Linearized Carbonate Chemistry for Efficient Modeling of Ocean-Based Carbon Dioxide Removal

Ocean-based carbon dioxide removal (CDR) relies on ocean models for measurement, reporting, and verification (MRV), because induced CO₂ uptake spans basin scales and decades. Explicit calculations with coupled physics–biogeochemistry models are computationally expensive, because biogeochemical models carry many tracers and each CDR intervention must be simulated separately. We introduce a CDR tracer method that represents each direct ocean removal (DOR) intervention by one passive tracer and each ocean alkalinity enhancement (OAE) intervention by two. Air–sea gas exchange is linearized using precomputed carbonate sensitivities, so that many interventions can be simulated in a single integration without a biogeochemical model. We evaluate the method against 24 explicit calculations with a 12 km ROMS configuration coupled to the Marine Biogeochemistry Library (MARBL), and reproduce all 1,380 explicit 1° CESM/MARBL calculations of existing DOR and OAE efficiency atlases in two CESM integrations. The CDR tracer method is 13.5–28× faster than explicit calculations. Its relative errors in CDR efficiency, predominantly positive owing to the linearization, peak shortly after intervention and then decay to less than 1% within a few years. In ROMS, peak errors reach 2–8% for extreme interventions but stay below 1% for plausible ones; in CESM, they average 3.5 ± 2%. Larger local errors, including in pH estimates, arise only where extreme interventions accumulate in semi-enclosed passages. The computational savings enable large ensembles across deployment scenarios and ocean models. Combined with the option to use carbonate sensitivities from different biogeochemical models or observation-based products, these ensembles support uncertainty quantification for MRV.