Here is an animation of the changes in river flow across the globe from 1870 until 2100 based on the Hadley Centre's climate model predications and a warming scenario known as A1B. This is what's known as a mid-range emissions scenario and you can find more details about this in the IPCC's Special Report on Emissions Scenarios. The animation shows changes from -3.5 (red) to +3.5 (purple) m3 per second. No change in flow is signified by the pale green colour.