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 carbon in atmospheric

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

is the annual emission rate (GtC/yr), and τ is CO2 atmospheric resident time. The value of

is constrained to be always larger than

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

firmly negative). For more information, see [1]. For the Socolow–Lam paper, see [2].