Associate ULF Sferics of the ISUAL Sprites

Chapter 3 Effects of Notch-Filtering in the Lulin ULF Recording System

3.3 The Physical Characteristics of the Sprite-Inducing Discharges

3.3.1 Associate ULF Sferics of the ISUAL Sprites

Partly due to the lack of adequate supports and damages from lightning, the Lulin notch-filtering ULF station was out of service for an extended period of time as reported in Section 2.3.3. Only during June to September of 2008, the Lulin station and the FORMOSAT-2/ISUAL were able to operate concurrently. In this period, 29 TLEs (14 pure sprites and 15 sprites with halos and/or elves) were screened out as

potentially-coincident events based on the proximity of the event time. After further considering the bearing angles inferred from the magnetic Lissajous figures of the ULF sferics, only 20 events are considered to be coincident TLEs. The other nine events are ruled out due to the bearing angle deviated more than 30 degrees from the TLEs [Füllekrug and Sukhorukov, 1999], or there were too many ULF sferics in the timing uncertainty window of both systems. For the coincident TLEs, the event distance ranges from 1.6 to 15.6 Mm (~10 Mm on average) and the average deviation of the bearing

angle is 9.7±7.9 degrees.

After reconstruction, the average event time shifts back by 9.2±0.4 milliseconds relative to the notch-filtered sferics. This result is consistent with the ~9 milliseconds peak shift found in the lab-experiment (Section 3.2.2). As a further check, we also computed the bearing angles pointing of the notch-filtered and the reconstructed sferics.

The average difference between each pair of ULF sferics is 0.39±3.69 degrees. This difference is minimal and can safely be treated as no difference. Hence it can be further concluded that the notch-filtering process affects the signal amplitude, the phase, but not the directional bearing.

3.3.2 Formulae for Extraction Current Moment Amplitude ( ), Time Constant (τ), and CMC

To infer the CMC of the sprite-inducing discharges, the methods and procedures suggested in Wait [1996], Jones [1967], Ishaq and Jones [1977], Huang et al. [1999], and

Sato and Fukunishi [2003] are applied. The magnetic component of a sferic can be

expressed as

, (2)

In Equation (2), is the complex amplitude spectrum of the magnetic field projected into the (phi) direction, I(f)ds is the complex vertical current moment spectrum of the discharge, a is the radius of the Earth (~6378 kilometers), h is the height of the

ionosphere (80 kilometers), n is an integer, is a complex modal eigenvalue which describes the propagation and dissipation of the waves [Ishaq and Jones, 1977],

is the associated Legendre function of order n and the first degree, and is the angular great circle distance between the discharge source and the recording system.

Under the assumption of a single exponential decay current moment form [Sentman, 1996], and using the current moment amplitude ( ) and the time constant ( )

estimation method described in Huang et al. [1999], the following equation can be derived:

, (3)

Using Equations (2), the reconstructed can be applied to infer the current moment spectrum I(f)ds, then the time constant ( ) and the CMC can be computed via equation (3).

3.3.3 Current Moment Amplitude ( ), Time Constant (τ), and CMC Inferred From the Reconstructed Sferics

Among the 20 sprite-associated Lulin ULF sferics, the procedures and methods discussed in Section 3.2.1 and Section 3.3.2 can be reliably applied to 18 of them. It is worth to mention that we apply the frequency components only below 100 Hz to estimate the CMC. Ideally, frequency components in the entire radiation band are required to accurately estimate the shape of the lightning source current. Missing high frequency components may potentially result in an underestimate of current moment amplitude and an overestimate of time constant since a narrower but taller pulse may produce the same waveform after passing through the 100 Hz low pass filter. However, this does not change the estimated CMC due to the fact that any low pass filtering does not change the

