Antenna orientation and polarization
A monopole antenna is one half of a proper dipole antenna. If you rotated the proper dipole through 90 degrees then the polarization direction follows the rotation. Because a monopole needs a ground plane to operate correctly, rotating it thru 90 degrees creates a bit of a mess mathematically and it becomes a bit unclear how the polarization changes precisely.

This is how a (ground referenced) monopole is "derived" from a free-space dipole (position c in the diagram below): -



This derivation is based on the fact that all lines of electric field along the horizontal centre-line of the dipole are effectively 0V and therefore can be replaced with a central ground-plane (without affecting dipole performance). The implication of this is that the lower half of the centre-ground-planed dipole can be discarded leaving a single monopole on a ground-plane.

The words that accompany this diagram in wiki are: -


  Showing the monopole antenna has the same radiation pattern over
  perfect ground as a dipole in free space with twice the voltage


In other words I believe the basic premise of the question is slightly flawed.