5.1 Sprite halos

Classification of high-altitude optical flashes caused by tropospheric lightning as ``sprites'' and ``elves'' has been guided as much by theorized physical causes as it has by distinct sets of observed phenomena. The electric field which causes heating, ionization, and optical emissions in sprites is caused by the charge moment changes (e.g., 250 to 3250  $\ensuremath{{\rm C\hbox{-}km}}$ according to Cummer and Inan [1997]) associated with the movement of large thundercloud charges, usually in association with intense positive cloud-to-ground lightning. On the other hand, the electric field causing heating, ionization, and optical emissions in elves is that of an electromagnetic wave which is launched by, and occurs in proportion to, changing current moments associated with very impulsive ($>$60 kA) return stroke currents [e.g., Barrington-Leigh and Inan, 1999]. As a result, elves last no longer than $\sim$1 ms, while the durations of sprites vary greatly, ranging from a few to many tens of milliseconds.

Due to their fleeting ($<$1 ms) existence, elves have been somewhat harder to study optically than have sprites, whose lifetime is more on par with the exposure time of standard video fields ($\sim$17 ms). As described in Chapter 4, a high speed photometric array lends itself well to the identification of elves. In recent years ostensible elves have also routinely been identified by others based on the existence of diffuse glows, often preceding or accompanying more filamentary ``sprites,'' in intensified video recordings. While Barrington-Leigh and Inan [1999] did not claim to identify any elves without the photometric evidence described in Section 4.1, these diffuse glows seem generally to occur when the photometric signature of elves also exists.

For instance, Figure 5.1 shows a (dim) diffuse optical emission which was associated with a negative cloud-to-ground lightning return stroke and with the photometric signature of elves, but without any subsequent streamer-type sprites. These optical flashes are very rarely observed on more than one successive video field, indicating that the luminosity persists for much less than 17 ms.

Figure 5.1: Misinterpreted diffuse glow in video observations. (a) Figure from Barrington-Leigh and Inan [1999], showing what was at the time thought to be the video signature of a ($-$CG) elve (shown in inverse video for clarity). In retrospect, and based on the discussion in the present section, this diffuse glow is probably not an elve but instead the ``sprite halo'' produced entirely by QE heating. (b) The photometric signature of elves, not apparent in the video, was also seen for this event.

However, upon critical inspection, these rather compact ($\sim$40 km horizontal extent) flashes do not bear a strong resemblance to the expected form of an elve, which is predicted (Figure 4.3 on page ) and observed (see Sections 4.1.2 and 4.1.4) to be relatively uniform in brightness over a horizontal scale of $>$150 km.

Below we demonstrate that the diffuse glows previously misidentified as elves are well described by models of electrical breakdown in sprites due to the thundercloud quasi-electrostatic (QE) field. The recent analysis of the temporal and spatial scales which characterize the electrical breakdown at different altitudes above sprite producing thunderstorms has demonstrated that the upper extremities of sprites are expected to appear as amorphous diffuse glows, while the lower portions exhibit a complex streamer structure [Pasko et al., 1998a]. We refer to the diffuse region of sprite breakdown, especially as observed optically, as a ``sprite halo''^5.1 and to the lower portion as the streamer region of sprites.

In Figure 5.1 the intensified video shows the signature of a sprite halo while the photometric array shows primarily that of an elve for the same lightning event, reflecting the complementary capabilities of each instrument. The difficulty of recording luminosity due to elves was discussed in Section 4.1.4 on page . Elves are largely undetectable using video equipment with a 17 ms or 33 ms temporal resolution.

5.1.1 Modeled optical signatures

A computer simulation of the effects of tropospheric currents on the lower ionosphere was described in Section 2.4 and applied in Section 2.5 to two cases in which the electric field in the upper atmosphere was dominated by either the quasi-static (QE) component or the radiated (EMP) component. In Section 4.1.1 optical signatures as seen from the ground were predicted for the case of elves (EMP). Below, the same electromagnetic model is used in an analogous way to predict ground observations of emissions for the QE case in order to compare with observations and with the EMP results already shown in Figures 4.2 and 4.3.

5.1.2 High speed video observations

Stanley et al. [1999] reported the use of a high-speed triggered image-intensified video system for sprite observations which included recordings of several cases of diffuse flashes preceding streamer formation in sprites. The recordings reported here were acquired at 3000 frames/second on 6 October 1997 from Langmuir Laboratory while observing the atmosphere above a storm $\sim$875 km to the south. These data provide an opportunity to compare in more detail the appearance of diffuse video flashes with the predictions of a numerical model.

