The glacial/interglacial rise in atmospheric pCO2 is one of the best known changes in paleoclimate research, yet the cause for it is still unknown. Forcing the coupled ocean-atmosphere-biosphere box model of the global carbon cycle BICYCLE with proxy data over the last glacial termination, we are able to quantitatively reproduce transient variations in pCO2 and its isotopic signatures (δ13C, Δ14C) observed in natural climate archives. The sensitivity of the Box model of the Isotopic Carbon cYCLE (BICYCLE) to high or low latitudinal changes is comparable to other multibox models or more complex ocean carbon cycle models, respectively. The processes considered here ranked by their contribution to the glacial/interglacial rise in pCO2 in decreasing order are: the rise in Southern Ocean vertical mixing rates (>30 ppmv), decreases in alkalinity and carbon inventories (>30 ppmv), the reduction of the biological pump (~20 ppmv), the rise in ocean temperatures (15--20 ppmv), the resumption of ocean circulation (15--20 ppmv), and coral reef growth (<5 ppmv). The regrowth of the terrestrial biosphere, sea level rise and the increase in gas exchange through reduced sea ice cover operate in the opposite direction, decreasing pCO2 during Termination I by ~30 ppmv. According to our model the sequence of events during Termination I might have been the following: a reduction of aeolian iron fertilization in the Southern Ocean together with a breakdown in Southern Ocean stratification, the latter caused by rapid sea ice retreat, trigger the onset of the pCO2 increase. After these events the reduced North Atlantic Deep Water (NADW) formation during the Heinrich 1 event and the subsequent resumption of ocean circulation at the beginning of the B¿lling-Aller¿d warm interval are the main processes determining the atmospheric carbon records in the subsequent time period of Termination I. We further deduce that a complete shutdown of the NADW formation during the Younger Dryas was very unlikely. Changes in ocean temperature and the terrestrial carbon storage are the dominant processes explaining atmospheric δ13C after the B¿lling-Aller¿d warm interval.