Strengths and weaknesses of three Machine Learning methods for pCO₂ interpolation

Abstract. Using the Large Enemble Testbed, a collection of 100 members from four independent Earth system models, we test three general-purpose Machine Learning (ML) approaches to understand their strengths and weaknesses in statistically reconstructing full-coverage surface ocean pCO₂ from sparse in situ data. To apply the Testbed, we sample the full-field model pCO₂ as real-world pCO₂ collected from 1982–2016 for each ensemble member. We then use ML approaches to reconstruct the full-field and compare with the original model full-field pCO₂ to assess reconstruction skill. We use feed forward neural network (NN), XGBoost (XGB), and random forest (RF) approaches to perform the reconstructions. Our baseline is the NN, since this approach has previously been shown to be a successful method for pCO₂ reconstruction. The XGB and RF allow us to test tree-based approaches. We perform comparisons to a test set, which consists of 20% of the real-world sampled data that are withheld from training. Statistical comparisons with this test set are equivalent to that which could be derived using real-world data. Unique to the Testbed is that it allows for comparison to all the "unseen" points to which the ML algorithms extrapolate. When compared to the test set, XGB and RF both perform better than NN based on a suite of regression metrics. However, when compared to the unseen data, degradation of performance is large with XGB and even larger with RF. Degradation is comparatively small with NN, indicating a greater ability to generalize. Despite its larger degradation, in the final comparison to unseen data, XGB slightly outperforms NN and greatly outperforms RF, with lowest mean bias and more consistent performance across Testbed members. All three approaches perform best in the open ocean and for seasonal variability, but performance drops off at longer time scales and in regions of low sampling, such as the Southern Ocean and coastal zones. For decadal variability, all methods overestimate the amplitude of variability and have moderate skill in reconstruction of phase. For this timescale, the greater ability of the NN to generalize allows it to slightly outperform XGB. Taking into account all comparisons, we find XGB to be best able to reconstruct surface ocean pCO₂ from the limited available data.