A 3D Numerical Model to Estimate Lightning Types for PyroCb Thundercloud

Abstract

Pyrocumulonimbus (pyroCb) thunderclouds, produced from extreme bushfires, can initiate frequent cloud-to-ground (CG) lightning strikes containing extended continuing currents. This, in turn, can ignite new spot fires and inflict massive harm on the environment and infrastructures. This study presents a 3D numerical thundercloud model for estimating the lightning of different types and its striking zone for the conceptual tripole thundercloud structure which is theorized to produce the lightning phenomenon in pyroCb storms. More emphasis is given to the lower positive charge layer, and the impacts of strong wind shear are also explored to thoroughly examine various electrical parameters including the longitudinal electric field, electric potential, and surface charge density. The simulation outcomes on pyroCb thunderclouds with a tripole structure confirm the presence of negative longitudinal electric field initiation at the cloud’s lower region. This initiation is accompanied by enhancing the lower positive charge region, resulting in an overall positive electric potential increase. Consequently, negative surface charge density appears underneath the pyroCb thundercloud which has the potential to induce positive (+CG) lightning flashes. With wind shear extension of upper charge layers in pyroCb, the lightning initiation potential becomes negative to reduce the absolute field value and would generate negative (−CG) lightning flashes. A subsequent parametric study is carried out considering a positive correlation between aerosol concentration and charge density to investigate the sensitivity of pyroCb electrification under the influence of high aerosol conditions. The suggested model would establish the basis for identifying the potential area impacted by lightning and could also be expanded to analyze the dangerous conditions that may arise in wind energy farms or power substations in times of severe pyroCb events.

1. Introduction

Pyrocumulonimbus (pyroCb) thunderclouds commonly form above bushfires, expanding to substantial heights and influencing the chemical composition as well as the concentrations of aerosol in the upper part of the troposphere [1]. In the formation of pyroCb thunderstorms, the presence of aerosol particles produced by smoke serves as cloud condensation nuclei (CCN), exerting a significant influence on the advancement of the storms. One of the most crucial impacts of pyroCb is the initiation of additional wildfires by cloud-to-ground (CG) lightning. Similar to conventional thunderclouds, pyroCb clouds can result in both positive and negative cloud-to-ground (+CG and −CG) lightning, with +CG being more likely to trigger secondary spot fires and cause extensive harm to nature [1,2,3].

Over 90% of all lightning strikes are of negative polarity, which is frequently observed in thunderstorms that occur in humid conditions [4]. Conversely, +CG strikes are often observed in dry environments with higher cloud bases [5]. These +CG flashes also occur in thunderstorms such as pyroCb, which release significant amounts of smoke into the atmosphere [6]. Multiple investigations have shown that CG strokes of either positive or negative having large continuous currents could start most of the fires [2,7,8,9]. The emergence of secondary bushfires ignited by CG lightning has become a significant concern for firefighting management on a global scale. Although there has been a notable rise in the number of pyroCb events in the literature, only a few investigations have been conducted in recent years. In August 2013, Western North America experienced the occurrence of 88 massive wildfires, which gave rise to 26 highly intense pyroCb storms [10]. Over the period of 1973–2020, the southeastern part of Australia faced several distinct pyroCb storms where recent events reported as Black Saturday (Victoria, 2009) and Black Summer (New South Wales, 2019–2020) observed the ignition of new spot fires by lightning as well as the longevity of the pyroCb storms [11,12,13,14]. The Black Saturday wildfire events (Figure 1a) produced three distinct pyroCb storms, with the largest reaching an altitude of 15 km and generating hundreds of lightning strikes in Southeast Australia, as depicted in Figure 1b [11]. According to the Victorian State Government records, the “East Tyers–Thomson” fire event began at 1800 LT and was attributed to lightning strikes occurring on Black Saturday. During the 2019–2020 Black Summer fire season, dry lightning strikes in East Gippsland ignited three fires, eventually expanding into a widespread bushfire disaster that raged for months [12]. On 8 January 2003, lightning strikes ignited 87 separate fires in northeastern Victoria, leading to the Alpine Fire [14]. These fires were exacerbated by several consecutive days of unprecedented high temperatures and dry weather conditions.

