We develop and test a theory for the relationship of atmospheric p CO2 and the solubility pump of CO2 in an abiotic ocean. The solubility pump depends on the hydrographic structure of the ocean and the degree of saturation of the waters. The depth of thermocline sets the relative volume of warm and cold waters, which sets the mean solubility of CO2 in the ocean. The degree of saturation depends on the surface residence time of the waters. We develop a theory describing how atmospheric CO2 varies with diapycnal diffusivity and wind stress in a simple, coupled atmosphere-ocean carbon cycle, which builds on established thermocline theory. We consider two limit cases for thermocline circulation: the diffusive thermocline and the ventilated thermocline. In the limit of a purely diffusive thermocline (no wind-driven gyres), atmospheric pCO2 increases in proportion to the depth of thermocline which scales as κ1/3, where κ is the diapycnal mixing rate coefficient. In the wind-driven, ventilated thermocline limit, the ventilated thermocline theory suggests the thickness of the thermocline varies as wek1/2. Moreover, surface residence times are shorter, and subducted waters are undersaturated. The degree of undersaturation is proportional to the Ekman pumping rate, wek, for moderate amplitudes of wek. Hence, atmospheric pCO2 varies as wek3/2 for moderate ranges of surface wind stress. Numerical experiments with an ocean circulation and abiotic carbon cycle model confirm these limit case scalings and illustrate their combined effect. The numerical experiments suggest that plausible variations in the wind forcing and diapycnal diffusivity could lead to changes in atmospheric pCO2 of as much as 30 ppmv. The deep ocean carbon reservoir is insensitive to changes in the wind, due to compensation between the degree of saturation and the equilibrium carbon concentration. Consequently, the sensitivity of atmospheric pCO2 to wind-stress forcing is dominated by the changes in the upper ocean, in direct contrast to the sensitivity to surface properties, such as temperature and alkalinity, which is controlled by the deep ocean reservoir.