Abstract

Combined multiparameter radar, dual-Doppler, thermodynamic sounding, and lightning observations of 11 thunderstorms (6 from the midlatitudes, 5 from the Tropics) are examined. The thunderstorms span a wide spectrum of intensities, from weak monsoontype to severe tornadic, and include both unicellular and multicellular convection. In general, the kinematically strongest storms featured lower production of negative cloud-to-ground lightning (typically <1 min−1 flash rates for large portions of the storms' lifetimes) when compared with more moderate convection, in accord with an elevated charge mechanism. The only significant differences between intense storms that produced predominately positive cloud-to-ground (CG) lightning for a significant portion of their lifetimes (PPCG storms) and intense storms that produced little CG lightning of any polarity (low-CG storms) was that PPCG storms featured much larger volumes of significant updrafts (both >10 and >20 m s−1) and produced greater amounts of precipitation (both rain and hail). Otherwise, peak updrafts and vertical airmass fluxes were very similar between the two types of storms, and both types were linked by anomalously low production of negative CG lightning. PPCG effects in storms may result from an elevated region of negative charge (reducing negative CG flash rates) combined with enhanced net positive charge regions created by the larger volume of significant updrafts.

1. Introduction

How do convective storm microphysical and dynamical processes affect lightning production, including flash rate, type, and polarity? This is a fundamental question in atmospheric electricity research, but it is a difficult question to answer, as there are a variety of convective storm types as well as different lightning patterns, as manifested in cloud-to-ground lightning flash rates, dominant polarity of cloud-to-ground lightning, total and intracloud lightning flash rates, the ratio of intracloud to cloud-to-ground lightning, and so on. Indeed, with the advent of lightning data for operational use in the “nowcasting” of thunderstorms, in particular severe thunderstorms, this question takes on additional weight. Answers to this question may provide better insights into the short-term prediction of severe weather, such as large hail and tornadoes.

Past studies have shown that “typical” convection (e.g., an airmass storm, or perhaps a cell within a multicell complex) lasts approximately 1 h and becomes electrically active after the ice phase develops (Workman and Reynolds 1949; Mazur et al. 1986; Goodman et al. 1988; Williams et al. 1989a,b; Carey and Rutledge 1996). Initial flashes are typically intracloud (IC) flashes (Workman and Reynolds 1949; Livingston and Krider 1978; Goodman et al. 1988; Williams et al. 1989b; Maier and Krider 1986). Cloud-to-ground (CG) lightning flashes tend to occur as the main core of the cell descends to lower altitudes (Larson and Stansbury 1974; MacGorman et al. 1989; Goodman et al. 1988, 1989; Williams et al. 1989a; Carey and Rutledge 1996). Thus, CG flashes typically peak after the ICs. Typical peak total flash rates are around 10 min−1 (Livingston and Krider 1978; Piepgrass et al. 1982; Williams et al. 1989a,b; Carey and Rutledge 1996), with CGs averaging around 2 min−1 and sometimes as high as 10 min−1 (Peckham et al. 1984; Williams et al. 1989a; Carey and Rutledge 1996). In typical warm season convection, the majority of the CG lightning is of negative polarity [90% or more of the flashes transfer negative charge to the ground; Orville (1994) and Orville and Silver (1997)].

By contrast, many severe thunderstorms feature high total lightning flash rates (greater than 15 min−1, and often greater than 30 min−1). These storms also may produce very little CG lightning (often <1 min−1 and sometimes no CGs for 10 min or more), which implies large IC flash rates and, thus, a high IC:CG ratio. This ratio can become infinite for brief periods of time. These so-called low-CG storms are a topic of recent interest (MacGorman et al. 1989; Billingsley and Biggerstaff 1994; Maddox et al. 1997; Williams et al. 1999; Lang et al. 2000; McCaul et al. 2002).

In addition, recent research has focused on the phenomenon of predominantly positive CG producing (PPCG) severe storms (Reap and MacGorman 1989; Branick and Doswell 1992; Curran and Rust 1992; Seimon 1993; MacGorman and Burgess 1994; Stolzenburg 1994; Carey and Rutledge 1998). By definition, at least 50% of the CG lightning in PPCG storms is of positive polarity. PPCG storms are often severe (producing hail, damaging winds, or tornadoes), and can have high IC flash rates.

What distinguishes low-CG from PPCG storms? Both have the potential for severity. Both tend to have high IC flash rates and high IC:CG ratios. Both lack significant production of negative CGs. But PPCG storms can produce significant numbers of positive CGs and low-CG storms do not.

One approach to addressing this question is to illuminate possible kinematic, microphysical, and environmental differences between low-CG and PPCG storms, as well as differences between these storms and more general convection. This study will focus on identifying these differences through radar and lightning observations of a variety of storms. By examining how lightning output changes as a function of radar-observed storm kinematics and microphysics, we hope to better understand how such properties may affect lightning production.

2. Hypotheses

MacGorman et al. (1989) first suggested that low-CG storms might be caused by an “elevated charge mechanism,” where intense updrafts loft the main negative charge layer to greater altitudes than normal. For a variety of reasons, most notably the reduced electric field between the main negative charge and ground due to the greater spatial separation, a reduction in the CG lightning flash rate (and in particular negative CG flash rate) would be expected. However, the total lightning (and thus IC) flash rate increases due to stronger charging driven by the intense updrafts in combination with less separation between the main negative charge layer and upper positive charge. Figure 1 presents these concepts in schematic form. For normal convection, as kinematic (updraft) intensity increases, the storm electrifies more and negative CG lightning flash rate increases. However, at the high end of the kinematic intensity scale, the negative charge becomes elevated enough that negative CG flash rates are reduced back to values typical of weak convection (or even become zero). Total flash rate continues to increase, at least conceptually.

Fig. 1.

Schematic representation of the impact of the elevated charge mechanism on lightning flash rates. Note that total flash rate and negative CG flash rate are plotted on different scales

Fig. 1.

Schematic representation of the impact of the elevated charge mechanism on lightning flash rates. Note that total flash rate and negative CG flash rate are plotted on different scales

Lang et al. (2000) found CG flash rate to be anticorrelated with storm intensity as measured by multiparameter radar, which supports the elevated charge hypothesis. In addition, balloon-borne electric field meter data presented by Stolzenburg et al. (1998a–c) support a direct correlation between updraft speed and height of the negative charge layer. Finally, a modeling study by Ziegler and MacGorman (1994) supports the concept of the elevated charge mechanism. We will provide further evidence for the elevated charge mechanism during the course of this study.

