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Numerical simulations of electromagnetic (EM) pulses propagation in the troposphere are presented in this letter with using the time-domain paraxial wave equation (TDPE) method. The TDPE is proved to be an efficient solution to single EM pulse problem. We propose an improved TDPE model considering realistic atmospheric refraction and irregular terrains. The impedance boundary conditions of vertical and horizontal polarization are respectively taken into account. Numerical examples are given to demonstrate the correctness of the proposed time-domain algorithm.