Simplified accurate new method for the calculation of the ground-wave in the exponential atmosphere

The ground-wave calculation software GRWAVE is based on Rotheram's method, and it has been recommended by the International Telecommunication Union Radio communication Sector(ITU-R). But it has two problems which are the complex programming and the lack of the phase value. Aiming at the issues, a new method is presented, which combines Fock's method of residue series for the smooth and electrically homogeneous earth and Rotheram's equivalent radius method to consider the influence of the exponential atmosphere. Firstly, the mode equation is transformed into differential equation, then the differential equation is solved by 4th order Runge-Kutta algorithm. Secondly, the ground-wave field is calculated in flat region and spherical region respectively, and Rotheram's equivalent radius is used to consider the influence of the exponential atmosphere. Lastly, the field strength of the vertical electric dipole antenna of 1kW has been calculated. It is found that the error is within 0.2dB when it is compared with that of the ITU-R. The curves of the ground-wave field strength drawn by this method is in excellent agreement with that of the ITU-R. This paper simplifies the calculation of the ground-wave field strength in the exponential atmosphere while it can give the phase value. So it has some theory guidance significance and practical engineering value for the application of the ground-wave communication system.