SeaFlux: harmonization of air-sea CO 2 fluxes from surface pCO 2 data products using a standardised approach

. Air-sea flux of carbon dioxide (CO 2 ) is a critical component of the global carbon cycle and the climate system with the ocean removing about a quarter of the CO 2 emitted into the atmosphere by human activities over the last decade. A common 20 approach to estimate this net flux of CO 2 across the air-sea interface is the use of surface ocean CO 2 observations and the computation of the flux through a bulk parameterization approach. Yet, the details for how this is done in order to arrive at a global ocean CO 2 uptake estimate vary greatly


Introduction
Surface ocean partial pressure of CO2 (pCO2) observations play a key role in constraining the global ocean carbon sink. This is because variation in surface ocean pCO2, ultimately driven by increases in atmospheric pCO2 levels, is the driving force governing the exchange of CO2 across the air-sea interface, which is commonly described through a bulk formula (Garbe et al. 2014;Wanninkhof 2014): where kw is the gas transfer velocity, sol is the solubility of CO2 in seawater, in units mol m -3 µatm -1 , 0 is the partial pressure of surface ocean CO2 in µatm, and 0 234 in units of µatm represents the partial pressure of atmospheric CO2 in the marine boundary layer. Finally, to account for the seasonal ice cover in high latitudes, the fluxes are weighted by 1 minus the ice fraction (ice), i.e. the open ocean fraction.
With the increasing number of observations of pCO2 available in each new release of the Surface Ocean Carbon Dioxide Atlas (SOCAT; Bakker et al. 2016) and the adoption of various pCO2 mapping techniques, multiple observation-based estimates of the pCO2 field are now publicly available and updated on an annual basis. Despite these advancements, the intercomparison of the products' global and regional flux values is hindered (1) by different areal coverage and (2) by a lack of a consistent approach to calculate the sea-air CO2 flux from pCO2 (Table A1). These differences in flux calculations, specifically differing spatial coverage, complicate comparisons between the products and Global Ocean Biogeochemistry Models (GOBM). In this work, we harmonize these products' flux estimates, specifically addressing three key differences between product methodologies. The resulting flux estimates can then be more directly compared with respect to uncertainty attribution with no source of difference that is not implicit in the mapping method or flux calculation.
The first step addresses the variable spatial coverage of current pCO2 products. Many of the current mapped products only cover roughly 90% of the ocean surface, missing continental shelves and high latitude regions. A newly released global pCO2 climatology product (Landschützer et al. 2020b) includes coverage in the coastal and Arctic regions. We use this climatology to fill any missing areas in each individual product to create consistent full global ocean coverage.
The second methodological step is the choice of flux parameterization, and appropriate scaling of wind speed data. Roobaert et al. (2018) presented uncertainty in air-sea carbon flux induced by various parameterizations of the gas transfer velocity and wind speed data products. Utilizing the MPI-SOMFFN pCO2 product (Landschützer et al. 2020a) and a quadratic parameterization (Wanninkhof 1992;Ho et al. 2006) they find flux estimates that diverge by 12% depending on the choice of wind speed products. Additionally, they find regional discrepancies to be much more pronounced than global differences, specifically highlighting the equatorial Pacific, Southern Ocean, and North Atlantic as regions most impacted by the choice of wind product. Roobaert et al. (2018) stress that to minimize the uncertainties associated with the wind speed product chosen, the global coefficient of gas transfer must be individually calculated for each (Wanninkhof 1992(Wanninkhof , 2014. In this work, we assess the impact of wind speed product choice and scaling on six pCO2 products' calculated air-sea flux estimates. By applying a consistent flux calculation methodology to each pCO2 product, we minimize the methodological divergence of fluxes within the ensemble. Here, we present SeaFlux, a dataset that provides a consistent approach specifically targeting the most commonly used pCO2 data products to deliver an end-product for intercomparisons within assessment studies such as the Global Carbon Budget (Friedlingstein et al. 2020) and the Regional Carbon Cycle Assessment and Processes (RECCAP). The SeaFlux dataset is accompanied by a Python package, called pySeaFlux (https://github.com/lukegre/pySeaFlux), that enables users to calculate fluxes for other configurations, use cases and resolutions. Specifically, by first addressing differences in spatial coverage between the observation-based products we can better present a true global pCO2 estimate for each product. SeaFlux also provides gas transfer velocities calibrated to a consistent 14 C inventory. Further, the data set includes estimates of atmospheric pCO2 and the solubility of CO2 in seawater. Finally, by calculating fluxes using multiple scaled gas transfer velocities for different wind products, we present a methodologically consistent database of air-sea CO2 fluxes calculated from available pCO2 products. SeaFlux is thus an ensemble data product with documented code (pySeaFlux) allowing the community to reproduce consistent flux calculations from various data-based pCO2 reconstructions now and in the future.