Currently, there are three mechanisms proposed to explain PPCG behavior: the tilted dipole, the inverted dipole, and precipitation unshielding. The tilted dipole mechanism (MacGorman and Nielsen 1991; Branick and Doswell 1992) posits that upper positive charge is displaced laterally by strong upper-level winds, thereby unshielding it from negative charge below and exposing the positive charge to ground. The inverted dipole mechanism (MacGorman and Nielsen 1991; Williams et al. 1991) suggests that in PPCG storms the lower positive charge layer may become dominant, effectively causing the classic dipole to become inverted, with negative charge situated atop positive charge. The lower positive charge would favor positive CGs instead of negative CGs. The precipitation-unshielding mechanism (Carey and Rutledge 1998) suggests that in intense storms the precipitation mass flux becomes sufficiently large such that the negative charge center is effectively removed (or greatly reduced) by the fallout of precipitation particles. The resultant large precipitation current suggests that the role of negative CGs in neutralizing charge may be diminished in these cases. Such a mechanism is consistent with the dearth of negative CGs in PPCG (and even low-CG) storms. In addition, the unshielding and exposing of upper positive charge by the reduction of negative charge could cause positive CG flash rates to increase.

The modeling study by Mansell et al. (2002) showed that positive CGs require negative charge underlying positive charge, in order to initiate positive leaders to ground. (In the precipitation-unshielding case, the assumption is that enough negative charge remains to provide some downward bias.) If upper positive charge is the dominant origin of positive CG lightning, then in the Stolzenburg et al. (1998c) model this underlying negative charge region would be the main negative charge layer. In intense storms, this layer would be elevated, while upper positive charge would tend to be constrained by the tropopause. The decreased distance between charge layers should lead to enhanced IC flashing, but it also could favor positive CG lightning through improved downward bias for positive leaders. If lower positive charge is the dominant origin for positive CG flashes, then in the Stolzenburg et al. (1998c) model the underlying negative charge would have to be a minor or screening charge layer (like one of the many charge layers found in thunderstorm downdrafts in that model). The total charge production in these layers should be enhanced by larger updraft volumes.

These hypotheses will be tested in this study in a variety of different ways, by utilizing unique datasets. Our datasets feature combined dual-Doppler, multiparameter radar, and lightning observations of 11 different cases, spanning a broad spectrum of storms, including weak monsoontype storms, ordinary (airmasslike) convection, moderate intensity storms, and severe (and even tornadic) thunderstorms. Both unicellular and multicellular convective storms are included. Six cases are from the midlatitudes, and five are from the Tropics.

3. Overview of data platforms

This study examines five case studies using the Colorado State University (CSU)-CHILL-Pawnee dual-Doppler radar network in northeast Colorado (1, 15, 21, 25, and 30 July 1998), the only research dual-Doppler network in the United States. To broaden the scope of the analysis, five cases (26, 13, 15, and 17 January and 20 February 1999) were selected from the Tropics, specifically from the Tropical Rainfall Measuring Mission/Large-Scale Biosphere–Atmosphere Experiment (TRMM/LBA; e.g., Rutledge et al. 2000) field project in the southwestern Amazon region of Brazil. Finally, the sixth midlatitude case (29 June 2000) was obtained from the Severe Thunderstorm Electrification and Precipitation Study (STEPS; see additional information online at http://radarmet.atmos.colostate.edu/steps/), which occurred in eastern Colorado/western Kansas.

These cases were selected to span a broad spectrum, from weakly electrified to PPCG and low-CG intense storms. Each case typically features 1–2 h of combined dual-Doppler and multiparameter radar data. Data from CG lightning detection networks were available for each case. Field change meters (FCMs) provide some information on total lightning flash rates for at least a portion of many cases (CHILL-Pawnee and TRMM/LBA). The STEPS case features data from a VHF lightning mapper (Krehbiel et al. 2000), which provides higher quality total/IC lightning data than do FCMs. Finally, all cases have sounding data to characterize storm environment. The data platforms are described below. Methods to quality control, analyze, and synthesize the datasets in this study are provided in the appendix.

The CHILL-Pawnee cases feature multiparameter radar data from the CSU-CHILL radar, and when combined with Pawnee data, dual-Doppler coverage of storm kinematics. The TRMM/LBA cases feature multiparameter radar data from the National Center for Atmospheric Research (NCAR) S-band dual-polarization Doppler radar (S-Pol) radar, and dual-Doppler coverage when combined with data from the National Aeronautics and Space Administration (NASA) Tropical Ocean Global Atmosphere (TOGA) radar. The STEPS case was covered by the CSU-CHILL radar (located near Burlington, Colorado, for STEPS) and the S-Pol radar. The specifics of all radars are summarized in Table 1. The variables measured by the multiparameter CSU-CHILL and S-Pol radars include horizontal reflectivity (Zh), radial velocity (Vr), differential reflectivity (Zdr), linear depolarization ratio (LDR), correlation coefficient at zero lag (ρhv), and differential phase (Φdp). These variables give information on the size, shape, orientation, thermodynamic phase, and radial velocity of hydrometeors in a bulk sense. The other nonpolarimetric radars provide information on radar reflectivity and radial velocity. For a thorough review of all the radar variables see Doviak and Zrnic (1993).

Table 1. 

Specifics of the radars used in this study

Specifics of the radars used in this study
Specifics of the radars used in this study

The National Lightning Detection Network (NLDN) provided CG lightning data for CHILL-Pawnee and STEPS cases. Detection efficiencies in northeastern Colorado are thought to be 90% or better (80% or better in the STEPS domain), with a median location accuracy of 0.5 km (Cummins et al. 1998). According to Cummins et al. (1998), positive discharges with peak currents under 10 kA may be IC discharges, and not positive CGs. Therefore, such flashes were eliminated.

A network of four combined direction finder (DF) and time-of-arrival (TOA) sensors provided CG data for TRMM/LBA cases. When all four sensors were operational, estimated detection efficiency within the LBA dual-Doppler lobes was 70%–80% or better, with a median location accuracy of 1–2 km. However, not all stations were operational during the entirety of TRMM/LBA, which affected location accuracy significantly. In addition, to account for misidentified IC flashes detected positive CGs with peak currents less than 15 kA were not included in the analysis (R. Blakeslee 2001, personal communication).

