The aim of this paper is modeling and parameter identification of the leader stage preceding the positive stroke of natural cloud-to-ground lightning. This research is based on electric field and 3D Doppler radar data recorded during thunderstorms in Poland, as supplied by database information from long range lightning location systems. The numerical simulation performed in the MATLAB platform showed that a high number of assumed model parameters, such as non-uniform leader tip speed and lightning channel charge density, allowed us to obtain greater compliance between simulated and measured electric field signatures than in the classical approach. The proposed model can be implemented in lightning location systems and forest fire warning systems, operating globally to reduce the risk of damages caused by positive cloud-to-ground flashes being one of the most dangerous type of lightning events. An alternative application of the model can be for research, including ground-based lightning data supplementation for the corresponding satellite and airborne registrations.