The recently released UN's Intergovernmental Panel on Climate Change (IPCC) report says the following about the effect on sea level rise on "Small Islands":

"Small islands have characteristics which make them especially vulnerable to the effects of climate change, sea-level rise and extreme events," the report said.

"Sea-level rise is expected to exacerbate inundation, storm surge, erosion and other coastal hazards, thus threatening vital infrastructure, settlements and facilities that support the livelihood of island communities."

It's happened already: