Explicit Physical Knowledge in Machine Learning for Ocean Carbon Flux Reconstruction: The pCO2‐Residual Method

The ocean reduces human impacts on global climate by absorbing and sequestering CO2 from the atmosphere. To quantify global, time‐resolved air‐sea CO2 fluxes, surface ocean pCO2 is needed. A common approach for estimating full‐coverage pCO2 is to train a machine learning algorithm on sparse in situ pCO2 data and associated physical and biogeochemical observations. Though these associated variables have understood relationships to pCO2, it is often unclear how they drive pCO2 outputs. Here, we make two advances that enhance connections between physical understanding and reconstructed pCO2. First, we apply pre‐processing to the pCO2 data to remove the direct effect of temperature. This enhances the biogeochemical/physical component of pCO2 in the target variable and reduces the complexity that the machine learning must disentangle. Second, we demonstrate that the resulting algorithm has physically understandable connections between input data and the output biogeochemical/physical component of pCO2. The final pCO2 reconstruction agrees modestly better with independent data than most other approaches. Uncertainties in the reconstructed pCO2 and impacts on the estimated CO2 fluxes are quantified. Uncertainty in piston velocity drives substantial flux uncertainties in some regions, but does not increase globally integrated estimates of uncertainty in CO2 fluxes from observation‐based products. Our reconstructed CO2 fluxes show larger interannual variability than smoother neural network approaches, but a lesser trend since 2005. We estimate an air‐sea flux of −1.8 PgC/yr (anthropogenic flux of −2.3 ± 0.5 PgC/yr) for 1990–2019, agreeing with other data products and the Global Carbon Budget 2020 (−2.3 ± 0.4 PgC/yr). Plain Language Summary The ocean absorbs carbon dioxide from the atmosphere, moderating the human impact on Earth's climate. To quantify how much carbon dioxide is removed from the atmosphere each year, we must know how much gas is exchanged at each location across the ocean over time. The observations necessary to quantify this gas exchange are very sparse and require gap‐filling in both space and time. Because of the heterogeneity of this gas exchange, complex relationships between the ocean observations with near global coverage and ocean carbon are determined using machine learning algorithms and other statistical techniques. A concern is that these statistical algorithms do not require inputs to be linked to outputs in a manner consistent with oce