Transient currents in the global electric circuit due to cloud-to-ground and intracloud lightning

Intracloud (IC) and cloud-to-ground (CG) lightning flashes produce transient changes in the electric field (E) above a thundercloud which drive transient currents in the global electric circuit (GEC). Using in-cloud and above-cloud E data from balloons, ground-based E data, and Lightning Mapping Array data, the above-cloud charge transfers due to lightning transients are estimated for five IC and five CG flashes from four thunderstorms that occurred above the mountains in New Mexico, USA, in 1999. For the five CG flashes (which transferred − 4 to − 13 C to the ground), the transient currents moved + 1 to + 5 C of charge upward from cloudtop toward the ionosphere, with an average transient charge transfer of about 35% of the charge transferred to ground. For the five IC flashes (which neutralized 6 to 21 C inside the cloud), the transient currents moved − 0.7 to − 3 C upward, with an average transient charge transfer of about 12% of the lightning charge. Estimates for three thunderstorms indicate that the transient currents made only a small GEC contribution compared to the quasi-stationary Wilson currents because of the offsetting effects of IC and CG flashes in these storms. However, storms with extreme characteristics, such as high flash rates or predominance of one flash type, may make a significant GEC contribution via lightning transients.     

Fine-resolution simulation of cloud-to-ground lightning and thundercloud charge transfer

2-D 12.5 m-resolution simulations of cloud-to-ground (CG) lightning discharge processes have been performed using an improved stochastic lightning model for different types of cloud charge distributions, such as dipole, tripole, bi-dipole and multi-layer charge structures produced from the numerical simulation of thundercloud electrification. The modelling produced the fine branched channel structure of CG lightning and the results illustrate the relations between CG lightning channel propagation and cloud charge distribution. The simulated features of CG lightning are associated with the observed results. The simulation studies are essential in our understanding of complex charge transfer processes caused by CG lightning discharges in thunderclouds. The induced charges of opposite polarity are deposited or embedded in the local volumes where the bidirectional leaders passed during a CG lightning discharge. Although the embedding affects charge structure only in a pair of significant positive and negative charge regions closest to the ground, the electric field strength acutely weakens and electrostatic energy in thunderclouds is significantly consumed when the discharge terminates. In addition to simulating the upward and downward breakdown of the initial leader to ground and the ensuing return stroke (RS), the simulation assumes that current continues to flow in the channel to ground and determines the upward breakdown until the end of the discharge. For the subsequent discharge sub-process, the upward leader channel tends to transfer the charges with the same polarity as the RS, while the downward leader channel favors transfer of opposite charge to ground. In the sub-processes of a few CG flash simulations, the magnitude of the opposite charges from the downward leader exceeds that of charges with the same polarity from the upward leader so that the net charges transferred to the ground have a reversed polarity to the RS. The simulation presents similar features of CG lightning as those observed in realistic bipolar CG lightning.     

Charge source of cloud-to-ground lightning and charge structure of a typical thunderstorm in the Chinese Inland Plateau

GPS-synchronized measurements of electric (E) field changes induced by lightning flashes were recorded at six stations in the northeastern verge of the Tibetan Plateau. The height and magnitude of charge neutralized by 65 return strokes, including 16 negative cloud-to-ground (CG) flashes and 2 positive CG flashes, have been fitted with the nonlinear least-square method based on the E field changes of CG flashes observed in a typical thunderstorm with larger-than-usual lower positive charge center (LPCC). Results show that the height of the charge region neutralized by negative CG flashes ranges from 3 km to 5 km above the ground, corresponding to an ambient temperature between − 2 °C and − 15 °C. For the two positive CG flashes, the neutralized charge regions are located at a height of about 5.5 km and the ambient temperature is about − 18 °C, indicating the existence of upper positive charge in the thunderstorm.     

