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