Our analysis is based on two recently published sea surface pCO2 data products. The first one, updated from , covers broadly the open ocean at a distance of 1∘ off the coast, and the second dataset, by , covers the coastal domain plus the adjacent open ocean up until 400 km away from the shoreline for a total surface area of 70×106 km2. Both datasets are based on the same neural network interpolation method, i.e., the SOM-FFN (Self Organizing Map – Feed Forward Neural Network) method . While the individual datasets (from here onward “NNopen” for the open-ocean dataset and “NNcoast” for the coastal-ocean dataset) have been extensively described and validated in their individual publications , we present here a short summary of each product including their most recent updates and the procedure used to merge both datasets.

The SOM-FFN method consists of a two-step interpolation approach. First, a marine region (i.e., either open ocean or coastal ocean) is divided into biogeochemical provinces based on similarities within selected environmental CO2 driver data. These provinces are illustrated in and . Secondly, the nonlinear relationship between a second set of driver data and available sea surface pCO2 data from the gridded SOCAT database is established and can then be used to fill gaps where no observations exist see. The gridded SOCAT data consist of measurements that received a quality flag of D and lower, illustrating a measurement uncertainty within 5 µatm. Both open- and coastal-ocean applications rely on satellite and reanalysis data, but different sets of environmental driver variables are used. For the open-ocean analysis, sea surface temperature, salinity, mixed layer depth, chlorophyll a and atmospheric CO2 are used as proxy variables.

While leaving NNcoast unchanged to its original publication , we here provide two updates to NNopen compared to its previous publications see. Firstly, we replaced the mixed layer depth proxy of the NNopen from to the MIMOC product as it allows us to expand our analysis region, creating a maximum overlap area between NNopen with NNcoast. We tested the impact of this change and found that SOCAT observations are reconstructed bias free with a root mean squared error of less than 20 µatm similar to . Secondly, for completeness, we also include the Arctic Ocean in NNopen, allowing the comparison between products to be extended to the high latitudes. In order to achieve this, the Arctic Ocean was assigned its own stand-alone oceanic biome in the SOM procedure see. Previous global-scale studies avoided the Arctic Ocean , however more recent studies by illustrate that the increase in measurements makes a reconstruction feasible. Due to its uniqueness in its seawater properties, we find that assigning the Arctic Ocean a stand-alone biome, which is not varying in time, provides the best reconstruction. This way, the Arctic pCO2 is only determined by Arctic Ocean measurements (starting at 79∘ N in the Atlantic Ocean), while Arctic Ocean measurements do not influence other biomes. Hence, the remainder of the global ocean remains unchanged by this addition, and the pCO2 product is thus considered the same as the one presented in .

The NNopen and NNcoast are all available at the same monthly temporal resolution but are applied at different spatial resolutions. While NNopen uses a 1∘×1∘ resolution, the coastal pCO2 data product is constructed at a higher 0.25∘×0.25∘ resolution to better capture the spatial heterogeneity of the coastal zone. Thus, in order to combine and compare the products at the same spatial resolution, we divided each 1∘×1∘ grid cell of the open ocean into 16 equal 0.25∘×0.25∘ bins. NNcoast combines observations from 1998 through 2015 using SOCATv4, whereas NNopen uses SOCATv5 data from 1982 through 2016. In this study, we constructed a climatological mean for the common period covered by both products (1998–2015). Despite the use of different versions of the SOCAT database used to generate the two pCO2 products (SOCATv4 vs SOCATv5), we expect little influence on our results, since most of the new data introduced into SOCATv5 compared to SOCATv4 were added in the later years and, in particular, 2016, which is excluded from our analysis. Figure 1 illustrates the temporal mean of all available pCO2 observations extracted from the SOCATv5 dataset for the 1998–2015 period.

Figure 2 shows the climatological mean pCO2 for both NNopen and NNcoast . The data products rely on sea masks that lead to a common overlap area at the coastal–open-ocean transition of roughly 42×106  km2, reflecting the lack of a commonly recognized definition of the boundary between both environments. While the landward limit of the NNopen is located at 1∘ (and therefore varies in  km depending on the geographical position) offshore, NNcoast extends from the coastline to either 400 km offshore or the 1000 m isobath, whichever is encountered first. The bathymetry used follows the SOCAT coastal definition and excludes estuaries and inner water bodies . This overlap area is the subject of our error analysis described below.