Comparative analysis of the initial stage in two artificially-triggered lightning flashes

The initial discharge stages of two flashes during the Shandong Artificially Triggering Lightning Experiment (SHATLE) are analyzed based on the synchronous data of the current and close electromagnetic field. For a lightning flash, named 0503, the wire was connected, not electrically, but via a 5 m length of nylon, with the lightning rod; while for another, named 0602, the wire was connected with the rod directly. Results show that the discharge processes of the initial stage (IS) in flash 0503 are quite different from that of the usual classical-triggered flash 0602 and altitude-triggered flashes. A large pulse with a current of about 720 A resulted from the breakdown of the 5 m air gap during flash 0503, and the corresponding electric field at 60 m from the lightning rod was 0.38 kV/m. The upward positive leaders (UPLs) propagated continuously from the tip of the rocket after this breakdown. The geometric mean (GM) of the UPL peak current was 23.0 A. Vaporization of the wire occurred during the initial continuous current (ICC) stage and the largest current pulse was about 400 A. Compared with triggered flash 0503, the discharge processes of IS in flash 0602 were simple, only two large pulses similar to each other occurred before dart leader/return stroke sequences. The peak current of the first pulse was 2.1 kA and its corresponding electric field and magnetic field at a distance of 60 m from the lightning rod were 0.98 kV/m and 7.03 μT, respectively. During the second pulse, the wire disintegrated. The current decreased to the background level at the moment of the wire disintegration. The current of the second pulse in triggered flash 0602 was 2.8 kA, and the corresponding electric field and magnetic field at 60 m from the lightning rod were 1.22 kV/m and 9.01 μT, respectively.     

Study of the total lightning activity in a hailstorm

A thunderstorm that developed over northeastern Spain on 16 June 2006 is analyzed. This severe thunderstorm produced hailstones as large as 40 mm and had a lifetime of 3 h and 30 min. Radar cross-sections show strong vertical development with cloud echo tops reaching an altitude of 13 km. The specific characteristics of the lightning activity of this storm were: (i) a large amount (81%) of negative cloud-to-ground (−CG) flashes with very low peak currents (< 10 kA in absolute value), (ii) a very large proportion of intra-cloud (IC) flashes with an IC/CG ratio reaching about 400, (iii) a large number of “short” IC flashes (with only 1-VHF source according to SAFIR detection), (iv) a large increase of the −CG flash rate and of the CG proportion near the end of the storm. The rate of −CG flashes with a low peak current were observed to evolve similarly to the rates of IC flashes. Most of them have been assumed to be IC flashes misclassified by the Spanish Lightning Detection Network (SLDN). They have been filtered as it is usually done for misclassified +CG flashes. After this filtering, CG flash rates remained very low (< 1 min^− 1) with +CG flashes sometimes dominant. All the particular lightning activity characteristics similar to those observed in the Severe Thunderstorm Electrification and Precipitation Study (STEPS) campaigns support the hypothesis that this thunderstorm could have had an inverted-polarity or complex charge structure. The maximum IC flash rate (67 min^− 1) peaked 24 min before the presence of reflectivity higher than 60 dBZ. The IC activity abruptly decreased during the period when reflectivity was dramatically increasing. The time of maximum reflectivity observed by radar was consistent with the times of reported hail at the ground.     

The characteristics of cloud-to-ground lightning activity in hailstorms over northern China

The characteristics of cloud-to-ground (CG) lightning for ten hailstorms in Shandong Province of China were analyzed statistically. It is found that the hailstorms in this study present dominant positive CG flashes during periods of falling hail. One specific hailstorm on 16 June 2006 was studied in detail using the data from a CG lightning location network, Doppler radar and cloud images. Comparison between the brightness temperature of cloud-top and CG flash locations indicated that most flashes occurred in the region with temperatures lower than − 40 °C, while dense positive CG flashes occurred in the range between − 40 °C and − 50 °C. Negative CG flashes occurred mostly in the relative weak radar echo region, and positive CG flashes were distributed in the strong echo region especially with a large gradient of echo intensity. CG flashes tended to occur in the cloud region with reflectivity between 25 dBZ and 35 dBZ. Comparison between the wind field retrieved from Doppler radar and the location of CG flashes indicated that the flashes were located in the convergent region at lower to middle levels.     

Lifetime of the thunderstorm electric energy in the global atmospheric circuit and thunderstorm energy characteristics

The lifetime of electric energy in the atmosphere is introduced and investigated as is the total electric energy of the atmosphere related to the total mean rate of electric energy dissipation. This lifetime, as determined from general estimations and convenient analytical expressions, turns out to be very small – from about 10 to about 100 s, depending on the assumptions on the control parameters of principal sources in the global electric circuit. In particular the energy lifetime is less than the relaxation time of the “global condenser” and field relaxation time near the ground surface. It is explained by the high dissipative rate of the electric energy in the atmosphere, taking into account that the regions mainly contributing to the total energy and its dissipative rate are connected to the altitudes of active parts of electrified (thunderstorm) clouds in the atmosphere with exponentially increasing conductivity.     

