Blue Flashes as Counterparts to Narrow Bipolar Events: The Optical Signal of Shallow In-Cloud Discharges

Narrow Bipolar Events (NBEs) are powerful radio emissions from thunderstorms, which have been recently associated with blue optical flashes on cloud tops and attributed to extensive streamer electrical discharges named fast breakdown. Combining data obtained from a thunderstorm over South China by the space-based Atmosphere Space Interactions Monitor, the Vaisala GLD360 global

surface discharges (sometimes called blue glimpses) that appear to "dance" on the upper layer of the cloud at a rate of about 120 per min (Chanrion et al., 2017) and the gnomes that emerge directly from the cloud top within ∼1 km, similar to blue starters, but with brighter and more uniform optical emission and much more compact shape (Lyons et al., 2003). We do not classify Giant jets, which travel from cloud tops to the lower ionosphere, as BLUEs, since they involve significative emissions in the 777.4-nm band (van der Velde et al., 2019).
Each of these types of phenomena exhibits a different morphology but they likely share common physical processes. The blue color indicates the presence of electron-impact excitation of molecular nitrogen (Gordillo-Vázquez & Pérez-Invernón, 2021;Pasko, 2008;Surkov & Hayakawa, 2020) and the weak or absent atomic oxygen line at 777.4 nm, indicates that air does not reach high temperatures, typically associated with lightning leaders at ground level. This points to streamer coronas being the key component of BLUEs, a conclusion supported by the close association between BLUEs and narrow bipolar events (NBEs) (F. Liu et al., 2018;Soler et al., 2020), which are radio emissions also attributed to corona discharges in thunderclouds (N. Liu et al., 2019;Rison et al., 2016;Tilles et al., 2019). It is thus likely that both BLUEs and NBEs are electromagnetic manifestations of large streamer coronas (or fast breakdown, a term coined by Rison et al., 2016 that we also adopt here).
Some distinctive features of each type of BLUE arise from their extension and their location inside the thundercloud. For example, Soler et al. (2020) analyzed a set of 10 BLUEs associated with positive NBEs and at a considerable depth inside the cloud, presumably between the main negative and the upper positive charge region of the cloud. As these events are deeply buried in the cloud, the scattering by cloud droplets and ice crystals blurs their image as observed from above, resulting in a diffuse blob that can be identified with the blue glimpses reported by Chanrion et al. (2017).
Here, we focus on events that are close to the cloud top, perhaps partially outside the cloud. This location suggests an origin between the upper positive region of the cloud and the negatively charged screening layer, and this is supported by radio detections that associate these events with negative-polarity NBEs (positive charges moving upward) Smith et al., 1999;Wu et al., 2012). Because the emissions come from close to the cloud top, optical radiation is less affected by scattering, leading to a more robust inferrence of source characteristics. This allows us to compare to radio observations of fast breakdown.

