Efficiency metrics for ocean alkalinity enhancements under responsive and prescribed atmospheric <i>p</i> CO ₂ conditions

Abstract. Ocean alkalinity enhancement (OAE) and direct ocean removal (DOR) are emerging as promising technologies for enacting negative emissions. The long equilibration timescales, potential for premature subduction of surface water parcels, and extensive horizontal transport and dilution of added alkalinity make direct experimental measurement of induced CO2 uptake challenging. Therefore, the challenge of measurement, reporting, and verification (MRV) will rely to a great extent on general circulation models, parameterized and constrained by experimental measurements. A number of recent studies have assessed the efficiency of OAE using different model setups and different metrics. Some models use prescribed atmospheric CO2 levels, while others use fully coupled Earth system models. The former ignores atmospheric feedback effects, while the latter explicitly models them. In this paper it is shown that, even for very small OAE deployments, which do not substantially change atmospheric pCO2, the change in oceanic CO2 inventories differs significantly between these methods due to atmospheric feedback causing some ocean CO2 off-gassing. An analogous off-gassing occurs during direct air capture (DAC). Due to these feedback effects, care must be taken to compute the correct metrics when assessing OAE efficiency with respect to determining negative emissions credits, as opposed to determining the effect on global temperatures. This paper examines the commonly used metrics of OAE efficiency, their exact physical meanings, the assumptions inherent in their use, and the relationship between them. It is shown that the efficiency metric η(t), used in prescribed pCO2atm simulations, equals the equivalent schedule of a gradual DAC removal and storage in a fully coupled system.