Methods
SeaFlux is based on six observation-based pCO2 products and spans the years 1990-2019 (Table 1). These six products include three neural network derived products (CMEMS-FFNN, MPI-SOMFFN, NIES-FNN), a mixed layer scheme product (JENA-MLS), a multiple linear regression (JMA-MLR), and a machine learning ensemble (CSIR-ML6). These products are included as they have been regularly updated to extend their time period and incorporate additional data that comes with each annual release of the SOCAT database.
All of these methods provide three-dimensional fields (latitude, longitude, time) of the sea surface pCO2 and the air-sea CO2 flux. In their original form, each product may utilize different choices for the inputs to Equation 1 (Table A1). While the choices made by each product's creator, listed in Table A1, are not incorrect, by utilizing a uniform methodology in flux calculation, provided by pySeaFlux, the differences in the resulting flux estimate can be attributed to the pCO2 mapping method itself. In this work we recompute the fluxes using the following inputs to the bulk parameterization approach Equation 1: kw is the gas transfer velocity (further discussed in Sect. 2.3), sol is the solubility of CO2 in seawater, in units mol m -3 uatm -1 , calculated using the formulation by Weiss (1974), near-surface EN4 salinity (Good et al. 2013), NOAA Optimum Interpolation Sea Surface Temperature V2 (OISSTv2) (Reynolds et al. 2002), and European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 sea level pressure (Hersbach et al. 2020); ice is the sea ice fraction from NOAA Optimum Interpolation Sea Surface Temperature V2 (OISSTv2) (Reynolds et al. 2002); pCO2 is the partial pressure of oceanic CO2 in µatm for each observation-based product after filling, as discussed in Sect. 2.1, and pCO2 atm is the dry air mixing ratio of atmospheric CO2  (Hersbach et al. 2020) at monthly resolution, and applying the water vapor correction according to Dickson et al. (2007). All of the components of Equation 1 are available in the SeaFlux dataset.
Throughout this study, flux is defined as being positive when CO2 is released from the ocean to the atmosphere and negative when CO2 is absorbed by the ocean from the atmosphere. In the following sections, we discuss the three steps that have the greatest impact on the inconsistencies between flux calculations in the six pCO2 products and the approach that we utilize for the SeaFlux ensemble product.

Step 1: Area filling
Machine learning methods aim to maximize the utility of the existing in situ observations by extrapolation using various proxy variables for processes influencing changes in ocean pCO2. Extrapolation with these independently observed variables is possible due to the nonlinear relationship between pCO2 in the surface ocean and the proxies that drive these changes. However, not all of the proxy variables have complete global ocean coverage for all months; therefore, the resulting pCO2 products are  (Rödenbeck et al. 2013). For this reason, it is not utilized in SeaFlux as a potential product for filling missing areas in the other pCO2 products.
To account for differing area coverage, past studies (Friedlingstein et al. 2019(Friedlingstein et al. , 2020Hauck et al. 2020) have adjusted simply by scaling based on the percent of the total ocean area covered by each observation-based product ( Figure A2). This does not account for the fact that some areas have CO2 flux densities that are higher or lower than the global average and their adjustment would be based on that mean value (Table 1, A comparison of the overlapping regions between the MPI-ULB-SOMFFN and OceanSODA-ETHZ product shows good agreement ( Figure A3). We have confidence moving forward using solely MPI-ULB-SOMFFN for area-filling, as including OceanSODA-ETHZ would not result in substantially different results and would be constrained by its limited Arctic coverage.
For each observationally-based product, we fill missing grid cells with a scaled value based on the global-coverage MPI-ULB-SOMFFN climatology ( Figure 2). The scaling accounts for year-to-year changes in pCO2 in the missing areas (given that the extended MPI-ULB-SOMFFN product is a monthly climatology centered on the year 2006) and is obtained as follows.
To extend the open and coastal merged climatology (MPI-ULB-SOMFFN) to 1990-2019, we calculate a global scaling factor based on the product-based ensemble mean pCO2 for regions that are covered consistently by all six pCO2 products. We first mask all pCO2 products to a common sea mask before taking an ensemble mean (pCO2 ens ). Next, we divide this ensemble mean by the MPI-ULB-SOMFFN climatology (pCO2 clim ) at monthly 1° by 1° resolution (Equation 2). The monthly scaling factor (sfpCO2) is calculated by taking the mean over the spatial dimensions. An alternative method of calculating the scaling factor individually for each pCO2 product yields very similar results; the benefit of the ensemble approach is it allows for the scaling factor to be quickly utilized for any other pCO2 product under development.
The scaling factor calculation can be represented as where DEF G is the one-dimensional scaling factor (time dimension), 0 WXY is the ensemble mean of all pCO2 products at three-dimension, monthly 1° by 1° resolution, 0 Z[\4 is the MPI-ULB-SOMFFN climatology, also at three-dimension but limited to just one climatological year. The x and y indicate that we take the area-weighted average over longitude (x) and Deleted: Shutler et al (2016) report that subtle differences in regional definitions can cause differences of >10% in the calculated net fluxes. Deleted: which latitude (y) resulting in the monthly 1D scaling value. If a product mean is exactly equal to the climatology mean, the scaling factor is 1. The value ranges from 0.91 to 1.06 over the 30-year period. The one-dimensional scaling factor is then multiplied by the MPI-ULB-SOMFFN climatology for each spatial point resulting in a three-dimensional scaled filling map. These values are then used to fill in missing grid cells in each observation-based product.
Globally, the area-filling adjustments result in a difference of less than 17% of the total flux in all products, with the mean adjustment for the six products at 8%. In the Northern Hemisphere, however, the filling process can drive adjustments of up to 32% due to missing coverage in the North Atlantic specifically ( Figure 1, Table 3). As expected, the observationally-based products with more complete spatial coverage tend to have smaller flux adjustments. However, the impact on the final CO2 flux depends on both the DpCO2 and wind speed of the areas being filled (Figures 2-3, Table 1,3). The only product that does not change during this adjustment process is the JENA-MLS mixed layer scheme-based product (Rödenbeck et al. 2013) which is produced with full spatial coverage and therefore needs no spatial filling; any difference between filled/unfilled for this product is due to the ocean mask applied in SeaFlux.
Our approach is not without its own assumptions and limitations. We rely on a single estimate to fill the missing pCO2 given that this is the only publicly available coastal-resolution product currently existing. Nevertheless, the fact that common missing areas along coastal regions and marginal seas are reconstructed using specific coastal observations provides a step forward from the linear-scaling approach currently used by the Global Carbon Budget (Friedlingstein et al. 2019(Friedlingstein et al. , 2020 Figure A2). Furthermore, our scaled filling methodology assumes that pCO2 in the missing ocean regions is increasing at the same rate as the common area of open-ocean pCO2 used to calculate the scaling factor. Research from coastal ocean regions and shelf seas reveal that, in spite of a large spatial heterogeneity, this is a reasonable first-order approximation ).
Any method of artificially filling in missing areas introduces additional uncertainty to the flux estimates. However, this introduced uncertainty is necessary for true global intercomparison efforts. A concern is that the filling method would artificially lower the spread of the products in the SeaFlux ensemble. We do not find this to be the case. The standard deviation of the mean flux for a most conservative mask, which includes only those grid cells with values reported for all six pCO2 products for all months, is nearly identical to the standard deviation of the final version of the SeaFlux product ensemble. This comparison indicates that our filling method does not in fact artificially lower the uncertainty or decrease the spread of the products.  Table A2.

