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Such characteristics are described in Answer 1 below, as sourced in a study of antenna engineering textbooks, and by generating NEC4.2 studies.

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           VERTICAL MONOPOLE, EARTH, and BURIED RADIALS
         as FACTORS in ANTENNA SYSTEM RADIATION EFFICIENCY

Considerations:

  1. The components shown in the graphic below, and the soil where they are located/buried are elements of the complete antenna system.

  2. R-F currents flowing on/in the earth within a radius of 1/2 wavelength from the monopole as a result of its radiation must be collected and returned to the 2nd terminal of the transmit/antenna system. The sum of those currents is equal to the current flowing along the monopole, itself.

  3. The r-f resistance of the Earth+radial path through which those currents travel is a series element of the transmit system. Reducing the r-f resistance of that path increases the radiation efficiency (gain) of the antenna system.

  4. R-F currents flowing in the earth beyond a radius of 1/2 wavelength from the monopole are not collected by buried radials of any length(s),and so do not affect the radiation efficiency of the antenna system.

  5. The e-m fields existing just beyond 1/2-wavelength from the monopole are fully formed, and will propagate outward into space.

  6. Fields radiated by the monopole toward higher* elevation angles decay at an inverse distance (1/r) rate.

  7. Fields radiated by the monopole toward lower* elevation angles decay at a rate greater than 1/r, due to the effects of their (lossy) interface with the earth.

  8. The radiation efficiency/gain of a monopole antenna system is independent of the conductivity values of the earth existing in the areas beyond 1/2 wavelength from the radiator.

  9. Received fields beyond a 1/2-wavelength radius of the monopole do vary as a functions of frequency, length of the propagation paths, and the physical conditions along and near those paths (earth conductivity, ionospheric reflection, obstructions etc).

    *The elevation angle separating lower from higher elevation angle radiation is arbitrary, but generally thought of as ranging from 5 to 10 degrees.

enter image description here

Author: Richard Fry - March 2020

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    $\begingroup$ Please be more specific with your question. The "answer" could be an entire textbook on electromagnetic engineering. For example, what goal(s) are you trying to achieve and under what constraint(s)? $\endgroup$
    – Brian K1LI
    Apr 16, 2020 at 18:49

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