Journal of Geophysical Research: Atmospheres
RESEARCH ARTICLE
10.1002/2016JD025832
Key Points:• Windmill coronas radiate larger
power and possibly develop to higher
altitudes than tower coronas do• Windmill corona production isperiodic, but only two out of threeblades of the windmill produce
detectable radiation• Coronas are not related with upward
leader initiation, but nearby lightning
can increase corona production rates
right after the ﬂash

Correspondence to:T. Wu,
tingwu@gifu-u.ac.jp

Citation:
Wu, T., D. Wang, W. Rison,
R. J. Thomas, H. E. Edens, N. Takagi,
and P. R. Krehbiel (2017), Corona
discharges from a windmill andits lightning protection tower
in winter thunderstorms, J.
Geophys. Res. Atmos., 122, 4849–4865,
doi:10.1002/2016JD025832.

Received 24 AUG 2016
Accepted 11 APR 2017
Accepted article online 18 APR 2017
Published online 8 MAY 2017
Corrected 16 JUN 2017

This article was corrected on 16 JUN
2017. See the end of the full text for
details.

©2017. American Geophysical Union.
All Rights Reserved.

WU ET AL.

Corona discharges from a windmill and its lightning
protection tower in winter thunderstorms
Ting Wu1 , Daohong Wang1 , William Rison2
Nobuyuki Takagi1 , and Paul R. Krehbiel2, Ronald J. Thomas2, Harald E. Edens2 ,1 Department of Electrical, Electronic and Computer Engineering, Gifu University, Gifu, Japan, 2 Langmuir Laboratory for

Atmospheric Research, Geophysical Research Center, New Mexico Institute of Mining and Technology, Socorro, New
Mexico, USA

Abstract This paper presents lightning mapping array (LMA) observations of corona discharges from awindmill and its lightning protection tower in winter thunderstorms in Japan. Corona discharges from thewindmill, called windmill coronas, and those from the tower, called tower coronas, are distinctly diﬀerent.
Windmill coronas occur with periodic bursts, generally radiate larger power, and possibly develop to higher
altitudes than tower coronas do. A strong negative electric ﬁeld is necessary for the frequent production of
tower coronas but is not apparently related with windmill coronas. These diﬀerences are due to the periodic
rotation of the windmill and the moving blades which can escape space charges produced by corona
discharges and sustain a large local electric ﬁeld. The production period of windmill coronas is related withthe rotation period of the windmill. Surprisingly, for one rotation of the windmill, only two out of the threeblades produce detectable discharges and source powers of discharges from these two blades are diﬀerent.
The reason for this phenomenon is still unclear. For tower coronas, the source rate can get very high only
when there is a strong negative electric ﬁeld, and the source power can get very high only when the source
rate is very low. The relationship between corona discharges and lightning ﬂashes is investigated. There isno direct evidence that corona discharges can increase the chance of upward leader initiation, but nearby
lightning ﬂashes can increase the source rate of corona discharges right after the ﬂashes. The peak of thesource height distribution of corona discharges is about 100 m higher than the top of the windmill and the
top of the tower. Possible reasons for this result are discussed.

1. Introduction
It is well known that in the enhanced electric ﬁeld under thunderstorms, pointed objects on the groundsuch as towers, trees, and grass can produce corona discharges. Corona discharges are conﬁned in a small
region around conductive points where the electric ﬁeld is larger than that necessary for electrical breakdown.
Corona discharges produce space charges in front of the electrode, which shield the electrode and decrease
the local electric ﬁeld. However, if the ambient electric ﬁeld is strong enough and there are large quantitiesof space charges, the electric ﬁeld produced by the space charges can generate further ionization and resultin weakly conducting streamer channels. If the ambient electric ﬁeld keeps growing, the current of streamers can get large enough to heat the streamer stem and turn it into a hot, conducting, and self-propagating
leader channel [Cooray, 2015].
Corona discharges also emit electromagnetic radiation but are much less powerful than lightning discharges.
As a result, direct observations of corona discharges under thunderstorms are quite scarce and most studies
about corona discharges are carried out by laboratory experiment [e.g., Waters, 1975] and numerical simulation [e.g., Becerra et al., 2007]. Early studies also paid attention to the inﬂuence of space charges producedby corona discharges on the electric ﬁeld under thunderstorms [Toland and Vonnegut, 1977; Standler andWinn, 1979; Soula and Chauzy, 1991]. Recently, Montanya et al. [2014] and Rison et al. [2015] both successfully observed corona discharges from windmills using the lightning mapping array (LMA). Montanya et al.
[2014] reported observation of periodic corona discharges at regular intervals of about 3.15 s from a windmill in Spain. Most detected VHF radiation sources were below 2 km in altitude and had powers of about−5 dBW. Rison et al. [2015] made a similar observation in a wind farm in Kansas. They found that the period
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of corona discharge groups was the same as the rotation period of the windmill, indicating that only one outof the three blades produced detectable discharges. They also found that the altitude of the corona sources
centered between the hub of the windmill and the blade tips.
During the winter campaign in 2014, we set up a nine-station LMA around a windmill and its lightning protection tower in Uchinada, Japan [Wang et al., 2015]. We have been making winter lightning observation formany years, mainly using high-speed optical systems supplemented with electric ﬁeld mills, and fast andslow antennas [Wang et al., 2008; Wang and Takagi, 2012]. This is the ﬁrst time that LMA has been used forwinter lightning observation in Japan. Winter lightning in Japan has many special characteristics including ahigh percentage of positive cloud-to-ground ﬂashes [e.g., Takeuti et al., 1978], frequent bipolar ﬂashes [e.g.,
Narita et al., 1989] and upward ﬂashes [e.g., Wang et al., 2008], a very small time diﬀerence between preliminary breakdown and the return stroke [Brook, 1992; Wu et al., 2013], and some discharge processes that havenot been observed in summer thunderstorms [Wu et al., 2014]. With the help of LMA, we intend to further
investigate the initiation and propagation characteristics of upward and bipolar ﬂashes, and the relationship between lightning types and the charge structure of winter thunderstorms. An analysis of the LMA data
showed that the system was triggered most frequently by corona discharges. As a ﬁrst report, this paper will
describe the observation of corona discharges from a windmill and its lightning protection tower. We will
describe diﬀerent characteristics of corona discharges from the windmill and the tower and investigate possible relationships between corona discharges and lightning ﬂashes. Based on the observation results, we will
discuss the physical processes responsible for the observed corona discharges.

