Roy Lewallen wrote:

Modeling will show that at great distances from the antenna, the
horizontally radiated field is zero from any horizontally polarized
antenna over ground.

I need to clarify this. It's based on a theoretical model which doesn't
apply in many practical cases. It assumes that the signal reaches the
destination by two paths, direct and via reflection from the ground;
that the ground is perfectly flat at the point of reflection; and the
destination is very far from the source. The lower the elevation angle
being observed, the farther the destination has to be for this effect to
occur. For example, consider the field strength at an elevation angle of
one degree from an FM transmitter whose antenna is 1000 feet above the
average terrain. Neglecting Earth curvature (which probably shouldn't be
neglected in this case), at a very distant point, the reflected signal
which will interfere with the direct signal strikes the ground at a
point about 11 miles from the transmitter. The receiver would have to be
more than 22 miles away (and of course, higher in elevation than the
transmitting antenna) for reasonable cancellation to occur. At a half
degree elevation angle, the receiver would have to be twice that
distance; at a quarter degree, four times, and so forth. Full
cancellation at zero elevation angle would occur only at an infinite
distance. In many practical situations, you can safely assume that the
potentially interfering ground reflection takes place beyond the
receiver, so a better estimation of received signal strength can be
obtained by looking at the free space pattern.

Roy Lewallen, W7EL