Background to the Sea Level Videos. Also useful are the pages: Paleoclimate and Ice & sea level and Key Element.
 
The videos show the equilibrium sea level rise in the centuries to come for A] a 2oC average global warming since 1880, and B] for the average global warming from business as usual or flat CO2 emission volumes over the next 30 and 40 years followed by declining annual emissions to levels consistent with 5% of current CO2 emission volumes by the year 2100 and held at this levelL [using this table including CO2e]. C] The 350ppm scenario in the videos assumes near zero CO2 emissions within 30 or 40 years.
 
The calculations are based on paleoclimate research into the relationship between the atmospheric life of CO2 , CO2 concentrationsaverage global temperatures, the ice sheet size of Antarctica and Greenland, and sea levels. 21st Century CO2 emission budgets [Spread sheet] and equilibrium temperature forecasts are the drivers of changeL.

Global Average Surface Temperature Change [surface waters 71% & land air 29%] from 1880 to ..... to historic comparable
Percentage Change in Earth’s Global Average Surface Temperature
Base: 13.8oC [+/-0.1oC] in 1880
Equilibrium Sea Level Adjustment in Meters relative to 1880
+
Atmospheric CO2
Size of Ice Sheets in meters of sea level rise potential once equilibrium reached
% change in 
global average temp of air over land surface
Base: 8.5oC in 1880. Use 1.5x uplift factor
- 4.8oC to Last Glacial Maximum 20,000 years ago
- 29%  to a global average of 9.7oC
120 meters lower
CO2 170ppm
190 meters
- 84.7% to land average of 1.3oC
0.8 oto 2010 link occurred already
+ 5.7% to 14.5oC
occurred already
3 meters higher
CO2 393 ppm in 2012
67 meters
+14% to 9.7oC
occurred already
+1.5 oto Eemian 125,000 years ago
+10.9% to 15.3oC
4 to 6 m higher (perhaps 9m) link
CO2 300ppm
61 to 66 meters
+26.5% to 10.75oC
+2 to 3oC to Pliocene 3 to 5m years ago
+ 14.5% to 15.8oC
+22% to 16.8oC
15 to 25 meters
CO2 340 - 390ppm
50 to 55 meters
+35.3% to 11.5oC
+53% to 13oC
+4 oC to Miocene 14 to 16m yrs ago
+28.9% to 17.8oC
30 to 45 meters
CO2 450ppm
25 to 40 meters
+70.5% to 14.5oC
+6 oC to Eocene 35 to 40m yrs ago
43.5% to 19.8oC
60 meters+ higher
CO2 550 to 650ppm
less than 10 m
+106% to 17.5oC
 
The Greenland ice sheet and the seabed grounded Antarctic ice sheets, containing 25m in sea level rise potential, have never in the last 65 million years of Earth's history fully formed or even remained 50% intact when CO2 has been 350ppm or more [Link]. Atmospheric CO2 is 394 ppm in 2012. Atmospheric CO2eq is approaching 500ppm. After netting out for human aerosols the CO2eq level is just under 400ppm CO2eq [eq=equivalent].
 
Sea levels have been 40 t0 60 meters higher for average global temperatures 3oC to 5oC warmer than present climate [Diagram] for atmospheric CO2 of 450ppm+. They were 15 to 25 meters higher for climates just 1oC to 1.5oC warmer than present climate for CO2 of 340 to 380ppm. 125,000 years ago, during the Eemian period, sea levels were 4 to 6 meters [perhaps even 9m, link] higher for a global average climate just 0.6oC warmer than present for CO2 of 280ppm [Orbit change had caused this warming]. 
 

The projected rate of warming [4oC+ CO2 600ppm+] for the 21st Century under business as usual is easily 60 times faster than the rate of the 4oC to at most 5oC global average warming during the 8,000 year emergence from the last ice age [or 160 times faster than  the PETM 55.6m years ago]. That's a 1oC rise in global average temperatures every 26 years in the 21st Century. In the exit from the last ice age it was a gradual 1oC rate every 1,600 to 2,000 years, cumulating to a 4oC to 5oC from a 100ppm CO2 rise in 8,000 years, and 120 meter sea level adjustment over 11.000 years.