Intracloud discharge and the correlated basic charge structure of a thunderstorm in Zhongchuan, a Chinese Inland Plateau region

The intracloud (IC) discharge is closely related to the charge structure of thunderstorms. The location, charge moment and polarity of intracloud discharges have been analyzed by using the electric field changes from a 7-site network of slow antennas synchronized by GPS with 1 μs time resolution in the area of Zhongchuan in the Chinese Inland Plateau. Ten IC flashes, from a storm on August 20, 2004, have been fitted by using the non-linear least-square solution. The results show that five IC flashes occurred between the main negative charge region and the lower positive charge region and other five between the main negative charge region and the upper positive charge region during the mature stage of the thunderstorm. The centers of discharge were 3.2–5.6 km and 6.8–7.7 km above sea level. The neutralized moments were about 4.56–61.0 C km and 1.06–15.9 C km. It suggests that the charge structure related to the lightning discharge can be represented by a tripole but with a strong positive charge region in the lower part of the thunderstorm, with the lower positive charge region taking an active role in the discharge.     

Analysis of thunderstorm and lightning activity associated with sprites observed during the EuroSprite campaigns: Two case studies

During the summers of 2003 to 2006 sprites were observed over thunderstorms in France by cameras on mountain tops in Southern France. The observations were part of a larger coordinated effort, the EuroSprite campaigns, with data collected simultaneously from other sources including the French radar network for precipitation structure, Meteosat with images of cloud top temperature and the Météorage network for detection of cloud-to-ground (CG) flash activity. In this paper two storms are analyzed, each producing 27 sprite events. Both storms were identified as Mesoscale Convective Systems (MCS) with a trailing stratiform configuration (ST) and reaching a maximum cloud area of ~ 120,000 km². Most of the sprites were produced while the stratiform area was clearly developed and during periods of substantial increase of rainfall in regions with radar reflectivity between 30 and 40 dBZ. The sprite-producing periods followed a maximum in the CG lightning activity and were characterized by a low CG flash rate with a high proportion of + CG flashes, typically around 50%. All sprites were associated with + CGs except one which was observed after a − CG as detected by the Météorage network. This − CG was estimated to have − 800 C km charge moment change. The peak current of sprite-producing + CG (SP + CG) flashes was twice the average value of + CGs and close to 60 kA with little variation between the periods of sprite activity. The SP + CG flashes were further characterized by short time intervals before a subsequent CG flash (median value < 0.5 s) and with clusters of several CG flashes which suggest that SP + CG flashes often are part of multi-CG flash processes. One case of a lightning process associated with a sprite consisted of 7 CG flashes.     

Characteristics of cloud-to-ground lightning in warm-season thunderstorms in the Central Great Plains

In July 2005, a field campaign was conducted in the Central Great Plains to obtain 60-field/s video imagery of lightning in correlation with reports from the U.S. National Lightning Detection Network (NLDN) and broadband electric field waveforms from the Los Alamos Sferic Array (LASA). A total of 342 GPS time-stamped cloud-to-ground (CG) flashes were recorded in 17 different sessions, and 311 (91%) of these were correlated with reports from the NLDN. Only 6 of the 17 recording sessions were dominated by flashes that lowered negative charge to ground, and 11 were dominated by positive CG flashes. A total of 103 flashes recorded on video were correlated with at least one NLDN report of negative CG strokes, 204 video flashes were correlated with one or two positive stroke reports, and 4 had bipolar reports. In this paper, we will give distributions of the estimated peak current, I_p, as reported by the NLDN, of negative and positive first strokes that were recorded on video, the multiplicity of strokes that were recorded on video, and the number of ground contacts per flash that were resolved on video. 41 (40%) of the negative flashes produced just a single-stroke on video, and 62 (60%) showed two or more strokes. The observed multiplicity of negative flashes averaged 2.83, which becomes about 3.14 after correcting for the finite time-resolution of the video camera. 195 (96%) of the positive flashes produced just a single-stroke on video, and 9 (4%) showed two strokes; therefore, the observed multiplicity of positive flashes averaged 1.04. Five out of 9 (56%) of the positive subsequent strokes re-illuminated a previous channel, and 4 out of 9 (44%) created a new ground contact. Simultaneous video, LASA, and NLDN measurements also allowed us to examine the classification of NLDN reports during 3 single-cell storms (one negative and two positive). Based on the LASA waveforms, a total of 204 out of 376 (54%) NLDN reports of CG strokes were determined to be for cloud pulses. The misclassified negative reports had |I_p| values ranging from 3.8 kA to 29.7 kA, but only 58 (24%) of these had |I_p| > 10 kA, and only one misclassified positive report had I_p > 20 kA. Radar analyses showed that most of the negative and positive CG strokes that were recorded on video were produced within or near the convective cores of storms. The radar imagery also showed that single-cell storms tended to produce one polarity of CG flashes at a time, and that such storms could switch rapidly from negative to positive CG flashes when the reflectivity was near maximum. Multiple-cell storms produced both negative and positive flashes over a broad region, but each polarity tended to cluster near regions of high-reflectivity.     