Step 3: Calculation of gas transfer
We employ the quadratic wind speed dependence (Wanninkhof 1992;Ho et al. 2006) and calculate the gas transfer velocity (kw) for each of the wind reanalysis products as where the units of kw are in cm h -1 , Sc is the dimensionless Schmidt number, and 〈 0 〉 denotes the square of average 10-m height winds (m s -1 ), also referred to as the second moment of the wind speed. We choose the quadratic dependence of the gas transfer velocity as it is widely accepted and used in the literature (Wanninkhof 1992;Ho et al. 2006) however we acknowledge that the actual relationship could vary from less than linear (Krakauer et al. 2006) to a cubic (Wanninkhof et al. 1999;Stanley et al. 2009 We calculate the square of the wind speed at the native resolution of each wind product and then average to 1° by 1° monthly resolution (see Table A2). The order of this calculation is important, as variability is lost when resampling data to lower resolutions because of the concavity of the quadratic function. For example, taking the square of time-averaged wind speeds would result in an underestimate of the gas transfer velocity Sweeney et al. 2007). The resulting released from nuclear bomb testing (hence bomb-14 C) in the mid-twentieth century has since been taken up by the ocean. The number of bomb-14 C atoms in the ocean, relative to the pre-bomb 14 C, can thus be used as a constraint on the long-term rate of exchange of carbon between the atmosphere and the ocean. This coefficient, a, is not consistent for each wind product and must thus be individually calculated via a cost function that optimizes the coefficient of gas transfer where parameters are as defined in Equation 3. The units of the coefficient a are (cm h -1 ) (m s -1 ) -2 . In the cost function, a global average of kw is set for which several estimates exist in the literature (ranging from 15.1 cm hr -1 to 18.2 cm hr -1 ), introducing another source of "disharmony" as shown in all wind products reduces the spread of flux estimates, but it does not reduce the uncertainty which remains ~20%. This uncertainty must be accounted for when reporting fluxes (Naegler 2009;Wanninkhof 2014). In this work, we refer to this uncertainty, which is inherent to the formulation and scaling of kw, as intrinsic uncertainty, which we do not try to reduce with SeaFlux and include in our reported uncertainty estimate. However, by correctly scaling kw for each wind product we reduce the disharmony associated with incorrect scaling by up to 9%, depending on which pCO2 and wind reanalysis product are considered. This is consistent with previous results shown by Roobaert et al. (2018Roobaert et al. ( , 2019. Deleted: A probability distribution of wind speed is used to optimize the coefficient of gas transfer based on these observed natural and bomb 14 C invasion rates. This coefficient must be individually calculated and is not consistent for each wind product. Further, the gas transfer velocity used by the different pCO2 mapping products are not scaled to the same bomb-14 C estimate (Table A1). The range of the different bomb-14 C estimates is within the range of the uncertainty from the associated studies (Naegler, 2009), but the choice would introduce inconsistency that is easily addressed here.

