Probabilistic model of lightning initiation and propagation in thundercloud using a one-dimensional electric circuit

Abstract Lightning initiation and propagation is complex and probabilistic in nature. In this study, we attempt to replicate these phenomena using an electric circuit model. We reproduce lightning behaviors numerically by dividing an air column into discrete cells of resistor and capacitor components. First, we reproduce the attributes of classical tripole structure of electric field in thunderclouds. We represent charging mechanisms due to electrification and precipitation as current sources in the circuit. As a cell charges, the electric field increases to near dielectric strength limit causing its resistor to breakdown probabilistically and create a discharge path for the current to flow. Then, the voltage and electric field across the cells are measured by solving the finite difference form of the circuit equation with a Gaussian solver package for Java in Eclipse IDE. The electric discharge paths revealed that lightning is initiated at the negative charge pole 4.5 km from the ground. However, a propagation path toward the center of the thundercloud can be produced once an initiation leader induces electric breakdown in nearby cells. With our model, three types of natural lightning propagation paths were reproduced consisting of split intra-cloud (IC), downward cloud-to-ground (CG), and upward intra-cloud. Numerical trials of 1000 simulations identified the occurrence of 284 downward CG, 709 split IC, and 7 upward IC lightning. We observed a ratio of 2.52 from the numerically generated IC and CG lightning paths, which is in good agreement with observations from satellite- and surface-based recorded lightning measurements.