2. Experiment and Data
During the winter of 2014, a nine-station LMA was deployed near the Japan Sea coast in the Hokuriku region
where winter lightning frequently occurs. LMA is a widely used lightning location system working in the VHF
band [Rison et al., 1999]. It can accurately locate sources of VHF radiation of basically all types of lightning
discharges. Figure 1a shows the array. It covers an area of about 18 × 18 km2 , forming a compact network,
which is capable of detecting discharges with very weak radiation, such as corona discharges. A windmill islocated at (0, 0), and its lightning protection tower is about 45 m away. The ground level is about 50 m. The
height of the windmill (from the base to the tip of a blade pointing upward) is 100 m, and the height of thetower is 105 m. So the altitude of the tower top is 155 m and the maximum altitude of the windmill is 150 m.
Details of the tower and the windmill are also described by Wang and Takagi [2012].
From Figure 1a we can see that all sources of corona discharges are located near the windmill and the tower(at this scale, we cannot diﬀerentiate the windmill and the tower from corona sources). An enlarged image
for the region near the windmill is shown in Figure 1b. Most of the sources are centered around the windmill
and the tower. Sources around the windmill seem to have higher power than those around the tower. Overall,
the source power of corona discharges is quite low, mainly below −10 dBW (about 0.1 W). This is comparedto source powers from 0 dBW up to 40 dBW for normal intracloud discharges [Thomas et al., 2001].
Corona discharges analyzed in this paper are observed in two periods: 15:00–21:00, 14 November and13:50–23:00, 2 December 2014 (universal time). In these two periods, the LMA was operated continuously
without any trouble, and a large number of corona discharge sources were located. Figures 1c and 1d show
the time series of corona discharges in these two periods. Most of the sources were lower than 600 m. Duringsome short periods, some sources reached about 1000 m.
Figure 2 shows height distributions of all corona sources on 14 November and 2 December. It also shows theground level, the top of the tower, and the top of the windmill. We can see a predominant peak at 50–60 m
on both days. At ﬁrst, we thought this peak was produced by corona discharges on the ground. However, LMA
in this study does not seem to be able to detect corona discharges on the ground. During this observation,
almost all corona discharges are located at the tower and the windmill. If this peak was produced by corona
discharges on the ground, there should have been corona discharges detected everywhere inside the array.
It seems that LMA is only capable of detecting relatively strong corona discharges from tall objects, and all
sources in Figure 2 should be produced from the tower and the windmill. Figure 2c shows the distribution of
reduced chi-square values (𝜒v2 ) versus heights for all corona discharge sources. As discussed by Thomas et al.
[2004], 𝜒v2 is an indication of the location error, and we are only using location results with 𝜒v2 smaller than 5.
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Figure 1. Sources of corona discharges located by the LMA. (a) Network of LMA. All sources of corona discharges arelocated near the windmill (0, 0) and a nearby tower. (b) Locations of corona discharges and the windmill (red cross), thetower (red triangle), and the ﬁeld mill (black dot). (c) Time sequence of source height of corona discharges on 14
November. Red curve represents electric ﬁeld. Red and blue horizontal lines indicate periods of windmill coronas andtower coronas, respectively. (d) The same as Figure 1c but for 2 December. Source color indicates radiation power
determined by LMA.

