<span>The ocean takes up roughly 25% of anthropogenic CO<sub>2</sub> emissions, yet quantifying the magnitude and variability of this sink is limited by the uneven, sparse sampling of surface-ocean partial pressure of CO₂ (pCO<sub>2</sub>). Here we present FDU-BTR, a global monthly 1° × 1° reconstruction of surface-ocean pCO<sub>2</sub> for 1982–2024, produced with a background–thermal residual (BTR) ensemble learning framework that embeds first-order physical structure in a machine-learning workflow</span> <span>(Wang and Fu, 2026, <a href="https://doi.org/10.5281/zenodo.20152530">https://doi.org/10.5281/zenodo.20152530</a>). Observed pCO<sub>2</sub> is decomposed into a multi-product background climatology, an explicit thermal-anomaly term, and a residual field; region-specific CatBoost ensembles then reconstruct the residual, with boundary blending ensuring spatial continuity. This decomposition simplifies the learning target while preserving physically meaningful constraints. Validated against the independent Hawaii Ocean Time-series (HOT) and Bermuda Atlantic Time-series Study (BATS) observations, FDU-BTR achieves a correlation of 0.93 and a root-mean-square error of 8.34 µatm, comparable to leading products, with a mean total uncertainty of 12.90 µatm. Cross-product comparisons and coverage–entropy diagnostics localize structural disagreement to coastal, marginal, and high-latitude regions where observations are sparse and processes are complex. Controlled thinning experiments further reveal a strong asymmetry in the observational error budget: reducing spatial coverage degrades reconstruction skill approximately twice as much as equivalent reductions in temporal coverage. FDU-BTR therefore provides a physically constrained, uncertainty-quantified pCO<sub>2</sub> product for air–sea CO₂ flux assessment and identifies spatial observational sparsity – not algorithm choice – as the dominant remaining limit on reconstructing the global ocean carbon sink, with direct implications for the design of future ocean carbon observing systems. </span>