Numerous studies in the past have investigated the electrical conditions that promote the formation of CG lightning strikes could serve as a crucial indicator for understanding specific phenomena associated with pyroCb events. Multiple hypotheses have been developed recently to explain the electrical configurations of charge regions and situations that result in both −CG and +CG lightning strikes and their association with thunderstorms [15,16]. The overall charge distribution of the conventional thundercloud developed in a moist environment is commonly visualized as a vertical tripole having three charge layers: a predominantly positive layer at the upper portion, a dominant negative layer in the middle, and an auxiliary positive layer below the main negative, typically of smaller magnitude [17]. This lower positive charge layer, in particular, has a crucial role in generating −CG flashes [18,19]. On the other hand, the presence of an enlarged region of positive charge at the bottom of thunderclouds may begin the progression of positive downward leaders to initiate +CG strikes [15,16,19,20,21,22]. Therefore, there has been considerable focus recently on the specific significance of the lower positive charge region. To date, there has been no literature work on the distribution of charges or investigations into the electrical circumstances conducive to lightning discharges in pyroCb events. The conditions present in pyroCb storms, characterized by strong wind shear and undiluted updrafts, increase the likelihood of exhibiting tripole charge structure while forming pyroCb thunderclouds [10,11]. Certain studies consider the tilted tripole charge structure in severe thunderstorms, where the charge centers in the upper cloud region are shifted towards the direction of the strong wind shear [23,24]. This displacement can separate the positive and negative charge regions, allowing both +CG/−CG flashes to occur from the displaced positive charge region.

In recent years, a method widely used to develop and understand thundercloud charge structures is the physical thundercloud model which incorporates several complex factors, including induced electric charge, the state of lightning leaders, and the formation of corona regions [25,26,27]. For analyzing the actual thunderstorm process at the mirco-physical level, this method highly relies on observation data, which makes it computationally expensive over large-scale domains. Nowadays, the numerical thundercloud model coupled with the empirical governing equations become widely popular in studying the configuration and dynamics of thunderclouds [18,23,24,28,29]. This stochastic model based on electrostatic concepts presents the cloud model in an axisymmetric manner, employing the non-inductive charging approach to describe the electrification of the thundercloud. Although this modeling technique is complex and requires significant time, it is remarkably efficient in capturing the dynamic evolution of a thundercloud that could be useful to identify the precise locations on Earth’s surface or any object in danger due to thunder or lightning.

Previous studies [30,31,32,33] have shown that aerosols affect cumulus clouds, implying that aerosols generated by fires might influence the formation of pyroCbs. For cumulus clouds, an increase in aerosol concentration leads to the formation of a large number of smaller cloud droplets. This process lowers the efficiency of droplet collisions, which delays and inhibits the formation of raindrops. Studies in [34,35,36,37,38,39] have identified a positive correlation between lightning activity and aerosol concentrations. Additionally, those works demonstrate that high aerosol concentrations can significantly enhance the electrification process, according to the bulk microphysical model, or even weaken the electrification on further increase. However, the scientific community still lacks a thorough understanding of fire-induced aerosols’ role in forming pyroCb thunderclouds and their electrification process. There is limited research on how variations in aerosol loading affect pyroCb development, with only a handful of studies conducted to date [40,41,42].

In this paper, a 3D stochastic thundercloud model is demonstrated to simulate the conceptual tripole cloud structure, which is proposed as a representation of a pyroCb thundercloud. More attention is placed on the lower positive charge layer to comprehensively analyze different electric states that benefit CG flash generations. In addition, the behavior of the pyroCb thundercloud under strong wind shear is investigated. The suggested model demonstrates how alteration in the size and intensity of the charge layers can impact both thundercloud potential and field distributions, along with surface charge density. Lastly, the model is utilized to investigate how varying aerosol concentrations impact the electrical parameters which may help to obtain a parametric knowledge of how the smoke-induced aerosols influence the lightning process in pyroCb. This analysis can be valuable in understanding and predicting the occurrence of lightning flashes of different types and their striking zones.

