters defined in Section 3.2.1 along with the eight new parameters defined above are used totrain the Random Forest classifier. The accuracy of five tests ranges from 98.86% to 99.32% with an average of
99.02%, and the efficiency ranges from 98.02% to 98.66% with an average of 98.34%. It is clear that these newparameters representing the relative strength are very effective in the classification of RSs.
3.3. Tradeoff Between Accuracy and Efficiency
From the above result, we can see one feature of the classifier is that the accuracy is always higher than theefficiency. It is obvious that increasing the efficiency usually implies decreasing the accuracy. However, it isdesirable if we can control the tradeoff between the accuracy and the efficiency. For example, in some situations,
it may be required to identify as many RSs as possible, so a high efficiency is essential while a low accuracy istolerable. Next we will investigate two factors that influence the tradeoff between the accuracy and the efficiency.
3.3.1. Influence of Sample Size Imbalance
One reason for the higher accuracy in the classifier built in the previous section is a much larger sample of IC
discharges compared with the sample of RSs. With such a biased data set, the classifier is more likely to misclassify RSs, as also noted by Zhu et al. (2021). We can simply duplicate the sample of RSs to make the classifier
identify more RSs, though at the cost of more misclassifications of IC discharges. Note that the duplication
should only be made for the training set.
With the original data set, 247 of 14,898 RSs (1.7%) are misclassified, but only 145 of 159,277 IC pulses(0.091%) are misclassified. If we duplicate the data set of RSs in the training set, the number of misclassified
IC pulses increases to 162 while the number of misclassified RSs decreases to 199. We tried to make more
duplications and tested the classifier, and the results of the accuracy and the efficiency are shown in Figure 3a.
With one duplication of the RS training set, the accuracy decreases from 99.02% to 98.91% but the efficiency
increases from 98.34% to 98.66%. With two duplications, the accuracy decreases to 98.84% but the efficiency
increases to 98.76%, very close to the accuracy. With further duplications, we can see that both the accuracy andthe efficiency are generally very similar, changing between 98.75% and 98.85%, indicating that the sample size
imbalance does not have a significant effect any more.
If we use the average value of the accuracy and the efficiency as the indicator of the overall performance of aclassifier, we can see from Figure 3a that with four duplications of the RS training set, the classifier has the highest performance with an accuracy of 98.84% and an efficiency of 98.81%. We treat this as the best performanceof the classifier for negative RSs and this classifier will be used for further evaluations in the following section.
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Figure 3. Variations of the accuracy and the efficiency with (a) different times of duplications of return stroke (RS) training set and (b) different thresholds ofprobability to classify RSs.