Characteristics of negative lightning flashes presenting multiple-ground terminations on a millisecond-scale

By using a high-speed video camera system (1000 frames s^− 1) in correlation with fast and slow antenna systems, the negative cloud-to-ground (CG) flashes that struck the ground with more than one termination have been analyzed. This kind of stroke, named as multiple-ground terminations stroke (MGTS), was produced by different branches of the same stepped leader during quite a short time. Based on optical images, the 2D progression speed of leader branches was estimated to be in the range (0.9–2.0) × 10⁵ m s^− 1. The distance between adjacent striking points of MGTS was from 0.2 km to 1.9 km. The percentage of flashes with multiple-ground terminations occupied about 15% (9 out of 59) of the total negative CG flashes, with a range of 11%–20% in different areas in China. The time intervals between the two adjacent peaks ranged from 4 μs to 486 μs based on the E-field change caused by the MGTS. The flashes which had multiple striking points on the ground during quite a short time may be a common phenomenon in the lightning discharge process. It might produce more serious damage to facilities on the ground and should not be neglected in the design of lightning protection.     

一次多回击负地闪放电过程的甚高频辐射和传输特征分析

利用短基线时间差甚高频(VHF)辐射源定位系统对一次多回击负地闪放电过程进行详细研究发现, 负地闪的预击穿、梯级先导、直窜先导及回击后云内放电过程伴随有较强烈的VHF辐射。结合同步观测的闪电快、慢电场变化资料, 分析VHF辐射源时空发展特征发现, 预击穿阶段辐射源在云中的放电通道为双向发展, 平均速度均在104 m s-1量级, 预击穿下行分支直接转化为梯级先导, 并产生多个分支通道同时向地面发展, 先导平均速度在105 m s-1量级。继后回击之前先导过程均产生多个分支通道, 直窜先导平均速度在105～106 m s-1量级, 新开辟的梯级先导速度在105 m s-1量级。闪击间及地闪后期云内放电活动较为复杂, 主要表现为辐射源从闪电起始区域发展, 进一步延伸云内闪电通道。地闪后期多次负极性K变化过程(Kitagawa and Kobayashi, 1958)主要表现为负极性流光沿之前的正极性电离通道快速发展, 平均速度在106 m s-1量级。     

Contribution of the MODIS instrument to observations of deep convective storms and stratospheric moisture detection in GOES and MSG imagery

Past studies based on the NOAA/AVHRR and GOES I-M imager instruments have documented the link between certain storm top features referred to as the “cold-U/V” shape in the 10–12 μm IR band imagery and plumes of increased 3.7/3.9 μm band reflectivity. Later, similar features in the 3.7/3.9 μm band have been documented in the AVHRR/3 1.6 μm band imagery.The present work focuses on storm top observations utilizing the MODIS data. The MODIS instrument (available onboard NASA's EOS Terra and Aqua satellites) provides image data with significantly better geometrical resolution (in some of its bands) and broader range of spectral bands as compared to that from AVHRR/3 observations. One of the goals of this study is to evaluate the contribution of this new instrument to observations of convective storm tops. Besides the cloud top features linked to storm top microphysics and morphology, the paper also addresses the possibility of detection of lower stratospheric water vapor above cold convective storm tops. This issue is explored utilizing MODIS as well as GOES and MSG imagery.In addition, the paper discusses an alternative interpretation of the “cold-U/V” patterns at the top of intense storms by a mechanism of “plume masking” as suggested by some of the observations.     

