Reconstruction of <i>δ</i> ¹³ C _DIC in the Atlantic Ocean: a probabilistic machine learning approach for filling historical data gaps

Abstract. Stable carbon isotope composition of marine dissolved inorganic carbon (DIC), δ13CDIC, is a valuable tracer for oceanic carbon cycling. However, its observational coverage remains much sparser than that of DIC and other physical or biogeochemical variables, limiting its full potential. Here, we reconstruct δ13CDIC in the Atlantic Ocean using a probabilistic machine learning framework, Gaussian Process Regression (GPR). We compiled data from 51 historical cruises, including a high-resolution 2023 A16N transect, and applied secondary quality control via crossover analysis, retaining 37 cruises for model training, validation, and testing. The trained GPR model achieved an average bias of −0.007 ± 0.082 ‰ and an overall uncertainty of 0.11 ‰, arising from measurement (0.07 ‰), mapping (0.08 ‰), and input-variable (0.009 ‰) errors. To address validation limitations related to sparse observations, we further supplemented this work with numerical model-based validation (Claret et al., 2021), confirming the GPR model's robustness in δ13CDIC reconstruction. Using the GLODAPv2.2023 Atlantic dataset as predictors, the reconstruction expanded the number of acceptable δ13CDIC samples by a factor of 7.65, from 8941 to 68 435 across the Atlantic basins. The resulting dataset markedly improves the spatial resolution in longitude, latitude, and depth, and provides enhanced temporal continuity over the past four decades, offering great advantages in decadal trend assessment. Compared to the sparse original measurements, the reconstruction also reduces spatial discontinuities and reveals finer vertical structures consistent with other high-resolution biogeochemical observations. Additionally, the validated GPR framework was applied to the GLODAPv2 1° × 1° global interior ocean mapped climatology (Lauvset et al., 2016), producing a climatological gridded 3D δ13CDIC dataset for the Atlantic Ocean. These reconstructed δ13CDIC datasets provide new opportunities to resolve regional carbon cycle dynamics, validate Earth system models, refine estimates of oceanic carbon uptake on at least decadal timescales, and extend climate reanalysis records. The reconstructed δ13CDIC data, quality-controlled observational data from 51 cruises, and gridded δ13CDIC product are available at https://doi.org/10.5281/zenodo.18481145 (Gao et al., 2025).