2. Thundercloud Model Description

The main aim of this paper is to explain the electric states in a pyroCb thundercloud that favor the generation of CG flashes of different types, depending on its charge structure. For modeling, the conventional tripole charge structure contains a negative screening layer (SC) at the top, along with upper positive (UP), middle negative (MN), and lower positive (LP) layers that are considered to represent the pyroCb thundercloud. For straightforward visualization, a vertical cross-sectional view (in xz plane) of the conceptual tripole structure-based pyroCb thundercloud is depicted in Figure 2a. The x-axis represents the horizontal dimension of the Earth’s surface beneath the thundercloud, while the z-axis corresponds to the vertical extent of the charged region. To simplify the analysis, the permittivity in the atmospheric region above z is considered to be the same as that of a vacuum. Typically, the charge magnitude of both UP and MN charge layers ranges from tens to hundreds of coulombs [43,44]. The LP charge region, which is located below the freezing level (a few km above the ground surface), is generally thought to be responsible for increasing the field magnitude at the bottom of the MN charge layer and initiating −CG lighting leader toward the ground [29]. The exact position of the LP charge region is highly influenced by factors such as the season and latitude. This tripole charge configuration in pyroCb can be influenced by the intense and undiluted updrafts in case of severe wildfire events, enhancing the LP charge to overpower the MN charge layer. This disruption can impact the lightning types (either +CG or −CG) produced by the pyroCb thundercloud and its striking locations on the ground. Another atmospheric complex factor known as the vertical wind shear can cause the main positive change region at the top to shift towards the thundercloud’s forward flank as shown in Figure 2b. The absence of a negative charge region no longer provides shielding for the positive charge region. As a result, a +CG flash can now originate directly from the displaced positive charge region. In Figure 2b, parameter d represents the difference between the initial and present position of the extended boundary on the right side of the UP and SC charge layers.

The proposed tripole structure-based pyroCb model is built in 3D, using a 30 km × 30 km × 30 km cartesian domain. This simulation domain is discretized using 61 × 61 × 61 equidistant node points by keeping the distance between the neighboring points along three axes equal. For modeling, each charge region is regarded as having an elliptical shape with a proportional charge density. This relationship can be demonstrated by (1) below, which states the characteristics of the distribution.

$${\rho }_n(x,y,z)={\rho }_n\left(0\right)exp\left[\frac{{(x-x_{0n})}^2}{{r_{xn}}^2}+\frac{{(y-y_{0n})}^2}{{r_{yn}}^2}+\frac{{(z-h_n)}^2}{{r_{zn}}^2}\right]$$

(1)

where ${\rho }_n\left(0\right)$ denotes the amplitude of maximum charge density of n^th charge layer with $n=1,2,3,...$; $x_{0n}$ and $y_{0n}$ act for representing the lateral center of n^th charge layer, and $h_n$ determines its corresponding altitude. Parameters $r_{xn}$ and $r_{yn}$ define the corresponding lateral extents in both x and y directions while $r_{zn}$ presents the vertical range in the z-axis. Two different configurations for the tripole charge structure are provided in

Table 1. Parameters related to the dimensions and electrical properties of tripole structured pyroCb thundercloud.

Config.	Charge Layer	Altitude, ${\mathit{h}}_{\mathit{n}}$ (km)	Lateral Range, ${\mathit{r}}_{\mathit{x}}$ & ${\mathit{r}}_{\mathit{y}}$ (km)	Vertical Range, ${\mathit{r}}_{\mathit{z}}$ (km)	Lateral Centre, ${\mathit{x}}_0$ & ${\mathit{y}}_0$ (km)	Charge Density, $\mathit{\rho }$ (nC/m3)	Charge, Q (C)
1	SC	11.75	6	0.5	15	−1.1	−19
	UP	9.75	6	1.5	15	2.2	77
	MN	6.75	5	1.5	15	−2.5	−73
	LP	4.25	3	1	15	1.0	18
2	SC	11.75	6	0.5	15	−1.1	−19
	UP	9.75	6	1.5	15	2.2	77
	MN	6.75	5	1.5	15	−2.5	−73
	LP	4.25	4	1.2	15	1.5	30

, with the magnitude of LP charge in the second configuration extended from 18 C to 30 C. The vertical range and lateral extents are enhanced from 1 km to $1.2$ km and from 3 km to 4 km, respectively, in the second configuration. The electrical and dimensional parameters of each charge region are derived from the studies documented in [23,29]. Based on the satellite data, the average cloud-base heights of pyroCb clouds ranged from 3 to 5 km, as reported in [41], which differs by approximately 7% compared to the simulated data. In this model, the cloud-base height of tripole structure-based pyroCb thunderclouds is represented by the altitude of its lower charge layers estimated from the ground surface.