Electric FCMs, stationed at the principal radars and elsewhere, were used to characterize total lightning flash rates for the CHILL-Pawnee and TRMM/LBA storms. These sensors have a nominal range of 40 km, and through comparisons with the NLDN and VHF lightning mappers are expected to detect 60%–70% of all lightning within this range. FCMs provide no direction or range information, so multiple cells within range cannot be distinguished.

The New Mexico Tech Lightning Mapping Array (LMA) was operated in the STEPS project area from mid-May to mid-August 2000. LMA coverage included and extended well beyond the CHILL/S-Pol dual-Doppler lobes. Within this range detection efficiency of lightning flashes is near 100%. The system locates the sources of impulsive VHF radio signals from lightning by measuring the time that the signals arrive at the various receiving stations. Synthesis of the TOA measurements allows three-dimensional reproduction of the lightning channels inside storms. For more information on the LMA see Krehbiel et al. (2000).

4. Observations

To briefly summarize each midlatitude case, the storm of 1 July 1998 was a severe supercell that produced large hail (D > 2 cm) and featured a tornado warning, although no visual confirmation was obtained. The storm of 15 July 1998 was a severe squall line that produced large hail. The 21 July 1998 storm was an intense storm, but no severe reports were logged. The storm of 25 July 1998 was a collection of nonsevere, but significant, convective cells. The storm of 30 July 1998 was a weak monsoonlike storm. The storm of 29 June 2000 was a tornadic supercell that produced large hail.

As for the tropical cases, the storm of 26 January 1999 was a large, intense squall line. The storm of 13 February 1999 was a collection of scattered and disorganized cells. The 15 February 1999 storm was initially a collection of cells that gradually merged into a convective line. The storm of 17 February 1999 comprised scattered cells, as did the 20 February 1999 case.

Table 2 summarizes some of the key observations (for the available analysis periods) from the midlatitude cases. The storms of 1 and 15 July were by far the most intense storms of the CHILL-Pawnee set by virtually every measure. The 15 July 1998 had greater peak volumes of significant updrafts in the mixed phase region (0° to −40°C; 3–9 km AGL for the midlatitude cases, 4–10.5 km AGL for the tropical cases), although 1 July 1998 had a larger peak vertical velocity. The 15 July 1998 storm produced larger amounts of rain and hail. This is interesting to note, since the 15 July 1998 storm had a much larger peak positive CG flash rate than 1 July. The 15 July 1998 storm was not necessarily more intense than 1 July (in terms non-area- and non-volume-based measures), just larger in storm volume. Peak negative CG flash rates were fairly modest for both storms.

Table 2. 

Summary of kinematic, microphysical, and lightning observations for the midlatitude cases. Note that flash rates are not corrected for detection efficiency

Summary of kinematic, microphysical, and lightning observations for the midlatitude cases. Note that flash rates are not corrected for detection efficiency
Summary of kinematic, microphysical, and lightning observations for the midlatitude cases. Note that flash rates are not corrected for detection efficiency

Figure 2 shows horizontal and vertical cross sections of CSU-CHILL radar reflectivity for the 1 July 1998 storm, near the time of its peak CG flash rate. Also shown are the ground-strike locations and polarities of CG flashes in a 10-min period centered on this time. Most CG flashes were not associated with the highest reflectivity (>60 dBZ) region of the storm, a region which showed very strong development in the vertical. Based on these observations, we define 1 July 1998 as a low-CG storm, as the peak CG flash rate for the area immediately surrounding the highest reflectivity region was under 1 min−1. The 15 July 1998 case is identified as a PPCG storm, due to the fact it produced greater than 50% positive CGs at peak, and peak positive CG flash rate exceeded 4 flashes per minute. Unfortunately, reliable total flash rate data were not available for these two storms.

Fig. 2.

(a) Horizontal cross section of CHILL radar reflectivity at 0.5 km AGL, at 1925 MDT 1 Jul 1998. Also shown are ground strike positions (plus signs for positives, minus signs for negatives) of NLDN CGs that occurred during 1920–1930 MDT. (b) Vertical cross section of reflectivity from the same time through 10 km N. Distances are relative to CHILL

Fig. 2.

(a) Horizontal cross section of CHILL radar reflectivity at 0.5 km AGL, at 1925 MDT 1 Jul 1998. Also shown are ground strike positions (plus signs for positives, minus signs for negatives) of NLDN CGs that occurred during 1920–1930 MDT. (b) Vertical cross section of reflectivity from the same time through 10 km N. Distances are relative to CHILL

The 29 June 2000 storm from STEPS had larger volumes of significant updrafts than either 1 or 15 July 1998 (particularly 1 July), but its rain production was comparable to 15 July, and it had a smaller peak hail area than 15 July. The peak vertical velocity on 29 June 2000 was larger than any other midlatitude storm, although not that much larger than that of 1 July 1998 considering the error expected in vertical velocity estimates (see the appendix). The 29 June 2000 storm produced very few negative CGs, but it had a peak positive CG flash rate that fell between the 1 and 15 July 1998 storms. Thus, 29 June 2000 had the greatest volume of updrafts in excess of 10 and 20 m s−1, but was not necessarily that much stronger than the other two. Based on these observations, 29 June 2000 is identified as a PPCG storm. About midway through the analysis period, around a time of rapid growth of total flash rate from the LMA, the 29 June storm produced a tornado. During most of the analysis period, lightning was occurring nearly continuously, making this storm similar in character to the severe storms observed by Williams et al. (1999).

The 21 and 25 July cases were less intense than the severe storms (1 and 15 July 1998, 29 June 2000) by nearly every measure (Table 2), but produced far more negative CGs. In particular, the 21 July storm produced negative CG flashes at a rate that was consistently well above average. It was less intense overall than 25 July 1998, which had CG flash rates that were typical of ordinary convection. Detected total flash rates were modest for both storms, 18 per 5 minutes for 21 July and 40 per 5 minutes for 25 July. Note that the peak total flash rates for 21 and 25 July 1998 are less than the peak CG lightning flash rate, due to the lower detection efficiency of the FCMs and the fact that CGs outside the range of the FCMs were considered in computing CG flash rates. Interestingly, both 21 and 25 July 1998 produced more rain at peak than the 1 July 1998 low-CG storm. The monsoonal storm of 30 July was the least intense of the set and also had the lowest lightning output, with very few CGs or ICs (maximum detected total flash rate of 2 per 5 minutes).