The warming since 1970 to 2010 has been 15 times faster, and the increase in atmospheric CO2 120 times faster than the exit from the last ice age. The 21st Century projected rate of CO2 increase is 300 times faster for business as usual, and 60 times faster under the 450ppm overshoot 2oC scenario. These abrupt changes mean accelerated change in the cryosphere, and sea levels. NASA Ice Viewer

Multi-meter sea level rise per century has often happened in paleoclimate for global average warmings 60 times slower than that forecast in the 21st Century. [Diagrams: Antarctic Ice sheet formation, Global surface temp 65m years, 35m year sea level record]

Quotes of NASAs Head of GISS: "A CO2 amount of order 450 ppm or larger, if long maintained, would push Earth toward the ice-free state." .... "Thus goals to limit human-made warming to 2°C are not sufficient — they are prescriptions for disaster. Link".... "The important point is that the uncertainty is not about whether continued rapid CO2 emissions would cause large sea level rise – it is about how soon the large changes would begin. Link" [NASA GISS] J. Hansen NASA GISS Director @ TEDX 18 mins      
 
Sea level did rise at rates of 1.5cm per year or 1.5m per century, even 4m, during the exit from the last ice age: Link. Given the speed of the heat shock we are subjecting the planet to, and the atmospheric life of CO2, one can only accept that huge sea level rise will be compressed into narrower time frames of centuries[Revised 21stC Sea Level Rise forecasts].
 
The surface carbon reservoirs (ocean, permafrost, soils, forests) easily contain 50 times the sum of all carbon in the atmosphere. 100ppm of atmospheric CO2 is equal to less than 0.5% of the surface reservoirs stores of carbon. They must only release 2% to 7% of their carbon stores to create a net 100ppm increase in COby the year 3100 when compared to that in the 21st Century. It is warming which triggers the release of carbon from the biosphere. Given the pace of change, regrowth will not be able to compensate and these calculations may be overly optimistic. It could be much worse and it will certainly be no better. 1000 years of sustained warming 50 times faster than ever before on Earth is plenty of time for the ice sheets to melt. 
 
* Incremental temperature & CO2 change 2020 - 2098 from the UK Committee on Climate Change median A1B representation of the IPCC scenario
** Model equilibrium temperatures are dependent upon CH4 & N20 tracking CO2 as in the past and sulphate aerosols declining to natural levels over time
*** Solomon et al 2009, Archer et al 2009, 40% of airborne fraction remains in air in 1,000 years for no feedbacks. Permafrost and Ocean feedbacks are 80%. Together these two sources contain 47 times the carbon that is in the atmosphere. Only some must be released as feedbacks. Mac Dougall et al 2012, Schaefer et al 2011. 100ppm = 213bn tons of carbon or just 0.5% of carbon in the land and ocean sinks.
**** If we decide to artificially reduce atmospheric CO2 the ocean will, irrespective of temperature, release CO2 as atmospheric CO2 falls to maintain the partial pressure [Revelle Factor]. As a consequence and when combined with the earlier start date the true level of CO2 that would have to be sequestered by humans from the atmosphere to return to 280 ppm is likely to be 100% larger than shown above. Once large amounts of fossil carbon are introduced to the surface reservoirs [atmosphere, ocean, surface soil & vegetation] it must be pumped back under ground to get rid of it, otherwise it is part of the main carbon cycle.
For a full explanation of above table read the end notes on this page link.
 
One can see in these 3 diagrams of the last 2,000 years that sea level has responded to increased temperature which was caused by increased GhGs: GHG levels, Global Temperature & Sea Level. We are on track for atmospheric CO2 concentrations greater than 650ppm later this century which is consistent with average global temperatures being more than 4oC warmer than 1880.  
 
Less than 5% of global energy comes from non CO2 producing sources. But if we want to avoid flooding our cities, we must rapidly reducing atmospheric CO2 to 350ppm and lower, to limit global average warming to less than 1.1oC since 1880. This means reducing our CO2 emissions to near zero levels, within 30 to 40 years, to both prevent atmospheric CO2 from increasing further, and to give Nature a chance to draw down the excess CO2. Levels are at 393ppm in 2012 - a forcing consistent with temperatures 1.5oC higher than present and sea levels 20 to 25 meters higher. [7 mins on 21stC sea level          ]
 
 *UK Committee on Climate Change analysis: Emission Budget Spreadsheet, Technical appendices. IPCC Table on CO2 & Emissions. Climate Science history & why the message does not get through: 1hr     
 
An excellent 30m lecture on some aspects of the technicalities of SLR past and future: