A fresh look at the pre-industrial air–sea carbon flux using the alkalinity budget

Abstract. Disparities between observational and model-based estimates of the ocean carbon sink persist, highlighting the need for improved understanding and methodologies to reconcile differences in both magnitude and trends over recent decades. A potential key source of uncertainty lies in the pre-industrial air–sea carbon flux, which is essential for isolating the anthropogenic component from observations. This flux, thought to result globally from an imbalance between riverine discharge and sediment burial of carbon, remains highly uncertain, limiting the confidence in impactful applications such as the Global Carbon Budget (GCB). In this study, we present a new theoretical framework that enables direct estimation of the riverine/burial-driven pre-industrial carbon outgassing using both carbon and alkalinity budgets. This approach is validated with a series of ocean biogeochemical simulations, which also highlight the main factors influencing its regional distribution. We then demonstrate the utility of the framework through two proof-of-concept applications. The first revisits the pre-industrial riverine/burial-driven air–sea carbon flux using existing carbon and alkalinity budgets, offering a simple method for reassessment as these budgets are updated. The second application leverages sensitivity simulations to construct a composite simulated estimate that aligns with both carbon and alkalinity budgets to assess the regional distribution of the pre-industrial riverine/burial-driven air–sea carbon flux. This approach is well suited for model intercomparisons, enabling an efficient reassessment of regional flux patterns and helping to reduce biases related to ocean model physics or biogeochemical parameterizations.