To model the impact of wind shear extension on tripole structure in pyroCb, the positioning and lateral extents of both SC and UP charge layers are consistently adapted while keeping their left boundary fixed. The electrical charge within the anvil section of the pyroCb is assumed to have initially formed within the central region of the thundercloud and subsequently moved towards the forward flank due to lateral air currents originating from the electrified area. Throughout this adjustment, the extension parameter d has been changed by 2, 4, and 8 km while the charge distribution within the upper thundercloud regions remains unchanged. The simulation assumes the ground surface (positioned at $x=0$ and $y=0$) beneath the pyroCb thundercloud as an unconstrained conducting plane with uniform potential. Electric potential, denoted as $V(x,y,z)$ produced by the n^th charge region in the thundercloud represented by their respective charge density ${\rho }_n(x,y,z)$, can be determined by solving the Poisson equation:

$${\nabla }^{2}V=-\frac{{\rho }_n(x,y,z)}{{ϵ}_0}$$

(2)

where ${ϵ}_0$ represents the free space’s permittivity. In computational terms, the total potential for the pyroCb thundercloud can be achieved by combining the influences from all individual nodes $(i,j,k)$ within the computational domain, along with their respective reflections or images given in (3).

$$\begin{array}{c}\hfill {V_{i,j,k}}^{\left(m\right)}={V_{i,j,k}}^{(m-1)}+\omega [A({V_{i+1,j,k}}^{(m-1)}+{V_{i-1,j,k}}^{\left(m\right)})+B({V_{i,j+1,k}}^{(m-1)}+{V_{i,j-1,k}}^{\left(m\right)})\\ \hfill +C({V_{i,j,k+1}}^{(m-1)}+{V_{i,j,k-1}}^{\left(m\right)})+\frac{D}{{ϵ}_0}\sum _n{\rho }_n(x,y,z)]\end{array}$$

(3)

where

$A=\frac{\delta y^2\delta z^2}{2(\delta x^2\delta y^2+\delta y^2\delta z^2+\delta x^2\delta z^2)}$

$B=\frac{\delta x^2\delta z^2}{2(\delta x^2\delta y^2+\delta y^2\delta z^2+\delta x^2\delta z^2)}$

$C=\frac{\delta x^2\delta y^2}{2(\delta x^2\delta y^2+\delta y^2\delta z^2+\delta x^2\delta z^2)}$

$D=\frac{\delta x^2\delta y^2\delta z^2}{2(\delta x^2\delta y^2+\delta y^2\delta z^2+\delta x^2\delta z^2)}$

Here, superscripts $\left(m\right)$ and $(m-1)$ represent their respective present and previous iteration cycles. The grid spacing between the neighboring node points along three corresponding axes is represented by $\delta x$, $\delta y$ and $\delta z$, respectively. Considering $\delta x=\delta y=\delta z$ in the simulation simplifies the constants A, B, C and D equal $1/6$, after every cycle, the electric potential of the entire computational domain was updated by (3) using the successive over-relaxation (SOR) algorithm where the speed of convergence was governed by the relaxation parameter $\omega$. The electric field E of each computational grid can be obtained from V from the expression given in (4),

$$E=-\nabla V$$

(4)

The presence of tripole cloud structure in pyroCb thunderstorms significantly affects the charge distribution on the ground surface, especially with the dominant MN charge leading to the repulsion of negative charges on the ground. As a result, the ground surface or any object underneath the pyroCb thundercloud acquires positive charges. As the intensity of the LP charge layer increases, it initiates the repulsion of positive charges present on the ground surface. This repulsion stops the downward movement of the negative leader, impending its progression. The value of the surface charge density that appears on the ground ($x,y\to 0$) can be computed by (5).

$$\sigma =-{ϵ}_o\frac{\mathsf{\partial }}{\mathsf{\partial }z}V{|}_{x=0,y=0}$$

(5)

3. Simulation Results and Discussion

3.1. Tripole Structure with Large Lower Positive Charge

To investigate whether a large LP charge region affects the electrical conditions to generate CG lightning, simulations are carried out on two different configurations of pyroCb thundercloud with a tripole structure. Figure 3a,b illustrate the cross-sectional view of the simulated tripole charge configurations. These charge configurations are built at the midpoint of the y-axis within the computational space, specifically along the $xz$ plane. The electric potential generated by the tripole structure is analyzed and illustrated in Figure 4(a1,a2) and Figure 4(b1,b2), respectively. When the LP charge region of the pyroCb thundercloud is enhanced in the second configuration (Figure 3b), the overall potential of the pyroCb thundercloud shows a positive increment compared to its first configuration depicted in Figure 4(a2). With a relatively large LP charge, the magnitude of the electric field within the thundercloud decreases as evident in Figure 4(b2) in comparison to Figure 4(b1). This observation aligns with the characteristics dictated by the law of the electrostatic field.

