Simultaneous measurements of high-altitude optical emissions and magnetic fields produced by sprite-associated lightning discharges enable a close examination of the link between low-altitude lightning processes and high-altitude sprite processes. We report results of the coordinated analysis of high-speed sprite video and wideband magnetic field measurements recorded simultaneously at Yucca Ridge Field Station and Duke University. From June to August 2005, sprites were detected following 67 lightning strokes, all of which had positive polarity. Our data showed that 46% of the 83 discrete sprite events in these sequences initiated more than 10 ms after the lightning return stroke, and we focus on these delayed sprites in this work. All delayed sprites were preceded by continuing current moments that averaged at least 11 kA km between the return stroke and sprites. The total lightning charge moment change at sprite initiation varied from 600 to 18,600 C km, and the minimum value to initiate long-delayed sprites ranged from 600 for 15 ms delay to 2000 C km for more than 120 ms delay. We numerically simulated electric fields at altitudes above these lightning discharges and found that the maximum normalized electric fields are essentially the same as fields that produce short-delayed sprites. Both estimated and simulation-predicted sprite initiation altitudes indicate that long-delayed sprites generally initiate around 5 km lower than short-delayed sprites. The simulation results also reveal that slow (5–20 ms) intensifications in continuing current can play a major role in initiating delayed sprites.
 Since they were first documented in 1989 [Franz et al., 1990], sprites have been studied through measurements of high-altitude optical emissions and remote lightning radiated electromagnetic (EM) fields. According to the largely accepted conventional breakdown model [Pasko et al., 1997, 1998], sprites are produced by conventional electric breakdown of the upper atmosphere, which is itself produced by large postlightning quasi-electrostatic (QE) fields. These QE fields are close to linearly proportional to the vertical charge moment change (charge transfer to ground times the vertical cloud to ground channel length) in the lightning discharge [Inan and Inan, 1999].
 Numerous studies have reported lightning charge moment measurements in sprite-producing lightning [Cummer and Inan, 1997; Huang et al., 1999; Ohkubo et al., 2005], all of which have been found to be essentially consistent with conventional breakdown theory. It is a challenge, however, to precisely measure the lightning charge moment change at the time of sprite initiation using normal speed video because the lightning charge moment change can vary considerably across the 16.7 or 33 ms image integration period. Approaches to avoid this limitation include analyzing a subset of sprites whose initiation times can be narrowly bounded on the basis of additional information [Hu et al., 2002], and analyzing sprites recorded using high-speed video [Cummer and Stanley, 1999]. Another challenge arises when trying to measure the charge moment change for sprites that initiate tens or hundreds of milliseconds after the lightning stroke. Measurements have suggested that continuing currents are at least partly responsible for initiating these sprites [Bell et al., 1998; Cummer and Füllekrug, 2001], but continuing currents can be difficult to remotely measure. Measurements based on Schumann resonances [Burke and Jones, 1992] are capable of measuring these slowly varying currents but cannot generally provide sufficient time resolution to accurately measure the charge moment change at a specific time. It has also been suggested that sferic bursts, first reported by Johnson and Inan , may contribute to sprite initiation [Ohkubo et al., 2005].
 Since it is almost impossible to measure the electric field inside a sprite, numerical simulations [Hu et al., 2006] have been applied to test the QE model. Hu et al.  combined video observations, electromagnetic measurements, and numerical simulations to estimate the electric field responsible for generating short-delayed sprites. They found that values of normalized electric field (the ratio between the actual electric field and the air breakdown field) from about 0.2 to 0.8 led to sprite initiation, with larger values generally leading to larger and brighter sprites.
 Measurements in June through August 2005 of the low-frequency horizontal magnetic field produced by lightning simultaneously recorded at Duke University and Yucca Ridge, Colorado, with simultaneous high-speed sprite images recorded at Yucca Ridge have produced a data set without the above mentioned limitations. The high-speed images (1000–10,000 frames per second (fps)) enable determination of the sprite initiation time with millisecond or better precision, and both magnetic field sensors had sufficient bandwidth and low-frequency sensitivity to measure currents from the submillisecond time scale of the lightning return stroke to the hundred-or-more millisecond time scale of continuing current.
