Spatiotemporal upscaling of sparse air-sea pCO2 data via physics-informed transfer learning

Global measurements of ocean pCO₂ are critical to monitor and understand changes in the global carbon cycle. However, pCO₂ observations remain sparse as they are mostly collected on opportunistic ship tracks. Several approaches, especially based on direct learning, have been used to upscale and extrapolate sparse point data to dense estimates using globally available input features. However, these estimates tend to exhibit spatially heterogeneous performance. As a result, we propose a physics-informed transfer learning workflow to generate dense pCO₂ estimates that are grounded in real-world measurements and remain physically consistent. The models are initially trained on dense input predictors against pCO₂ estimates from Earth system model simulation, and then fine-tuned to sparse SOCAT observational data. Compared to the benchmark direct learning approach, our transfer learning framework shows major improvements of up to 56-92%. Furthermore, we demonstrate that using models that explicitly account for spatiotemporal structures in the data yield better validation performances by 50-68%. Our strategy thus presents a new monthly global pCO₂ estimate that spans for 35 years between 1982-2017.