From Figure 2 we can see that many sources near the ground have relatively large errors, also indicating thatsources near the ground may be not real and were caused by location errors. The large number of sources
mislocated near the ground may pose a signiﬁcant inﬂuence on the analysis, so we decided that only sources
above 100 m (black dashed lines in Figure 2) are used in this study.
The electric ﬁeld measured by an electric ﬁeld mill near the windmill is also shown in Figures 1c and 1d. The
ﬁeld mill has a sampling rate of 20 samples/s, shown as a black dot in Figure 1b. Due to the shielding eﬀect of
the windmill, the absolute value of the electric ﬁeld strength is underestimated. Atmospheric sign convention
is used for the electric ﬁeld record, so a positive value indicates a downward electric ﬁeld.
We also have high-speed video recordings of lightning ﬂashes striking at the windmill and the tower. These
data will not be analyzed in detail in this paper but will only be used to determine striking locations for someﬂashes of interest.
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Figure 2. Height distribution of all corona sources on (a) 14 November and (b) 2 December. (c) Reduced chi-squarevalues (𝜒v2 ) versus sources heights. Color indicates the source density. Purple dashed lines indicate the ground level. Bluedashed line in Figure 2a indicates the top altitude of the tower. Red dashed line in Figure 2b indicates the top altitude of
the windmill. Black dashed lines indicate the height of 100 m, sources below which are not analyzed in this study.

3. Results
3.1. Two Types of Corona Discharges
From Figure 1b we have already noticed that corona discharges from the windmill and the tower have quite
diﬀerent powers. The tower is at least 5 m taller than the windmill and has a sharper top (there is a lightning
rod at the top of the tower), so when the windmill is not rotating, corona discharges are more likely to be
produced from the tower. However, when the windmill is rotating, the moving blade is capable of escaping
the space charges produced by corona discharges and is likely to produce corona discharges more frequently.
Due to the fundamental diﬀerence between the tower and the windmill, more diﬀerences in their corona
discharges are expected. In this section, we will explore the diﬀerences between corona discharges from thetower and the windmill.
For this analysis, we need to ﬁrst classify all corona discharges into those from the tower and those from thewindmill. If we knew the periods when the windmill was or was not rotating, the classiﬁcation would be veryeasy. Unfortunately, we could not get this information from the windmill operator. As a result, we can only
make the classiﬁcation based on source locations. We carefully checked source locations of all corona discharges and found some periods during which sources were predominantly occurring near the tower (bluehorizontal lines in Figures 1c and 1d) and some periods during which sources were predominantly occurring
near the windmill (red horizontal lines in Figures 1c and 1d). In other periods, we were unable to determine
whether the tower or the windmill was playing a predominant role in producing the sources. In the following analyses, we will refer to corona discharges occurring around the windmill as windmill coronas and thosearound the tower as tower coronas. It should be noted that this classiﬁcation is not strict; periods of windmill
corona may also include a small number of tower coronas and vice versa. This is unavoidable as the tower andthe windmill are closely situated and will always have certain eﬀects on the production of corona discharges.
We have tried to select the periods during which most of the sources are clearly produced by either the tower
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Figure 3. A short period on 14 November during which a large number of windmill coronas occurred, followed by tower coronas. (a) Time series of source heightand electric ﬁeld. F1–F3 indicates the time when upward lightning ﬂashes occurred. Sources of these ﬂashes are not plotted. (b) Locations of windmill coronaswith respect to the windmill and tower. (c) Locations of tower coronas with respect to the windmill and tower. (d) Production frequency of sources of windmill
coronas and tower coronas.

or the windmill. Two of the periods are shown in detail in Figures 3 and 4, and the statistical results for all
selected periods will be analyzed in this section.
Figure 3 shows a segment of 28 min on 14 November (also shown in Figure 1c), during which a large numberof windmill coronas are followed by a large number of tower coronas. A black dashed line in Figure 3a divides
windmill coronas and tower coronas.
Figure 3b shows locations of windmill coronas (before the black dashed line), which are centered around thewindmill. Although some sources are located around the tower, we cannot see clearly the contribution of the
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Figure 4. The same as Figure 3 but for a period on 2 December.

tower to the production of these sources. By comparison, Figure 3c shows locations of tower coronas (after
the black dashed line), which are centered around the tower. Almost no sources are located near the windmill.
It seems that the majority of sources in Figure 3c are produced from the tower. An obvious diﬀerence between
the two types of discharges is that sources of windmill coronas are generally more powerful.
Figure 3d shows the frequency distribution of source production for the two types of discharges. The frequency is calculated by ﬁrst counting source numbers in every 0.1 s segment and then performing the Fouriertransform. The frequency for windmill coronas shows three clear peaks, at 0.2, 0.4, and 0.6 Hz, while the frequency for tower coronas does not show any clear peak. It clearly indicates the eﬀect of the windmill rotationon the production of windmill coronas.
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Figure 5. Comparison of windmill coronas and tower coronas. (a) Distribution of source power. (b) Distribution of source altitude. (c) Distribution of reduced
chi-square value (𝜒v2 ).