Optical observations of transient luminous events associated with winter thunderstorms near the coast of Israel

We report the results of two observation campaigns conducted during the Northern Hemisphere winters of 2005–6 and 2006–7 aiming to detect transient luminous events (TLEs) above winter thunderstorms in the vicinity of Israel and the eastern coastline of the Mediterranean Sea. In 10 out of 31 different observation nights we detected 66 events: 56 sprites and 10 Elves. The detection ranges varied from 250 to 450 km. Sprites were found to be produced by active cells with a vertical dimension of 5–9 km and cloud top temperature ~ − 40 °C, embedded in a much larger matrix of stratiform precipitating cloudiness. This configuration closely resembles the conditions for winter sprites in the Hokuriku region of Japan. Synchronized with the optical observations, ELF data were recorded at two observation stations in Israel and Hungary in order to qualify and quantify parameters of the parent lightning discharge associated with the TLEs. These stations are located 500 km and 2100 km respectively from the Eastern Mediterranean Sea, where most TLEs occur. Among the optically observed TLE events, we found that all the ELF signals were produced solely by positive cloud-to-ground flashes (+ CGs), most of which were recorded in Israel (88%) and Hungary (77%). Calculation of the Charge Moment Change showed average values of 1400 ± 600 C km, with some extreme events exceeding 3500 C km. The average time delay between the ELF transient of the parent + CG and the observed sprites was 55 ms, with shorter delays for column sprites (42 ± 34 ms) compared to carrot sprites (68 ± 34). Furthermore, based on the ELF data, there were no early identifiable precursors to TLE occurrence in the regional lightning activity. From the spatial formation of the observed columniform sprites, we propose that columniform sprites are sometimes arranged in a 3-dimensional circular pattern, thus mapping the instantaneous electric field in the mesosphere.     

In situ measurements of contributions to the global electrical circuit by a thunderstorm in southeastern Brazil

The global electrical circuit, which maintains a potential of about 280 kV between the earth and the ionosphere, is thought to be driven mainly by thunderstorms and lightning. However, very few in situ measurements of electrical current above thunderstorms have been successfully obtained. In this paper, we present dc to very low frequency electric fields and atmospheric conductivity measured in the stratosphere (30–35 km altitude) above an active thunderstorm in southeastern Brazil. From these measurements, we estimate the mean quasi-static conduction current during the storm period to be 2.5 ± 1.25 A. Additionally, we examine the transient conduction currents following a large positive cloud-to-ground (+ CG) lightning flash and typical − CG flashes. We find that the majority of the total current is attributed to the quasi-static thundercloud charge, rather than lightning, which supports the classical Wilson model for the global electrical circuit.     

The spatial and temporal variability of fog and its relation to fog oases in the Atacama Desert, Chile

Fog has been studied in the Atacama Desert of Chile for the past ten years. This paper analyzes its temporal and spatial variability, relying in part on satellite images (GOES) to analyze the frequent orographic fog and the low cloud deck (stratocumulus, Sc) that generates advective fog in the area. Fog water fluxes were measured with Standard Fog Collectors (SFC). Field trips and observers provided information on cloud top and base and the presence of fog. Vegetation in fog oases were used to confirm the results of these surveys.The Sc moves onshore into the continent with different intensities depending on season and time of day. The maximum spatial extent occurs during winter and at night. Fog is frequent in the coastal cliffs, where fog water fluxes of 7.0 L m^− 2 day^− 1 were measured using a SFC. It is less frequent 12 km inland, where the collection rates were less than 1 L m^− 2 day^− 1. The height of the fog collector above the ground affected the collection rate. The highest fog water fluxes were recorded at Alto Patache at altitudes of between 750 and 850 m a.s.l. The growth or thickness of the cloud is important in the collection of fog water. The information that GOES provides on the altitude of the top of low clouds is used to analyze this factor. Fog oases are described and analyzed in relation to how the geographical location of fog influences the growth of vegetation.     