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3.3.2. Influence of Probability Thresholds
When classifying a pulse, the Random Forest classifier can output the probability that the pulse is a true RS.
By default, the classifier determines a pulse as an RS when the probability is larger than 50%. By changing theprobability threshold, we can conveniently tune the accuracy-efficiency tradeoff.
Figure 3b shows variations of the accuracy and the efficiency related with the probability threshold. We can seethat as the probability threshold increases, the accuracy increases while the efficiency decreases. This is easy tounderstand; a higher probability threshold represents stricter criteria to classify RSs, so naturally the identified
RSs are more likely true RSs (higher accuracy), but at the same time fewer RSs can be identified (lower efficiency). In practice, when using the classifier we can set a customized probability threshold that fits the specificrequirements of an application to achieve desired accuracy or efficiency.
3.4. Parameter Importance and Parameter Reduction
The Random Forest classifier outputs a value indicating the relative importance of each parameter in contributing
to the performance, from which we can evaluate the effectiveness of each parameter in the classification of RSs.
The results are shown in Figure 4a. Values of the importance of all parameters combined equal to 1. We can seethat parameters related with the pulse strength relative to previous pulses (red parameters in Figures 2 and 4a) are
generally more important than other parameters. This is easy to understand as an RS pulse is preceded by leader
pulses which are usually much weaker than the RS pulse. By contrary, an IC pulse is usually preceded by otherIC pulses with comparable amplitudes. Therefore, parameters related with the relative strength are very effectivein the classification of RSs.
We can also see that parameters related with pulse characteristics (blue parameters) have relatively low importance,
which is why the classifier performance is very poor with only these parameters as described in Section 3.2.1.
It also indicates that traditional RS classification methods based on pulse characteristics are not very reliable.
Using the information of the relative importance of each parameter, it is possible to simplify the parameterization by removing some parameters with low importance. Based on the model built in Section 3.3.1, we investigated how the accuracy and the efficiency change when removing some parameters with low importance. Whenremoving the parameter Rap1, which has the lowest importance, the accuracy decreases from 98.84% to 98.78%,
although the efficiency increases slightly from 98.81% to 98.83%. When further removing Rap2, which has thesecond lowest importance, the accuracy stays unchanged as 98.78%, but the efficiency decreases to 98.72%.
We tried to further remove other parameters in order of importance, from lowest to highest, and the results areshown in Figure 4b. We can see that with fewer parameters, the accuracy and the efficiency generally decrease
as expected, but the decreasing is not significant when removing parameters with low importance. Specifically,
when removing the six parameters with lowest importance and using only the remaining five parameters to train
the classifier, the accuracy is 98.44% and the efficiency is 98.07%, which are still satisfactory results. Therefore,
in applications with limited computational resources, parameters with low importance can be removed to makethe classifier easier to be implemented.
3.5. Comparison of Different Machine-Learning Models
Apart from the Random Forest classifier, another popular machine-learning model for classification is the SVM
classifier, which was used by Zhu et al. (2021) for the classification of lightning pulses. Here we make a brief
comparison of the Random Forest and the SVM classifiers. Note that the same classifier may have very different performances in different types of applications, and the comparison here is only of the Random Forest andthe SVM classifiers for the classification of lightning radiation waveforms with the parameterization schemes
described in this paper. First we use the scheme described in Section 3.2.2 (using 11 parameters illustrated in
Figure 2) to train the classifiers, and the results are shown in Table 1 (upper part). We can see the SVM classifier has slightly lower accuracy and efficiency than the Random Forest classifier. Further, we use the scheme
described in Section 3.3.1 (duplicating the RS training data set) to train the classifiers, and again, the SVM classifier has slightly lower accuracy and efficiency. Another difference is in the time needed to train a classifier; ittakes less than 30 s to train an Random Forest classifier while the time needed to train an SVM classifier is around
100 s. A significantly shorter time to build a classifier is potentially very useful as it would be more convenient toexperiment various combinations of parameters in order to boost the performance of the classifier.
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Figure 4. (a) Relative importance of waveform parameters. Definitions of these parameters are illustrated in Figure 2. (b) Variations of accuracy and efficiency whenreducing the number of parameters. Parameters are reduced in order of importance, from low to high, that is, Rap1, Rap2, Trise, Thalf, Ran2, Rbp2, and Ran1.

3.6. Classification of Positive Return Strokes

Table 1Comparison of the Random Forest Classifier and the Support Vector
Machines (SVM) Classifier
Classifier

Accuracy (%)

Efficiency (%)

Time cost (s)Eleven parameters (Section 3.2.2)
Random forest

99.02

98.34

20

SVM

98.43

97.42

96

Duplicating return stroke training set (Section 3.3.1)
Random forest

98.84

98.81

28

SVM

97.98

98.09

108

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The methods described above can also be used to build a classifier for theclassification of positive RSs. However, positive CG flashes are very rare insummer thunderstorms in central Japan. As reported by Wu et al. (2018b),
only 46 positive CG flashes consisting of 53 positive RSs were observed andcould be located in 3-D during the summer observation of 2017. Therefore,
here we also include the data obtained in other periods. First we use the 690
positive RSs observed during the winter of 2018 (Wu et al., 2022) to build apreliminary classifier for the identification of positive RSs. Then we use thisclassifier to search the data recorded in about 1 year from September of 2021
for possible positive RSs. As described in Section 2, during this period, we
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set up a FALMA network with long baselines for 2-D locating of both summer and winter lightning. Waveformsof the identified positive RSs by the preliminary classifier are manually confirmed to exclude obvious false classifications. Indeed, the preliminary classifier identified many pulses that were clearly IC pulses and we painstakingly excluded all apparent IC pulses by manual inspections. In this way, we collected the data of 8700 positive
RSs, locations of which are shown in Figure 1b. Note that there is no height information for these positive RSs, so
this data set is not as accurate as the negative RS data set in 2017 summer used in previous sections.
For IC data, we also use the data of summer observation of 2017 as these data have accurate 3-D location results.
However, different from the IC data set for the negative RS classifier, IC pulses for building positive RS classifiershould have the same polarity as positive RSs. So we located IC pulses having the same polarity as positive RSs
and selected those with heights larger than 3 km, the same treatment as that in building the negative RS classifier.
On the other hand, as the size of positive RS data set is relatively small, we do not need too many IC data, so
for simplicity, we only located one IC pulse in every 50-ms window. Finally, we collected a total of 113,922 IC
pulses.
Using these data sets, and with the same scheme for building negative RS classifier described in Section 3.3.1, we
built and tested the classifier for positive RSs. It is found that with the RS training set duplicated for one time, theclassifier has the best overall performance with an accuracy of 99.04% and an efficiency of 98.37%. This result
demonstrated that as long as there are enough data of positive RSs, we can also build a high-accuracy classifier
for positive RSs in the same way as building the negative RS classifier.
Although the data set of positive RSs does not have 3-D location information, and the usage of the preliminaryclassifier to assist the selection of positive RSs may also introduce some biases, as positive RSs are much rarer
than negative RSs and it is very difficult to collect a large and reliable sample, we believe our classifier is very
valuable for future observations and researches. Moreover, as all waveforms of identified positive RSs have been
manually confirmed, the classifier likely has an accuracy similar to that of the manual classification.