Figure 4 shows a segment of 34 min on 2 December (also shown in Figure 1d). During this period, a large
number of tower coronas are followed by windmill coronas. Figure 4b shows the locations of tower coronas(before the black dashed line). The majority of sources are located around the tower. A few sources are scattered, but it seems that the windmill has little contribution to the production of these sources. Figure 4c shows
the locations of windmill coronas (after the black dashed line). In this case, the sources are scattered aroundthe windmill. Some sources (green ones near the tower) seem to be produced from the tower. It looks like they
were produced alongside with the corona discharges from the windmill. As is the case in Figure 3, sources ofwindmill coronas are generally more powerful than tower coronas.
Figure 4d shows source production frequencies. The frequency for tower coronas still does not have any clear
peak, similar to the case in Figure 3. The frequency for windmill coronas shows some peaks but not very clear.
However, we can still identify three frequency components as indicated by three arrows in Figure 4d. The f2 isabout 2 times of f1 , and f3 is about 3 times of f1 , the same as the case in Figure 3. The values of the frequencies
are diﬀerent, indicating that the rotation speed of the windmill was diﬀerent.
Based on the above two cases, diﬀerences between windmill coronas and tower coronas are further analyzed
and summarized as follows.
1. Windmill coronas generally have larger powers than tower coronas. From the Figures 3b, 3c, 4b, and 4c we
can see that sources of windmill coronas are much more powerful than those of tower coronas. Figure 5ashows source power distributions for the two types of discharges in all selected periods (as indicated in
Figure 1). The source power of tower coronas centers in −27 to −18 dBW while the source power of windmill coronas has a wide distribution from −24 to −6 dBW. The average values are −21.7 and −15.5 dBW,
respectively, for tower coronas and windmill coronas. The smallest source power that could be detectedin the observation by Rison et al. [2015] was −20 dBW, and they only detected one short period of corona
discharges from towers. The typical source power detected in the observation by Montanya et al. [2014]
was about −5 dBW, and apparently, they did not detect any corona discharges from towers or other stationary objects. These results also indicate that the power of windmill coronas is stronger than that of
tower coronas.
2. Sources of windmill coronas can reach higher altitudes than those of tower coronas. From the Figures 3aand 4a, we can see that most of the sources of tower coronas are below 400 m, while for windmill coronas a signiﬁcant portion of the sources are between 400 and 600 m. Figure 5b shows the distribution ofsource altitudes for two types of discharges in all selected periods (as indicated in Figure 1). The distribution
for windmill coronas is much wider, with a much higher percentage of sources reaching altitudes above
400 m. The average values are 230.5 and 321.0 m, respectively, for tower coronas and windmill coronas. It
should be noted that sources below 100 m are not used for this analysis, so these average values may beoverestimated. As shown in Figure 5c, windmill coronas also have a wider distribution of 𝜒v2 , indicating thatlocation errors for windmill coronas are larger, and it is possible that the height diﬀerence between tower
and windmill coronas are due to diﬀerent location errors. More will be discussed on this issue in section 4.2.
3. The production of windmill coronas shows three characteristic frequency components: f1 , f2 , and f3 , in which
f2 = 2f1 and f3 = 3f1 . These frequency components are caused by the periodic rotation of the windmill,
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Figure 6. (a) A segment of windmill coronas. Red and blue arrows are both separated by 5 s. The time diﬀerence
between successive red and blue arrows is 1.67 s. (b) A segment of tower coronas.

so tower coronas do not show such characteristic frequency components. The relationship between thesefrequency components and the rotation of the windmill will be further analyzed in section 3.2.
4. Tower coronas are usually accompanied by a large negative electric ﬁeld. This is especially obvious when alarge number of lower power (dark blue) sources are produced (19:40–21:40 in Figure 3, 10:30–12:00 and
17:00–21:00 in Figure 4). On the other hand, no special characteristics can be identiﬁed for the electric ﬁeld
during the period of windmill coronas. The electric ﬁeld is usually much weaker and can also be positive
when windmill coronas are produced. This indicates that a strong electric ﬁeld is essential for the productionof tower coronas but is not necessary for windmill coronas.
One feature in Figures 3 and 4 that we do not understand is that sources of tower coronas always show anelongated shape oriented in a ﬁxed direction. This should not be due to the network conﬁguration, as sourcesof windmill coronas do not have such a shape. This should not be due to the inﬂuence of the windmill, as the
direction is not right to the windmill. This should not be due to the wind eﬀect, as the shape is symmetrical to
the tower. This should not be due to some local objects or landforms around the tower, as we made a survey
and did not ﬁnd anything corresponding the orientation. This can be due to some unknown properties of
tower coronas, but further observations are needed to make sure that this is not a local phenomenon and is
not due to systematic location errors.
3.2. Frequency Analysis for Windmill Coronas
As shown in Figures 3d and 4d, the production of windmill coronas shows three characteristic frequency
components, which are apparently related with the rotation of the windmill. However, how these frequency
components are related with the windmill rotation is not yet clear.
Figure 6 shows segments of windmill coronas and tower coronas. The production of windmill coronas is apparently periodic, but this is not the case for tower coronas. In Figure 6a, we have drawn some red and blue arrows,
both of which are separated by T = 5 s, and successive red and blue arrows are separated by ΔT = 1.67 s. T
corresponds to f1 = 0.2 Hz in Figure 3d, and ΔT = T∕3. It seems that each red arrow corresponds to a columnof relatively bright sources, and each blue arrow corresponds to a column of relatively dark sources. We speculate that for one rotation of the windmill, during which the three blades pass the highest point, one blade
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Figure 7. Simulation of the frequency components of windmill corona production. (a) Simulated time series of source
numbers. (b–e) Frequency distribution under diﬀerent values of ΔT .