 The general statistics of the lightning-to-sprite delay for all of the observed events show that there is a clear breakpoint in the overall delay distribution at ≈10 ms delay. Taking 10 ms as the definition of a delayed sprite, we further analyze the subset of these data associated with delayed sprites. All of the delayed sprites were preceded by continuing current with mean time-averaged current moment (lightning source current times the vertical cloud to ground channel length) between the return stroke and sprites of 42 kA km. The minimum time-averaged value was 11 kA km and the maximum was 132 kA km. The total lightning vertical charge moment change at sprite initiation varied from 600 to 18,600 C km (note that many of these were not the first sprite event in the sprite sequence caused by a single lightning event), and in most cases the continuing current contributed significantly more to this total than the lightning return stroke. This confirms that lightning continuing current is an important driver of delayed sprites and in many cases is the primary driver. We also test the initiation mechanism of long-delayed sprites by combining video observations, electromagnetic measurements, and simulations in the same manner as Hu et al. . The results show that normalized fields responsible for initiating delayed sprites are essentially the same as those previously found for short-delayed sprites. Thus, the quasi-static electric field driven by vertical lightning charge transfer is the primary cause of short and long-delayed sprites. These observations further reveal the relationship between sferic bursts, continuing current and sprite initiation.
2. Instrumentation and Method of Analysis
 From 24 June to 15 August 2005, we measured broadband low-frequency electromagnetic radiation from lightnings at two observation sites: the Yucca Ridge Field Station (40.702°N, −105.031°E) near Fort Collins, Colorado, and Duke University (35.864°N, −79.101°E). At the Duke site, two pairs of magnetic induction coils recorded the vector horizontal magnetic field from 0.1 Hz to 500 Hz (BF-4 coils built by EMI, Inc.) and from 50 Hz to 30 kHz (custom designed coils). At the Yucca Ridge site, one pair of coils continuously sampled signals from ∼2 Hz to 30 kHz (coils built by Quasar Federal Systems, Inc). National Lightning Detection Network (NLDN) data provided all of the return stroke locations presented in this work. The lightning location and two orthogonal horizontal measurements of the magnetic field from each pair of the coils enable us to derive the azimuthal magnetic field, which is the magnetic field in azimuthal () direction defined by a cylindrical coordinate system with the origin at the lighting location. A photometer and a high-speed intensified camera were used to record the optical emissions from sprites from the Yucca Ridge site. The P30A-05 photodetector (built by Electron Tubes, Inc.) recorded total sprite luminosity across the 280 to 870 nm range at 100 kHz. The high-speed camera was a Vision Research Phantom 7.1 monochrome high-speed imager coupled to an ITT Gen III image intensifier with spectral response from 450 to 900 nm. The phosphor persistence of this intensifier was measured with controlled sources to have a half-life between 0.35 (dim features) and 0.70 ms (bright features). Across the entire campaign, images were recorded at rates from 1000 to 10,000 frames per second. The camera time stamps every image with the end of the integration time as computed from an external GPS-synchronized IRIG time code. The absolute image timing accuracy was confirmed to be better than 10 μs by imaging an LED driven by the one pulse per second output from a TrueTime XL-AK GPS receiver. The same GPS unit provide absolute timing for the photometer and magnetic field channels with an accuracy of better than 10 μs.
 The resulting data set comprises synchronized, high time resolution images, overall brightness, and wideband (∼0.1 Hz–30 kHz) magnetic field measurements at two locations. For the events analyzed here, we extracted from the magnetic field data the estimated source current moment waveforms using a modified version of the deconvolution method described by Cummer and Inan  in which we apply regularization parameters that enforce more smoothness on the later part of the current moment waveform. This enables reliable extraction of both the fast return stroke current moment and the slow continuing current moment that is present in essentially all of the analyzed strokes. The needed estimates of the propagation impulse response are computed using a full wave 2-D cylindrical Finite difference time domain (FDTD) simulation [Hu et al., 2006].