time integration of the signal. Moreover, the high frequency components are hard to be measured due to their high attenuation rates. The inferred current moment amplitudes, the time constants, and the CMCs of the sferics are tabulated in Table 3-1. Most notably, the CMCs of the sprite-inducing discharges are found to range from 1,500 C-km to 14,000 C-km; whereas those computed from the reconstructed sferics falls between 1,300 C-km and 10,000 C-km. When the reconstructed sferics are used in place of the notch-filtered counterparts, on average the current moment amplitude increases by 69±55%, the time constant reduces by 52±15%, and the CMC lowers by 22±21%. Also as shown in Section 3.2.2, Figure 2-7 and Figure 3-1, the signal reconstruction suppresses ringing in the notch-filtered signals and recovers some of the signal amplitude lost in passing through the modulator. Hence comparing with the notch-filtered sferics, the reconstructed sferics are expected to have larger current moment amplitude and shorter time constant. The combined influence of these two factors reduces the over-estimation of CMC, and produces a smaller value that is closer to the true CMC of the causative discharge.

Table 3-1. The current moment amplitude ( ), the time constant ( ), and the charge moment change (CMC) of the 6 coincident pure sprites and the 12 coincident sprites with halos and/or elves.

Event

To lend further support to the above assertion, quantitative comparisons of the model sferics computed using Equations (2) and (3), the notch-filtered sferics, and the reconstructed sferics are performed. The inferred parameters in Table 3-1, from the notch-filtered and the reconstructed sferics are used as the inputs to the Equation (3). The

derived current moment I(f)ds is then plugged into Equation (2) to obtain the model sferics for the notch-filtered and the reconstructed sferics, respectively. Figure 3-2 shows the results for the associate Lulin ULF sferics of a pure sprite recorded on 12 August 2008. In this particular example, the correlation coefficients (R) between the models (Figure 3-2 (a) and (b); black dashed lines), the notch-filtered (Figure 3-2 (a); blue solid line), and the reconstructed sferics (Figure 3-2 (b); red solid line) improve from 0.78 to 0.94. For the twenty sferics analyzed in this work, the average correlation coefficient improves from 0.80 (notch-filtered) to 0.85 (reconstructed). The results indicate that, owing to the reconstructed sferics having a higher degree of similarity to the true sferics, the CMCs computed from the reconstructed sferics are closer to the true values

comparing with those inferred from the notch-filtered sferics.

Figure 3-2. (a) Comparison of the notch-filtered sferics (blue solid line) and the model sferics (black dashed line) computed using Equation (2); the correlation coefficient (R) is 0.78, and (b) comparison of the reconstructed (red solid line) and the model sferics (black dashed line); R = 0.94. This sferic is associated with a pure sprite observed on 12 August 2008.

3.4 Time‐Integrated Total Photons of the Coincident ISUAL Sprites

From previous studies, the brightness of sprites is known to be correlated to the CMC of the causative lightning [Pasko et al., 1997; Huang et al., 1999; Takahashi et al., 2010]. As an additional illustration of the effects of sferics reconstruction, the N₂1P brightness (in units of mega-Rayleigh) of eight ISUAL sprites, that were not

contaminated by lightning emissions, is computed using the method described in Kuo et

al. [2005; 2008] and Lee et al. [2010]. Since the image data were recorded through a

N₂1P-filter, the N₂1P brightness of sprites in units of photons therefore has to be corrected for the known transmission of the ISUAL imager N21P band (14% at 70 kilometers altitude) [Mende et al., 2005; Kuo et al., 2008]. The sprite N₂1P emission in units of photons, therefore, is the mega-Rayleigh brightness ( )

multiplied the imager integrating time (29 milliseconds) and the size of the sprite in cm². For the eight analyzable ISUAL sprites, the brightness is found to be between 0.2 × 10²⁴ and 8.9 × 10²⁴ photons. The resulting sprite brightness is plotted against the CMC of the causative lightning in Figure 3-3. As shown in Figure 3-3, the data point scatter is substantially lower for the set of CMC inferred from the reconstructed sferics. The correlation coefficients (R) for the straight line fit of these two sets of data (CMC versus imager N21P intensity) are 0.76 for the notch-filtered sferics and 0.92 for the

reconstructed sferics. Arguably, the assumed linear sprite brightness versus CMC relationship is not well mirrored by the data points, since the linearity seems to depend heavily on the outlier point at 12,000 C-km. With the outlier point removed, the linear correlation would drop down to 0.4, which clearly cannot be used to support a linearity

claim. However, a clear linear relation between the causative lightning CMC and the relative sprite brightness [Huang et al., 1999] has long been reported since the early years of the TLE research. More recently, Takahashi et al. [2010] have also found the linear relationship between the absolute luminous intensity of fourteen ISUAL sprites and the CMC of parent lightning. Therefore, even the data set reported in this work is relative small, but the result is consistent with the previous works.

