Climate changes affect the ocean's biological carbon pumps by modifying the sources of macro- and micro-nutrients to the euphotic zone, cloud cover, surface alkalinity, and phytoplankton assemblages. We use a global model of coupled oceanic cycles of carbon, phosphorus and iron to investigate controls on global productivity and the ocean carbon cycle. We use the adjoint of the model to comprehensively and efficiently map the sensitivity of biological productivity and air-sea carbon fluxes to decadal perturbations in the external sources of iron and photosynthetically active radiation (PAR), the availability of phosphate, and the relative export of particulate organic and particulate inorganic carbon (rain ratio). Productivity and air-sea carbon flux in the high nitrate, low chlorophyll regions are most sensitive to perturbations in the iron source while the Atlantic ocean is most sensitive to additional sources of phosphorus and the high latitudes are most sensitive to perturbations in PAR. Air-sea carbon fluxes are most sensitive to variations of the rain-ratio in the equatorial oceans.