The carbonate pump, sometimes called the carbonate counter pump, starts with marine organisms at the ocean's surface producing particulate inorganic carbon (PIC) in the form of calcium carbonate (calcite or aragonite, CaCO). This CaCO is what forms hard body parts like shells.  The formation of these shells increases atmospheric CO due to the production of CaCO in the following reaction with simplified stoichiometry:Coccolithophores, a nearly ubiquitous group of phytoplankton that produce shells of calcium carbonate, are the dominant contributors to the carbonate pump. Due to their abundance, coccolithophores have significant implications on carbonate chemistry, in the surface waters they inhabit and in the ocean below: they provide a large mechanism for the downward transport of CaCO.  The air-sea CO flux induced by a marine biological community can be determined by the rain ratio - the proportion of carbon from calcium carbonate compared to that from organic carbon in particulate matter sinking to the ocean floor, (PIC/POC).  The carbonate pump acts as a negative feedback on CO taken into the ocean by the solubility pump.  It occurs with lesser magnitude than the solubility pump.
The carbonate pump is sometimes referred to as the "hard tissue" component of the biological pump. Some surface marine organisms, like coccolithophores, produce hard structures out of calcium carbonate, a form of particulate inorganic carbon, by fixing bicarbonate. This fixation of DIC is an important part of the oceanic carbon cycle.
:Ca + 2 HCO → CaCO + CO + HO
While the biological carbon pump fixes inorganic carbon (CO) into particulate organic carbon in the form of sugar (CHO), the carbonate pump fixes inorganic bicarbonate and causes a net release of CO. In this way, the carbonate pump could be termed the carbonate counter pump. It works counter to the biological pump by counteracting the CO flux from the biological pump.