Figure 3-3. Correlation between the charge moment charge (CMC) of the causative discharges and the brightness of sprites. The CMCs are computed from the notch-filtered (blue pluses) and the reconstructed (red circles) sferics. The correlation coefficient (R) and the zero-crossing point for the line fit to the data are 0.76 and ~1,200 C-km for the notch-filtered sferics, and 0.92 and ~900 C-km for the reconstructed sferics.

In Figure 3-3, the interception of the straight line fit of the reconstructed CMC data to the x-axis is ~900 C-km, which is 25% lower than that inferred using the notch-filtered sferics. This threshold value seems to be significant higher than the ~600 C-km reported in Takahashi et al. [2010] and in Hu et al. [2002]; a value believed to be needed for a

positive CG discharge to induce sprites. However, due to the sferic sources studied in this works are all far away events (~10,000 kilometers), the relative uncertainty of the

inferred CMC may range from 10% to more than 100% [Williams et al., 2010]. Also the number of data points available to perform the straight line fitting is low. Hence the uncertainty in the zero-crossing point of the straight line is expected to be high, but the value reported here is still in a reasonable range.

3.5 Conclusion

For ULF recording systems that use hardware notch-filters to remove the 50/60 Hz power grid emissions, the content of the recorded sferics will be altered. For the sferics recorded by notch-filtered ULF station and the sferics further undergo signal

reconstruction, some of the significant differences are:

 The recorded event time is typically delayed by ~9 milliseconds after passing through the signal modulator.

 The inferred current moment amplitude ( ) increases by an average of 69±55%

using the reconstructed sferics.

 The inferred time constant ( ) decreases by an average of 52±15% using the reconstructed sferics.

 The inferred charge moment change (CMC) decreases by an average of 22±21%

using the reconstructed sferics.

 Using the reconstructed parameters, the average correlation coefficient between the model and the recorded sfeircs improves from 0.80 (notch-filtered) to 0.85

(reconstructed).

 The threshold of CMC needed to produce sprites is inferred to be ~900 C-km from

the reconstructed sferics, which is closer to the accepted value of ~ 600 C-km and is 25% lower than that infers using the notch-filtered sferics.

 With closer-to-true CMC values, a tighter linear correlation (0.92 versus 0.76) between the sprite N21P brightness and the CMC of the causative lightning was obtained.

Hence notch-filtered ULF systems can still be very useful, provided a proper signal reconstruction has been performed to reconstruct the recorded sferics.

Chapter 4 Optical and Radio Signatures of Negative Gigantic Jets

4.1 Overview: Negative Gigantic Jets From Typhoon Lionrock (2010)

On 31 August 2010, more than 100 TLEs were observed to occur over Typhoon Lionrock when it passed at ~210 kilometers to the southwest of the NCKU site in Taiwan.

Among them, 14 negative gigantic jets with clear recognizable morphologies and radio frequency signals are analyzed. These gigantic jets are all found to have negative

discharge polarity, and thus are type-I GJs [Chou et al., 2010]. Morphologically, they are grouped into two previous reported forms (tree-like, Figure 4-2 and carrot-like, Figure 4-3) [Su et al., 2003] and a new intermediate form, termed as “tree-carrot-like GJs”

(Figure 4-4). The ULF and ELF/VLF band signals of these events contain clear signatures associate with GJ development stages including the initiating lightning, the leading jet, the FDJ, and the trailing jet. Though the radio waveforms for each type of GJs always contain a fast-descending pulse linked with the surge current upon the

