It is not. Water is transported by motion of the atmosphere, the energy source behind is the Sun. Yes, it goes up because its density decreases, but its density decreases because of the temperature change.
i beg your pardon, my response was unclear
the mass of water of given GPE changed to KE and thus to electricity has energy input by the sun
once the phase change occurs from liquid to solid, the same mass of water occupies a larger volume. the density has decreased
due to decrease in density, the an equivalent volume of atmosphere displaces that volume of water vapour into the atmosphere by exhausting GPE of that equivalent atmosphere volume
why does it the equivalent volume of atmosphere displace the water vapour? because there is a weight force of the atmosphere defined by the mass of that atmosphere volume accelerated by gravity. this force is greater and seeks to get under the water vapour's weight force thereby displacing it
so the GPE of the displacing atmosphere volume is exhausted to raise the water vapourised by the sun
this is my flow of logic, i beg your criticism