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

Stable carbon isotope composition of marine dissolved inorganic carbon (DIC), δ 13 C DIC , 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 δ 13 C DIC 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 valida