The combination of the two data products takes place in three steps, which are illustrated in Fig. 3. In a first step, we divide the globe into a raster of coarse 30∘×30∘ boxes starting at 90∘ N and 180∘ W. The large box size ensures that, even in remote regions, observations from both open ocean and coastal ocean are represented in the overlap area. We then investigate the overlap area for each raster box individually. In a second step, within each 30∘×30∘ box, the pixels that are only covered by either NNopen or NNcoast are assigned their respective pCO2 value. In a third step, all pixels where open-ocean and coastal-ocean pCO2 products overlap, that is, all 0.25∘×0.25∘ pixels with co-located pCO2 values in the open-ocean and coastal-ocean datasets, are identified. To assign a pCO2 value in this overlap area, we weight the open and coastal pCO2 estimates by their standard error relative to the SOCATv5 open and SOCATv5 coastal-ocean datasets, respectively. We calculate the standard error at the scale of each 30∘×30∘ raster, as in these larger-scale regions enough observations are available to provide an error statistic. To implement this scheme, we first calculate the standard error on each 30∘×30∘ box as 1σi=RMSEiNi, where RMSE is the root mean square error of the open and coastal datasets with respect to the SOCATv5 gridded observations, N is the number of available gridded data from SOCATv5 available in a given 30∘×30∘ raster box, and the subscript i refers to either NNopen or NNcoast, respectively. Since we have simply divided the open ocean from a 1∘×1∘ grid into 16 equal 0.25∘×0.25∘ bins, we use an effective number of Neff=N/16 for the open ocean. We do not account for autocorrelation in our calculations since we are only interested in the difference between the standard errors and assume autocorrelation lengths of similar magnitude between the SOCATv5 gridded datasets located in the coastal-ocean and open-ocean domains, respectively. Next we calculate the total error for each 30∘×30∘ degree raster region r: 2σr=σr,o+σr,c. We also calculate the scale, for each grid cell in the overlap area, the weight given to the open-ocean and coastal-ocean local pCO2 value by the standard error of each raster region: 3pCO2,overlap=1-σr,oσr⋅pCO2,o+1-σr,cσr⋅pCO2,c.

Substantial differences exist between the mean difference and standard deviations of NNopen and NNcoast and the respective measurements from the SOCAT database within each 30∘×30∘ degree raster. Figure 4 illustrates these differences. While both NNopen and NNcoast have a near 0 bias for the mean difference, some rasters show differences exceeding 15 µatm. While more variability appears in NNcoast, this can largely be explained by the overall smaller number of gridded measurements. The larger number of gridded measurements in NNopen is a result from the division of the 1∘×1∘ cells into 16 quarter degree boxes. Therefore, we reduce the number of effective degrees of freedom for the open ocean by 16. To generate the final merged product we perform an additional smoothing using a 8×8 grid point running mean filter (roughly 200 km by 200 km at the Equator).

The long term mean pCO2 field at 0.25∘ resolution for NNopen and NNcoast is shown in Fig. 5. In most oceanic regions, the transition from open to coastal ocean occurs without steep gradients, particularly in the subtropics (∼20–50∘ N) of the Northern Hemisphere. However, exceptions exist in the tropics like the Peruvian upwelling system, the Namibian–Angolan coast in the South Atlantic, and off Somalia and the Arabian Peninsula. Moreover, abrupt spatial gradients in pCO2 have been observed in large river plumes such as that of the Amazon or on continental shelves influenced by large rivers. The identification of such gradients, however, results only from a first order visual inspection between the two products. In what follows, we perform a quantitative analysis of the merging procedure and of the resulting pCO2 fields in the overlap area.

Figure 6 reports the absolute pCO2 difference in % between NNcoast and NNopen along the common overlap area relative to the mean partial pressure of the merged climatology. Figure 6 shows a clear latitudinal pattern with the lowest difference in the low and subtropical latitudes and the largest differences in the high latitudes, especially in the Northern Hemisphere. We find in particular, that discrepancies are large in the newly added Arctic Ocean, but also in other seasonally ice-covered areas that have been previously described in NNopen and NNcoast publications (e.g., the Labrador Sea). One significant contributor to this difference might be that NNcoast uses information about sea ice in reconstructing the surface ocean pCO2. Acknowledging this discrepancy in seasonally ice-covered regions, we further focus our error analysis and products comparison on ice-free areas, based on the sea-ice product of . There are some exceptions to this general latitudinal trend consistent with our first qualitative inspection, such as along the Pacific coastline of South America, the African coast in the South Atlantic and the Arabian Sea, i.e., the regions with steep gradients already identified above. Furthermore, a gradient of decreasing pCO2 from the coast to the open ocean has been reported over the continental shelves of the eastern US and Brazil and may exist in other regions as a consequence of the influence of rivers oversaturated in CO2 combined with a limited estuarine filter . It is thus possible that the pCO2 predicted by the coastal SOM-FFN is slightly skewed towards higher values in some regions because of the presence of overall higher pCO2 observations in the calibration data pool. While there is no clear basin-wide bias structure, systematic differences can be found regionally such as in the southeastern Pacific Ocean and the Southern Ocean (south of 35∘ S). Overall, the largest relative differences are located in the overlap areas of the Arctic Ocean.

