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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. Since a sky wave reaches the antenna at an angle with the ground plane, there is reflection from the ground plane, and the virtual quarter-wave antenna element is functioning. A groundwave is a surface wave that travels along the surface of the ground plane, and there is no reflection at the receiving antenna, and the virtual antenna element is not present when the receiving antenna intercepts a groundwave. The lack of the virtual antenna element causes the effective height of the receiving antenna to be half of what it is when receiving a sky wave. Halving the effective height of the antenna causes the effective aperture of the antenna to be reduced by a factor of 4. This is the cause of the 6 dB difference between the gain of the receiving antenna when receiving a sky wave and when receiving the ground wave.
A quarter-wave transmitting monopole above ground depends on reflection from the ground plane to function, so its gain has a single fixed value, which is 3 dB higher than for a half-wave dipole remote from earth.
It is this the 6 dB reduction in the gain of the quarter-wave monopole when receiving a groundwave that accounts for the fact that two quarter-wave monopoles above ground (one is a transmitting antenna and the other is a receiving antenna) have the same systen gain as two parallel half-wave dipoles remote from the earth, separated by the same distance as the two monopoles. For the monopoles, the transmitting antenna has a gain that is 3 dB greater than for a dipole. The receiving antenna has a gain that is 3 dB less than for a dipole. The transmitting antenna creates a groundwave, and the receiving antenna receives the groundwave. So, the system gain for the two monopoles is the same as for the two dipoles.
For both the dipoles and the monopoles, the system gain remains the same if the transmitting and receiving antennas are interchanged. So there actually is reciprociry for these two antenna systems.