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Ermi: The reason that a vertical quarter-wave monopole above ground has 6 dB less gain when receiving a groundwave compared to when receiving a sky wave is that there is no reflection from the ground plane when the groundwave is received. It is reflection that creates the virtual quarter-wave element below the level of the ground surface that adds to the real quarter-wave element to creates an antenna that is something like a half-wave dipole.
A base-driven, 1/4-wave monopole working against a perfect, infinite, flat ground plane has 1/2 the feedpoint impedance of a 1/2-wave dipole in free space (37.5 ohms instead of 73 ohms). Therefore for equal applied power, twice the current will flow in the 1/4-wave monopole as in each arm of the 1/2-wave dipole, which means that the peak power “launched” by each of these radiator forms is the same. The ground plane reflection (or “image”) adds 3 dB to the net far-field radiation of the monopole system, so that its peak, far-field system gain for the groundwave is 5.15 dBi.
The base impedance of a 1/4-wave monopole is a constant, whether it is in receive or transmit mode. Therefore a 6 dB difference in its receive gain is not possible, even if the monopole in receive mode was unaffected by reflections from the ground plane.