The objectives of the Framework Convention on Climate Change imply the
conflicting constraints of minimising concentrations and maximising e
missions (i.e. minimising emission restrictions). Carbon cycle models
are readily used for 'forward' calculations of future CO2 given specif
ied emissions and the 'inverse' problem of deducing the emissions requ
ired to achieve specified concentration profiles. However these approa
ches (a) are each geared to only one side of the problem; and (b) each
requires the specification of a particular pathway in terms of either
emissions or concentrations. These limitations can be avoided by anal
ysing the relations between future emissions and concentrations of CO2
using a formalism that optimises over all possible future emission pr
ofiles, subject to relevant constraints on both emissions and concentr
ations. We present specific calculations indicating which combinations
of upper bounds on concentrations and lower bounds on emissions are m
utually inconsistent and which are consistent. We also calculate the (
smaller) consistency regions that apply if emission reductions are res
tricted to less than 0.5% p.a. or less than 1% p.a. In each case, two
reference periods (1990-2100 and 1990-2200) are considered.