A numerical model is used to calculate the electric field enhancement in a thundercloud due to the propagation of a growing system of positive corona streamers, such as might be initiated by a hydrometer. These streamers intensity if the ambient electric field E exceeds a critical value E0, which is experimentally determined. The positive charge carried in the head of the system increases in magnitude, and the negative charge is deposited in the trail, and thus an electric dipole that tends to enhance the original field is created. The growth is calculated by solving an energy balance equation for the system, including the potential energy of the dipole, the losses due to ionization and excitation, and the production of new streamer tips. Several systems may propagate sequentially, each one passing into the debris of its predecessors and growing more rigorously as a result. For representative values of E and E0 at 6.5-km altitude it is shown that a series of three to seven such systems can give rise to local enhancement of the ambient electric field up to 15¿105 V/m over a distance of a few meters, which is sufficient to insure dielectric breakdown and possibly launch the stepped leader.