Product Information

Product Description

The UExP-FNN-U approach is described in detail within Ford et al. (2024a) and therefore we provide a summary of the algorithm for interpolating the fugacity of CO₂ in seawater (fCO_{2 (sw)}). The UExP-FNN-U is a two step neural network interpolation technique, the self-organising map feed forward neural network (SOM-FNN) (Landschützer et al., 2014, 2016). The first step is a self-organising map (SOM) which was used to divide the global oceans into regions, or provinces, of similar oceanic conditions. The inputs to this step were monthly climatology of sea surface temperature (SST) from the European Space Agency Climate Change Initiative (ESA-CCI) SST, merged sea surface salinity (SSS) from the CCI and the CMEMS reanalysis (GLORYS12V1; merged using a hierarchy approach described in Gregor et al., 2024), CMEMS GLORYS12V1 mixed layer dapth (MLD), and spatailly and temporally complete OC-CCI chlorophyll-a (chl-a) (Ford et al. 2026a; Sathyendranath et al. 2019) and the Takahashi et al. (2009) fCO_{2 (sw)} climatology updated in Fay et al. (2024). The SOM produces 16 provinces, and two manual provinces are implemented to cover the Arctic Ocean and Mediterranean + Red Sea using Longhurst biogeochemical provinces (Longhurst, 1998). The second step uses a feed forward neural network (FNN) ensemble (10 members) for each province to estimate the relationships between the target variable (i.e in situ fCO_{2 (sw)} from the recalculated SOCAT dataset; Bakker et al., 2016; Ford et al., 2025; Ford et al. 2026c) and oceanic properties that likely control their variability. For the UExP-FNN-U v2026-pre1 these were SST, SSS, MLD, chl-a and xCO_{2 (atm)} and anomalies of each.

In v2026-pre1, we implemented a probability based SOM approach, which provides a probability that each monthly 1 degree pixel is assigned to each of the 18 provinces. To achieve the probabilities, the SOM training occurs as in Ford et al. (2024a) and then the inputs are perturbed within the limits of their uncertainties and the resulting SOM provinces retrieved for 400 ensembles. The probability that each monhtly 1 degree regions fall within a province are calculated. If a province probability is found to be less than 5%, this is set to 0 % to reduce computation. Locations where the sum of the probability is greater than 1 or less than 1 are scaled linearly to equal 1. In the FNN training stage the provinces are defined for the initial SOM (i.e the hard provinces that the SOM predicts with the data unperturbed). In the mapping stage the fCO_{2 (sw)} and the uncertainties are predicted for each location and province, and a weighted sum of the resulting fCO_{2 (sw)} and uncertainties is taken. This approach was shown to reduce large biases at the edge of provinces and reduced the appearance of provinces in the geographical outputs within a model testbed approach within the Surface Ocean CO₂ mapping intercomparison (SOCOMv2 Experiment 2; Roobaret et al. 2026). Additionally, the global ocean CO₂ sink for v2026-pre1 using the standard SOM approach as in Ford et al. (2024a) compared to this updated probability approach showed only minor differences (~2%). We have used this same probability based apporach in v2026-1.

Expansion to Total Alkalinity using a consistent SOM-FNN

The UExP-FNN-U approach was expanded to estimate Total Alkalinity (TA) on the same monthly 1 degree grid. The first step, the SOM, was trained on a monthly climatology of CCI-SST, CCI+CMEMS SSS and an annual TA climatology (DIVA interpolated in situ TA). Gregor and Gruber (2021) use the gridded GLODAPv2.2016 surface TA field for this step, but these have not been updated in recent years. Therefore, we use a merged in situ TA dataset produced from observations in GLODAPv3 (Lange et al. submitted) , SNAP-O-CO2v2 and Sharkweb datasets to produce a surface TA annual climatology using DIVA interpolation (Schlitzer and Reiner 2025). Data are currently too sparse to produce a monthly climatology of TA (highlighted in Gregor and Gruber; 2021). The SOM produces 16 provinces for the second FNN step, and there were no manual province modifications for TA.

For the FNN step, as described in Gregor and Gruber (2021) the available TA observations are much lower than that for fCO_{2 (sw)}. Gridding the TA observations onto a monthly 1 degree grid before input into the UExP-FNN-U would greatly reduce the available constraints. Consistent to Gregor and Gruber (2021), the individual bottle observations were provided to the neural network (as the target), and the coincident temperature, salinity, and the WOA phosphate and silicate (WOA nutrients extracted from the monthly 1 degree climatology and linear interpolated to the spatial location). This parameter combination was consistent to Gregor and Gruber (2021), and testing indicated from the quality assessment this was the optimal parameter choice.

For the mapping to a monthly 1 degree global grid, the CCI-SST, CCI+CMEMS SSS and WOA phosphate and silicate (for the WOA nutrients monthly climatologies) were used. The selection of CCI-SST and CMEMS SSS ensures that the TA fields are produced to the same SST and SSS as the fCO_{2 (sw)}, and therefore consistency in the carbonate system. In 2026-1 we also use the probability based SOM approach for the TA mapping as descirbed in the fCO_{2 (sw)} section.