Figure 1 demonstrates this measurement with the azimuthal magnetic fields (magnetic field in tangential direction) from one sprite-producing lightning flash measured at Duke and Yucca Ridge and the extracted current moment waveforms from each. Despite different ranges, sensors, and ambient noise, the extracted current waveforms agree well and the total charge moment changes differ less than 10% at 180 ms. The two station measurements provide redundancy that ensures the accuracy of the extracted source currents. With the estimated lightning current moment waveform, we are able to simulate the vertical electric fields at high altitudes above the lightning discharge with a 2-D FDTD model [Hu et al., 2006]. This electric field is a function of both time and altitude. Then we normalized this field by the air breakdown field at different altitudes. This procedure is basically the same as the method described by Hu et al. . However, Hu et al.  focused on short-delayed sprites and could not always precisely determine the sprite initiation time. In contrast, we use extracted current moment waveforms of 200 ms duration for long-delayed sprites, and in all cases the sprite initiation time is measured with submillisecond precision from high-speed video.
3. Data Overview
 During the campaign period, the high-speed camera recorded 67 sprite sequences on 7 different days. Of these, 64 were associated with NLDN detected lightning strokes, all of which were positive polarity.
Figure 2 shows the locations of these 64 sprite-producing positive CGs detected by NLDN network and the two observation sites. These lightning events occurred ∼300–800 km from the Yucca Ridge station (YR) and ∼1600–2100 km from Duke University. The magnetic field data clearly showed that remaining three sprite sequences were also produced by positive polarity strokes that were not classified as CGs by the NLDN. Many of the sprite sequences contained several discrete sprites that occur at different times. We define a sprite that initiated at least 5 ms after any previous sprite as a single “sprite event.” Per this definition, the 67 observed sprite sequences contained a total of 86 discrete sprite events. A single sprite event may contain a cluster of sprites that occurred at about the same time but different locations. We then measured the time delay between the lightning return stroke and the initiation of a sprite event determined from the high-speed video, accounting for speed of light propagation delays for both the sprite optical emissions and lightning radio emissions. One of the sprite events was captured on video after its initiation, and for two of them we do not accurately know the propagation time to Yucca Ridge, and thus their delays could not be measured. Figure 3 shows the histogram of the remaining 83 lightning-to-sprite initiation delays, binned in 5 ms windows (except for the last bin).
 There were 37 sprites that occurred within 5 ms of a return stroke, and 8 events that occurred 5 to 10 ms after the lightning return stroke. These events constitute about 54% of the total number of single sprite events, and the histogram shows a natural break point in the distribution after 10 ms, above which the time delays are almost uniformly distributed up to several hundred milliseconds. We thus empirically define a delayed sprite event as one that initiates more than 10 ms after a lightning return stroke. We also note that among these 83 events, sprite currents [Cummer et al., 1998, 2006] were detected in 21. This 32% rate is higher than the ∼10% reported in previous observations [Cummer, 2003], which is probably due to our smaller data set. More than half of these sprite currents were observed in a thunderstorm on 4 July 2005 that produced 53 sprites and thus dominates our statistics. Excluding this day, the rate of measurable sprite currents is only 7%. The 4 July storm produced relatively more delayed sprites than sprite-producing storms observed on other days.
4. Long-Delayed Sprites
 Measurements of charge moment change in lightning strokes followed quickly by sprites have been shown to be generally consistent with conventional breakdown theory [Hu et al., 2002, 2007], but the degree to which this is true for delayed sprites is not known. If a sprite initiates more than 10 ms after a return stroke, some nonreturn stroke lightning process must contribute substantially to the mesospheric electric field. The wide sensor bandwidth and high-speed imaging employed in this work enable accurate measurement of continuing current and of sprite initiation time to answer these open questions. Consequently, these delayed sprites are the focus of the following analysis.