Moved (insertion) [1]
Deleted: Global winds from the wind speed products differ and therefore even with the same bomb-14 C observations the scaled coefficient (a) can have a 40% range (Wanninkhof 2014). By determining the optimal a coefficient for each of the reanalysis winds, uncertainty in the global fluxes can be decreased.
Deleted: . Differences in the coefficient will also result from the time period considered and definition of global area and ice fraction applied in the calculation.

Further parameters for flux calculation
The remaining parameters of Equation 1 are the solubility of CO2 in seawater (sol), the atmospheric partial pressure of CO2 (pCO2 atm ), and the area weighting to account for sea ice cover. While the choices of products used for these parameters can also result in differences in flux estimates, the impacts are much smaller as compared with the parameters discussed above.
Atmospheric pCO2 is calculated as the product of surface xCO2 and sea level pressure corrected for the contribution of water vapor pressure. The choice of the sea level pressure product or absence of the water vapor correction can have a small, but not insignificant, impact on the calculated fluxes. Additionally, some products utilize the output of an atmospheric CO2 inversion product (e.g. CarboScope, Rödenbeck et al. 2013; CAMS CO2 inversion, Chevallier, 2013) which can introduce differences in the flux estimate outside of the sources related to a product's surface ocean pCO2 mapping method. Importantly, we do not advocate that our estimate of pCO2 atm is an improvement over other estimates thereof; rather we provide an estimate of pCO2 atm that has few assumptions and leads to a methodologically consistent estimate of DpCO2. We maintain the same philosophy in our estimates of solubility of CO2 in seawater and sea-ice area weighting and therefore we do not elaborate on them here.

SeaFlux air-sea CO2 flux calculation
Following Equation 1, CO2 flux is calculated individually for each of the six observation-based products with three available wind products (CCMPv2, ERA5, JRA55) as discussed in Sect. 2.2 (Table 4). Since we account for spatial coverage differences via our filling method (Sect. 2.1), taking a global mean flux for each of the data products truly follows the definition of "global" for each original product. Figure 4 shows the difference these wind products generate on the resulting global mean flux of the CSIR-ML6 product as one example (other products in Figure A4). The three wind products show very consistent fluxes throughout the time series, however, the importance of appropriate scaling of the coefficient of gas transfer (a) is evident by the significant differences between global mean fluxes calculated with unscaled and scaled a values ( Figure 4, Table 2). It is clear that the impact of applying the appropriate coefficient of gas transfer through proper scaling has a larger impact on the resulting flux time series than solely the choice of wind product.

SeaFlux ensemble flux
By calculating each product's air-sea CO2 flux using consistent inputs described in Section 3.1, we permit for a more accurate comparison of fluxes with the SeaFlux ensemble. Combining all fluxes, we derive a mean flux estimate of -1.97 ± 0.45 PgC yr -1 (Table 4). We discuss the calculation of the uncertainty in the following section. This flux estimate is strengthened by the use of multiple observation-based pCO2 products and wind products which we consider to be independent estimates for the purpose of the uncertainty calculation. These flux values are different from those produced by the observation-based pCO2 Deleted: ¶ This scaling of the gas exchange coefficient (a) for each wind product is an essential, and an inconsistently applied step (Table  A1), that has large implications for air-sea flux estimates (Figure 4). Without individual scaling, and instead utilizing a set value for the gas transfer coefficient (a) regardless of wind product, our results show that calculated global fluxes could be as high as 9% different depending on which pCO2 and wind reanalysis product considered (Roobaert et al. 2018 product's original creator, both spatially and on the mean (Figure 5, A5, Table A1, A3). However, by calculating fluxes in such a consistent manner, we on the one hand gain more confidence in the ensemble mean estimate as it considers representations using a variety of pCO2 reconstructions, gas transfer parametrizations and wind products, and on the other hand, we have a more realistic uncertainty representation than previous estimates based on a single pCO2 reconstruction.