Table 3 summarizes key observations (for the available analysis periods) for the tropical cases. The 26 January 1999 storm featured the highest peak reflectivity of the tropical cases (>60 dBZ), the largest updraft volume in the mixed phase region (for updrafts >10 m s−1), the largest area of heavy rain, and the highest rain mass flux. It also had the second highest altitude of the 30-dBZ contour, the second strongest peak updraft, and the second largest total flash rate. The 13 February 1999 storm had substantially weaker measurands, and the smallest peak negative CG flash rate. However, the Brazil Lightning Detection Network (BLDN) had detection problems for a substantial portion of this case, in fact not detecting any CG lightning within the LBA domain for the period 1700–1800 UTC (during which time the storm peaked in updraft strength and rain production), so this peak value is probably an underestimate. The 13 February 1999 storm did feature the highest vertical extent of the 30-dBZ contour.

Table 3. 

Summary of kinematic, microphysical, and lightning observations for the tropical cases. Hail and positive CG values not shown because they were negligible. Note that flash rates are not corrected for detection efficiency

Summary of kinematic, microphysical, and lightning observations for the tropical cases. Hail and positive CG values not shown because they were negligible. Note that flash rates are not corrected for detection efficiency
Summary of kinematic, microphysical, and lightning observations for the tropical cases. Hail and positive CG values not shown because they were negligible. Note that flash rates are not corrected for detection efficiency

The strongest peak updraft and the largest updraft volume (>20 m s−1) were associated with the 15 February 1999 storm. This case also had the highest total flash rate (79 detected flashes per 5 minutes vs 64 for 26 January and 32 for 17 February) and the second highest negative CG flash rate. The 17 February 1999 case was smaller compared to the 26 January and 15 February cases, although its updraft speed was comparable (considering the expected error; see the appendix) and it did produce the largest negative CG flash rate in the set. The 20 February 1999 case was typically in the middle to bottom half of all storms in any particular category, including featuring the second lowest peak negative CG flash rate. Note that over the entire tropical set the peak 10-min negative CG flash rate was in the range of 2–6.5 min−1. This falls just below the rates seen in the moderate midlatitude cases like 21 and 25 July 1998, but is comparable to peak CG rates observed in past studies of moderate convection (e.g., Peckham et al. 1984). Overall, total flash rates for these storms were significant, but not anomalously high (note no measurements were available for 13 and 20 February). Positive CGs and hail were not produced in significant amounts by any of the tropical events, and are not shown in Table 3. Indeed, peak positive CG flash rates were at or near zero for all storms.

One parameter of potential importance to thunderstorm electrification is vertical airmass flux, particularly positive (upward) vertical airmass flux, the product of air density and updraft velocity. Large mass fluxes are important since they deliver larger mixing ratios of precipitation-sized particles critical for electrification.

Figure 3a shows vertical profiles of area-averaged upward mass flux profiles for each midlatitude storm, at the time of peak updraft speed for each event. The 1 and 15 July 1998 storms, as well as 29 June 2000, clearly had greater fluxes than the other storms, particularly in the lower half of the storm volumes. The mixed phase region (defined as 0° to −40°C) generally spanned between 3 and 9 km AGL for the midlatitude storms, and here 1 and 15 July, as well as 29 June, generally exceeded the other storms' fluxes by a large margin (roughly a factor of 2), especially near the base of the mixed phase region. The 30 July storm had a larger positive flux than the 21 or 25 July storms below the mixed phase region, but the 21 and 25 July storms had larger positive fluxes within the mixed phase region itself. The 21 July 1998 storm had a somewhat larger flux in this region than 25 July.

Fig. 3.

(a) Average positive vertical airmass flux as a function of height at the times of peak updrafts for the midlatitude storms. (b) Same as in (a) except for the tropical cases

Fig. 3.

(a) Average positive vertical airmass flux as a function of height at the times of peak updrafts for the midlatitude storms. (b) Same as in (a) except for the tropical cases

Mass fluxes for the tropical cases are shown in Fig. 3b. These fluxes are similar within the mixed phase region (roughly 4–10.5 km AGL). Thus, while storms like those on 26 January and 15 February had more intense updrafts, their average vertical mass fluxes were comparable to the other storms. The tropical mass fluxes were very similar to the values posted for the midlatitude storms of 21 and 25 July 1998 (Fig. 3a), which suggests that these tropical thunderstorms were of comparable kinematic intensity to moderate midlatitude convection. Mass fluxes in all tropical cases were substantially less than the strongest midlatitude cases, especially in the mixed phase region.

Note that most of the midlatitude cases, in particular the more intense cases, do not show as much of a monotonic dropoff in mass flux with height, when compared with the tropical cases. In fact, some cases, like 21 July 1998, show a midlevel maximum in vertical airmass flux. In addition, many tropical cases (and some kinematically similar midlatitude cases like that on 25 July 1998) show an upper-level maximum in vertical airmass flux. This is likely due to two causes, one a data issue and the second a physical issue. At upper levels, there are fewer data points and so a few large numbers skew the average there to higher values. The physical cause is related to the fact that these storms achieved their peak vertical velocities at upper levels. This is consistent with precipitation loading of the updraft at lower levels, which does not recover until one moves well above the reflectivity core. Contrast this with the intense midlatitude cases (1 and 15 July 1998, 29 June 2000), which show no such upper-level peak. In fact, in these storms the updrafts were large throughout the midlevel regions, consistent with peak thermal buoyancy being situated there (though below the altitude of the peak updraft speed). The likely result is that more robust charging occurred in the most intense storms, leading to higher total flash rates when compared to more moderate midlatitude and tropical events. However, due to the lack of total flash rate data for the 1 and 15 July storms, we cannot verify this hypothesis.

5. Synthesis

If the elevated charge mechanism is valid, a relationship between kinematic intensity and negative CG flash rate (Fig. 1) is expected. To study this, we must determine what quantity best measures kinematic intensity (KI). Peak vertical velocity is a common measure, but perhaps is not the best since it only reflects the value of a single grid point at a particular time. Volume occupied by significant updrafts within the mixed phase region is another potential measure. Still another measure might be vertical airmass flux, in particular, mass flux in the mixed phase region.

