I'm reading about synthetic aperture radar (SAR), and one of the basic concepts is that the transmitted and received signals can have "horizontal" (H) or "vertical" (V) polarization, but I can't find anywhere what that means in terms of the real-life physical direction. If the radar were on top of a building and transmitting a wave parallel to the surface of the earth, then I can understand that horizontal and vertical would mean relative to the surface of the earth. But if the radar is on a satellite, then the direction of propagation of the wave is more like perpendicular to the surface of the earth, so both of the polarizations would be nearly horizontal in that sense (and in the case where the radar is looking directly downward (zero "incidence angle"), both polarizations would be exactly horizontal relative to the surface of the earth). So what do horizontal and vertical refer to in this context? Is vertical the direction that's in the plane containing the direction of the satellite's movement and the direction of the wave (and is perpendicular to the direction of the wave), and horizontal the direction that's perpendicular to that plane?
I think you have the gist of it. From Iain H. Woodhouse's text "Introduction to Microwave Remote Sensing" (a great resource on SAR and RADAR):
For convenience, in remote sensing the horizontal axis, x, is defined to be parallel to the surface of the Earth when we are taking oblique (off-nadir) measurements. The vertical axis, y, is then defined as being perpendicular to this so that the x-y plane is defined at the instrument, not the ground (i.e. it need not be vertical with respect to the Earth's surface). When viewing towards the nadir, the choice is completely arbitrary since there would be no distinction between the horizontal and vertical at the ground surface. In such a case the instrument designers would choose the axes based on the instrument configuration. If the field of view is large enough (or if it is a scanning instrument) so that part of the data is effectively oblique, then the surface in this direction can be taken as the horizontal axis. Otherwise, the horizontal is taken as parallel to the motion of the platform.