4.1. Typical Long-Delayed Sprite
 A typical long-time-delayed sprite-producing lightning return stroke was observed on 4 July 2005 at 0539:02.873 UT. Figure 4 shows the time-synchronized measurements of optical emissions and the low-frequency magnetic field. Figure 4a shows the images recorded at 3600 fps. The vertical bar on the right represents the altitude in kilometers estimated by star field analysis assuming that the sprite is directly above the lightning discharge. The effect of atmospheric refraction has been taken into account. The unknown offset between the lightning discharge and sprite (a few tens of kilometers) contributes an overall altitude uncertainty of ∼5 km for this event. Figure 4b shows the sprite luminosity recorded by the photometer, confirming that the sprite occurred when seen in the video. Figures 4c and 4d show the azimuthal magnetic field measured at Yucca Ridge and at Duke University. Figure 4e shows the extracted current moment waveform and accumulative total charge moment change.
 At 144.4 ms after the lightning return stroke, the first visible light of the sprite appears at both ∼80 km and ∼70 km altitudes. This could be caused by the dimness of the sprite at its initiation stage, which cannot be clearly observed on the image. Thus the sprite initiation altitude cannot be accurately estimated but is between 70 and 80 km. This sprite reached its maximum brightness about 1.7 ms later, and its development followed the downward then upward streamer sequence reported from other high-speed sprite recordings [Stanley et al., 1999; Cummer et al., 2006]. The dark bands in the sprite body are due to clouds along the line of sight. An ELF radiation peak is seen in the magnetic field data whose source current moment is aligned to about 0.1 ms with the sprite brightness. This is the signature of high-altitude current in the body of the sprite [Cummer et al., 1998; Cummer, 2003; Cummer et al., 2006].
 The impulse charge moment change (total charge moment change within the first 2 ms after the lightning return stroke) of the lightning return stroke is 193 C km, which is large but smaller than the usual charge moment change required to initiate a sprite [Hu et al., 2002, 2007]. This is not surprising since we know that the sprite initiated long after the return stroke, and thus the impulse charge moment change was not responsible for the sprite initiation. The postreturn stroke quasi-static magnetic field seen in the Duke and Yucca Ridge magnetic field data is a signature of continuing current [Cummer and Füllekrug, 2001]. From the lightning discharge to the sprite initiation time, the average amplitude of current moment is greater than 16 kA km. Integrating the total current moment waveform extracted from these data yields a total charge moment change at the time of sprite initiation of 2650 C km. In this case, the impulse charge moment change is almost negligible compared to the charge moment change produced by the continuing current, and the continuing current is clearly the primary driver of the quasi-static electric field in the mesosphere that initiated the sprite.
 From ∼125–144 ms after the lightning return stroke, the measured magnetic field and estimated current moment steadily increased by a factor of 2. This current increase is similar to the perturbations of continuing current caused by lightning M component [Malan and Schonland, 1947; Rakov et al., 1995], which is associated with the temporary increase in continuing current. However, the shape and the risetime may not fit the characteristic of a typical M component [Rakov and Uman, 2003]. We show below that significant increases in continuing current amplitude on time scales from several to several tens of milliseconds are frequently seen in lightning that produce delayed sprites, and we call this feature a slow intensification (SI). The YR magnetic field data further show that this SI is accompanied by a clear sferic burst (SB) [Johnson and Inan, 2000]. We explore this SI-SB relationship in more detail below, but it appears that distinct SBs are almost always accompanied by SIs. This suggests that SBs may be produced by an expansion of the lightning channels inside the cloud that taps into new charge centers and thus increases the continuing current to ground. This in turn suggests that SBs frequently occur in close association with sprite initiation because SBs are linked to SIs, which increase the mesospheric electric field by increasing the rate of vertical charge transfer to ground.
4.2. Charge Transfer and Continuing Current Statistics
 Among the 38 discrete sprite events delayed more than 10 ms, the exact lightning location of 4 events are not available from the NLDN network. Figure 5 shows the average amplitude of current moment and total charge moment change of the remaining 34 events. Data from different days are represented by different symbols. Continuing current was detected in every one of these lightning strokes, and the average amplitude of the continuing current moment between the return stroke and sprite varies from 11 to 132 kA km with a mean value of 43.2 kA km. Assuming a 6 km channel length [Marshall et al., 2001], these current moment values correspond to a continuing current range of ∼1.8 kA to 22 kA with an average value of 7.2 kA. These values are much larger than typical continuing currents which are usually below 1 kA [Rakov and Uman, 2003].
