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.