一次中尺度对流系统的电场演变特征

综合雷达、卫星、电场、闪电定位仪等资料,分析了2009年6月5日经过南京地区的中尺度对流系统(MCS)的地闪、电场演变过程及特征。本次过程中,MCS的发展阶段正地闪占主导地位,成熟阶段负地闪占主要地位,消亡阶段层状云区的正地闪相对较频繁。将该过程电场划分为4个阶段,重点对MCS对流区的电场进行了演变过程和特征分析,并用准正态分布模式模拟了MCS的对流区电场。结果表明,准正态分布模式能够更细微地反映电场变化,模拟得到的电场和实际观测相符。     

闪电起始过程时空特征的宽带干涉仪三维观测

闪电的起始位置和起始阶段发展速度是闪电研究中的重要问题。2010年夏季,使用架设在广州市从化区的两套甚高频 (VHF) 宽带干涉仪对闪电的起始阶段放电过程进行三维定位观测。对观测数据给出的地闪和云闪的起始高度分布特征以及起始阶段击穿过程的时空发展特征进行统计和对比分析,结果表明:闪电的起始高度分布呈双峰值特征,分别在5.0 km和8.8 km有两个明显的分布峰值,符合雷暴云三极性总体电荷结构的描述。对起始阶段闪电放电发展速度的计算表明,云闪和地闪在起始阶段的前15 ms内的平均发展速度均在104~105 m·s-1量级之间;多数云闪、地闪起始阶段前15 ms内的平均发展速度表现出减速趋势,但云闪个例中起始阶段前10 ms存在减速趋势的比例更高,且其中在前15 ms一直保持减速趋势个例所占比例也大于地闪。云闪和地闪的起始阶段放电过程的发展方向有向上、向下和水平发展3种情形,可用于指示闪电始发位置的环境电场方向。     

Statistical analysis of lightning electric field measured under Malaysian condition

Lightning is an electrical discharge during thunderstorms that can be either within clouds (Inter-Cloud), or between clouds and ground (Cloud-Ground). The Lightning characteristics and their statistical information are the foundation for the design of lightning protection system as well as for the calculation of lightning radiated fields. Nowadays, there are various techniques to detect lightning signals and to determine various parameters produced by a lightning flash. Each technique provides its own claimed performances. In this paper, the characteristics of captured broadband electric fields generated by cloud-to-ground lightning discharges in South of Malaysia are analyzed. A total of 130 cloud-to-ground lightning flashes from 3 separate thunderstorm events (each event lasts for about 4–5 hours) were examined. Statistical analyses of the following signal parameters were presented: preliminary breakdown pulse train time duration, time interval between preliminary breakdowns and return stroke, multiplicity of stroke, and percentages of single stroke only. The BIL model is also introduced to characterize the lightning signature patterns. Observations on the statistical analyses show that about 79% of lightning signals fit well with the BIL model. The maximum and minimum of preliminary breakdown time duration of the observed lightning signals are 84 ms and 560 us, respectively. The findings of the statistical results show that 7.6% of the flashes were single stroke flashes, and the maximum number of strokes recorded was 14 multiple strokes per flash. A preliminary breakdown signature in more than 95% of the flashes can be identified.     

Comment on “Glory phenomenon informs of presence and phase state of liquid water in cold clouds” by Anatoly N. Nevzorov

In a recent publication “Glory phenomenon informs of presence and phase state of liquid water in cold clouds” Nevzorov [Nevzorov, A., 2006. Glory phenomenon informs of presence and phase state of liquid water in cold clouds. Atmospheric Research 82, 367–378] claims that “the convincing evidence has been provided that this sort of glory forms as a first-order bow from spherical particles with a refractive index of 1.81–1.82 and diameter over 20 μm”. This is a highly unusual finding because the refractive index of liquid water and ice is between 1.30 and 1.35 in the visible spectral range. The author concludes that “once more corroboration is gained […] of droplets of liquid water in specific phase state referred to amorphous water, or A-water”. Here we show that the phenomena described by the author are easily explained assuming liquid water with a refractive index of 1.33 and a realistic droplet size distribution with an effective radius of around 10 μm. We conclude that this type of observations does not corroborate the existence of amorphous water in the atmosphere. In a recent publication we showed how to quantitatively derive cloud optical thickness, effective droplet radius, and even the width of the size distribution from observations of the glory [Mayer, B., Schröder, M., Preusker, R., Schüller, L., 2004. Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study. Atmospheric Chemistry and Physics 4, 1255–1263].