 The total charge moment change at the time of delayed sprite initiation is extremely variable, from 600 to 18,600 C km. There is some evidence of a lower bound, however, that increases slowly with delay from about 600 C km for a few tens of milliseconds to about 2000 C km above 120 ms. An initiation threshold that follows this bound is not inconsistent with the predictions of conventional breakdown theory [Pasko et al., 1997] in which longer delays enable relaxation of fields at higher altitudes, pushing the initiation altitude somewhat lower and thus increasing the electric field required to initiate a sprite. We quantitatively examine the relationship between lightning charge transfer, mesospheric electric field, and delayed sprite initiation in section 4.3.
 It is also not surprising that some sprites initiate after charge moment changes much larger than this apparent threshold. Lightning strokes with large continuing currents like these can remove charge over a very large horizontal region [Krehbiel et al., 1979], and only a small fraction of the total vertical charge moment change may contribute to the mesospheric electric field in the region of sprite initiation. This is because the charge removal far away does not cause significant vertical electric fields because vertical electric fields caused by a dipole are small when the distance is much greater than the dipole length [Inan and Inan, 1999]. In other words, consider a sprite that initiates at one edge of a wide (many tens of kilometers) region of charge removal. Any charge removal from the opposite side of the region will not contribute significantly to the electric field where the sprite initiated but will contribute to the total vertical charge moment change. Many of these long-delayed sprites are found in sprite sequences in which different sprite events occur with wide horizontal separation [Lyons et al., 2000; Neubert et al., 2001; Hardman et al., 2000], as we would expect if the above were true.
4.3. Testing of Initiation Mechanism for Long-Delayed Sprites
 With the estimated current moment waveform, we are able to test the initiation mechanism of long-delayed sprites by simulating the electric field at mesosphere altitudes and comparing it with air breakdown field (Ek). Hu et al.  first applied this approach to test the initiation mechanism for short-delayed sprites and reported the electric fields to initiate typical, dim, and bright sprites immediately after lightning return stroke. The issue we address here is primarily whether the lightning generated quasi-static electric field that initiated long-delayed sprites is similar to that which produced short-delayed sprites, or whether some other process appears to contribute to delayed sprite initiation. It should be noted that the fields we computed from the measured lightning source current are the background fields at sprite locations for a smooth ionosphere profile. Inhomogeneities, like irregularities and ionization patches, are not included in our computations because their time scale, spatial scale and enhancement factor are highly variable. These inhomogeneities, which are required to initiate streamers, will enhance the local fields [Ebert et al., 2006]. Thus we expect that our inferred field (En) to be less than 1 and we are not claiming that streamers initiate in regions where E/Ek is less than 1.
 Different from short-delayed sprites, where the high-altitude electric field may be dominated by the lightning return stroke, the electric field to initiate long-delayed sprites is caused by the slow varying continuing current. Thus the electric relaxation time plays an important role in long-delayed sprite initiation. This electric relaxation time depends on the properties of the medium or the environment. When the electric field at mesosphere altitude is intense enough, it is able to modify the environment through the heating and ionization processes [Pasko et al., 1997; Hu et al., 2007]. This change of environment condition will further affect the electric relaxation time and thus the electric field as a feedback. At altitude above 60 km, both of the heating and the attachment increase the electric relaxation time [Hu et al., 2007] when the electric field exceeds a certain threshold and below the air breakdown field. These nonlinear effects of heating and ionization are included in the FDTD model applied. Here we discuss the simulation results for examples of typical, dim and bright sprites before reaching a general conclusion with more simulation results.
