Description of a one-dimensional carbon cycle model calibrated using techniques of constrained inversion

A quasi one-dimensional carbon cycle model is discussed. The ocean is divided into two zones; thus the mixing processes can be parameterized in terms of both eddy diffusion and advective circulation. All the model processes are parameterized so as to allow, so far as is possible, for independent geophysical (or biogeochemical) estimates of the model parameters. The model is then calibrated by using a constrained inversion approach in which the independent estimates of the parameters act as the constraints. This calibration scheme has proved stable and robust. The model is used for a number of studies in which various indirect observations of the carbon cycle constrain the range of possibilities for the history of biospheric change over the last 200 years. The estimates of current net releases of biotic carbon are small and possibly negative and all the estimates give negative values for the current rate of change of biotic carbon release. This is in conflict with results recently deduced from analysis of Mauna Loa CO₂ data using the unjustifiable assumption of a constant airborne fraction.