In this study, we decided on a combination of all three of these variables to approximate kinematic intensity. They were combined (with equal weights) to form a kinematic intensity index. In particular, for each storm, peak vertical velocity, peak storm volume containing updrafts in excess of 10 m s−1, peak storm volume containing updrafts in excess of 20 m s−1, and peak average upward airmass flux within the mixed phase region (0° to −40°C; basically the average of the mixed phase points in Fig. 3) all were normalized to the respective values for the 25 July 1998 storm (since this case was of intermediate intensity), and then averaged together to form the KI index. (Information on how we obtained the variables to calculate KI and other indices can be found in the appendix.) The storm volume indices were averaged together before combining with the other measures, so that each category (vertical velocity, updraft volume, and mass flux) had a weight of one-third. The advantage of an index is that it is not completely sensitive to any one measure of intensity. As will be seen, using a composite KI with equal weights is an efficient way to investigate relationships between kinematics, microphysics, and lightning.

Peak values (over the available dual-Doppler analysis periods) were used to construct the index because each of the cases generally had only 30 min or less of optimal dual-Doppler. Thus, averages over storm lifetimes could be misleading, since storms not well placed within the dual-Doppler lobes for a majority of their lifetimes would appear to be less intense than those that were optimally situated, regardless of their actual updrafts. Note that, due to radar coverage issues, the true peak times could be missed if they lay outside the available analysis periods, and so only a minor peak may be sampled. This would tend to bias any constructed indices lower than they were in reality.

Figure 4 shows kinematic intensity index versus peak negative (panel a) and positive (panel b) CG flash rates for each case. The three low negative CG storms (1 and 15 July 1998, 29 June 2000) stand out in the lower-right portion of the plot (Fig. 4a), with high kinematic indices yet low peak negative CG flash rates. Note how KI for the PPCG storms exceeds the indices for the other intense storms, 1 July 1998. This was mainly due to the large volume of intense updrafts observed in the PPCG storms. The remaining storms fell within a KI index range of 0.5 to 1.5, or within 50% of the 25 July 1998 storm. In this range of moderate intensities, peak negative CG flash rates varied significantly, and there was no obvious correspondence between KI and peak negative CG flash rate. However, there was a tendency for storms within this moderate intensity range to exhibit greater peak negative CG flash rates compared to storms with larger KI, behavior consistent with the elevated charge mechanism (Fig. 1). Note that the monsoonal storm, 30 July 1998, was very low on the intensity scale and produced no negative CG lightning. This is consistent with this case lacking strong enough updrafts to electrify significantly.

Fig. 4.

(a) Kinematic intensity index vs peak negative CG flash rate for all the storms in this study. (b) Same as in (a) except for positive CG flash rate. Open points denote midlatitude cases; filled points denote tropical cases. Note that flash rate scale is greater for negative CG flashes than for positive CGs

Fig. 4.

(a) Kinematic intensity index vs peak negative CG flash rate for all the storms in this study. (b) Same as in (a) except for positive CG flash rate. Open points denote midlatitude cases; filled points denote tropical cases. Note that flash rate scale is greater for negative CG flashes than for positive CGs

The two PPCG storms, 15 July 1998 and 29 June 2000, both had significantly higher KI than any other storm, even 1 July 1998 (Fig. 4b). However, as mentioned above, the discrepancy in KI between the low-CG 1 July 1998 storm and the PPCG storms was mainly due to the vastly greater volumes of intense (i.e., >20 m s−1) updrafts in the latter storms. The other components of the index were not as different between these storms. Given such a small sample size, it is difficult to draw firm conclusions, but one key difference between low-CG and PPCG storms may be that, although both types of storms can have comparable peak vertical velocities and vertical airmass fluxes, PPCG storms have far larger volumes of intense updrafts. As we argue later, a larger volume of strong updrafts (i.e., >20 m s−1) would imply significantly greater production of positive charge, which could be tapped for subsequent positive CG flashing.

Along the same lines as the KI index, a rain intensity index was constructed for each storm. This index comprised a peak area of heavy (>60 mm h−1) rain at 0.5 km AGL and a peak rain mass flux, both of which were normalized to their respective values for 25 July 1998, and then averaged together. The rain index (RI) is advantageous over any one particular measure of rain intensity because it balances very heavy rain producers (area of heavy rain) against storms that produce large rain totals despite the absence of large rain rates (rain mass flux). Peak values were used for similar reasons to the kinematic index.

Figure 5 shows RI versus peak negative and peak positive CG flash rate for each storm in this study. The 15 July 1998 and 29 June 2000 storms were by far the most intense rain producers. No well-defined relationship between RI and peak negative CG flash rate is evident (Fig. 5a). However, based on our sample, PPCG storms featured the greatest rainfall production. The PPCG storms stand out at the high end of the spectrum, suggesting that very intense rainfall may be related to enhanced positive CG activity (Fig. 5b). This is broadly consistent with the precipitation unshielding mechanism discussed in section 2. However, a low-CG storm like 1 July 1998 actually had a lower rainfall intensity index than more prolific negative CG producers such as 21 and 25 July 1998. This observation seems inconsistent with a precipitation unshielding mechanism, where storms with the heaviest rainfall should have the lowest negative CG flash rates. An additional factor that could be important for precipitation unshielding, peak rain rates, was not included in the RI. Maximum rain rates for all storms generally were within 20% of one another (i.e., not significantly different from expected measurement error), so it is difficult to draw favorable conclusions for the unshielding mechanism based on this additional factor.

Fig. 5.

(a) Rain intensity index vs peak negative CG flash rate for all the storms in this study. (b) Same as in (a) except for positive CG flash rate. Open points denote midlatitude cases; filled points denote tropical cases

Fig. 5.

(a) Rain intensity index vs peak negative CG flash rate for all the storms in this study. (b) Same as in (a) except for positive CG flash rate. Open points denote midlatitude cases; filled points denote tropical cases

A hail intensity (HI) index was constructed for the midlatitude cases, comprising a peak hail area at 0.5 km AGL and a peak hail mass flux, both normalized to 25 July 1998 and then averaged. The HI index was not calculated for the tropical cases.

Figure 6a is very similar to the midlatitude portion of Fig. 4a, suggesting that KI and HI are strongly related. Moderate hail producers like 21 and 25 July 1998 featured significantly higher negative CG flash rates than more intense hail producers. In Fig. 6b, which is very similar to the midlatitude portion of Fig. 4b, the most distinctive feature is that the PPCG storms were associated with significantly larger HI.

Fig. 6.

(a) Hail intensity index vs peak negative CG flash rate for the midlatitude storms. (b) Same as in (a) except for positive CG flash rate

Fig. 6.