GJ-ionosphere contact, the details actually vary substantially. Cross-analysis of the optical and radio frequency signals for these GJs indicates that a large surge current

moment (CM; >60 kA-km) appears to be essentially associate with the tree-like GJs. In contrast, the carrot-like and the tree-carrot-like GJs are both related to a surge current moment less than 36 kA-km, and a continuing current moment less than 27 kA-km further separates the carrot-like GJs from the tree-carrot-like GJs. Furthermore, on the peak current moment-versus-charge moment change diagram for the initiating lightning (Figure 4-5), different types of GJs seem to exhibit different trends. This feature suggests that the eventual forms of negative GJs may have been determined at the initiating lightning stage.

4.2 Occurrence of GJs in Typhoon Lionrock (2010)

Typhoon Lionrock (2010) was the first of five typhoons with warning issued by the Central Weather Bureau (CWB) in Taiwan and was named in number as ‘1006’. It formed as a tropical depression in the vicinity of Dongsha Atoll (20.6997°N and

116.7277°E; in the lower left of Figure 4-1) over the northern South China Sea on August 27 and dissipated in southeastern China on September 3. At the beginning, Lionrock moved northward and intensified into a weak typhoon. Later, the movement of Lionrock was slowed down due to the presence of Typhoon Namtheun (numbered as ‘1008’), which formed rapidly in northern Taiwan. On August 30, the Fujiwhara effect (binary interaction; Wu et al. [2003]) between the two typhoons drifted Lionrock eastward and east-southeastward. As Lionrock continued to intensify, it reached the lowest mean sea-level pressure of about 985 hPa around 12:00 UTC, 30 August. On 31August, by combining (merging) the circulation and rainband associate with Namtheun, Lionrock further intensified. Lionrock then changed its course to the north-northeast and reached the maximum sustained winds of 23 meters per second. Between 15:00 and 20:00 UTC, the balloon sounding in the synoptic environment of Lionrock inferred relatively high convective available potential energy (CAPE) of 1980 J/kg and relatively low convective inhibition (CIN) of 70 m²s², thus providing favorable thermodynamic conditions to support vigorous convection in the inner-core eyewall region of Typhoon Lionrock with strong dynamic forcing (i.e., convergence in the boundary layer under the eyewall).

When Lionrock approached the southern tip of Taiwan, the radar reflectivity measured from Taiwan was around 50-60 dBz and the cloud top temperature was ~190 K (-83℃), as estimated from the infrared satellite image. Eventually, Lionrock crossed Taiwan Strait northwestward and made landfall in southeastern China on September 2. Lionrock then

weakened into a tropical storm quickly and dissipated in the next day.

Figure 4-1. MTSAT-2 infrared map for the surrounding region of Taiwan at 17:32 UTC, 31 August 2010.

Typhoon Lionrock can be identified as the big patch of clouds toward the southwest of Taiwan. Inset is the cropped radar reflectivity for the GJ occurring region from the Kenting radar station (21.9010°N and 120.8550°E; effective range ~250 kilometers) at 17:30 UTC provided by the Central Weather Bureau in CWB. Overlapping markers on the map respectively are: red square, the optical observation site at NCKU, Tainan City; yellow cross, Lulin ULF station; green triangle, Cingcao ELF/VLF station, which also have the same symbols in Figure 2-1. The two black lines extend from the NCKU campus represents the FOV (30.8°) of the cameras. The color circles (blue and green) indicate the storm centers during the observation period between 15:45 and 20:01 UTC (23:45 and 04:01 in local time), with the time listed to the right. The color dots denote the inferred locations of the fourteen observed GJs that occurred within a one-hour bin centering on the time of the storm center in same colors.