Figure 5.2a shows VLF sferic, wide field-of-view photometer, and high speed video recordings from Langmuir Laboratory for an event at 05:00:04.716 UT on 6 October 1997. The data are time-tagged and co-aligned to $<$50 $\mu$s accuracy. Less than 0.5 ms after the arrival of the sferic, a photometric enhancement corresponds to a diffuse, descending glow in the imagery. Following this by $\sim$1 ms, a group of sprite columns develops and subsequently brightens in a manner similar to that described by Cummer and Stanley [1999].

Figure 5.2: Modeled and observed diffuse flash at 05:00:04.716 UT. (a) A time-resolved sprite halo, with VLF sferic and photometer data; (b) theoretical lightning currents used as input to the model; and (c) comparison of observations (false color) and the modeled QE and EMP cases, which show emissions in the ${\rm N}_2(1{\rm P})$band.

Figure 5.3: Sprite halo following lightning at 04:45:48.962 UT. 6 October 1997

Figure 5.4: Sprite halo following lightning at 04:52:11.981 UT.

Figure 5.2b shows the two hypothetical lightning currents used to model emissions resulting predominantly from the EMP and QE fields. While all fields are encompassed within the same fully electromagnetic model, the slow and fast input currents will be referred to as the ``QE case'' and the ``EMP case,'' respectively. The EMP case has a 30 $\mu$s current rise time and thus radiates $\sim$10 times as intensely as the QE case which has a 300 $\mu$s rise time. However, on time scales $>$0.2 ms the QE case brings about a much larger vertical charge moment change.

The three sequences shown in Figure 5.2c compare observations of the diffuse flash with video signatures predicted by the model, given the lightning currents shown in (b) and the precise video frame timing (with respect to the lightning return stroke) and viewing geometry in effect during the observations. Scales show altitude above the source lightning discharge. The optical signature for the EMP case is that of elves, but the field-of-view shown reveals only a small part of the elve around its center. A wider field-of-view would reveal that the elve extends over hundreds of km horizontally and begins before the luminosity recorded in high speed video and well above the recorded field-of-view.

A more realistic lightning current profile may have a fast rise time, like that of our EMP case, but a slow relaxation, like the QE case. For the parameters used in the model, the elve (EMP case) is less than one sixth as bright as the diffuse flash of the QE case. Thus, even if both optical emissions were produced in the observed event, the elve may not have been bright enough to be detected by the high speed imager. Nevertheless, the timing, altitude, shape (including upward curvature), and development of the observed luminosity match closely those of the modeled response to a slow lightning current producing a charge moment change of $\sim$900  $\ensuremath{{\rm C\hbox{-}km}}$ in $\sim$1 ms.

By comparison with the model, it can be inferred that this luminosity occurs at altitudes of 70 to 85 km, localized ($\sim$70 km wide) over the source currents, and descends in altitude in rough accordance with the local electrical relaxation time $\index{electric field!relaxation time ($\tau_{\rm E}$)}\ensuremath{\tau_{\rm E}}=\ensuremath{\epsilon_{}}/\sigma$ [Pasko et al., 1997b]. In contrast, the luminosity in elves is confined to higher (80 to 95 km) altitudes and its time dynamics are dominated by an outward expansion in accordance with the speed of light propagation of the lightning EMP, as described in Section 2.5.

Modeling also indicates that the upward curvature apparent in the luminosity (Figure 5.2c) after its first appearance is due to the `expulsion' of the electric field by the enhanced ionization. The ionization enhancement for this modeled event was presented in Figure 2.7. While optical luminosity, especially at the higher altitudes ($>$80 km) of the diffuse upper portion of a sprite, can occur without extra ionization, the upwardly-curved shape of the observed event indicates that significant ionization did occur.

Two other similar events were observed in high-speed video recordings from 6 October 1997 and are shown in Figures 5.3 and 5.4. The three events showed varying delays between the beginning of the sprite halo and the first development of streamer structure. In particular, in the two events not shown in Figure 5.2, the streamers initiated $\sim$0.3 ms and $\sim$3.6 ms after the halo onsets, based on the high speed video.

Altogether, 42 sprite clusters were recorded at video frame rates of 1000 to 4000 s$^{-1}$ during observations on October 3, 6, and 7, 1997. Sprite halos were recorded by the high speed video for only four of these events. All four of the lightning events which did produce sprite halos exhibited unusually large vertical charge moment changes during the initial $\leqslant$1 ms of the return stroke, as inferred from ELF filtering of the sferics measured at Langmuir Laboratory.^5.2 This time scale is fast enough for the electric field to penetrate to lower ionospheric altitudes (see Section 5.1.6).

5.1.3 Sprite halos in normal-rate video

Figure 5.5: Comparison of two sprite halos observed in normal and high speed video.

