The way i see it, water is increasingly concentrated on cities in the imperial core because these are the main destination of imports, so the imperial core will have even bigger problems of immigration.

Agricultural production will slowly plummet due the lack of water and the lack of labour in the countryside, the reason of this is that the countryside is exporting more water than it imports to the cities in the manner of grain/meat/milk/etc. The fall of the main economic activity of the countryside will cause migration from the countryside to the cities (something that already is happening).

Food will become scarce and will cause massive famines, large cities will have, one way or another, to adapt the cities to do agricultural production in order to survive.