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The radiated horizontal electromagnetic field of a lightning channel acts as the excitation when the lightning-induced voltages on overhead lines are under study. To accelerate the calculation of the horizontal electric field of a lightning channel, a piecewise Hermite interpolation model is proposed, which exploits the distinct feature of the transmission line whose height keeps unchanged. In the piecewise Hermite interpolation model, the key technique is fast evaluating the derivative of the horizontal electric field expressed by the generalized Sommerfeld integral. In this paper, the moment technique is utilized to calculate the derivatives efficiently. As demonstrated in the numerical examples, the piecewise Hermite interpolation model can reach a high accuracy with a very low computation cost.