4.3.1. Typical Long-Delayed Sprites
Figure 6 shows the simulated electric fields between 50 and 90 km altitude for the typical long-delayed sprite shown in section 4.1. For convenience, Figure 6a again shows the extracted current moment waveform and charge moment change. The sprite initiated at 144.4 ms after the lightning return stroke and is represented by a vertical line in the time window. Photometer data in Figure 4 show that the maximum sprite luminosity is about 500 for this sprite. Figure 6b shows the simulated electric fields with the nonlinear effects of heating and ionization. The color intensity represents the amplitude of normalized electric field (En). The sprite initiation altitude estimated from high-speed images is between 70 and 80 km, which is represented by an altitude bar. At about 2 ms, En increased to ∼0.4 caused by the lightning return stroke. This value is right on the border of what has produced short-delayed sprites [Hu et al., 2007]. After the return stroke, the field decreased to ∼0.2 at 100 ms because of the combination of continuing current balanced by dielectric relaxation of the electric field. After that, the field again increased because of the slow intensification (SI) of the continuing current. At the time of sprite initiation, the maximum En is 0.45 at 72 km altitude, which falls in the 70–80 km range estimated from high-speed images. Although the maximum En is less than unity, En = 0.45 is the same as for typical short-delayed sprites that are neither remarkably bright or dim [Hu et al., 2007]. This simulation result also revealed that the SI before the sprite initiation increased the electric field from 0.26 to 0.45 in about 20 ms even though it only contributes a small fraction of the total lightning charge moment change. The detailed effect of SIs on electric field is discussed in section 5.
4.3.2. Small and Dim Sprites
 Two small and dim sprites in a TLE sequence were detected on 2 July 2005, 0442:06 UT. The parent lightning discharge is 438 km away from the Yucca Ridge station. Figure 7a shows the optical emissions recorded at 3600 fps. There are two dim sprites in the TLE sequence. The first sprite initiated 15.0 ms after the lightning return stroke at ∼71 ± 2.5 km altitude estimated from high-speed images. The second sprite initiated 23.1 ms after the lightning return stroke, also at ∼71 ± 2.5 km altitude. Figure 7b shows the measured azimuthal magnetic field, extracted current moment waveform and total charge moment change. The total charge moment is 639 C km at the initiation time of the first sprite. This total charge moment change is about the smallest among all the delayed sprites. At the initiation time of the second sprite, the total charge moment change is 740 C km, which is also at the lower end. The average amplitude of the continuing current to the initiation time of the second sprite is about 16 kA km. Thus these two dim sprites are associated with relatively small continuing current and total charge moment change among all the delayed sprites. Our photometer data did not show these two dim sprites since they are below the noise level. Figure 7c shows the simulated electric fields. The estimated initiation altitude is represented by a dot with an altitude uncertainty bar of ±2.5 km. At 15 ms, the maximum En is 0.26 at 72 km altitude. And at 23.1 ms, the maximum En is 0.23 at 69 km altitude. In this example, the simulation-predicted altitudes agree well with the estimated altitudes within 2 km. This maximum En of about 0.25 is also typical for small and dim short-delayed sprites [Hu et al., 2007].
4.3.3. Big and Bright Sprites
 We next examine two relatively bright events caused by a lightning discharge which occurred 4 July 2005, 05:25:17.570 UT. Figure 8 shows the optical emissions in 3600 fps, sprite luminosity, measured azimuthal magnetic field, extracted current moment waveform and simulated electric fields of two bright sprites in a TLE sequence. The first sprite occurred at 4.1 ms after the lighting return stroke with a total charge moment change of 737 C km. This is a very bright sprite with a maximum luminosity of 1500. The second sprite occurred at 88.6 ms after the lightning return stroke with a total charge moment change of 4400 C km. The maximum luminosity is about 650. From the lightning return stroke to the initiation time of the second sprite, an intense continuing current that averages 31 kA km is detected. At 4.1 ms, the maximum En increased to 0.67 caused by lightning return stroke and the simulation-predicted altitude is 79 km. After the first sprite, En decreased to a value of ∼0.4 at about 60 ms because of electric relaxation. After that, the electric field increased again to ∼0.58 at 88.6 ms and the simulation-predicted altitude is 80 km. For these two events, we are not able to estimate the sprite initiation altitudes because of the lack of background star fields. However, the simulation-predicted altitudes are consistent with typical long-delayed sprite initiation altitude (70–80 km). The maximum En responsible for initiation is closer to unity than for typical or dim sprites, again consistent with bright short-delayed sprites analyzed by Hu et al. .
