Bacastow <1996>, Broecker et al. <1999>, and Archer et al. <2000> have called attention recently to the fact that box models and general circulation models (GCMs) represent the thermal partitioning of CO2 between the warm surface ocean and cold deep ocean in different ways. They attribute these differences to mixing and circulation effects in GCMs that are not resolved in box models. The message that emerges from these studies is that box models have overstated the importance of the ocean's polar regions in the carbon cycle. A reduced role for the polar regions has major implications for the mechanisms put forth to explain glacial - interglacial changes in atmospheric CO2. In parts 1 and 2 of this paper, a new analysis of the ocean's carbon pumps is carried out to examine these findings. This paper, part 1, shows that unresolved mixing and circulation effects in box models are not the main reason for box model-GCM differences. The main factor is very different kinds of restrictions on gas exchange in polar areas. Polar outcrops in GCMs are much smaller than in box models, and they are assumed to be ice covered in an unrealistic way. This finding does not support a reduced role for the ocean's polar regions in the cycling of organic carbon, the subject taken up in part 2.