(a) Hail intensity index vs peak negative CG flash rate for the midlatitude storms. (b) Same as in (a) except for positive CG flash rate

Given the apparent strong relationship between KI and HI, it would be difficult to decouple the two to state unambiguously that hail was a driving factor in causing PPCG storms. In addition, hail is not likely produced in high enough number concentrations (e.g., Cheng and English 1983), even in storms like 15 July 1998 and 29 June 2000, to be significant from an electrical perspective compared to graupel. Moreover, observations of a PPCG storm by Carey and Rutledge (1998) suggest that hail may be electrically neutral in such storms, in that it does not carry enough aggregate charge to significantly affect lightning production.

6. Discussion and conclusions

The elevated charge mechanism is consistent with our observations. Storms that featured high KI, such as those on 1 and 15 July 1998, and on 29 June 2000, consistently featured smaller peak negative CG flash rates compared to storms with less KI, whether these latter storms were tropical or midlatitude. This conclusion is strengthened by the fact that it was independent of the particular kinematic descriptor. The low negative CG producers had higher peak updrafts, greater vertical mass fluxes, larger volumes containing updrafts greater than virtually any arbitrary threshold (e.g., 20 m s−1), and so on.

The HI index was found to be highly correlated to KI (for the midlatitude cases), and thus the most significant hail producers were also the lowest producers of negative CGs (save for a weakly electrified case like that of 30 July 1998). Unlike hail, rain production was only loosely correlated to KI and negative CG production. Thus, one cannot identify probable low negative CG storms by simply looking for the storms that produce the largest rain mass fluxes or heavy rain areas.

This dataset contained two PPCG storms (15 July 1998 and 29 June 2000) and one low-CG storm (1 July 1998). From a kinematic perspective, both of these types of storms were very similar, having nearly identical peak updrafts and mass fluxes. Reflectivity statistics were also similar. In fact, the only true differences between these two storm types from a kinematic perspective was that the PPCG storms had greater volumes of significant updrafts (e.g.,>20 m s−1). This was primarily due to the larger area covered by the strong updrafts; the total depth was similar among the two types of storms. PPCG storms also produced more hail than the low-CG storm.

Due to the lack of in situ charge measurements and the small sample size it is difficult to make definitive conclusions; however, the implications of the observed differences in terms of the proposed PPCG mechanisms (tilted dipole, inverted dipole, precipitation unshielding) can be examined in a basic sense. Given the Stolzenburg et al. (1998c) thunderstorm charge model, positive charge must come from some part of the thunderstorm, whether a region of lower positive charge (inverted dipole mechanism) or a region of upper positive charge (tilted dipole and precipitation unshielding). To first order, a larger volume of significant updrafts likely would produce a greater reservoir of positive charge in both of these regions. Based on noninductive charging theories, a larger volume of significant updrafts should result in more condensate and more opportunities for charge-separating collisions. Indeed, Williams (1985) showed that thunderstorms tend to obey scaling laws, which dictate that charge production and electrical power output increase as thunderstorm size increases. Hence, larger storms should have greater charge production, and more CGs of both polarities, as well as more total lightning overall. But we have argued that stronger updrafts and the elevated charge mechanism should counteract the tendency for increased negative CGs. This should tend to increase positive CG flashes, in both a relative and an absolute sense.

We should note, however, that increased condensate and charge-separating collisions are not the only explanations for enhanced positive charge. For example, Berdeklis and List (2001) found in laboratory experiments that the value of relative humidity can play an important role in the sign of charge imparted to the riming ice particles. We do not have the measurements to explore such additional factors, but these can be important, and larger updraft regions would tend to enhance their effect.

In the two storms that are best characterized as PPCG, those of 15 July and 29 June, there is some limited evidence to favor a tilted dipole. Examining horizontal and vertical radar cross sections and NLDN CG lightning from the storms at their peak positive CG output (Fig. 7), the ground-strike locations of the positive CGs in general were positioned outside the vertically deep 60-dBZ cores of these storms. However, many positive CGs were still within the 50-dBZ contours and thus were situated within substantial precipitation. Moreover, many positive CGs came to ground not far from a 60-dBZ core, often within 10 km. Since ground-strike position does not necessarily correspond to the flash origin, or even mean flash location, it cannot be ruled out that a substantial portion of the positive CGs in these storms started within the main core and not the adjacent anvil. Finally, while 29 June 2000 positive CGs during 2340–2350 UTC (the time of peak positive CG flash rate) showed some evidence of coming to ground in the downshear (eastern) part of the storm (Fig. 7c), consistent with the tilted dipole mechanism, Fig. 7a shows no such preferential behavior for 15 July 1998, with positive CGs coming to ground in all directions from the main 60-dBZ core. Interestingly, the vertical cross sections reveal some downshear tilting and a weak-echo region of the reflectivity for the 15 July storm, but little for the 29 June storm. Thus, if the tilted dipole mechanism was active in these storms, it did not manifest itself very obviously.

Fig. 7.

(a) Horizontal cross section of CHILL radar reflectivity at 0.5 km AGL, at 1804 MDT 15 Jul 1998. Also shown are ground-strike positions of NLDN CGs that occurred during 1800–1810 MDT. (b) Vertical cross section of reflectivity from the same time through 30 km N. (c) Horizontal cross section of CHILL radar reflectivity at 0.5 km AGL, at 2343 UTC 29 Jun 2000. Also shown are ground-strike positions of NLDN CGs that occurred during 2340–2350 UTC. (d) Vertical cross section of reflectivity from the same time through 35 km N. Distances are relative to CHILL

Fig. 7.

(a) Horizontal cross section of CHILL radar reflectivity at 0.5 km AGL, at 1804 MDT 15 Jul 1998. Also shown are ground-strike positions of NLDN CGs that occurred during 1800–1810 MDT. (b) Vertical cross section of reflectivity from the same time through 30 km N. (c) Horizontal cross section of CHILL radar reflectivity at 0.5 km AGL, at 2343 UTC 29 Jun 2000. Also shown are ground-strike positions of NLDN CGs that occurred during 2340–2350 UTC. (d) Vertical cross section of reflectivity from the same time through 35 km N. Distances are relative to CHILL

The positive CG lightning peaked as the rain and hail production of the 15 July and 29 June storms increased significantly, as shown in Fig. 8. This is broadly consistent with the precipitation-unshielding mechanism. However, other storms, most notably those of 1, 21, and 25 July 1998, featured substantial precipitation (particularly rain in the cases of 21 and 25 July) as well, and sparse positive CG lightning. In those cases, though, no major intensification was observed during the analysis periods. As best as could be determined, the storms typically fluctuated around a given intensity level, or diminished in intensity during the analysis times. Thus, it appears that if a mechanism like precipitation unshielding was active, it may have been only active during major intensification periods in the storms. An additional potential inconsistency between our data and the precipitation unshielding mechanism is that there was no notable decrease in negative CG flash rate as precipitation production climbed. Negative CG flash rates were low throughout the analysis periods and showed limited trends of any sort.