Instruments and Observations
The MMIA is a component of the ASIM, a mission launched on April 2, 2018 and installed on the ISS Neubert et al., 2019). MMIA observes in ultraviolet and near-infrared wavelengths, points towards the nadir and contains three photometers and two cameras. The three photometers, with a temporal sampling rate of 100 ksamples/s, include one in the UV band at 180-230 nm, and two others sensitive to the same wavelengths as two installed cameras: in the near-UV at the strongest spectral line of the nitrogen second positive system (337 nm) and at the strongest lightning emission line, OI (777.4 nm). The spatial resolution of the cameras is around 400 × 400 m at the nadir point and their integration time is 83.3 ms.
On the evening of August 7, 2019, above an intense localized thunderstorm over Southern China, there were eight BLUEs simultaneously detected by MMIA, the ground-based Vaisala GLD360 global lightning network and the ground-based very low frequency (VLF)/low frequency (LF) sensor at Guangzhou (see Table 1 for further details). All of them were detected by MMIA's photometer and camera filtered at 337 nm; some events had a detectable signal in the 180-230 nm photometer but there was no signal in the 777.4 nm photometer and camera at the 3σ confidence level. Depending on the event this implies that the 777.4-nm flux was at least between 50 and 300 times weaker than the 337-nm flux (see Figure A1 and the text there in Appendix A for more details). The rise times of the events in the 337 nm photometer are below 56 μs, with the shortest of them being unresolved by the 10 μs sampling time of the photometer. The peak brightness ranges from 20 to 140 μW/m 2 , which is among the brightest signals detected by MMIA. The brightness and quick rise of the events indicate that they originate close to the cloud tops or perhaps slightly above them. Note that below, we show that most of the emissions were partially scattered by the cloud and that the photometer light curve is not indicative of the true source duration.
We sketch the context of the eight BLUEs in Figure 1 which, in panels (a) and (b), plots the intra-cloud (IC) and cloud-to-ground (CG) flashes and the eight BLUEs superimposed on the cloud top height (CTH) provided by the Fengyun-4A (FY-4A) satellite (Yang et al., 2017) for the time period from 13:04:00 to 13:07:00 UTC. During these three minutes, there were 522 lightning events with 240 CG and 282 IC flashes reported by GLD360 (see Figure 1). Two of the BLUE events (with ID 5 and 7) were missing from GLD360 so for all the BLUEs, we use the location provided by the lightning location systems (LLSs) in Guangzhou province (Chen et al., 2012).
The absolute timing uncertainty of MMIA is on the order of tens of milliseconds but we can correct the MMIA times to sub-millisecond accuracy by comparing flash times provided by GLD360 to MMIA 777.4 nm-pulses. In our case, we found that the systematic time shift with respect to the ground-based measurements experienced a time adjustment at around 13:06:07, the time corrections before and after the time adjustment are −23.3 ± 0.3 ms and −6.2 ± 0.5 ms, respectively (see Figure B1 in Appendix B for further details). Note that the time shift −23.3 ms is similar to the estimations for other thunderstorms such as the −28.7 ms inferred by Soler et al. (2020) or the −16.37 ms from Neubert et al. (2021).
With this time correction we find that each of the eight BLUEs has a radio signal that, when back-propagated to the source, is within 0.7 ms of the optical peak. All VLF/LF waveforms of the BLUEs were unambiguously classified as negative NBEs measured by the vertical electric field antenna (frequency bandwidth 800 Hz-400 kHz) located about 105 km away at Guangzhou station of Jianghuai Area Sferic Array (Qin et al., 2015;F. Liu et al., 2018). Figure 1 shows in panels (c) and (d) a composition of all camera images for the BLUE events (always from the 337 nm-filtered camera). To produce this picture we have added the projection of each of the eight MMIA images into the Earth surface according to coordinates introduced by the ASIM pipeline. The resulting locations differ noticeably from those provided by LLSs and the distribution is more spread out. We attribute this to uncertainties in the camera orientation. Note also that several of the images exhibit LI ET AL. Note. All the detection times have been corrected to the time with respect to the BLUEs source locations. Abbreviations: BLUEs, blue luminous events; LF, low frequency; MMIA, Modular Multispectral Imaging Array; VLF, very low frequency. a Rise time is calculated using the linear interpolation by taking the time for the amplitude of a photometer signal to rise from 10% to 90%. Note that the sampling time is 10 μs so the rise is unresolved in several events. b Time duration is calculated using the linear interpolation by the time interval for the amplitude of a photometer signal to rise from 10% and fall to 10%.

Table 1
The Eight BLUEs Simultaneously Detected by MMIA, Ground-Based Vaisala GLD360 Global Lightning Network and the Ground-Based VLF/LF Sensor at Guangzhou a sharp peak that appears to emerge from the middle of the diffuse blob: this is a blooming artifact of the CCD camera.
To understand better the relation between the BLUE emissions and their parent thunderstorm, we examined the progression of the cloud Top Blackbody Brightness temperature (TBB in K) provided by the Himawari-8 satellite (Bessho et al., 2016) with ten-minute resolution. Figure 2 displays the TBB around the time of our detections. The BLUE events originated from the boundary of a rapidly evolving thunderstorm cell. This suggests that rapid turbulent mixing of the screening layer plays a role in the inception of fast breakdown (Krehbiel et al., 2008;Lyons et al., 2003) or the occurrence of groups of localized NBEs is associated with dynamically intense convection (Bandara et al., 2021). Note that the cloud top heights provided by FY-4A that we use here are likely underestimates 2-3 km comparing with radar data (B. F. Liu et al., 2021). Since the negative NBEs are usually associated with deep convection and detected in overshooting cloud tops (F. Liu et al., 2018;Wu et al., 2013), which might also cause uncertainties.
LI ET AL.