Illustrating two distinct configurations of the pyroCb thundercloud, Figure 5(a1,a2) and Figure 5(b1,b2) display the projected electric potential values at the maximum field and longitudinal electric field, respectively. These are measured along the z-axis at the core (at $x=15$ km and $y=15$ km) of the simulation domain. In Figure 5(a1,a2), the symbol “x” denotes the particular node point where the maximum electric field with discharge initiation occurs. The mathematical expression in (6) [45] represents the relationship between altitude z and the initiation threshold value $E_{th}\left(z\right)$, marked as red dotted lines in Figure 5(b1,b2). As observed in Figure 5(a1,a2), the maximum potential shows gradual incremental trends while the minimum potential decreases when the LP charge region is enhanced. At the same time, the lightning flash initiation point of the pyroCb thundercloud has shifted from −51.73 MV (in the first configuration) to a positive value of 203.397 MV in the second configuration. This analysis agrees with the findings reported in [46], which indicate that the CG lightning initiation (regardless of their polarity) occurs only when the absolute potential value at the initiation point is significantly higher than 0 MV. In contrast to the first configuration, the longitudinal electric field ($E_z$) at the thundercloud bottom exhibits a negative shift with the increase in the LP charge layer (Figure 5(b2)).

$$E_{th}\left(z\right)=\pm 201.7exp\left(-\frac{z}{8.4}\right)$$

(6)

The results of simulated surface charge density $\sigma$ on Earth’s surface are graphically presented in Figure 6a and 6b, respectively, for two different configurations of pyroCb thunderclouds. This analysis helps in understanding the probable lightning types associated with two distinct tripole charge setups and is summarized in

Table 2. Possible lightning categories for simulated pyroCb thunderclouds with tripole charge configuration.

${\mathit{r}}_{\mathit{x}}$ and ${\mathit{r}}_{\mathit{y}}$ of LP (km)	${\mathit{r}}_{\mathit{z}}$ of LP (km)	Charge of LP (C)	Range of x and y (km)	Polarity of $\mathit{\sigma }$	Peak Value of $\mathit{\sigma }$ (nC/m2)	Probable Lightning Types
3	1	18	3.5 ≤ x ≤ 26.5 km, 3.5 ≤ y ≤ 26.5 km	Positive	0.2087 nC/m2 at x = 14, 14.5 ≤ y ≤ 15.5 km	−CG
4	1.2	30	0 ≤ $x,y$ ≤ 30 km	Negative	0.2454 nC/m2 at $x,y$ = 15 km	+CG

. As observed in the first configuration (Figure 6a), surface charge density $\sigma$ becomes positive within the ranges of 3.5 ≤ x ≤ 26.5 km and 3.5 ≤ y ≤ 26.5 km on the projected ground surface beneath the pyroCb thundercloud. This would trigger the start of −CG flashes. This corresponds to the theory that says the presence of an LP charge layer below the pyroCb thundercloud amplifies the electric field and triggers −CG flashes [15,19]. A similar simulation for $\sigma$ is carried out for the second configuration of the pyroCb thundercloud by enlarging the lateral and vertical extents of the LP charge region, along with adjusting its charge magnitude. As depicted in Figure 6b, the value of $\sigma$ turns negative across the entire simulation domain, reaching its peak of 0.2454 nC/m² at the thundercloud’s core. This simulated negative peak is larger in magnitude than the maximum value of $\sigma$ (0.2087 nC/m² at x = 14, 14.5 ≤ y ≤ 15.5 km) that appeared in the first configuration of the pyroCb thundercloud. The negative value of $\sigma$ in the second configuration could trigger the initiation of a downward positive leader, ultimately causing a +CG flash to form as it reaches the ground. These projected outcomes align with the findings in [29], which concluded that the existence of a large LP charge layer hinders negative lightning leader progression to the ground. Consequently, this terminates the incidence of −CG flashes while raising the likelihood of positive +CG lightning. This phenomenon takes place when a negative electric field other than a positive or zero value appears at the thundercloud’s bottom.

