James Hansen was a director of NASA climate research, and he has published papers showing that the unexplained part of the rise is due to a cleaner atmosphere, with less sulphur in it. This has substantially reduced the amount of cloud cover which reduces the reflection of sunlight and allows the sun to heat the land and the ocean.
This has caused some discussion from other scientists but Hansen has been proven right many times before and is probably right now.
Sometimes its easy to get lost in the detail of calculations and it can pay to go back to look at paleological records and se what happed the last time the planet was in a similar state with 400 + parts per million of CO2 in the atmosphere.
New Zealand scientist, Tim Naish, of Victoria University is a geologist and has been researching Antarctica to discover what happened to the ice shelves, sea level rise and the temperature during the Pliocene period three million years ago, which was the last time the planet had 400 ppm of CO2 in the atmosphere.
He participated in the ANDRILL project that, remarkedly, took core samples from the seabed under the McMurdo Sound ice shelf and he and his team were able to study them, to work out what the climate was like. Sealife and detritus sink to the seabed and can be examined to deduce the conditions of the time. An ice free ocean would have sealife only found in an open ocean and other indicators such as pollen can indicate the temperature.
This showed that the ice had disappeared three million years ago and the temperature was in the range of 3 C to 8C warmer. The ice only recovered when the temperature reduced due to the biosphere locking up the CO2 in the soil and sea bed.
Having established a time period for this situation it was relatively straightforward to find places around the world to establish the height of the sea for that period and it was 21 metres higher than today.
For times les than 800 thousand years ago there are good records in ice cores taken from the 3 kilometre deep ice in Antarctica and these show how the planet has cycled though ice ages and brief warm periods every 125 thousand years. These show that in the last warm period, when CO2 was only 300 ppm, the sea level was 7 metres higher than today.
What is missing here is the sensitivity of the planet to change and here Hansen claims that the current climate models are much too conservative which is why they are consistently forecasting temperatures less than the consequent facts, even in the short time we have been conducting research.