4. Atypical Intracloud and Return Stroke Waveforms
As described in Section 3.1, the whole data set of 2017 summer is divided into five parts, with each part in turnused as the testing set and the remaining four parts combined used as the training set. In this way, all pulses can betested and we can identify as many pulses as possible that are potentially difficult to classify. Using the classifierbuilt in Section 3.3.1 with the RS training set duplicated for four times, all pulses are classified. Of the 14,898
RSs, 178 were misclassified as IC discharges, and of the 159,277 IC pulses, 173 were misclassified as RSs. Waveform figures of all these misclassified pulses are provided in the data repository.
There are several common reasons for misclassifications of RS pulses as IC pulses. Waveforms of four examples
are shown in Figures 5a–5d, all of which are misclassified as IC discharges and whose source heights have been
confirmed to be close to the ground. First, it is well known that RSs striking tall grounded objects usually produce
very narrow pulses (Araki et al., 2018; Cai et al., 2022; Pavanello et al., 2007; Zhu et al., 2018), making it easy to
misclassify them as IC discharges. One example is shown in Figure 5a. This pulse is located near a transmission
tower, and its pulse width is only about 9 μs, indicating that it is likely produced by an RS striking the tower.
Second, two RSs sometimes occur sequentially with a very small time difference of a few tens of microseconds,
and if the second RS has a larger peak than the first one, the second RS may be misclassified as an IC pulse.
One example is shown in Figure 5b. Such RSs are likely the so-called “multiple-termination strokes” (Konget al., 2009; Sun et al., 2016) or “forked strokes” (Ballarotti et al., 2005), with two RSs induced by two branchesof the same leader. Third, an RS may occur almost simultaneously with IC discharges of other lightning flashes,
resulting in a peculiar waveform and thus misclassified as an IC discharge. One example is shown in Figure 5c.
While the positive pulse is confirmed to be produced by an RS, the preceding negative pulse labeled as “IC”
is produced by IC discharges in an independent lightning flash and is located about 87 km away from the RS.
Such large negative pulse is normally not seen right before negative RSs, and as a result the overall waveform is
misclassified as an IC discharge. Finally, some RSs apparently produce waveforms that are largely different fromtypical RS waveforms but the reason is not yet clear. One example is shown in Figure 5d. The pulse has a rise timeof about 18 μs while its fall time is only about 9 μs.

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Figure 5. (a)–(d) Atypical E-change waveforms produced by return strokes (RSs) but misclassified as intracloud (IC) discharges. (e)–(h) Atypical E-change waveforms
produced by IC discharges but misclassified as RSs. The value of d represents the distance between the discharge and the observation site recording the waveform. The
value of h represents the source height of the IC discharge.

Another example of an RS producing abnormal waveform is shown in Figure 6 along with location results of thepreceding leader. This RS is a subsequent RS. We can see from the location results in Figure 6a a dart leader witha speed of about 4 × 10 6 m/s preceding the RS, and the RS is located very close to the ground as indicated by thecross sign. From Figure 6c, we can see details of the RS waveform. It contains two peaks with the second peakmuch larger than the first one, resulting in a much larger rise time than the fall time. Without the 3-D location
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Figure 6. Location result and E-change waveforms of a return stroke (RS) misclassified as an intracloud discharge. (a) Height-time location results of the dart leader
preceding the RS. The cross sign represents the RS. (b) E-change waveform of the RS and preceding discharges. (c) E-change waveform of the RS. The value of drepresents the distance between the RS and the observation site recording the waveform.

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results, it is very difficult to determine that the waveform is produced by an RS. Waveforms of this RS recordedby all sites are shown in Figure S2 in Supporting Information S1.
The major reason for IC discharges misclassified as RSs is that waveforms of some IC discharges have somesimilar features as those of RSs. Four examples are shown in Figures 5e–5h. All of these waveforms appear
very similar to those of RSs. However, their source heights range from 5.9 to 15.1 km, indicating that they
are produced by IC discharges. We also manually located these pulses to make sure that there were no large
errors in the source height results. We can see that these pulses have relatively short rise times and much
longer fall times. Pulses in Figures 5e–5g also have fine structures superimposed on the falling part, similar to
waveforms of first RSs, and the pulse in Figure 5h resembles the waveform of a subsequent RS. These similarfeatures as RS waveforms make it almost impossible to correctly classify them as IC discharges without the
3-D location results.
Another example of an IC pulse appearing similar to RS pulses is shown in Figure 7 along with location resultsof preceding discharges. From the height-time location results in Figure 7a, we can see that a leader first propagated above 6.5 km and then descended to a height of about 5.5 km, and then the large IC pulse is produced,
represented by the cross sign. From the E-change waveform in Figure 7c, we can see that the large IC pulse isvery similar to an RS pulse, with preceding pulses resembling stepped leader pulses. With the help of the 3-D
location results, we can be sure that this RS-like pulse is produced by IC discharges. Waveforms of this IC
discharge recorded by all sites are shown in Figure S3 in Supporting Information S1. We are not aware of any
study reporting such RS-like IC pulses, and the reason for their abnormal waveforms is not immediately clear
even by looking at their 3-D mapping results. In our future studies, we will explore the mechanism responsible
for these special IC pulses.
These examples of special RS and IC waveforms illustrate the fact that some RSs and IC discharges produce
atypical radiation waveforms from which the discharge types cannot be accurately determined, resulting in afundamental difficulty to achieve very high accuracy and efficiency using only waveform information. This
result also illustrates the importance of accurate 3-D location results in scientific investigations of lightning
phenomena.

5. Conclusions
Using a large data set with 3-D location results, we built a classifier for radiation waveforms of negative
RSs based on the Random Forest classifier. Eleven simple parameters are defined for building the classifier,including three parameters related with pulse characteristics and eight parameters related with relative strengthof pulses. A classification accuracy of 98.84% and an identification efficiency of 98.81% are achieved. We
also demonstrated methods to tune the tradeoff between the accuracy and the efficiency so the classifier canbe used in applications with different requirements of the accuracy or the efficiency. The importance of the
11 parameters was analyzed and we demonstrated that it is possible to reduce the number of parameters withrelatively low importance and at the same time keep the high performance of the classifier. With the same
methods, we also built a classifier for positive RSs which has similarly high accuracy and efficiency as theclassifier for negative RSs.
Misclassified RS and IC waveforms are examined and some common reasons for misclassifications are analyzed.
We demonstrated that RSs sometimes produce radiation waveforms that are largely different from normal RS
waveforms, and IC discharges sometimes produce waveforms that appear very similar to RS waveforms. Therefore, some RS and IC waveforms are fundamentally difficult to be correctly classified without 3-D location
information, and it is likely that such misclassifications commonly exist in most LLSs. The results also imply theimportance of 3-D location results in detailed analyses of lightning phenomena.

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Figure 7. Location result and E-change waveforms of an intracloud (IC) pulse misclassified as a return stroke pulse. (a) Height-time location results of the IC pulse andpreceding discharges. The cross sign represents the location of the IC pulse. (b) E-change waveform of the IC pulse and preceding discharges. (c) E-change waveform of
the IC pulse. The value of d represents the distance between the IC discharge and the observation site recording the waveform.

Data Availability Statement
Data sets for building and testing the classifiers, waveform figures of all positive and negative RSs, data ofthe trained classifiers and a simple Python script demonstrating the usage of the classifiers can be found athttps://doi.org/10.5281/zenodo.7900171 (Wu, 2023).
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Acknowledgments
This study was supported by the Ministryof Education, Culture, Sports, Science,
and Technology of Japan (Grants
20H02129 and 21K03681).

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