When averaged over 2 ms, the observed sprite of Figure 5.2 appears as a diffuse halo capping a cluster of columnar features. Figure 5.5 compares this averaged image to a commonly observed form for sprites in normal-speed video, and suggests that broad upper halos occasionally seen in video of sprites are also sprite halos preceding the onset of streamer formation. When the frames of this high speed video sequence are averaged over the entire duration of the sprite ($\sim$4 ms, still much less than a normal video frame) the sprite halo is mostly washed out and becomes hard to perceive. It is thus likely that only in exceptionally bright cases are the diffuse upper portions of sprites visible in a normal video field as sprite halos.

5.1.4 Sprites and elves in photometry

No elves were recorded by the high speed video system in the three mentioned nights of observation in 1997. With much higher temporal resolution than that afforded by even this system, one may be able to resolve in two dimensions the dynamic temporal evolution of an elve, dominated by the propagation time between the source of optical emissions and the observer. As shown in Figure 4.1, these dynamics result in later emissions being observed before earlier ones, and in an apparent downward and outward development of the flash, consistent with the predictions of Inan et al. [1996c].

Figure 5.6: Modeled temporal development of elves and sprite halos. (a) 10 $\mu$s-long snapshots every 100 $\mu$s, viewed from ground level 745 km from the causative CG (from Figure 4.2). The QE and EMP sequences begin 17 $\mu$s and 517 $\mu$s after the lightning sferic would be received by the observer. Note the horizontal and vertical scale difference. (b) The flashes are shown integrated over 2 ms. Superimposed are the fields-of-view of two typical photometer arrays. The EMP cases were already shown in Figures 4.2 and 4.3.

Figure 5.6a shows the same model events as in Figure 5.2 but as seen from 745 km away with a broader field-of-view and with a higher time resolution. Both sequences show a flash which descends over the course of about 1 ms and exhibits the same upwardly concave curvature that was noted in connection with Figure 5.2. While the descent and curvature of the sprite halo represent true descent and curvature of the optical source, these features in elves are instead a result of the propagation geometry between the highly extended source and the observer.

Figure 5.6b shows $28^\circ$$\times$$8^\circ$ images of the predicted emissions from the QE and EMP cases, as would be observed from 745 km away by an instrument integrating over 2 ms. Modeled optical intensities shown here and in Figure 5.2 correspond to the total output of the first positive band of N$_2$ over its entire spectrum from 570 to 2310 nm. About 15% of this intensity would reach the Fly's Eye's red-filtered photometers in their passband of 650 to $\sim$780 nm. For the lightning parameters used here, the elve is only 8% as bright as the sprite halo when integrated over 2 ms. This example illustrates the fact that sprite halos are much easier to image with a 17 ms video field than are elves. However, the intensity of each phenomenon varies strongly with electric field strength, so either emission could be much brighter or dimmer than the cases modeled here, depending on the characteristics of the causative lightning current.

Figure 5.7: Predicted photometric array signatures. Predicted contributions from both EMP (solid lines) and QE (dotted lines) emissions are given for the horizontal and vertical arrays shown in Figure 5.6b.

It has previously been established (see Section 4.1.2) that a horizontal photometer array with time resolution $\ll$1 ms is well suited for identifying elves. We now show how the photometric signatures of sprite halos compare to those of elves. Overlaid on the model images in Figure 5.6b are the fields-of-view of the Fly's Eye array (in blue) and of a 16$\times$($0.5^\circ$$\times$$9^\circ$) multianode photometer (in green) similar to that used by Fukunishi et al. [1998].

Predicted photometric signatures are shown in Figure 5.7 in corresponding colors for EMP (solid lines) and QE (dashed lines) emissions. In both the vertical and horizontal photometer arrays, the initial signature of the ``front'' of the elve (i.e., luminosity produced at a point nearer than the CG to the observer -- see Figure 4.1) is unambiguous. However, at later times, the ``back'' of the elve (i.e., luminosity produced beyond the CG, as seen by the observer) may be confused with that due to the upper part of the sprite. This feature could make it somewhat difficult to measure the downward propagation of the sprite halo in the vertical array,^5.3 and also makes the horizontal array (Fly's Eye) configuration very sensitive to its viewing elevation angle. The modeled response of the Fly's Eye array takes into account the imperfect array alignment. This imperfection is reflected in the fact that photometers P1, P2, and P3 are viewing the ``front'' of the elve in Figures 5.6b and 5.7a, while P5 through P9 view the ``back.''

