Since the onset of the industrial era, humankind has profoundly modified the global carbon (C) cycle. The use of fossil fuels, cement production, and land use change added 700±75 PgC (best estimate ±1σ) to the atmosphere between 1750 and 2019 (Friedlingstein et al., 2020). An estimated 285±5 PgC of this excess C stayed there; the remainder was taken up by the ocean (170±20 PgC) and the land biosphere (230 ± 60 PgC). While the fraction of total CO2 emissions sequestered by the ocean has remained rather stable (22 %-25 %) over the past 6 decades (Friedlingstein et al., 2020), the global ocean sink has varied significantly at interannual timescales (Rödenbeck et al., 2015). Global ocean biogeochemical models (GOBMs) are used within the framework of the annual assessment of the global carbon budget (Friedlingstein et al., 2020) to annually re-estimate the means of and variations in CO2 sinks and sources over the global ocean and major basins. However, these recent model-based estimates need to be benchmarked against observation-based estimates in order to better understand the global carbon budget as well as its yearly re-distribution in the biosphere (Hauck et al., 2020).
In situ measurements of sea surface fugacity of CO2 collected by an international coordinated effort of the ocean observation community and combined into the Surface Ocean CO2 Atlas (SOCAT, https://www.socat.info/, last access: 16 June 2020; Bakker et al., 2016) provide an observational constraint on the assessment of the surface ocean partial pressure of CO2 (pCO2) and the ocean C sinks and sources. Despite an increasing number of observations since the 1990s, data density remains uneven in space and time. While, for instance, data coverage is sparse over the southern basins of the Atlantic and Pacific oceans, observations are seasonally biased towards the summers at high latitudes (Landschützer et al., 2014; Denvil-Sommer et al., 2019; Gregor et al., 2019).
Various data-based approaches have been proposed to infer gridded maps of surface ocean pCO2 from the sparse set of observation-based data. They have been successful in obtaining similarly low misfits between the reconstructed and evaluation data and reasonable estimates of air-sea CO2 fluxes (see Rödenbeck et al., 2015; Gregor et al., 2019; Friedlingstein et al., 2020) although model design and implementation are quite different (e.g. the proportion of SOCAT data used in model fitting and evaluation). Aside from data reconstruction built on a single model mapping pCO2 data with machine learning, classical regression, or mixed-layer schemes (e.g. Rödenbeck et al., 2013; Landschützer et al., 2016; Iida et al., 2021), ensemble-based approaches have recently emerged but with their own concepts and objectives. For example, Denvil-Sommer et al. (2019) designed a two-step reconstruction of pCO2 climatologies and anomalies based on five neural network models and selected the one that reproduced the pCO2 field with the smallest model-data misfit. Gregor et al. (2019) and Gregor and Gruber (2021) introduced machine-learning ensembles with 6 to 16 different two-step clustering-regression models mapping surface pCO2 and suggest that the use of their ensemble mean is better than each member estimate. In a broader context, Rödenbeck et al. (2015) presented an intercomparison of 14 mapping methods targeting the identification of common or distinguishable features of different products in long-term mean, regional, and temporal variations. Hauck et al. (2020) and Friedlingstein et al. (2020) also synthesized pCO2 mapping products and took an ensemble of their observation-based estimates of air-sea CO2 fluxes as a benchmark to compare with the one derived from ocean biogeochemical models.
Despite positive conclusions overall, statistical data reconstructions are still subject to further improvements. In Rödenbeck et al. (2015), Hauck et al. (2020), Bushinsky et al. (2019), and Denvil-Sommer et al. (2021), the authors explain that substantial extensions of surface ocean observational network systems are essential to better determine pCO2 and fluxes at finer scales and reduce mapping uncertainties. So far mapping uncertainties have been estimated by using misfits between the model outputs and SOCAT data (e.g. the root-mean-square deviation, RMSD). By construction, such uncertainty estimates are restricted to oceanic regions and periods when observations are available (Rödenbeck et al., 2015; Lebehot et al., 2019; Gregor et al., 2019), and the uncertainty quantification of an averaged pCO2 or an integrated flux over the space and time of interest is with low confidence due to sparse data density. Also, most of the aforementioned mapping methods target pCO2 data and estimate air-sea fluxes solely over the open ocean, with the coastal data excluded or not fully qualified. In Laruelle et al. (2014), the authors present spatial distributions of air-sea flux density and estimates of the total coastal C sink inferred from spatial integration methods on coastal SOCAT data. Laruelle et al. (2017) adapted the two-step neural network approach described in Landschützer et al. (2016) to the coastal-ocean pCO2. The coastal and open-ocean products were combined into a single reconstruction to yield a global monthly climatology of pCO2 presented in Landschützer et al. (2020). Notwithstanding these advances, a global reconstruction and its uncertainty assessment of monthly varying coastal surface ocean pCO2 and air-sea fluxes are still missing.
In this work, we propose a new inference strategy for reconstructing the monthly pCO2 fields and the contemporary air-sea fluxes over the period 1985-2019 with a spatial resolution of 1∘ × 1∘. It is based on a Monte Carlo approach, an ensemble of 100 neural network models mapping sub-samples drawn from the monthly gridded SOCATv2020 data and available data of predictors. This ensemble approach was developed at the Laboratoire des Sciences du Climat et de l'Environnement (LSCE) as both an extension of and an improvement on the first version (LSCE-FFNN-v1; Denvil-Sommer et al., 2019). In the following sections, we first present the ensemble of neural networks designed with the aims of leaving aside the issue of discrete boundaries in the existing two-step clustering-regressions (see further discussion in Gregor and Gruber, 2021) and reducing the mapping uncertainties induced by the two-step reconstruction of the pCO2 fields (Denvil-Sommer et al., 2019) or by an ensemble-based reconstruction with a small ensemble size. In addition, each feed-forward neural network (FFNN) model follows a leave-p-out cross-validation approach, i.e. the exclusion of p gridded SOCAT data of the reconstructed month itself in model training and validation. This allows us to reduce model over-fitting and to leave many more independent data for model evaluation than in the previous studies. The mean and standard deviation computed from the ensemble of 100 model outputs are defined as estimates of the mean state and uncertainty in the carbon fields. As one of the novel key findings of this study compared to the existing ones, we compute and analyse the estimates of pCO2 and air-sea fluxes, model errors, and model uncertainties for different timescales (e.g. monthly, yearly, and multi-decadal) and spatial scales (e.g. grid cells, sub-basins, and the global ocean). We then suggest the use of an indicator map built on the space-time-varying uncertainty fields instead of model-data misfits for identifying regions that should be prioritized in future observational programmes and model development in order to improve data reconstruction. Last but not least, the model best estimates of and uncertainty in pCO2 and air-sea fluxes are analysed seamlessly over the open ocean to the coastal zone. Potential drivers of the spatio-temporal distribution and the magnitude of open-ocean and coastal CO2 fluxes are discussed with the aim to better identify underlying processes and to detect potential focus regions for further studies on the evolution of oceanic CO2 sources and sinks.