Light-Scattering Model
To better understand the MMIA observations we compare them now to a simple model where the light source is a thin, straight, uniformly bright segment and the cloud is homogeneous with a planar upper boundary. We neglect the intrinsic duration of the source, assuming that all light is emitted instantaneously. This is consistent with the source durations for NBEs of about 10 microseconds estimated by Rison et al. (2016), which is much shorter than the signal waveforms that last several hundred microseconds. The propagation velocity of the discharges is thus unresolved in our analysis.
Because photons can be scattered many times before they exit the cloud, an impulsive optical flash results in a temporally stretched light curve. To understand this curve, we start with the expression for a point-like source buried in the cloud. Using the diffusion approximation for the propagation of photons inside the cloud proposed by Koshak et al. (1994) and Soler et al. (2020) gave an analytical expression for this curve, which was derived in more detail by Luque et al. (2020). Adopting the normalization and the notation of the latter the photon flux exiting the cloud top has the following expression valid for t > 0, with the time origin being the moment of light emission: where F(t) is the flux per photon in the source, N is the total number of source photons, τ A is the mean absorption time of the photons inside the cloud and τ D = L 2 /4D is, given a diffusion coeffcient D, the characteristic time of diffusion for the distance L between the source and the cloud top. The derivation of these magnitudes from the microscopic properties of the cloud is given by Koshak et al. (1994) and reviewed by Luque et al. (2020). For a distant observer, differences in light travel time from different points in the cloud LI ET AL.
10.1029/2021JD035013 5 of 13 are not significant so one can reinterpret the time in Equation 1 with t = 0 being the arrival time of an unscattered photon.

Length of the Optical Source
To obtain the light curve for an extended source that spans altitudes from the cloud top to a maximum depth L 0 we integrate (N/L 0 )F(t)dL in Equation 1 from 0 to L 0 (the factor N/L 0 is the linear density of source photons, assumed uniform). The result is Note that this expression disregards any part of the source above the cloud top. Some photons emitted outside the cloud propagate directly to the detector and others are back-scattered by the upper cloud surface after a small number of scattering events. These emissions have an effect only on a few data points in a photometer with a 10 μs time resolution. We therefore do not account for these emissions which, although may be present, do not dominate the photometer light-curves.   (Peterson, 2020;Platt, 1997) also lead to absorption times significantly longer than the duration of our events. Hence here we assume τ A ≫ τ D .
As we show in Figure 3, most of the recorded BLUEs light-curves have the shape predicted by Equation 2. In the figure, we plot a least squares fit of the observational data to the model with two parameters: An overall amplitude factor and the decay time τ D . To reduce the effect of the emissions from outside the cloud discussed above, we disregard the data points at the peak of the light-curve. The good fit of most events indicate that indeed they originate from sources that extend below the cloud top. Event 5 is the only one that does not show a clear t −1/2 decay, possibly because there was a gap between the source and the cloud top or because light emissions were inhomogeneous or long-lasting. In events 1 and 7 there is weak secondary activity 1-2 ms after the main peak that distorts the estimate of the cutoff time τ D .
From Table 2, leaving aside events where τ D was estimated poorly, this cutoff time ranges between 0.5 and 1.6 ms. The smallest diffusion coefficient proposed by Soler et al. (2020), D = 3 × 10 9 m 2 s −1 yields a range of lengths for the optical sources of L 0 = 2.4-4.4 km. However, the evaluated results will be affected by the uncertainties that surround our modeling of the cloud composition.

