# A 3D Numerical Model to Estimate Lightning Types for PyroCb Thundercloud
## 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 (afew 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 \(\times\) 30 km \(\times\) 30 km cartesian domain. This simulation domain is discretized using 61 \(\times\) 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. \[\rho_{n}(x,y,z)=\rho_{n}(0)exp\left[\frac{(x-x_{0n})^{2}}{r_{xn} ^{2}}+\frac{(y-y_{0n})^{2}}{r_{yn}^{2}}+\frac{(z-h_{n})^{2}}{r_{zn}^{2}}\right] \tag{1}\]  
where \(\rho_{n}(0)\) 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, 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.