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

[1] 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×CO ₂/(I _B ln 2), ranging from 0.8 to 1.9 K (1000 PgC) ^-1 for surface air temperature, depending on the climate sensitivity ΔTsurface:2×CO ₂ and the buffered carbon inventory I _B. 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.