Monte Carlo Simulations
Next, we extend our model to include the propagation of the signal to the MMIA instruments, accounting for Rayleigh scattering by the atmosphere and for the non-isotropic (approximately Lambertian) emission pattern from the cloud tops. We use the radiative transfer Monte Carlo code CloudScat.jl  and run simulations of uniformly bright, straight vertical sources, with the lengths L 0 derived above, in a homogeneous cloud that spans altitudes from 7 km to the cloud top height derived by the Fengyun-4A (FY-4A) satellite LI ET AL.  with D = 3 × 10 9 m 2 s −1 , the total optical energy in the 337-nm band of the second positive system of nitrogen and an estimation of the number of streamer branching events in the fast breakdown processes that we assume that originated the events. a In events 1 and 7, there is secondary activity that distorted the estimation of the cutoff time τ D and the source length. b Event 5 has a light-curve that cannot be explained by an impulsive, uniformly bright source. (listed in Table 2). The scattering parameters in the cloud are those for a density of 10 8 m −3 spherical ice particles with 20 μm radius. The relative positions between the source and the observer reproduce the conditions of each of the eight BLUEs in our data set. Note that the optical length L 0 in our study is a relative extension from the cloud top to a maximum depth. The uncertainties of the cloud top heights provided by FY-4A satellite do not affect the modeling results.

Table 2 Model-Inferred Properties of the Eight BLUE Events
In Figure 4 we show the results of the Monte Carlo code comparing with 337-nm photometer and camera observations for the event 8 and 2 (Additional comparisons can be found in Figures S1-S8). The photometer light curves calculated from CloudScat model closely follow the analytical estimate of Equation 2 and are a good fit to the observations. The simulated camera images are also reasonably close to MMIA's records although they are slightly more compact. This is a possible indication of a non-negligible source width on the order of the camera resolution of about 400 m.
In the results presented here, we always consider that the top of the source coincides with the top of the cloud. As we discuss above, the effect of light emissions outside the cloud is too impulsive to compare against the MMIA photometer and is possibly dominated by the intrinsic time-dependence of the source. We performed additional Monte Carlo simulations that confirm that the photometer light-curves are compatible with source tops within a few hundred meters of the cloud top, either above or below it. The VLF/ LF waveforms of negative NBEs for event 8 and 2 are also shown in Figure 4. The radio signals of the eight events, along with other positive NBEs at deeper locations in the same thunderstorm, are analyzed with more details in a complementary publication (F. . The CloudScat.jl code outputs a photon flux at the observer's location in units of photons per unit time and unit surface that reach a detector for each photon in the source whereas the MMIA photometers are calibrated in terms of power per unit surface (irradiance). The conversion factor is the total energy of the event in the 337-nm band, E = Nhc/λ, where N is the total number of photons emitted by the source, h is the Planck's constant, c is the speed of light and λ = 337 nm. By comparing the results of our Monte Carlo code to the MMIA data we found the best-matching total energy of each event. Because the events that we analyze are close to the cloud tops and thus barely affected by in-cloud absorption, our estimates of E are weakly sensitive to our model assumptions and thus provide a reasonably precise picture of the actual source emission intensity of the BLUE events. The estimated energies are listed in Table 2.

