Sea level is currently rising at just over 3mm a year in the South Pacific islands - you can look this up - it's a matter of record. The trend currently seems to be accelerating but even if we take the current rate, by the end of the century sea levels will be 30+cm higher than in 2000. (This is lower than the mid-range IPCC predictions
which have been shown to underestimate current contributions from melting Greenland and Antarctic ice but lets stick with 30cm). 30cm may not seem much, but when your entire country rises no higher than 3m out of the sea and your island is barely more than a few paces across - and you have 100,000 people in overcrowded conditions on it, it is a serious issue. More frequent swamping of your landfill sites and what sewage systems there are contaminates the sea - from where you get your only source of protein. More frequent and more severe flood tides contaminate all your groundwater, freshwater and whatever crops you have - not to mention your homes and gardens. 30cm may be more than countries like Kiribati and the Marshall Islands can bear. And 30cm is about the most conservative estimate of likely sea level rise this century. I have visited both of these countries in recent years - I was in the Marshall Islands during a 'King tide' in 2015. During a King tide, there is effectively no island in large parts of the country - just shallow ocean with houses sticking out of it. I have seen the evidence of these effects first hand and my opinion, based on what I have seen, is that Kiribati is already doomed. I doubt it has a century left before it ceases to be a viable habitat for humans.
On desertification,
here's a paper on that that compares IPCC models to actual data and finds that on that too, the models underestimate the pressure on dry land under global warming.