Figure 5.8 shows normal-speed video and photometric responses for three events recorded with the Fly's Eye using slightly different pointing elevations with respect to the observed flash. All three events produced elves and sprite halos. The event in Figure 5.8a includes an elve and sprites with a halo, but all the photometers are pointing high enough to observe the front of the elve. In Figure 5.8b the sprite halo, which occurred without any further sprite development, may be contributing to the enhanced brightness in P5 and P6. In Figure 5.8c the response of P5 and P6 is clearly dominated by that of the sprite halo, which again occurred without any apparent streamer breakdown.

In the most energetic sprites, any sprite halo is often followed very closely ($<$1 ms) by the much brighter filamentary sprite breakdown, so that all these emissions may not appear as distinct peaks in the photometric record.

Figure 5.8: Photometry and enhanced video images from the Fly's Eye for three events exhibiting sprite halos. A sprite halo caused by a $-$CG is shown in Figure 5.1.

5.1.5 Dependence on the ambient electron density

The distinctive shape, motion, and altitude range of the sprite halo of Figure 5.2 represents the first instance of an observed large-scale feature of sprites which can be accurately modeled in detail. These detailed features can potentially serve as a diagnostic tool for the ambient electron density profile at the time of the discharge. Figure 5.9 shows the modeled luminosity for three initial electron density profiles, using the lightning parameters and timing of the QE case in Figure 5.2. The ambient electron density $\ensuremath{n_{e}}$ at altitude $h$ follows the form [Wait and Spies, 1964]

$$\ensuremath{n_{e}}(h) = 1.43\times 10^{7} {\rm cm}^{-3} \exp\left... ...\right] \exp\left[\left(\beta-0.15 {\rm km}^{-1}\right)\left(h-h'\right)\right]$$

where we use $\beta=0.5$ km$^{-1}$ for each effective reflection height (for VLF signals) $h'$ shown in Figure 5.9. For numerical efficiency, the ambient profiles were capped at ${\ensuremath{5\!\times\!10^{3}}}$ cm$^{-3}$. Both the intensity and shape of optical emissions vary with the $D$ region height. Following well characterized lightning discharges, these optical emissions could reveal information about the local electron density profile over a thunderstorm. The case of $h'$=85 km was chosen as a best match for the observed sprite halo development in Figure 5.2c, remarkably consistent with the well known nighttime VLF reflection height of $\sim$85 km [Bickel et al., 1970].

Figure 5.9: Ambient electron density profiles for three values of $h'$, and the resulting modeled sprite halos. The $h'=85$ km case corresponds to Figure 5.2c. Each image shows a region 30 km high by 105 km wide at a range of 875 km. Dashed lines show profiles used by Pasko et al. [1997b].

5.1.6 Independence of sprite halos and streamer breakdown

The diffuse region of sprites has been previously described in the context of a QE model [Pasko et al., 1995; Pasko et al., 1997b] with the shape, size, and dynamics of optical emissions closely resembling those observed in the high speed video presented here, and is modeled with a more general fully electromagnetic model and more realistic viewing geometry in this work. The direct large scale ($\sim$100 km) modeling of the lower portion of sprites dominated by streamers using the QE model or the electromagnetic model used in this study is computationally not possible at present due to the extremely fine spatial resolution which is required to resolve individual streamer channels [Pasko et al., 2000].

Ionization and optical emissions in the diffuse region and in the lower streamer region of sprites are observed to occur both as fairly separate events and as closely-coupled processes. The upper diffuse region of sprites [Pasko et al., 1998a] is characterized by very fast relaxation of the driving electric field due to the high ambient conductivity associated with electrons at the lower edge of the ionosphere. The ionization process in this region of high electron concentration is theorized to be simple collective multiplication of electrons. In the lower streamer region of sprites, formation of streamer channels follows strong dissociative attachment of electrons (e.g., Figure 2.7 on page ). The upwardly concave shape sometimes evident in sprite halos is due to enhanced ionization in the descending space-charge region. This extra ionization enhances the electric field outside (below) the region and appears to affect the formation of streamers.

However, because the time scale for electrical relaxation varies strongly with altitude, breakdown in the two regions can occur somewhat independently. A lightning discharge with a fast ($<$1 ms) charge moment change may be sufficient to cause diffuse emssions at higher altitudes, where the threshold for ionization and optical excitation is lower, but if lightning currents do not continue to flow, there may not be sufficient electric field to initiate streamers below $\sim$75 km. Conversely, slow continuing currents may cause a (delayed) sprite with streamers but without a significant initial flash in the diffuse region.

Although sprite halos in high speed video can be compared in detail with modeled luminosity, single-site recordings do not allow a robust experimental determination of their altitude distribution. Two-site triangulation of sprite halos was accomplished for the first time by Wescott et al. [1999], and further measurements using triangulation and high-speed imagers may be necessary to statistically characterize the initial development of either the halo or streamer regions of sprites.