Atmospheric carbon dioxide (CO2) measured in Antarctic ice coresshows a natural variability of 80 to 100 ppmv during the last four glacial cycles and variations of approximately 60 ppmv in the two cycles between 410 and 650 kyr BP.We here use dust and the isotopic temperature proxy deuterium (dD) from the EPICA Dome C Antarctic ice core covering the last 740 kyr together with other paleo-climatic records to force the ocean/atmosphere/biosphere box model of the global carbon cycle BICYCLE in a forward mode over this time in order to reconstruct the natural variability of pCO2. Our simulation results covered by our proposed scenario are based on process understanding gained previously for carbon cycle variations during Termination~I. These results match the pCO2 measured in the Vostok ice core well (r^2=0.80) and we predict prior to Termination V significantly smaller amplitudes in \pcoo variations mainly based on a reduced interglacial ocean circulation and reduced interglacial Southern Ocean sea surface temperature. These predictions for the pre-Vostok period match the new pCO2 data from the EPICA Dome C ice core for the time period 410 to 650 kyr BP equally well (r^2=0.79).This is the first forward modelling approach which covers all major processes acting on the global carbon cycle on glacial/interglacial time scales. The contributions of different processes (terrestrial carbon storage, sea ice, sea level, ocean temperature, ocean circulation, CaCO3 chemistry, marine biota) are analysed.