Fig. 8.

(a) Time series of storm volume in the mixed phase region (0° to −40°C) containing updrafts exceeding 20 m s−1, area of heavy rain (>60 mm h−1) at 0.5 km AGL, area of hail at 0.5 km AGL, and positive CG flash rate for the 15 Jul 1998 storm. (b) Same as in (a) but for the 29 Jun 2000 storm

Fig. 8.

(a) Time series of storm volume in the mixed phase region (0° to −40°C) containing updrafts exceeding 20 m s−1, area of heavy rain (>60 mm h−1) at 0.5 km AGL, area of hail at 0.5 km AGL, and positive CG flash rate for the 15 Jul 1998 storm. (b) Same as in (a) but for the 29 Jun 2000 storm

From Fig. 8a, it can be seen that the 15 July 1998 storm reached its peak positive CG flash rate as rain and hail production increased significantly. [Note that the 15 July 1998 storm was not well placed within the dual-Doppler lobes at the beginning of the analysis period, leading to unrealistically low updraft and precipitation estimates as not all of the strongest cores were completely scanned until after 1740 mountain daylight time (MDT).] Positive CGs peaked during 1750–1820 MDT, while hail area and mass flux (the latter is not shown) began their increase after 1750 MDT, and reached a peak immediately after 1820 MDT. This time period was also coincident with a significant increase in volume of intense updrafts (>20 m s−1). Due to the radar scanning strategy noted above, at least some of these updraft and precipitation fixes are fictitious and may have actually occurred prior to 1740 MDT. The 29 June 2000 storm showed similar behavior (Fig. 8b), with increases in positive CGs and volumes of significant updrafts preceding the increases in hail and rain, during the latter two-thirds of the observation period. Note that the 29 June storm produced a tornado near 2330 UTC, as updraft volumes and positive CG flash rates (as well as total flash rate) were increasing. The Carey and Rutledge (1998) precipitation identification matrix was applied to these storms to identify large (>2 cm) hail near the surface (0.5 km AGL), associated with enhanced LDR values. The matrix found no large hail during 15 July 1998, but did identify a large hail area up to 70 km2 during 29 June 2000 (2351 UTC radar volume). The area of large hail on 29 June (not shown) generally tracked the intensification of the storm, much like the other radar-derived variables.

These observations are at times convergent with and divergent with the PPCG case study of Carey and Rutledge (1998). By examining a PPCG storm that occurred in northeast Colorado on 7 June 1995, they found that large hail and positive CG lightning were anticorrelated in time, with peaks in positive CGs occurring 20–35 min after peaks in large hail. For the 29 June 2000 case examined in this study, large hail and positive CGs were largely coincident. However, like Carey and Rutledge (1998), the positive CG peaks during the storms of 15 July and 29 June occurred as the rain and hail production underwent significant increases. If positive charge formed on these hail/graupel particles as they descended through the charge-reversal layer (0° to −10°C), then these observations are broadly consistent with an inverted dipole, since the enhanced lower positive charge then could allow for a greater positive CG flash rate. In addition, a very preliminary analysis of the LMA data from the 29 June case suggests that the lightning observations were consistent with a major layer of positive charge underlying the main negative charge, that is, an inverted dipole (P. Krehbiel 2001, personal communication).

Overall, the evidence for any specific PPCG mechanism from this dataset appears ambiguous. It is entirely possible that multiple processes are active at once. However, there were no inconsistencies between our observations and the inverted dipole mechanism, while the observations were not entirely consistent with the tilted dipole and precipitation-unshielding mechanisms.

Kinematic intensification in the PPCG storms may be what distinguishes them from the low-CG storms. Both are kinematically strong, but it appears that if a storm intensifies even more, such that its volume of significant updrafts increases, then it may have the necessary ingredients to produce more positive CGs. That is, a further intensification increases the charge production in the storm due to an increase in size, leading to enhanced positive flashing. The 29 June 2000 storm provides a good example of this, as the storm was low CG prior to its intensification phase. As the updraft volume steadily grew during the intensification period, so did positive CG flash rates.

Figure 9 presents a schematic depiction of how these processes may work. In low-CG storms the charge structure is elevated when compared to an ordinary thunderstorm, resulting from stronger updrafts. In addition, there is more charging due to a larger storm volume containing strong updrafts. A low-CG storm has about the same updraft speeds as a PPCG storm, and similar altitudes of major charge regions, but the greater volume of strong updrafts (primarily due to larger areal coverage) results in more charging overall, leading to greater numbers of positive CGs.

Fig. 9.

Schematic diagram of possible charge structures within the updraft regions of ordinary, low-CG, and PPCG thunderstorms. Negative charge is denoted by negative signs; positive charge by plus signs. Updrafts are denoted by vector arrows, with the length of the arrow corresponding to the strength of the updraft. Relative size of the updraft is implied by the number of arrows

Fig. 9.

Schematic diagram of possible charge structures within the updraft regions of ordinary, low-CG, and PPCG thunderstorms. Negative charge is denoted by negative signs; positive charge by plus signs. Updrafts are denoted by vector arrows, with the length of the arrow corresponding to the strength of the updraft. Relative size of the updraft is implied by the number of arrows

Acknowledgments

The authors would like to thank the following people and organizations for their crucial help and support: Dr. Lawrence Carey, Dr. Walter Petersen, Dr. Robert Cifelli, and Ms. Margi Cech in the Radar Meteorology group at Colorado State University; the CSU-CHILL radar staff; the NCAR S-Pol radar staff; the NASA TOGA radar staff; the NASA Marshall Space Flight Center, especially Dr. Richard Blakeslee; and New Mexico Tech, especially Dr. Paul Krehbiel. This work was supported under NSF Grants ATM-9726464 and ATM-9912051.

