How warming and steric sea level rise relate to cumulative carbon emissions

Surface warming and steric sea level rise over the global ocean nearly linearly increase with cumulative carbon emissions for an atmosphere-ocean equilibrium, reached many centuries after emissions cease. Surface warming increases with cumulative emissions with a proportionality factor, ΔTsurface:2×CO2/(IB ln 2), ranging from 0.8 to 1.9 K (1000 PgC)−1 for surface air temperature, depending on the climate sensitivity ΔTsurface:2×CO2 and the buffered carbon inventory IB. Steric sea level rise similarly increases with cumulative emissions and depends on the climate sensitivity of the bulk ocean, ranging from 0.4 K to 2.7 K; a factor 0.4 ± 0.2 smaller than that for surface temperature based on diagnostics of two Earth System models. The implied steric sea level rise ranges from 0.7 m to 5 m for a cumulative emission of 5000 PgC, approached perhaps 500 years or more after emissions cease.