# Inversion of a Thunderstorm Cloud Charging Model Based on a 3D Atmospheric Electric Field
## 1 Introduction  
The charging model of thunderstorm clouds refers to the use of parameters to describe the characteristics of the charge distribution inside a cloud. Atmospheric electric field is an important parameter of atmospheric physics. The average intensity of the atmospheric electric field near the ground is about 130 V/m on fine days. The atmospheric electric field will increase significantly during the formation of thunderstorm clouds. The inversion of the thundercloud charge model from ground electric field measurement data has important theoretical value for monitoring lightning and early warning research. The most direct way to study the charge structure of thunderstorm clouds is to use sounding balloons to detect the thunderstorm clouds and obtain the electric field distribution characteristics of the detection equipment on the flight path. [PERSON], [PERSON], and others proposed the model of the tripole charge structure of a thunderstorm cloud by using sounding balloon observations [1]. Due to the short flying time of the sounding balloon, the measured electric field is the instantaneous charge structure of the thunderstorm cloud, so it is difficult to realize continuous monitoring. In recent years, scholars have used numerical simulation methods combined with the micro-dynamic factors of cloud physics to simulate the charge structure characteristics during the development of thunderstormclouds [2; 3; 4; 5; 6]. However, most of these methods are simulations, and there is no physical quantity that combines actual observations. Atmospheric electric field meters play an important role in the detection of thunderstorm clouds. Studies [7; 8; 9; 10] have looked at the improvement of atmospheric electric field meters and the method of electric field-based lightning warning. However, current techniques can only measure the vertical electric field component, ignoring the horizontal electric field caused by the charge of the thunderstorm cloud. The literature [11; 12; 13] has proposed the classical thunderstorm cloud charge model and used the atmospheric electric field data to study the structural parameters of the model. The data used are still derived from an atmospheric electric field that can only measure the vertical component [14]. As the horizontal component is neglected, it is necessary to invert the data from the joint observations of atmospheric electric field meters at different locations. However, the atmospheric electric field is greatly affected by the building and surface conditions at the installation site, leading to a difference in each atmospheric electric field measurement. The consistency is not high, and the quality of the data participating in the inversion is poor [15]. This paper attempted to develop a three-dimensional atmospheric electric field meter capable of simultaneously measuring horizontal and vertical components, and more comprehensively establish a functional relationship between the thunderstorm cloud charge structure and the electric field of the observation point. Combined with the particle swarm algorithm, the measurement data inversion using a single three-dimensional electric field meter was used. The structural parameters of thunderstorm clouds provides a new technical means for the study of the charge structure of thunderstorm clouds. In this paper, the electric field generated by thunderstorm clouds on the ground was observed by using the developed three-dimensional electric field meter, and compared with the radar observation data. The experimental results showed that the trajectory of the thunderstorm cloud could be analyzed by using the three-dimensional electric field data. At the same time, using the particle swarm algorithm (PSO) and the three-dimensional atmospheric electric field data, the thunderstorm cloud-charged structure of the observation point (Nanjing) can exhibit the classic dipole. These conclusions are not achievable with conventional single-dimensional electric field meters.