It depends on the mass of the ice,temperature around it and latent heat energy required to melt the ice.
However the furthest a ice berg can travel is estimately 32-40°n/s
While the state of China sees Tibet as its rightful territory that it has liberated, the Tibetan state and the vast majority of people see themselves as an independent state.
Rainwater is the main solution. There would need to be higher technology, to make that happen.
