ATCast asked for an official definition of groundspeed. Genghis the Engineer thought it is horizontal component of absolute velocity but could not pin a reference.
Pugilistic Animus thinks the two definitions are equivalent. Wizofoz thinks it is not the "horizontal component of absolute velocity" because "absolute velocity" is not defined, although I understood perfectly well what ATCast was asking, as did Genghis.
Tmbstory thinks it is "speed over the ground", and Checkboard "speed over that surface", so FEHoppy "speed relative to the surface of the earth". None of these contributors seem to have picked up that their "definitions" are ambiguous in just the way ATCast explained.
BOAC sees the difference, I think, but considers the discussion "twaddle".
I did what ATCast wanted. I looked it up in Kayton and Fried, Avionics Navigation Systems, 2nd edition, Wiley-Interscience 1997, otherwise known as The Book, when I had the chance.
Ground speed is the horizontal (i.e. tangential to the reference ellipsoid) component of the resultant vector of the air-velocity vector with the wind velocity vector (Figure 2.4, p30, notation Vg). Genghis is right.
As for PA, we may take it he doesn't build inertial nav instruments for a living. Serious nav takes altitude into account, for reasons which I hope I indicated in my earlier post.
PBL