Calculation of full surface ocean carbonate system

The remaining components of the carbonate system (i.e DIC, pH etc) were calculated from fCO_{2 (sw)} and TA using pyCO2SYS (v1.8.3.3) (Humphreys et al., 2022, 2024). The calculation also requires SST, SSS, phosphate and silicate, where the same temperature, salinity and nutrient datasets were used (as used in the neural network stages) to consistently calculate the carbonate system. pH was calculated on the total scale. The dissociation constants of Lueker et al. (2000), bisulfate dissociation constants of Dickson (1990) and total boron-salinity relationship of Uppström (1974) were used as recommended in Orr et al. (2015) and Raimondi et al. (2019) (and are the default sets used in pyCO2sys). The surface ocean carbonate system was therefore considered representative of ~0.2 m water depth.

Uncertainties due to the fCO_{2 (sw)}, TA, SST, SSS, phosphate and silicate were propaged through the caluclations providing a uncertainty due to each component and a total uncertainity. In v2026-1, we also add an uncertainty component due to the dissociation constants as provided in Orr et al. (2018). 

Calculation of air-sea CO₂ fluxes

The air-sea CO₂ fluxes (F) were calculated, such that vertical temperature gradients can be accounted for (Dong et al., 2022, 2024; Ford, Shutler, et al., 2024; Shutler et al., 2020; Watson et al., 2020; Woolf et al., 2016, 2019) as described in detail by Woolf et al. (2016), using FluxEngine v4.2.0 (Holding et al., 2019; Shutler et al., 2016). The CO₂ flux takes the form:

F = K₆₀₀ (Sc / 600)^-0.5 (α_subskin fCO_{2(sw, subskin)} – α_skin fCO_2(atm)) (1-ice)

where K₆₀₀ is the gas transfer coefficient estimated using the Nightingale et al. (2000) parameterisation and wind speeds from the CCMP (v3.1) (Mears et al., 2022; Remote Sensing Systems et al., 2022). Sc is the Schmidt number estimated using the calculation in Wanninkhof et al. (2014) and the ocean’s skin temperature. α is the solubility of CO₂ at the respective subskin or skin temperature and salinities which was estimated as in Weiss (1974). fCO_{2 (atm)} and fCO_{2 (sw,subskin)} are the fugacity of CO₂ in the atmosphere and the seawater subskin layer respectively. The CCI-SST and CCI+CMEMS SSS are considered representative of the subskin temperature and salinities and used in the calculation of α_subskin. For the atmospheric side, the ocean’s skin temperature was estimated from the CCI-SST with a cool skin deviation calculated with NOAA-COARE3.6 (Edson et al., 2013; Fairall et al., 1996) using CCMP wind speed, CCI-SST and ERA5 fields as inputs. Skin salinity was calculated assuming a +0.1 psu change from the CCI+CMEMS SSS (i.e a salty skin) as in Watson et al. (2020) and Woolf et al. (2019). fCO_{2 (atm)} was calculated using NOAA-GML atmospheric dry mixing ratio of CO₂ (xCO_{2 (atm)}; Lan et al., 2023), the skin temperature and ERA5 atmospheric pressure following Dickson et al. (2009). Sea ice concentrations from the OSISAF dataset (OSI SAF, 2022) were used for the ice component.

Variables

All variables are provided in a single netCDF file, that has been zipped to reduce file sizes with a filename: Fordetal_UExP-FNN-U_surface-carbonate-system_vXXXX-X.nc. XXXX-X refers to the version number.

Each variable contains an uncertainty estimate that follows the BIPM (2008) principles, comprising of multiple components and then a total uncertainty. We refer the user to the netCDF file for available uncertainties, but in most cases the total uncertainty is the required component.

Acknowledgements and Funding

This dataset has been funded by funding from the European Space Agency under the projects ‘Satellite-based observations of Carbon in the Ocean: Pools, Fluxes and Exchanges’ (SCOPE; 4000142532/23/I-DT) and ‘Ocean Carbon for Climate’ (OC4C; 3-18399/24/I-NB). This dataset was also funded by OceanICU which was funded by the European Union under grant agreement no. 101083922 and UK Research and Innovation (UKRI) under the UK government’s Horizon Europe funding guarantee [grant number 10054454, 1006367, 10064020, 10059241, 10079684, 10059012, 10048179]. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or European Research Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. This dataset also acknowledges the Convex Seascape Survey.

The Surface Ocean CO₂ Atlas (SOCAT) is an international effort, endorsed by the International Ocean Carbon Coordination Project (IOCCP), the Surface Ocean Lower Atmosphere Study (SOLAS) and the Integrated Marine Biosphere Research (IMBeR) program, to deliver a uniformly quality-controlled surface ocean CO₂ database. The many researchers and funding agencies responsible for the collection of data and quality control are thanked for their contributions to SOCAT. We acknowledge The Swedish Agency for Marine and Water Management (HaV) and the Swedish Meteorological and Hydrological Institute (SMHI) for providing access to hydrographic data through the Shark Archive (https://shark.smhi.se/en).

Changelog

Traceable input datasets

Traceable software

References

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