emits corona discharges relatively strongly, followed by a blade that emits relatively weakly, followed by thethird blade having even weaker emissions, which cannot be detected. Then a new rotation with the same
behavior follows.
In order to verify this speculation, we did a simple simulation. We simulated a 100 s series of source numbers.
At ti = 5i and tj = 5j + ΔT (i, j = 0, 1, 2, … , 20) s, sources with a Gaussian distribution are produced. The
probability density for the distribution has the form()(t−tj )2(t−ti )2
1
−
−
2
2
2𝜎
2𝜎
e
p(t) = √
+e
(1)
2𝜋𝜎 2
in which ti corresponds to the sources produced by the ﬁrst blade (red arrows in Figure 6a), and tj corresponds
to the sources produced by the second blade (blue arrows in Figure 6a). The parameter 𝜎 is the standard
deviation of the distribution. We set it as a constant 𝜎 = 0.5 s. We assume that source numbers producedby the two blades have the same distribution. For the case in Figure 6a, ΔT = 1.67 s, and the simulated
distribution of source numbers is shown in Figure 7a (only a segment of 0–20 s is shown). The corresponding
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Figure 8. Relationship between some parameters of tower coronas. Shown are scatterplots of (a) the source rate of
tower coronas versus the electric ﬁeld strength, (b) the source power versus the electric ﬁeld strength, and (c) the source
power versus the source rate.

frequency distribution is shown in Figure 7c, which is quite similar to the frequency distribution in Figure 3d.
We calculated the frequency distribution with diﬀerent values of ΔT as shown in Figures 7b–7e. Variation of
ΔT causes variations of relative strength of the three frequency components, and it seems that ΔT = 1.67 s
gives the most similar result.
With this simulation, we conclude that the three frequency components are indeed caused by corona
discharges emitted by two of the three blades, with the ﬁrst blade emitting relatively strongly and the second relatively weakly. It is likely that the third blade also emits some radiation, which is too weak to be
detected though.
We can also calculate the rotation period of the windmill from the frequency components.
1(2)
f1
For the case in Figure 3, f1 = 0.2 Hz, so the rotation period at that moment was 5 s. For the case in Figure 4,
f1 = 0.23 Hz, so the rotation period at that moment was 4.3 s. Although we do not have the data of thewindmill rotation period, we know that its rated rotation speed is 11–20 rpm, corresponding to the rotation
period of 3–5.5 s, in agreement with our calculations.
T=

Rison et al. [2015] observed corona discharges with a 10-station LMA in a wind farm in Kansas. They foundthat sources produced from the windmill had the same period as the rotation period of the windmill andconcluded that only one of the three blades was producing VHF sources. As the lowest power they could
detect was about 10 mW (−20 dBW), higher than that in our study, it is likely that other blades also emitted
corona discharges but were too weak to be detected. Montanya et al. [2014] also observed corona discharges
from a windmill with a 10-station LMA. They observed sources with a period of 3.15 s from the windmill andclaimed that this interval “corresponds to the time between each blade tip reaching the highest altitude.” This
corresponds to a rotation period of 9.45 s for the windmill, which is a relatively long period for a windmill. It
also seems that they did not have the data of the actual rotation speed of the windmill. Considering the factthat the power of the corona discharges detected by Montanya et al. [2014] was about −5 dBW, it is very likelythat Montanya et al. [2014] also only detected relatively powerful corona discharges from one blade similar to
Rison et al. [2015], and 3.15 s is actually the time for one complete rotation of the windmill.
3.3. Relationship Between Tower Coronas and the Electric Field
Characteristics of windmill coronas are controlled by the rotation of the windmill, so it is diﬃcult to study
the relationship between their characteristics and other factors such as the electric ﬁeld. On the other hand,
tower coronas do not have such a problem. Besides, tower coronas radiate more weakly, so have not been
observed by previous studies. In this section, we will explore the relationship between some characteristics
of tower coronas and the electric ﬁeld. Tower coronas in all selected periods (blue horizontal lines in Figure 1)
are analyzed, but periods when the electric ﬁeld is distorted by lightning ﬂashes are excluded. For every 10 s,source rate, average electric ﬁeld strength, and average source power are calculated and relations among
them are explored.
Figure 8a shows a scatterplot of the source rate of tower coronas versus the electric ﬁeld strength. Under apositive electric ﬁeld, the source rate is always very low (below 10 sources per 10 s). Under a relatively strong
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Figure 9. An intracloud ﬂash initiating an aborted upward leader (or just some high-altitude sources of corona
discharges, see text). In all views, colors indicate time with the earliest source in blue and the latest source in red.

negative electric ﬁeld, the source rate can be very high (up to 1000 sources per 10 s). This is consistent with
the notion that positive polarity corona discharge is easier to develop [MacGorman and Rust, 1998]. However,
although it is clear that a large negative electric ﬁeld is conducive to the production of corona discharges, there
is no straightforward relationship between the source rate and the electric ﬁeld strength. The possible reason
is that when the electric ﬁeld is strong enough and corona discharges frequently occur, the space charges
produced by corona discharges will hinder further development of corona discharges even if the electric ﬁeld
gets stronger.
Figure 8b shows a scatterplot of the source power versus the electric ﬁeld strength. When the electric ﬁeld is
positive, the source power seems to be relatively stable, around −15 dBW, without any clear relationship to theelectric ﬁeld strength. When the electric ﬁeld is negative, the source power tends to decrease with increasing
electric ﬁeld strength (absolute value). This is somewhat surprising. A related result is shown in Figure 8c,
which is a scatterplot of the source power versus the source rate. For sources with powers higher than about
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Figure 10. Height-time view of a self-initiated upward lightning from the tower. Color indicates the source power. (a) A
section of 5 s before and after the upward lightning. (b) An enlarged view of the upward leader.