4.3.4. Summary of Long-Delayed Sprite Measurements
 Analyzing more events yields the same conclusions as the examples shown above. Figure 9 shows the maximum En at sprite initiation time for 16 events with delay time from 15 to 177.8 ms. The maximum En varies from ∼0.2 to 0.6 with a mean value of ∼0.4. As mentioned earlier, the maximum En is expected to be less than 1 since the ionization patches can enhance the local electric fields [Ebert et al., 2006]. These field quantities are the same as that to initiate short-delayed sprites [Hu et al., 2007]. The range of En is related with brightness of the sprites. Bright sprites were associated with higher electric fields compared to dim sprites. We also compared the simulation-predicted altitudes with the estimated sprite initiation altitudes.
Figure 10 shows the estimated and simulation-predicted sprite initiation altitudes for 10 sprites with different time delays ranged from 1.8 to 144.4 ms. The estimated sprite initiation altitudes were computed from star fields with a total uncertainty of 5 km except the last event, in which the sprite initiation altitude cannot be accurately estimated but in the 70–80 km range. The simulation-predicted sprite initiation altitudes agree well with those estimations. For short-delayed sprites, the initiation altitude is about 75–80 km. As the time delay increases, the initiation altitude slightly decreases to around 70 km for long-delayed sprites. This slightly lower initiation altitude is likely produced by dielectric relaxation. For short-delayed sprites, the total charge moment change is mostly provided by the impulsive lightning return stroke. Thus electric fields can accumulate at higher altitudes around 80 km, where the electric relaxation time is short. For long-delayed sprites, most of the total charge moment change is provided by the slowly varying continuing current. Since electric fields relax faster at higher altitudes, they accumulate at slightly lower altitudes.
5. Effect of Sferic Bursts and Slow Intensifications
 Above we highlighted the sferic bursts (SBs) and slow intensifications (SIs) in the example of a typical long-delayed sprite in Figure 4. Here we further explore the SB-SI relationship. For all the 64 sprite-producing lightning events, we have examined the magnetic fields for 200 ms after the lightning return stroke. We identified all of the sferic bursts that satisfied two conditions: the sferic burst lasts at least 2 ms, and the peak-to-peak amplitude is at least two times the level of background noise. A total of 23 sferic bursts in 19 lightning flashes met these conditions. And of these 23 SBs, 19 are associated with clear slow intensifications of the continuing current. Figure 11 shows another two examples of the link between SBs and SIs observed on 28 June 2005. In Figure 11a, the SB lasted ∼20 ms during which the continuing current increased by a factor of 4. A delayed sprite initiated at 32.5 ms, which is represented by a vertical line in the time window. Figure 11e shows an example containing two SBs in a sequence. The first burst lasted ∼7 ms during which the continuing current increased by a factor of 3. The second burst lasted ∼5 ms during which the continuing current again increased significantly. A delayed sprite initiated at 26.5 ms, which is after the first burst but before the second.
 Sferic bursts are produced by a rapid succession of in-cloud current pulses [Johnson and Inan, 2000] that are likely linked to expansion of the in-cloud breakdown channels. We suggest that the observed strong link between SBs and SIs is because expansion of the extent of in-cloud breakdown enables the flash to tap into new charge centers in the cloud. If there is a preexisting channel to ground, this new charge will ultimately be delivered to ground as a slow intensification in the continuing current.
 Of these 19 SBs clearly connected to SIs, 12 of them occurred in advance of long-delayed sprites. These statistics clearly support the connection between sferic bursts and delayed sprite initiation reported by [Ohkubo et al., 2005]. We now demonstrate that SIs can play a critical role in delayed sprite initiation. Figure 11b shows the extracted current moment waveform (black solid line) and total charge moment change (gray solid line) for the first SI/SB shown. The black dashed line and gray dashed line represent the current moment waveform and charge moment change in which the SI has been artificially removed. At the sprite initiation time, about 360 C km is provided by the SI among a total charge moment change of 860 C km. Two simulation results of electric field for lightning source current without and with the SI are shown in Figures 11c and 11d, respectively. Without the SI, the maximum En is 0.14 at 70 km altitude at 32.5 ms. With the SI, the maximum En is 0.36 at 74 km altitude. The SI increases the total charge moment change at sprite initiation by 72% but increases the maximum normalized field by 157%. The reason for this nonlinear relationship is explained below.
