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The knowledge of the initiation and propagation of an upward moving connecting leader in the presence of a downward moving lightning stepped leader is a must in the determination of the lateral attraction distance of a lightning flash by any grounded structure. Even though different models that simulate this phenomenon are available in the literature, they do not take into account the latest developments in the physics of leader discharges. The leader model proposed here simulates the advancement of positive upward leaders by appealing to the presently understood physics of that process. The model properly simulates the upward continuous progression of the positive connecting leaders from its inception to the final connection with the downward stepped leader (final jump). Thus, the main physical properties of upward leaders, namely the charge per unit length, the injected current, the channel gradient and the leader velocity are self-consistently obtained. The obtained results are compared with an altitude triggered lightning experiment and there is good agreement between the model predictions and the measured leader current and the experimentally inferred spatial and temporal location of the final jump. It is also found that the usual assumption of constant charge per unit length, based on laboratory experiments, is not valid for lightning upward connecting leaders.

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The amount of the electric charge injected by the streamer corona bursts during the stage of leader inception determines the energy deposited to thermalize the corona stem into a leader segment. This paper is aimed at investigating the critical charge required for positive leader inception in air by using a thermo-hydrodynamic model with a detailed kinetic scheme. In order to simplify the analysis and to speed up the simulation, a reduced kinetic scheme for air is proposed. Numerical comparisons show that the reduced scheme can obtain almost the same results as the previous comprehensive kinetic scheme but with only half of the number of species and reactions. The thermo-hydrodynamic model with the reduced kinetics is then used to solve the radial dynamics of a single stem heated by current pulses typical of streamer corona bursts. The critical charge necessary for the direct transition of a first streamer corona into a leader under electrodes with large curvature radius is estimated between 0.08 and 0.5 µC per stem. Furthermore, the simulation shows that the gas heating of corona stem formed from electrodes with small curvature radius is mainly determined by the total accumulated charge injected by previous streamer corona bursts and the length of the dark periods in between the current pulses. The shape and the number of the corona current pulses in the discharge also play a role and their effects are discussed. It is suggested that the transition into a leader is triggered when a secondary streamer burst is initiated after the gas temperature is increased by the heating of previous streamers to about 1200 K. In addition, it is found that the heating produced by the charge injected by previous streamer corona bursts can be neglected if the dark period to the next burst is larger than few hundreds of µs for a corona stem with moderate initial stem radius. This indicates that the critical charge criterion obtained from laboratory experiments does not hold to evaluate the inception of positive leaders under conditions when long dark periods are present.

The evaluation of the upward connecting leader inception from a grounded structure has generally been performed neglecting the effect of the propagation of the downward stepped leader. Nevertheless, field observations suggest that the space charge produced by streamer corona and aborted upward leaders during the approach of the downward lightning leader can influence significantly the initiation of stable upward positive leaders. Thus, a physical leader inception model is developed, which takes into account the electric field variations produced by the descending leader during the process of inception. Also, it accounts for the shielding effect produced by streamer corona and unstable leaders formed before the stable leader inception takes place. The model is validated by comparing its predictions with the results obtained in long gap experiments and in an altitude triggered lightning experiment. The model is then used to estimate the leader inception conditions for free standing rods as a function of tip radius and height. It is found that the rod radius slightly affects the height of the downward leader tip necessary to initiate upward leaders. Only an improvement of about 10% on the lightning attractiveness can be reached by using lightning rods with an optimum radius. Based on the obtained results, the field observations of competing lightning rods are explained. Furthermore, the influence of the average stepped leader velocity on the inception of positive upward leaders is evaluated. The results obtained show that the rate of change of the background electric field produced by a downward leader descent largely influences the conditions necessary for upward leader initiation. Estimations of the leader inception conditions for the upper and lower limit of the measured values of the average downward lightning leader velocity differ by more than 80%. In addition, the striking distances calculated taking into account the temporal change of the background field are significantly larger than the ones obtained assuming a static downward leader field. The estimations of the present model are also compared with the existing leader inception models and discussed.