While the simple model of the total atmospheric carbon sink effect as a linear function of concentration has provided excellent prediction results, several problems remained to be investigated and solved. The most obvious open issue is the correct treatment of land use change emissions. It turns out that the model improves by mostly neglecting these emissions after 1950. This effectively implies that land use change emissions have been constant and small since then. The key investigation starts with the observation that the total carbon sink has a short-term component that can be explained by temperature changes. The apparent paradox, why contrary to the short-term changes no temperature-caused trend can be detected, despite the fact that several contributing processes exhibit clear temperature dependency, is analyzed and explained. The result of this analysis leads to the model extension, where the total effect of absorptions and natural emissions are a linear function of concentration and temperature. This extended model not only explains current measurements but also paleo-climate data from ice core time series.