−20 dBW, the source rate is usually very low, mostly lower than 10 sources per 10 s. When the source poweris below −20 dBW, the source rate can be very high. According to Figure 8a, high source rate corresponds
to a strong negative electric ﬁeld. It seems that only when a strong negative electric ﬁeld exists can tower
coronas occur frequently. However, when a large number of sources are produced, their source powers arealways very low. On the other hand, if a positive or a very weak negative electric ﬁeld exists, tower coronas canrarely occur, but once they occur, their source power tends to be large. This result may also be related withthe space charges produced by the corona discharges. High rates of corona discharges produce a signiﬁcantamount of space charges, which reduce the local electric ﬁeld and impede the further development of corona
discharges, resulting in relatively low source powers.

3.4. Relationship With Lightning Flashes
Windmill coronas are more powerful and possibly develop higher in altitude, so it is expected that they are
more likely to initiate lightning ﬂashes. In Figure 3a, there are three upward ﬂashes (F1–F3) from the tower or
the windmill. F1 is close to the end of the most frequent period of windmill coronas. Similarly, in Figure 4a there
is one upward ﬂash (F4), which occurred right at the end of a period of frequent windmill coronas. On the contrary, tower coronas do not show any evidence that they may be associated with any lightning ﬂashes. From
this respect, windmill coronas seem to be more likely to precede lightning ﬂashes. However, F1 in Figure 3a is
at least tens of seconds apart from the most frequent corona discharges. In other words, the activity of windmill coronas has already diminished before the onset of the ﬂash. For F4 in Figure 4a, a close look at its LMA
sources shows that there is an intracloud ﬂash near the windmill initiating an aborted upward leader from thewindmill as shown in Figure 9. We can see that an intracloud ﬂash occurred around the tower and windmill,and less than 0.1 s after, an upward leader was initiated. The leader propagated to nearly 2000 m altitude andthen stopped. This kind of other-triggered upward leader is commonly observed in winter [Wang et al., 2008],
and there is no evidence that the intracloud ﬂash has any connection with the corona discharges before it. It
is also possible that the aborted upward leader is actually some relatively high sources of corona discharges,
according to the time scale. Either way, we found no direct evidence that either windmill coronas or tower
coronas are associated with the initiation of lightning ﬂashes.
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In fact, all of the above ﬂashes (F1–F4) areother-triggered upward ﬂashes [Wang et al.,2008; Saba et al., 2016]. Such ﬂashes are
initiated by a rapid electric ﬁeld change
caused by other nearby lightning ﬂashes, so
it is an expected result that they do not have
any relationship with corona discharges.
In winter, self-triggered upward lightning
ﬂashes are also commonly observed [Wanget al., 2008]. These ﬂashes are caused bya slowly built up background electric ﬁeld.
During the period of the analysis for thisstudy, there are three self-triggered upward
ﬂashes, but still, we cannot ﬁnd any evidence that they are related with precedingcorona discharges. One example is shownin Figure 10. Figure 10a shows a section of
Figure 11. Source numbers of corona discharges within 2 s before
and after nearby lightning ﬂashes.
5 s before and after the upward ﬂash. We
can see there are only ﬁve sources within 5 s
before the ﬂash, an extremely low source rate as compared with Figure 8a. Therefore, the preceding corona
discharges do not seem to have any inﬂuence on the upward ﬂash.
On the other hand, lightning discharges nearby should be able to inﬂuence the space charges and the local
electric ﬁeld, so it is expected that lightning discharges may have certain impact on corona discharges. The
case in Figure 9 shows such a feature. There are few corona discharges within about 2 s before the intracloudﬂash, but right after it, numerous sources of corona discharges are detected, and they develop higher thanthose before the intracloud ﬂash. It seems that the intracloud ﬂash is capable of generating a burst of corona
discharges. Figure 11 shows the relationship between source numbers of corona discharges 2 s before and 2 s
after lightning ﬂashes within 5 km of the windmill. Cases with the source number of zero are not plotted in
the ﬁgure. We can see that for most cases, the source number of corona discharges after a ﬂash is larger thanthat before a ﬂash. Note that the axes are logarithmic scales, so there are usually far more sources within 2 s
after a ﬂash than within 2 s before a ﬂash. This result indicates that a lightning ﬂash near a tall object is indeed
able to increase the rate of corona discharges from the tall object right after the ﬂash. This is probably due tothe abrupt and large variation of the electric ﬁeld at the tip of the tall object caused by the lightning ﬂash.

