This work is devoted to the impact of random environmental constraints regarding the transient impedance of horizontal grounding wire. Deterministic modeling relies on solving the Pocklington equation in the frequency domain (antenna theory). First, the method is based upon the scattered voltage analytically computed at the input terminal of the grounding electrode; transient impedance is then extracted from Inverse Fast Fourier Transform. Finally, a methodology is proposed to precisely assess the respective influence of different parameters jointly by means of stochastic collocation method and sensitivity analysis.