NLDN data provided by the Global Hydrology Resource Center (GHRC) located at the Global Hydrology and Climate Center (GHCC), Huntsville, Alabama, through a license agreement with Global Atmospherics, Inc. (GAI). The data available from the GHRC are restricted to LIS science team collaborators and to NASA EOS and TRMM investigators.

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APPENDIX

Data Analysis Methodology

In all cases, the only radar scans used for analysis purposes were plan position indicator (PPI) sector volumes. Sector volumes typically varied between 4 and 6 min in length, enclosed at least 30-dBZ echoes and larger, and “topped” the storm of interest. Radar data were carefully edited for clutter, sidelobe, second trip, and other spurious echo. In addition, radial velocity fields from all radars were unfolded.

With multiparameter data from the CHILL and S-Pol radars, the differential phase field was filtered via the method of Hubbert and Bringi (1995) before a specific differential phase (Kdp) was calculated. Sidelobe contamination in the Zdr, LDR, and ρhv fields (Herzegh and Carbone 1984) was accounted for in a subjective manner, as these fields were not used in any objective analyses. Generally, these fields were examined to gain a better idea of the microphysical structure of the storms, and to supplement inferences from any objective multiparameter data analyses. For these purposes, data in areas of strong reflectivity gradients were subjected to considerable scrutiny. However, since the CHILL and S-Pol are high quality research radars with well-matched sidelobe patterns, sidelobe contamination was not a major concern.

All radar data were interpolated to a grid whose spacing was 1.0 km in the horizontal and 0.5 km in the vertical. CHILL-Pawnee data were gridded up to 16 km AGL, and STEPS and tropical data up to 20 km AGL.

The multiparameter data analysis focused on two objectives: 1) calculate near-surface rain and hail rates to derive estimates of storm-total mass flux for each precipitation type, and 2) distinguish different hydrometeor types in a subjective bulk sense. Toward these ends, a process that used mainly the reflectivity and specific differential phase fields was employed.

At a particular grid point, if the specific differential phase, Kdp, was greater than 0.25° km−1 (noise level), then it was used to calculate rain rate via the method of Sachidananda and Zrnic (1987). If Kdp was less than this threshold, then a radar reflectivity–rain rate (ZR) relationship was used to calculate the rain rate. In the midlatitudes, the ZR (Z = 486 R1.37) from Jones (1955) was chosen. In the Tropics, a preliminary ZR relationship (Z = 163R1.49) developed by analysis of S-Pol and rain gauge data (L. Carey 2001, personal communication) was used. If the relevant ZR gave a rain rate greater than 20 mm h−1, then it was assumed that the reflectivity was almost entirely due to hail at that point (small Kdp due to spherical particles), and the rain rate was set to zero.

The hail rate was calculated by first using Kdp to determine the reflectivity factor (in mm6 m−3) due to rain at a grid point by substituting the KdpR relationship from Sachidananda and Zrnic (1987) into the relevant ZR relationship. The resulting rain reflectivity factor was subtracted from the total Zh, with the remainder being the reflectivity factor due to hail. This value was used in the hail reflectivity–hail rate (ZH) relationship of Carey and Rutledge (1998), which is based on the Cheng and English (1983) hail size distribution, to determine hail rate in mm h−1 liquid equivalent. However, if the hail reflectivity was not within 7 dBZ of the rain reflectivity, then the hail rate was assumed negligible, after Balakrishnan and Zrnic (1990). Precipitation fluxes were computed by summing all the precipitation rates over the entire horizontal grid at a fixed vertical level (usually the lowest level—0.5 km AGL). Fluxes were calculated for the entire storm complex, not individual cells.

For dual-Doppler syntheses, gridded radial velocities from both radars were shifted to account for advection during the sampling interval by using an estimate of storm motion. The horizontal (U and V) wind fields were estimated by geometrically combining the radial wind fields within the dual-Doppler lobes. Then, to determine vertical velocity (W), the first step was to correct the initial estimates of U and V for the vertical fall speed of the precipitation using a reflectivity–terminal fall velocity (ZVt) relationship. The reflectivity field from the principal radar (CHILL in all midlatitude cases, S-Pol for LBA) was used for calculations of Vt. After this was done, the horizontal divergence calculated from the corrected U and V was numerically integrated downward from the top level (zero vertical velocity is the upper boundary condition) only to the next level in the column. The U and V at this next level were corrected for this air motion, and the divergence was recalculated and the integration downward was repeated, but from the top level to the next level in the column. Once the solution converged, an integration step then was done from this level to the next level, and so on. Nelson and Brown (1987) estimated vertical velocities from dual-Doppler analyses to be within 10%–20% of the actual value. For updrafts in excess of 20 m s−1 errors would tend toward the lower end of this range. Significantly smaller errors are expected for horizontal winds. For more on multiple-Doppler analyses, see Ray (1978, 1980).

The CG lightning data (time, strike location, peak current, multiplicity) from the NLDN (midlatitude) and Advanced Lightning Direction Finder (ALDF) network (Brazil; also known as the Brazil Lightning Detection Network or BLDN) were used to compute both positive and negative CG lightning flash rates during the entire radar analysis period of each case. The CG ground strike locations were compared to radar reflectivity fields at periodic times to identify strikes that were not close (subjectively chosen, but typically > 10 km away) to any radar echo. Extra leeway was granted in the TRMM/LBA cases due to reduced location accuracy with the BLDN. Distant strikes were not included in flash rate estimates.

Standard FCM data give voltage strength as a function of time. Flashes then manifest themselves as rapid changes in the voltage signal. With detected flashes and flash times, total lightning flash rates were computed. LMA data were only available for the STEPS case. This storm was similar to many of the severe storms presented in Williams et al. (1999), in that VHF signals often were continuous and filled a substantial volume of the storm, making actual calculations of flash rates difficult. As such, the results are not directly comparable to NLDN or FCM flash rates, so we used the LMA flash rates only for their trend information.

Limited thermodynamic sounding data were available in the midlatitude cases. Regular soundings in the immediate vicinity of the main observational area were available in the tropical cases. Soundings were used to determine important temperature levels (useful in radar analyses) and air density profiles (useful in determining vertical mass fluxes).

Footnotes

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Current affiliation: Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts

Corresponding author address: Dr. Timothy J. Lang, Division of Engineering and Applied Sciences, Harvard University, Pierce Hall 110I, 29 Oxford St., Cambridge, MA 01238. Email: tlang@deas.harvard.edu