Exponential analysis in assessing the contribution of greenhouse gases emissions to global warming

Several carbon cycle models listed in the IPCC materials are used for assessing the atmospheric CO₂ response to various scenarios for the CO₂ anthropogenic emission into the atmosphere. The same materials present the Green function expressions of these models in terms of this exponential approximation, i.e., in the form of a sum of exponents. The uncertainties that occur when the Green function is substituted by its exponential approximation are investigated. The reason of such an analysis is a classic conclusion that a general problem of the exponential approximation refers to the class of inconsistent problems.