Uncertainty discussion
All flux estimates using such parameterizations are not without significant uncertainties and SeaFlux is no exception. We estimate the uncertainty of the flux estimate to be 0.45 PgC yr -1 . Here, the stated spread represents √ ∑( wind 2 , pco2 2 , kw 2 ) where pco2 (0.19 PgC yr -1 ) is the mean standard deviation over the six filled pCO2 products and wind (0.09 PgC yr -1 ) is the mean standard deviation over the three wind products included in the SeaFlux product. kw 2 (0.39 PgC yr -1 ) is the 20% uncertainty in the gas transfer velocity and associated scaling flux parameterization (Wanninkhof 2014). This last estimate shows that there is significant intrinsic uncertainty inherent to the method of calculation as estimated by Naegler (2009) and Wanninkhof (2014).
Currently, there is only one product available designed to estimate the pCO2 of coastal oceans, the Arctic Ocean and marginal seas. It would be beneficial to likewise have an ensemble of estimates in these regions to better constrain the uncertainty attached to this filling approach. Therefore, while our current analysis shows that the chosen filling method does not itself reduce the spread in the products, we push the community to extend their products to the coastal ocean so as to eliminate the need for this correction in the future.
While the SeaFlux product is unable to further reduce these sources of uncertainty, the strength of the product is that it provides an estimated flux with no source of difference that is not implicit in the mapping method or flux calculation.

Issues not addressed by SeaFlux
While SeaFlux presents one approach to standardize the calculation of air-sea carbon flux, there remain issues that the ocean carbon community is still working towards understanding and incorporating. One such issue has been raised by Watson et al. (2020) who contend that a correction should be applied to in situ pCO2 observations to account for the vertical temperature gradient between the ship water intake depth and the surface skin layer where gas exchange actually takes place. A further correction should be applied when calculating fluxes to account for the "cool skin" effect caused by evaporation (Woolf et al. 2016;Watson et al. 2020). Applying these corrections results in an increasing CO2 sink by up to 0.9 PgC yr −1 . Here, we do not take such adjustments into account for two reasons. Firstly, the skin temperature correction to pCO2 needs to be applied directly to the measurements and not the final interpolated pCO2 from the data products. Hence, it is up to the developers of the SOCAT dataset and the developers of the pCO2 mapping products to decide on the inclusion of this correction. It would then be up to the developers of the data products to update their mapped products. Secondly, the cool skin correction would be equally applied to all methods and would not contribute to the inconsistencies in flux calculation that we are trying to address here. As the ocean carbon community moves towards consensus on such issues, SeaFlux will be updated to include revised protocols.
To compare these estimates of contemporary air-sea net flux (Fnet) from surface ocean pCO2 with estimates of the anthropogenic carbon flux (Fant) from interior data (Mikaloff Fletcher et al. 2006;DeVries 2014;Gruber et al. 2019), or from global ocean biogeochemical models (Friedlingstein et al. 2020;Hauck et al. 2020), it is necessary to account for the outgassing of natural carbon, which was supplied to the ocean by rivers, as well as the non-steady-state behavior of the natural carbon cycle (Hauck et al. 2020). Work is ongoing to quantify the lateral river carbon flux transported into the coastal and open oceans.  2020). Similar to the "cool skin" correction suggested by Watson et al. (2020) discussed above, in this work we have not included these adjustments here as they would not contribute to the inconsistencies between the different products for Fnet itself, which is our focus.