3.2. Impact of Wind Shear on PyroCb Thundercloud

To examine the consequences of wind shear on a pyroCb thundercloud and how the displacement of its charge layers influences potential lightning strike areas, the parameters $x_{0n}$ and $r_{xn}$ of both SC and UP charge layers are altered while keeping the MN and LP charge structures the same as configuration 2 in Table 1. The vertical cross-sectional view in Figure 7 illustrates how strong wind shear displaced the charge layers in pyroCb thunderclouds, causing an impact on the overall distribution of thundercloud-generated potential and electric field (see Figure 8). In Figure 7a–c, the extension parameter d is varied by 2, 4, and 8 km, respectively, while maintaining the value of ${\rho }_n\left(0\right)$ constant to ensure the overall charge of the affected charge regions remains constant. With the wind shear extension in the SC and UP regions, growth in negative potential is observed, particularly in the middle region of the pyroCb thundercloud, as depicted in Figure 8(a1–a3). Furthermore, the magnitude of the electric field (Figure 8(b1–b3)) within the thundercloud decreases with the rightward lateral extension of SC and UP charge layers, aligning with the principles of the electrostatic field.

Figure 9(a1–a3) and Figure 9(b1–b3) depict the variations in the electric potential V (measured at maximum field point) and longitudinal electrical field $E_z$ at the thundercloud’s core with the effect of wind shear extension. Figure 9(a1–a3) shows that as the UP charge layer shifts horizontally, the maximum potential decreases gradually, whereas the minimum potential experiences a concurrent rise. Consequently, the point at which discharge initiation occurs shifts negatively. The potential at the initiation point of the lightning flash is 178.81 MV for $d=2$ km as seen in Figure 9(a1). Then, a noticeable change in the potential value at the point of flash initiation becomes evident with an increase in the value of d and ends up at −64.07 MV for $d=8$ km (Figure 9(a3)). Moreover, the extension of wind shear leads to a reduction in the absolute peak value of the vertical field at the top, while it increases the absolute peak value of the vertical field at the bottom of the pyroCb thundercloud as observed in Figure 9(b1–b3). For various values of extension parameter d, the fluctuations in the simulated surface charge density $\sigma$ on the ground surface beneath the pyroCb thundercloud are illustrated in Figure 10a–c. The probable lightning types based on the polarity of simulated $\sigma$ and their identified locations on the ground surface are summarized in

Table 3. Effect of wind shear extension leading to possible lightning types in pyroCb thunderclouds.

Extension Parameter, d (km)	Absolute Peak Value of $\mathit{\sigma }$ (nC/m2)	Location on Earth’s Surface, $(\mathit{x},\mathit{y})$ km	Polarity of $\mathit{\sigma }$	Probable Lightning Types
2	0.2531	$(15,15.5)$	Negative	+CG
4	0.0065	$(15,7)$	Positive	−CG
	0.2035	$(15,16)$	Negative	+CG
8	0.0565	$(13,8.5)$	Positive	−CG
	0.1309	$(15,16.5)$	Negative	+CG

. When $d=2$ km, the value of $\sigma$ remains negative over the simulation domain having an absolute peak value of 0.2531 nC/m² which is higher than the peak value measured for configuration 2 of pyroCb in Table 2. But its location on the ground surface is shifted from 15 km to 15.5 km along the y-axis while remaining fixed at 15 km along the x-axis. For $d\ge 4$ km, the positive value of $\sigma$ becomes visible for pyroCb, and its absolute peak value is enhanced with increasing values of d, indicating a higher probability of an increase in the −CG flash rate. As indicated in Table 3, the coordinates of the peak negative $\sigma$ location are notably distant from the center. This spatial distribution suggests that the −CG lightning strikes tend to occur away from the thundercloud core. On the other hand, the absolute peak value of negative $\sigma$ starts to decrease when $d>2$ km, with the position slightly shifting away from the core along the y direction.

3.3. Influence of Aerosol Concentrations on PyroCb Electrification

PyroCb thunderstorms are a distinctive form of high-altitude storm, marked by the presence of aerosol particles emitted from fires. Wildfires are capable of generating high aerosol concentrations, typically ranging between 10,000 cm⁻³ and 20,000 cm⁻³, as reported in [41,47,48]. There is no significant observational evidence indicating that high aerosol concentrations increase cloud electrification in pyroCb storms. According to the sensitivity analysis presented in previous studies [34,36,39], there is a noticeable non-linear relationship between the values of positive and negative charge densities and aerosol concentrations which can significantly affect the cloud charge structure. However, this paper does not aim to determine any qualitative link between aerosol concentrations and electrification. Consequently, this study assumes a positive correlation between charge density and aerosol concentrations to conduct the sensitivity analysis of electrification in pyroCb thunderclouds under the effect of wind shear extension. To assess the influence of aerosol, further simulations are carried out for the tripole structure-based pyroCb thundercloud using four different values of aerosol concentration—N = 1000, 5000, 10,000, and 20,000 cm⁻³—while considering 100 cm⁻³ as the base value. During the initial stage of a pyroCb storm, the thundercloud charge structure is typically formed by strong undiluted updrafts, which can create a small volume of positive charge at the cloud’s bottom (low-temperature zone). According to the laboratory study by Saunders et al. [49], a highly effective liquid water content in the low-temperature zone results in graupel particles acquiring a positive charge and therefore can enhance the LP charge layer in tripole structure with a large background of aerosols. For $N=$ 100 cm⁻³, the magnitude of the peak density for different charge layers is considered similar to the value of configuration 2 of pyroCb given in Table 1. Similar to the method in Section 3.2, the same simulations are conducted after increasing the charge of the UP and MN regions by 10%, and the LP region by 20% of its initial value for each 1000 cm⁻³ increase in aerosol concentration (summarized in

Table 4. Increment rate of peak charge densities in tripole structure-based pyroCb.

Charge Structure	Charge Regions	Peak Charge Density (nC/m2) at $\mathit{N}=$ 100 cm−3	Percentage of Increment Rate of Density (per 1000 cm−3 Rise of Aerosol)
tripole	SC	−1.1	Constant
	UP	2.2	10%
	MN	−2.5	10%
	LP	1.5	20%

).

Figure 11(a1–c1,a2–c2) illustrate the variation in the electric potential V (at maximum field point) and vertical electric field $E_z$ value for different aerosol concentrations N in pyroCb under the effect of wind shear extension. For $d=2$ and 4 km, it is observed in Figure 11(a1,b1) that the potential V of the lightning initiation point increases and remains positive with high aerosol concentrations. When $d=8$ km, V becomes negative with a decline in its absolute value for concentrations ranging from $N=$ 1000 to 10,000 cm⁻³ (Figure 11(c1)). Moreover, the increase in aerosol concentration increases the vertical electric field in the lower dipole (between MN and LP) region of the thundercloud and is also observed to exceed the threshold field value for lightning breakdown as seen in Figure 11(a2–c2). The levels of aerosols also greatly affect the electrical charges on the ground beneath pyroCb thunderclouds. Figure 12 and Figure 13 depict the development of simulated surface charge density $\sigma$ under the influence of different aerosol concentration levels. The value of $\sigma$ consistently stays negative for aerosol concentrations ranging from 1000 to 20,000 cm⁻³. Moreover, beyond 1000 cm⁻³, there is a sharp increase in $\sigma$, which in turn boosts the probability of +CG strikes. For different aerosol concentrations, the simulated absolute value of peak $\sigma$ and their effect on developing probable lightning types are summarized in

Table 5. Effect of aerosol concentration on electrification in pyroCb thunderclouds.

Aerosol Concentration, N (cm−3)	Polarity of $\mathit{\sigma }$	Absolute Peak Value of $\mathit{\sigma }$ (nC/m2)			Lightning Types and Striking Location on Earth’s Surface
		$\mathit{d}=\mathbf{2}$	$\mathit{d}=\mathbf{4}$	$\mathit{d}=\mathbf{8}$	$\mathit{d}=\mathbf{2}$	$\mathit{d}=\mathbf{4}$	$\mathit{d}=\mathbf{8}$
1000	Positive	–	–	0.1187	–	–	−CG ($x,y=14.5,8.5$ km)
	Negative	0.3599	0.3039	0.0737	+CG ($x,y=15,16$ km)	+CG ($x,y=15,16$ km)	+CG ($x,y=15,16$ km)
5000	Positive	–	–	0.0747	–	–	−CG ($x,y=10.5,8$ km)
	Negative	0.7869	0.7089	0.3907	+CG ($x,y=15,15.5$ km)	+CG ($x,y=15,15.5$ km)	+CG ($x,y=15,15.5$ km)
10,000	Positive	–	–	0.0455	–	–	−CG ($x,y=9.5,7.5$ km)
	Negative	1.3214	1.2152	0.7878	+CG ($x,y=15,15$ km)	+CG ($x,y=15,15.5$ km)	+CG ($x,y=15,15.5$ km)
20,000	Positive	–	–	0.1377	–	–	−CG ($x,y=9.5,8$ km)
	Negative	1.9535	1.791	1.1453	+CG ($x,y=15,15$ km)	+CG ($x,y=15,15.5$ km)	+CG ($x,y=15,15.5$ km)

