[jamest (OP)]

Kate: 'How long does the water cycle take to complete a circuit from meltwater to evaporation to snow and ice and back again? Over what size of landmass and water area does the water cycle take place?'

[paul cotter]

No answers, well here is my two cents, for what it is worth(most likely very little). A question like that is so vague that there is no definitive answer. The water cycle may include the solid state(ice, snow) but it does not have to: it is quite possible for water to evaporate from the sea/lakes and rise into a cumulonimbus cloud and precipitate in the same/different location within hours. For evaporation from melt water the same applies but whether it freezes again depends largely on where it is deposited. If precipitation occurs in a part of the world where temperatures are below freezing then the cycle could in principle be quite short. Prevailing weather conditions might move the clouds to a warmer area and in this case the precipitation would have to be re-evaporated to have any chance of returning to an area where freezing could complete the cycle. No simple answer. The water cycle can occur just about anywhere except for deserts where it is infrequent.

[alancalverd]

The period between ice ages or global temperature maxima is about 100,000 years, and the periodicity is remarkably constant. So you could ascribe an effective half-life of 50,000 years to an ice molecule undergoing the complete cycle, at least for  the north pole where the ice is moving continuously.

But we have ice cores over land which can be reliably dated over at least 8 global temperature cycles, so whilst the antarctic ice shelf  would fit into the 50,000 year half-life, quite a lot of ice will "never"  reach the sea because it is trapped behind a mountain. "Never" in inverted commas because tectonic drift may eventually move the entire continent  away from the pole and turn parts of it into a dry desert like the middle of Australia (once a sea bed).