4. Discussion
4.1. Production Frequency of Windmill Coronas
The diﬀerences between windmill coronas and tower coronas are mainly caused by the periodic rotation of
the windmill. For a stationary object, the space charges produced by the corona discharges can reduce theelectric ﬁeld at the tip of the object and suppress the further development of corona discharges. For windmills,
however, the moving blades can get rid of the space charges produced by corona discharges and the electricﬁeld at the tips of the blades can be sustained, so windmill coronas are more powerful than tower coronas.
One mystery about the windmill corona is its production frequency. In section 3.2, we have demonstrated thatfor one rotation of the windmill, during which three blades pass the highest point, corona discharges from theﬁrst blade have the largest power (strong radiation), those from the second blade have relatively weak power(medium radiation), and those from the third blade have even weaker power, which could not be detected(weak radiation) (Figure 6a). This scenario is illustrated in Figure 12a. The observations by Rison et al. [2015]
and Montanya et al. [2014] showed diﬀerent phenomena, but as demonstrated in section 3.2, it is possiblethat they actually only detected the relatively strong radiation from the ﬁrst blade. The problem here is that
if the three blades are exactly the same, it is unclear why the variation period of the radiation power has tobe the same as the rotation period of the windmill. Instead of the observed pattern (Figure 12a), it should beequally possible to be strong to medium+ to medium− to weak and back to strong (Figure 12b), or strong tomedium to weak to medium and back to strong (Figure 12c), and the period for corona discharge production
would be four thirds of the rotation period. The fact that only the ﬁrst scenario has been observed in diﬀerent
regions of the world indicates that there are some fundamental mechanisms behind this phenomenon.
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Figure 12. Illustration of three possible scenarios of one period of corona discharge production on the windmill. (a) A
scenario that has been observed. (b, c) Scenarios that should also be possible if the three blades of the windmill are
the same.

One possible explanation may be related with the production and drifting away of space charges produced bycorona discharges. On the ﬁrst blade, powerful corona discharges produce a large amount of space charges.
These charges drift away slowly in the ambient electric ﬁeld. Corona discharges on the second blade are
weaker due to the space charges. At this stage, the space charge density is still increasing, which makes corona
discharges on the third blade even weaker. Extremely weak corona discharges result in a rapid decrease of
the space charge density, so corona discharges on the next blade become powerful again.
In the case of a tower, the production and drifting away of the space charges can reach an equilibrium so thepower of tower coronas is relatively stable. For the case of a windmill, the fast moving blade can get rid of
the space charges and produce more powerful radiation, which results in the higher density of space charges
and makes the subsequent blade produce less powerful radiation. As a result, the radiation power of windmill
coronas shows periodic ﬂuctuations.
However, it is still diﬃcult to explain why the scenarios in Figures 12b and 12c cannot happen. The time
constants for the production and drifting away of space charges must satisfy certain relationships with therotation period of the windmill to make it only possible for the scenario in Figure 12a.
Another possible explanation that is much simpler is that one of the three blades has developed an imperfection as suggested by Rison et al. [2015]. The imperfect blade can always produce relatively powerful radiation
so the variation period of the radiation power is always the same as the rotation period. Considering the factthat windmills are frequently struck by lightning, imperfections on any blade is possible. However, it is still
diﬃcult to explain the observation in our study that at least two blades produce corona discharges. We canconsider that two of the three blades of the windmill in our study have developed imperfections. The second
blade produced relatively weak radiation due to the space charges produced by the ﬁrst blade. However, fora wind farm as in the study of Rison et al. [2015] and Montanya et al. [2014], windmills with imperfections on
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one, two, or even three blades should all exist, and diﬀerent patterns of the variation of radiation power shouldhave been detected; but apparently, only one pattern has been observed by Rison et al. [2015] and Montanya
et al. [2014].
It would be interesting to know what would happen if the windmill rotated much more slowly or much more
rapidly and what would happen if the windmill had four or more blades. Further observation and simulation
works are needed to answer these questions.
4.2. Source Height of Corona Discharges
As shown in Figures 2 and 5b, the source height distributions of both windmill coronas and tower coronas
peak at around 250 m. Altitudes of the windmill and the tower are 150 m and 155 m above mean sea level.
It seems that most corona discharges occur about 100 m above the top of the windmill and the top of thetower. This is in disagreement with the observation by Rison et al. [2015] which showed that most sourceswere located between the hub and the blades of the windmill.
Figure 5b also shows that the source height of windmill coronas has a much wider distribution extending
higher in the sky than that of tower coronas. They have a diﬀerence of about 100 m on the average sourceheight.
One possible reason for these results is that corona discharges observed in this study include streamers emanating from the windmill and/or the tower and dying out several hundred meters above. Streamers from thewindmill carry larger energy and can develop higher above. For the case in Figure 9, if we consider the several upward propagating sources after the intracloud ﬂash as produced by corona discharges, it is evident
that corona discharges can develop upward propagations after an abrupt electric ﬁeld change. It is possiblethat corona discharges observed by Rison et al. [2015] are the so-called “glow corona” without any streamersdeveloping upward [e.g., Becerra, 2013].
Another piece of evidence for this speculation is the source power. The source power of corona discharges,
especially windmill coronas, observed in this study seems to be close to that of the initial portion of upward
leaders. Figure 10b shows the ﬁrst 17 ms of a self-initiated leader from the tower. The ﬁrst several sources havepowers of about −10 dBW, close to the typical source power of windmill coronas (Figure 5a). As the leader
develops upward, the source power gets much larger.
Corona discharges can consist of both electrical avalanches and streamer processes [Cooray, 2015], and it ispossible that a signiﬁcant portion of the sources observed in this study are produced by streamer processes.
Sources of the electrical avalanches may have even lower power and were not detected, or they may be thelow tail in the source power distribution (Figure 5).
However, one diﬃculty for this explanation is that there is no observational evidence that streamers near thesea level can develop for more than 100 m. It is also possible that the location error is the reason for the height
distributions and diﬀerences between windmill and tower coronas.
The estimated height error is given by the following relation [Thomas et al., 2004]:()
d+rΔz ≃ cΔtz(3)where c is the speed of light, Δt is the timing error, z is the source height above the ground, d is the horizontal
distance between the source and the closest station, and r is the slant distance. The timing error is assumed
to be the same as the timing error of GPS: Δt ≃ 40 ns. In our case, the closest site is about 1430 m fromthe windmill and the tower, and the source height is assumed to be the same as the top of the windmill andthe top of the tower (height above the ground), so d ≃ 1430 m, r ≃ 1433 m, and z ≃ 100 m. This gives us
Δz ≃ 344 m. This height error is relatively large compared with the error for normal lightning discharges dueto the fact that corona discharges occur near the ground. This error may account for the 100 m diﬀerence
between the peaks of height distributions in Figure 2 and the top heights of the windmill and the tower.
The location error may also be the reason for the diﬀerence of height distributions of windmill and tower
coronas in Figure 5b. As shown in Figure 5c, the distribution of 𝜒v2 is wider for windmill coronas, indicatingthat location results of windmill coronas have larger errors. As one reviewer suggested, windmill coronas may
produce pulses with higher powers and longer durations. The longer duration makes a larger timing error Δt,
and thus a larger height error Δz for windmill coronas.
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5. Conclusions
Observations of corona discharges from a windmill and its lightning protection tower with a nine-station LMA
are reported. Because of the moving blades capable of escaping shielding space charges, windmill coronas are
distinctly diﬀerent from tower coronas. Windmill coronas generally have larger powers and possibly develop
higher upward than tower coronas do. The average source powers are −15.5 and −21.7 dBW, and averagesource altitudes 321.0 and 230.5 m, respectively, for windmill coronas and tower coronas. Tower coronas tend
to be produced in a strong negative electric ﬁeld, but windmill coronas do not have a clear relationship withthe electric ﬁeld.
The source production of windmill coronas shows three frequency components: f1 , f2 , and f3 , in which f2 = 2f1
and f3 = 3f1 . These frequency components are caused by the periodic rotation of the windmill, so they do
not exist for tower coronas. Close examination of the time series of sources of windmill coronas and a simple
simulation showed that during one rotation of the windmill, in which three blades pass the highest point, theﬁrst blade produces sources with large power, the second blade produces sources with median power, andthe third blade produces sources with weak power which cannot be detected. The reason for such periodic
variation is still not clear.
The relationship between tower coronas and the background electric ﬁeld is investigated. Under a positive or
weak negative electric ﬁeld, the source rate of tower coronas is always very low (below 10 sources per 10 s).
Under a strong negative electric ﬁeld, the source rate can sometimes be very high (up to 1000 sources per10 s). The source rate of tower coronas is also related with the source power. Only when the source poweris lower than about −20 dBW can the source rate get very high. For sources with powers higher than about−20 dBW, source rates are mostly lower than 10 sources per 10 s.
The relationship between corona discharges and lightning ﬂashes is also investigated. We did not ﬁnd any
direct evidence that either type of corona discharge raises the chance of upward leader initiation. But lightning ﬂashes near the windmill and the tower can increase the production rate of corona discharges right after
the ﬂashes.
Source altitudes of corona discharges in this study are on average about 100 m higher than the top of the windmill and the top of the tower. We speculate that a signiﬁcant portion of corona discharge sources observedin this study are produced by streamer processes. However, this explanation also has some diﬃculties, andanother possible reason is that the location error caused this result. The estimated height error for corona
discharges is 344 m, which is relatively large due to low source altitudes of corona discharges. The heightdiﬀerence between windmill coronas and tower coronas may also be due to the location error.
Acknowledgments
The data for this paper were obtained
during the winter campaign in2014. Readers can request the datafrom the corresponding author(tingwu@gifu-u.ac.jp). This work
was supported by the Ministry of
Education,Culture, Sports, Science, andTechnology of Japan (grant 2336012)
and Japan Power Academy Special
Research 2013.

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Erratum
In the originally published version of this article, the height units in Figure 9 and Figure 10 should read ‘m’instead of ‘km’. The error has since been corrected and this version may be considered the authoritative
version of record.

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