. Increased aerosol concentrations within pyroCb events can amplify the negative value of $\sigma$, even amidst the horizontal displacement of UP charge by wind shear (see Figure 12 and Figure 13). This justifies the occurrence of excessive LP charges within low-temperature regions of thunderclouds during high aerosol conditions, consequently generating high field strength in lower dipole regions. Under extreme aerosol concentrations, such electrical conditions may induce the development of downward positive leaders toward the Earth’s surface. This results in the occurrence of +CG strikes primarily underneath the thundercloud core, as observed from the extracted $(x,y)$ coordinates given in Table 5. In the high aerosol case of $N\ge$ 1000 cm⁻³, the wind shear extension of UP charge by 8 km from the thundercloud core reduces the field strength between the UP and MN charge layers (Figure 11(c2)) so that the LP charge region no longer shields the MN charge layer above from the ground and −CG strikes will occur with probable locations far away from +CG striking zones (summarized in Table 5).

In brief, the objective of this research is to use numerical representation to depict the tripole structure of pyroCb thunderclouds and investigate the electrical states of the thunderclouds to approximate the probable lightning types and their striking zone on the ground surface. Through the model and simulation, the study has initially revealed the impact of enlarging the lower positive charge layer with the rise in potential and forming negative longitudinal electric field initiation at the thundercloud’s bottom. This enlargement leads to a negative surface charge density underneath the pyroCb thundercloud, which can trigger +CG lightning strikes on the ground surface near the core of the storm. Later, the consequences of the wind shear extension on the electrical conditions in a pyroCb storm are investigated. As seen, the lightning initiation potential shifts to the negative value with the wind shear extension of upper charge regions in pyroCb to reduce the absolute field value and can generate −CG lightning with a large lower positive charge region. Additionally, high concentrations of aerosol produced by wildfires can have a significant impact on pyroCb lightning activities. A parametric study has been conducted to examine the effect of increased aerosol concentration on electrical conditions under the assumption of a positive linear relationship between charge density and aerosol concentration in pyroCb. The research indicates that the frequency of both +CG and −CG lightning and their striking zones are significantly affected by the variations in charge densities resulting from different aerosol concentrations within pyroCb thunderclouds. This compact thundercloud model and its quick computational capabilities make it highly valuable for providing early warnings and protection, particularly in the context of pyroCb lightning events caused by wildfires. The proposed work has a high potential to provide a comprehensive explanation of the emergence of different cloud charge structures in pyroCb considering the charging current within the thundercloud and corona near the ground surface.

4. Conclusions

The generation of lightning-ignited secondary wildfires is a serious issue for global firefighting management. This study presents a significant advancement in understanding the complex electrification phenomenon within pyroCb storms. By developing a 3D numerical model that incorporates the conceptual tripole charge configuration, this paper has investigated the electrical conditions under which +CG and −CG flashes are likely to occur. The proposed model emphasizes the role of the lower positive charge layer, and the influence of strong wind shear and high aerosol concentrations on the electrical characteristics of pyroCb thunderclouds is also explored. The results confirmed the initiation of a negative vertical field at the cloud base and a rise in thundercloud potential coupled with the expansion of a lower positive charge region. The proposed model has demonstrated that the wind shear extension of upper charge layers in thunderclouds can facilitate the incident of different lightning types during a pyroCb event, depending on the estimated value of initiation potential and surface charge density. The parametric study on aerosol concentration’s effect also confirms the increased likelihood of both +CG and −CG lightning.

The correlation between aerosol concentrations and charge density further highlights the sensitivity of pyroCb lightning to environmental conditions, drawing attention to the necessity of comprehensive monitoring and modeling in high aerosol conditions. This understanding is particularly valuable for predicting and mitigating the impact of lightning-induced spot fires, which intensify the severity and duration of wildfire events. This model forms the basis for identifying high-risk zones prone to lightning flashes in times of extreme weather conditions. This capability is crucial for enhancing early warning systems and improving firefighting strategies. Such a model can be adapted further to explore the interactions between lightning and wind energy infrastructure, providing a foundation for assessing the risks posed by charged particles to spinning wind turbines and other critical assets. Future research should aim to refine the model by incorporating real-time data and extending its application to other severe weather phenomena. Investigating the effects of corona discharge and lightning leaders in greater detail will further enhance the understanding of pyroCb electrification.