Streamer Branching Events
N. Liu et al. (2019) analyzed radio spectra of NBEs and concluded that they can be understood as systems of 10 7 -10 8 streamers. In that analysis the key feature of a streamer is a current moment that increases rapidly on a time scale of about one nanosecond, which is the timescale of streamer initiation in numerical simulations. Here, in order to estimate the number of the streamer branching events for the BLUEs, we also consider that a single nanosecond event may produce more than one streamer, as is the case in a bifurcated tree. Denoting by b the mean number of streamers emerging from an event, we have M = bK, where M is the total number of streamers (unbifurcated branches) and K is the number of initiation events (most likely bifurcations from other streamers). Then the total streamer length contained in one fast breakdown process is ℓbK, where ℓ is the mean length between bifurcations (but see Nijdam et al., 2020 for a discussion of the difficulties involved in precisely defining this quantity). If a streamer emits η photons per unit length as it propagates, the total number of emitted photons is The value of η depends on the air density. We first estimate its value at atmospheric density, η 0 , by considering the numerical simulations by Malagón-Romero & Luque (2019). There we find a time-integrated photon yield of about n ph = 2 × 10 18 m −3 in a streamer of radius R ≈ 2 mm. The photon emission per unit length is then roughly where, we have also included a factor χ that accounts for the fraction of emissions of the second positive system of N 2 inside the 5-nm window of the 337-nm MMIA photometer. From the spectra presented by Gordillo-Vázquez et al. (2012), we estimate χ ≈ 0.3. This leads to η 0 ≈ 8 × 10 12 m −1 .
We now derive the photon yield η for a different air density n air by applying the scaling laws for streamers (Ebert et al., 2010). A length such as R scales like 1 air n . Because photons result from the electronic excitation of N 2 molecules into N 2 (C 3 Π u ), their density n ph is proportional to the electron density inside streamers, which scales as 2 air n . However the excited molecules are also collisionally quenched and the fraction of excited molecules that radiate is only where A is the Einstein radiative coefficient, k 1 and k 2 are the rate coefficients for the quenching of the N 2 (C 3 Π u ) state by collisions with, respectively, ground-state N 2 and O 2 and k′ = (k 1 [N 2 ] + k 2 [O 2 ])/ n air ≈ 0.8k 1 + 0.2k 2 . Capitelli et al. (2000) gives A ≈ 2 × 10 7 s −1 , k 1 ≈ 10 −17 m 3 s −1 , k 2 ≈ 3 × 10 −16 m 3 s −1 , which in our range of interest implies k′n air ≫ A, leading to f ≈ A/k′n air (i.e., f scales as 1 air n ). Combining all factors we conclude that η scales as 1 air n .
At an altitude of about 15 km, which is roughly the altitude of the events analyzed here, the air density is about 6 times lower than at ground value. The number of photons inside MMIA's 337-nm filter emitted by a streamer per unit length of propagation is about η ≈ 6η 0 = 5 × 10 13 m −1 .
To estimate the remaining factors in Equation 3, we first refer to Briels et al. (2008), who observed a ratio of branching length to streamer radius of about 20, so a radius of 2 mm at atmospheric pressure translates into ℓ ≈ 6 × 4 cm = 24 cm (Ebert et al., 2010). Finally, we take the branching number b to be 2, although there are evidences that it may possibly be slightly larger (Heijmans et al., 2013(Heijmans et al., , 2015. We can now solve for K in Equation 3 to find a number of branching events from the optical energies derived above. The results for all the BLUEs are listed in Table 2. Our results are 10-100 times above those derived from radio spectra by N. Liu et al. (2019). One possible reason for this disagreement is the uncertainties in our assumed parameters. For example, the estimated K is highly sensitive to the assumed streamer radius: had we chosen a radius of 5 mm at atmospheric pressure, the estimation of K would be reduced by about a factor 15. It is also possible that a large fraction of the optical signal in fast breakdown is emitted not close to streamer heads but from long-lived glows, as is the case in sprites (Luque et al., 2016;Pérez-Invernón et al., 2020).
Note, finally that our computations rely on extrapolations from streamer experiments and simulations at conditions that may turn to be different from those that prevail within a fast breakdown discharge inside a thundercloud. Nevertheless we find that the optical brightness of the BLUE events is compatible with an origin in extensive streamer coronas.

Discussion and Conclusions
The eight BLUE events that we analyze in this study expand and complete the picture of fast breakdown as the source of both optical blue-dominated emissions and radio pulses detected as NBEs in the VLF/LF bands or high-amplitude noise in VHF. All events were strongly detected in the photometer and camera filtred at 337 nm; in some events there was a weak signal in 180-230 nm but with no signal in 777.4 nm photometer and camera.
As in previous studies (Chanrion et al., 2017;Wescott et al., 1995;1996), the BLUEs appeared temporally isolated from either CG or IC flashes detected by the GLD360 network. However, all the BLUEs coincide with NBEs observed by the ground-based VLF/LF sensor at Guangzhou. This strengthens the connection between BLUEs and negative NBEs (Chou et al., 2018;F. Liu et al., 2018) and further supports that NBEs originate from non-thermal, streamer processes (Lyu et al., 2019;Rison et al., 2016;Tilles et al., 2019;Soler et al., 2020).
The rise times of the blue events in the 337 nm photometer are between 10 and 60 μs with peak irradiance varying from 20 to 140 μ Wm −2 . The brightness and short rise times suggest a source close or even slightly above the cloud tops and this is supported by our modeling results based either on the diffusion approximation by Koshak et al. (1994) or on a Monte Carlo radiative transfer code . Since all events are identified as negative NBEs, this is consistent with previous studies that place the initiation of most of negative NBEs between the upper positive charge region and the screening negative charge region of the thunderstorm Smith et al., 1999;Wu et al., 2012). The variation in the rise times between different events may be due to differences in the intrinsic time dependence of the optical sources but this is equally well explained by a finite distance to the cloud top or from nonuniformities of the optical sources below the cloud.
Our estimates of the total optical energy within the 337-nm band provide a new constraint for models of fast breakdown. The present understanding of these events is still limited and it is difficult to translate this energy into microscopical properties of fast breakdown. However our results confirm that fast breakdown involves more than 10 7 streamers, as inferred by N. Liu et al. (2019) and further analyzed by Cooray et al. (2020).
Future investigations should address the underlying physics of fast breakdown and its global significance, including its relation to lightning initiation. Data from the ASIM mission will likely play a decisive role in this research.

Appendix A: Constraints in the 777.4-nm Emission for Blue Luminous Events (BLUEs)
To establish rigorous bounds to the possible signal in the 777.4-nm photometer we proceed as follows. For each event first, we divide the photometer light-curve into temporal bins of m = 40 samples (0.4 ms) and compute the mean inside each bin b as where k b is the earliest sample inside b and y i is the value of each sample. These Y b = S b + η b contain a possible signal from the observed events S b as well as stochastic background noise η b . To characterize the statistical distribution of η b we find a bin where we can assume S b = 0 by selecting the bin with the largest Y b below the median of all Y b . We compute the empirical average μ 1 and standard deviation σ 1 for the samples inside this background bin. Then we approximate the distribution function of η b as a Gaussian with mean μ = μ 1 and standard deviation    1 / m . Hence we can mark bins with signals Y b above μ + 3σ as statistically significant (p-value < 0.0014).
The fact that we do not have any statistically significant 777.4-nm observation coinciding with the 337-nm peaks implies that in all cases the 777.4-nm signal is, if it exists, weaker than 3σ ≈ 0.1 μW/m 2 , which is between 200 and 1400 times below the different 337-nm peaks.
On the other hand, there are statistically significant emissions detected by the UV photometer sensitive to wavelengths in 180-230 nm. From our 8 events, 3 have UV detections coinciding with the 337-nm peaks at the 3σ level (events with ID 2, 3, and 5), 2 of them at the 5σ level (events with ID 4 and 6).
In Figure A1, we show the signals of the three photometers corresponding to event 6 in Tables 1 and 2 of the main text. This is the event with the strongest UV signal.

Appendix B: The Systematic Time Shift of MMIA With Respect to the Ground-Based Measurements
The systematic time shift of MMIA is estimated by using the 777-nm pulses and their simultaneous GLD360 events, which are (−23.3 ± 0.3) ms and (−6.2 ± 0.5) ms before and after the time adjustment τ, see Figure

Data Availability Statement
The Modular Multispectral Imaging Array (MMIA) data and Global Lightning Detection Network GLD360 data used in this study were obtained at (https://asdc.space.dtu.dk/). The cloud top height data is based on the data sharing proxy in Fengyun Satellite data center (http://satellite.nsmc.org.cn/PortalSite/Data/ Satellite.aspx?currentculture=en-US). The Himawari-8 gridded data in this study is supplied by the P-Tree System, Japan Aerospace Exploration Agency (JAXA)/Earth Observation Research Center (EORC) (https:// www.eorc.jaxa.jp/ptree/). The data that support the findings of this study are openly available in (http://doi. org/10.5281/zenodo.4588549).