The world carbon cycle model is based on the one-tank model of Socolow–Lam:

, where

is time (years) offset from the start of the 21st century,

is atmospheric

in GtC (divide by 2.1 to get ppmv, parts per million by volume), and

is the annual emission rate (GtC/yr). The value of

is constrained to be larger than -0.02 times the number of wedges ("wedge" as defined by Pacala–Socolow), and the maximum effort is reached after "transition years" (the approximate number of years needed by the world to make

firmly negative). For more information, see