Conclusions
We introduce SeaFlux, a data set that facilitates a standardized approach for flux calculations from observationally-based pCO2 products. Specifically, we address the two largest sources of divergence, namely the differences in spatial coverage between the products, and the scaling of the gas transfer velocity for available wind speed products based on global 14 C-based constraints. The area adjustment is the largest contributor to the methodological discrepancies, resulting in an increase in CO2 uptake of 0-17% relative to the original, possibly incomplete coverage (depending on pCO2 product). The global scaling of the gas transfer velocity can change the CO2 flux on average by 5% relative to non-standardized flux calculations. The impact of applying the appropriate gas exchange coefficient through proper scaling has a larger impact on the resulting flux time series than solely the choice of wind product. By accounting for these sources of differences, the global mean calculated air-sea carbon flux calculated from the six available products is adjusted by up to 21%. The SeaFlux ensemble mean air-sea carbon flux is estimated to be -1.97 +/-0.45 PgC yr -1 with the spread representing 1σ as calculated from the 18 realizations.
This work provides an ensemble data product of the sea-air CO2 flux based on observation-based pCO2 products. This ensemble product is meant to facilitate the use of the pCO2 observation-based ocean flux estimates in assessment studies of the global carbon cycle, such as the Global Carbon Budget or RECCAP-2. Note that the original pCO2 products still offer additional

Moved (insertion) [2]
Deleted: Data Availability Deleted: In addition to enhanced consistency, our area correction and the consistent scaling of gas exchange may help reduce the current carbon budget imbalance (Friedlingstein et al. 2019(Friedlingstein et al. , 2020. Note that the original sea-air CO2 flux information important in other applications, such as coverage over longer time periods, higher spatial or temporal resolution, or runs incorporating further auxiliary data sets or pCO2 data (e.g., SOCCOM float data, Bushinsky et al. 2019).
Along with the ensemble of CO2 flux fields, we also provide a public-use coding package (pySeaFlux) allowing users to apply the presented standardized flux calculations to their own data-based pCO2 reconstructions.

Data and Code Availability
Data (

Author Contributions
ARF and LG designed the experiment and LG developed the model code and performed the simulations with ARF focusing on analysis. ARF and LG collectively prepared the manuscript with contributions from all co-authors.    Tables   Table 1: Global area coverage and mean pCO2 for the six observation-based products. Area coverage listed represents the average annual area covered for 1990-2019 as this value changes monthly for many products ( Figure A1). Change is defined as the filled product -original product (i.e. a negative change implies the original product had a larger global/regional mean pCO2 than the filled product). Global and hemispheric mean pCO2 value for filled/original coverage is included in parentheses below the delta value.     Table 3: Mean air-sea fluxes (PgC yr -1 ), 1990-2019, using the mean of three wind products, calculated for the filled global area and the unfilled native "global" area for each pCO2 product. The northern hemisphere (NH) and southern hemisphere (SH) fluxes (unfilled/filled) are included to highlight the imbalanced regional effect of the spatial filling process.

Product
Global Flux unfilled/filled NH Flux unfilled/filled Table 4: Mean fluxes (PgC yr -1 ) for each observational pCO2 product over the period 1990-2019. Mean flux calculated from filled coverage pCO2 map and scaled gas exchange coefficient; global mean flux is for 3 wind products (CCMP2, ERA5, JRA55) and the average. The time series of the mean flux values for each product (rightmost column) are plotted in Figure 5 Table A3: Mean fluxes, PgC yr -1 , 1990-2019 for each observational pCO2 product. Mean flux calculated from unfilled (filled) coverage pCO2 map and unscaled/scaled coefficient of gas transfer (unscaled = 0.251); calculated for 3 wind products (CCMP2, ERA5, JRA55) with the average shown here. Percent change is calculated as the difference between the unfilled/unscaled and filled/scaled as a fraction of the filled/scaled; does not indicate an error in the product's flux but is a representation of the impact the filling and scaling can have on the end flux estimate. The mean flux as reported in the original pCO2 product is included for comparison ( Figure 5).    (a) and (c) in µatm (red colors correspond to regions in which the pCO2 from ETHZ-OceanSODA is higher than MPI-ULB Merged product). There is good agreement between the products on a regional scale. Figure A4: Air-sea CO2 flux time series (PgC yr -1 ) calculated using five wind speed products (CCMPv2, ERA5, JRA55, NCEP1, NCEP2); scaled (solid) and unscaled (dashed).