A Novel Back-Calculation Approach to Estimate Ocean Anthropogenic Carbon Using Carbon-Based Data and a Total Matrix Intercomparison Method

Abstract

Over the last decades, back-calculation (BC) techniques for ocean anthropogenic carbon (C_ant) estimation have improved and evolved into different methodologies that are not exempt from various assumptions and limitations. No single optimal BC method exists to date for computing C_ant; therefore, it is necessary to continue advancing the broad range of approaches. Here, we present a novel method based on the BC fundamentals that combines marine-carbonate-system (MCS) data and the Total Matrix Intercomparison (TMI) framework. This MCS-TMI approach differs from other BC methods by using the TMI to reconstruct deep-ocean biogeochemical properties and their preformed conditions. It also incorporates a global sea-air oxygen disequilibrium term, and a dynamic stoichiometric carbon-to-oxygen ratio that depends on the water-mass ideal time. The MCS-TMI yields a total C_ant inventory of 124 ± 7 Pg C (referred to 1995), in good agreement with previous global C_ant climatologies. The MCS-TMI method uncertainty (±5.6 μmol kg⁻¹) is controlled by input-data errors that, nonetheless, have a minimal impact on the total C_ant inventory. In contrast, our total C_ant inventory uncertainty is governed by methodological errors, specifically those related to the TMI's boundary conditions. Our study demonstrates the effectiveness of MCS data-based climatologies in reconstructing a 3D gridded C_ant climatology, and the validity of ocean circulation transport operators for obtaining BC preformed conditions.