Between 15:45 and 20:01 UTC (23:45 and 04:01 in local time) on 31August 2010,

when the center of Typhoon Lionrock was located at about 270 to 170 kilometers toward the southwest of Taiwan, more than 100 TLEs (including sprites and dozens of gigantic jets) occurred over the typhoon as observed from the NCKU site. Among the identifiable gigantic jets, their locations appear to move synchronously with the typhoon center; color dots in Figure 4-1. However in the FOV of the cameras, the front edge of the typhoon clouds blocked the lower half of the view and the severe light pollution from Tainan city also affected the observation in classifying some of the events. Therefore, only fourteen negative gigantic jets that have clear recognizable forms and identifiable ULF/ELF/VLF data are chosen for detailed analysis.

Based on the height inferred from the IRI-2007 model [Bilitza and Reinisch, 2008]

and the boundaries previously reported in Su et al. [2003], Cummer et al. [2009], and

Soula et al. [2011], the nighttime ionospheric boundary for the region above Lionrock is

estimated to be located at 90 kilometers in altitude during the occurring window of the observed GJs. The fully-developed jets of the GJs are thus assumed to terminate at this ionosphere height, and therefore the occurrence locations of the GJs are projected at the positions marked by the color dots in Figure 4-1. From the radar reflectivity reported by the Kenting radar station (21.89° N and 120.85° E; effective range ~250km) at 17:30 UTC, two regions in Lionrock in the GJ-occurring region show notable echoes; the inset in Figure 4-1. The strong echo region closer to the NCKU site is a convective cell at the eyewall with the cloud top temperature of about 200 K, which corresponds to cloud top height of about 14.5 kilometers. Similar strong echo regions from the deep convective cores also exist in radar reflectivity data obtained at the occurring time of other GJs.

Interestingly, the inferred locations of the GJs all collocate with the region with strong radar echoes that associate with the eyewall convective core of Lionrock, indicating the

observed negative GJs are likely originated from the protruding cloud top region. The soundings also indicate that the direction of the wind rotates clockwise with the height, with the westerly wind in the lower level and easterly wind at the cloud top at the location of the GJ-producing convective core; Figure 4-1. It is possible that the vertical wind shear may have dislocated the charge structure in the convective core and makes the GJs to occur more easily [Riousset et al., 2010]. Consequently, Lionrock serves as a prolific system in the production of gigantic jets and other TLEs.

To check the fairness of the inferred GJ locations, the WWLLN data are also used.

Only one GJ initiating lightning is found to be a WWLLN event, and the geolocation offset of this WWLLN lightning is found to be 15 kilometers with respect to that of the FDJ-inferred location, thus indicating that the inferred locations of the observed GJs are of reasonable accuracy. However, it should be noted that WWLLN [Rodger et al., 2006]

did not actually detect these GJ events. The locating of initiating lightning by no mean represents the occurrence location of GJ is known as well, since the location offset between initiating lightning and the GJ is not known. However, if we assume GJ and its initiating lightning have no occurring location offset, from the top elevation angle of the FDJ and the location of the WWLLN detected initiating lightning, the GJ termination height is inferred to be ~95 kilometers [Hsu et al., 2003]. Since these fourteen GJs evidently occurred over a relatively small area and their top elevation angles are all similar to the one having WWLLN detected initiating lightning, a 90km termination height for these GJs would be scientifically sound.

4.3 The Optical Features of the Negative Gigantic Jets

In this section, the optical band data, flashes associate with the initiating lightning, the morphology and the luminous duration of GJs are presented.

4.3.1 The Initiating Lightning of Gigantic Jets

For the fourteen GJs analyzed in this work, due to the obstruction of the clouds and the heavy light pollution, only the FDJ and the trailing jet stages were clearly discernible on the video footage. Although the GJs were at a relatively large distance of ~210

kilometers from the optical observation site, the accompanying in-cloud optical flashes at the GJ initiation are discernible. As a result, twelve out of the fourteen GJs (>80%) were found to have the associate optical flashes from the GJ initiation. The other two no-flash GJs occurred back to back within a 1.5-minute window. It may be that the clouds at this period were exceptionally thick and thus blocked the optical emissions from the initiating lightning to leak through. The ULF and the ELF/VLF signals are used to correlate the

在文檔中各類高空短暫發光現象的超低頻與極低頻至甚低頻電波特性 (頁 69-0)