Figures 11e–11h show another example. From total charge moment change of 600 C km at sprite initiation, 140 C km is provided by the SI for a 30% increase. However, the maximum En increases from 0.14 to 0.23 for a 64% increase because of the SI. Evidently a slow intensification can increase the normalized mesospheric electric field more than in linear proportion to the net charge transfer it contains. This is because of the nonlinear response of the ionosphere to large electric fields. As the electric field increases, electron mobility decreases and electron density decreases because of an increase in the electron attachment rate [Pasko et al., 1997]. These effects decrease the effective conductivity of ionosphere and thus temporarily increase the electric relaxation time. This enables higher-altitude electric fields (in the 70–75 km altitude range) to persist longer than they otherwise would in response to modest increases in continuing current on time scales of ∼10 ms. For this reason, slow intensifications as defined here significantly enhance the probability of sprite initiation, and, according to our simulations, are a direct cause of many long-delayed sprites. We conclude that the association of sferic bursts with sprite initiation is not due to the burst itself but is due to the continuing current increase that usually accompanies sferic bursts.
 In this work, we have reported the results from simultaneous high time resolution measurements of lightning radiated magnetic fields and high-altitude optical emissions. In our data, 46% of the sprites initiated more than 10 ms after the lightning return stroke and are empirically defined as long-delayed sprites. All these long-delayed sprites are associated with continuing current with a time-averaged current moment magnitude from 11 to 132 kA km. The total charge moment change varied from 600 to 18,600 C km and the minimum values required to initiate long-delayed sprites are from ∼600 C km for 15 ms delay to ∼2000 C km for time delay above 120 ms. These estimated total charge moment change and current moment amplitudes agree well with the long-delayed sprite events presented by Cummer and Füllekrug . Up to more than 90% of the total charge moment change in these events are provided by continuing current. Thus the intense continuing current, instead of the lightning return stroke, is the primary driver that initiates a long-delayed sprite.
 Numerical simulations were used to estimate the maximum electric field and sprite initiation altitude expected for the measured lightning discharges. For long-delayed sprites, although their total charge moment change is much greater than that of short-delayed sprites, the maximum normalized electric field, in the range of ∼0.2–0.6, is the same as the field to produce short-delayed sprites [Hu et al., 2007]. We conclude that both long-delayed and short-delayed sprites are driven by the same basic processes, and thus that the vertical charge moment change is the primary factor behind sprite initiation. Sprite initiation altitudes predicted by numerical simulations agree well with the estimated initiation altitudes. They both showed that the long-delayed sprites tend to initiate at slightly lower altitudes (∼70 km) compared with short-delayed sprites (∼75–80 km), which is caused by the shorter electric relaxation time at high altitudes.
 Our high-speed video recordings and wide band magnetic field measurements enabled us to accurately determine the sprite initiation time and clearly identify both fast and slow electromagnetic signatures, such as sferic bursts and slow intensifications of continuing current. We find that sferic bursts and slow intensifications almost always occur together. In our data, about one third of the long-delayed sprites appeared in a few tens of milliseconds after sferic bursts and slow intensifications. Simulations show that slow intensifications increase the total charge moment change by several tens of percent but increase the electric fields at high altitudes by a factor of two or more. This nonlinear electric field increase is due to the nonlinear response of the ionospheric electrical conductivity, and we find that the slow intensification are often a direct cause of sprite initiation. Consequently, although sferic bursts frequently appear near sprite initiation times, it is the vertical charge transfer in slow intensifications that is responsible for this apparent link. It appears that in-cloud processes influence sprite initiation predominantly through their connection to increases in the cloud-to-ground charge moment change in the lightning stroke.
 This research was supported by NSF Aeronomy Program grant ATM-0436585 to Duke University, by NSF Dynamic and Physical Meteorology Program grant ATM-0642757 to Duke University, and by NSF Dynamic and Physical Meteorology grant ATM-0221512 to FMA Research, Inc.