Lightning is a complicated phenomenon. People try to understand it using models from Electromagnetic theory. In the simplest possible case with static or slowly varying charge and current distributions, we could think of the charge distribution in a cloud as a point charge and the earth as an infinite conducting plane. With the method of images, we have an equation that describes the potential. Armed with an equation for the potential we could find an equation for the electric field at the surface of the earth. The figure below identifies the method of images and the equation for the potential.

Cleary the electromagnetic phenomenon of lightning is more complicated. If we model the path the lightning takes as a straight line, we can consider two spherical charge distributions connected by a wire where the charges are driven back and forth harmonically such that there is a dipole moment. With the help of Griffiths, we can calculate the electric magnetic field due to a dipole, the intensity of the dipole radiation, and the power radiated by the dipole. The figure below is a graph of the intensity profile and the associated equations.

If you're wondering how Snap, Crackle and Pop fit into all of this click on the scp link.