BP,
Remember reading somewhere that the radar can now pick up the movement of nitrogen molecules, well apparently they always could, just they were designed to filter them out in older radar types, newer types have better digital processing to allow this to be picked up.
Doppler only works on the axis of transmission, to get crosswind and vertical wind movements my thoughts would be multiple doppler units, say one on each wing tip and one on the tail, the sum of the momvement would get the movement of the air, as a vector, direction and speed.
However present day types are basically along only one axis, so the signal processing measures the head or tailwind change, and assumes this corresponds to a similar vertical movement.
Having been in 20+ of windshear on finals, or in CAT, without warning from these types of radars, they should be thought of as tools thats will not always show everything, but aid in your situational awareness