In spite of clear regional discrepancies, the mean difference, that is to say the bias, between the two estimates in the overlap area remains close to 0 µatm when integrated globally (Table 1), whether or not the comparison is limited to the locations where observations exist (Table 1 columns 1–3). Furthermore, the mismatch between the two products is in the range of the mismatch between the individual products and the available observations in SOCATv5. This result is a consequence of the neural network-based interpolation applied here at the global scale. In particular, the SOM-FFN is designed to minimize the mean squared error between available observations and the network output over the entire domain of application.

The global RMSE between NNopen and NNcoast as well as the SOCAT observations within the overlap area is in the range of previously reported global values by and . In general, the spread between open-ocean and continental-coastal pCO2 varies more than the spread between coastal estimates and SOCAT or between open estimates and SOCAT, possibly indicating that the SOM-FFN method is having difficulties generalizing the pCO2 in the coastal–open-ocean continuum.

A more detailed analysis is performed on the overlap of several regions selected to encompass a wide variety of conditions. These regions, indicated in Fig. 5, include three areas characterized by strong upwelling and offshore transport (Peruvian upwelling system, Canary upwelling system, US west coast) but contrasted data coverage, two data-rich regions (Sea of Japan, US east coast) of which one comprises a marginal sea (Sea of Japan), one region where seasonal data are scarce (west coast of Australia), and a region characterized by strong river outflow (Amazon river plume).

In order to further investigate the role of existing observations in upwelling regions, we first focus on the Canary upwelling system and the Peruvian upwelling system. These two regions are part of the eastern boundary upwelling systems and subject to many ecosystem stressors, such as ocean acidification or deoxygenation . Therefore, monitoring the full aquatic continuum is essential in these regions. Both are characterized by strong upwelling and significant offshore transport of carbon-rich water from depth see, e.g., resulting in elevated pCO2 levels exceeding atmospheric levels at the sea surface. Such values are consistent with observations in the Canary upwelling system (Fig. 7) extracted from either the open-ocean SOCAT dataset (, Fig. 7b) or the coastal SOCAT dataset (, Fig. 7c) and, consequently, the merged pCO2 product (Fig. 7a). Furthermore, the Canary upwelling system is well covered by both open-ocean and coastal-ocean observations. As a consequence – despite a few areas with larger differences – the overall mismatch between the coastal ocean and NNopen (Fig. 7d) is in the range of their relative mismatch towards the observations (see Fig. 7e–f) and generally within 10 µatm.

In contrast to the Canary upwelling system, the Peruvian upwelling system shows a steep pCO2 gradient between the offshore and nearshore regions (Fig. 8a), particularly just south of the Equator. A closer inspection of the available observations (Fig. 8b and c) reveals that, particularly in the nearshore domain at the Equator, several of the few available observations of the sea surface pCO2 indicate low partial pressures resulting in a low reconstructed coastal pCO2, as already identified by . The mismatch that results from the upscaling of the low pCO2 data in the coastal domain is further reflected in the difference between the coastal- and open-ocean pCO2 fields in the overlap area (Fig. 8d). The mismatch between the open ocean and NNcoast exceeds 30 µatm and is larger than the difference between the individual products and the observations (Fig. 8e–f), suggesting that the disagreement between the open ocean and NNcoast in the overlap area stems from their data treatment. The fewer existing coastal observations of low pCO2 are extrapolated in space, spreading a potential mismatch over a larger area. Likewise, the nearshore domain in the NNopen is influenced by the high CO2 partial pressures offshore. This data sparsity and spatial heterogeneity is a further challenge for model evaluation .

No steep pCO2 gradient can be identified along the west coast of Australia in the merged product (Fig. 9). The highest CO2 partial pressures are found nearshore along the Leeuwin current , and the lowest observed pCO2 can be found along the West Australian Current. The area is spatially covered both in the open- and coastal-ocean SOCAT datasets (Fig. 9b and c), and therefore the overall difference towards observed values remains among the smallest of all investigated regions. This is remarkable given the lack of seasonal observations, which will be discussed in the subsequent section. NNopen and NNcoast agree with each other spatially within 15 µatm (Fig. 9d), which is in the range of the mismatch between the individual products and the respective SOCAT observations (Fig. 9e–f). Both products tend to overestimate the low pCO2 towards the south of the domain. This is reflected in the positive mismatch towards the SOCAT observations (Fig. 9e and f) in the common overlap area where, the difference between the neural network estimates and the raw data exceeds 15 µatm for both products.

Observations in the Sea of Japan and adjacent Pacific Ocean suggest large variability in the pCO2 with the lowest observed values just north of the Korean Peninsula and the highest observed pCO2 in the Yellow Sea (Fig. 10b–c). Furthermore, low pCO2 is also observed south of the island of Hokkaido. These large spatial variations in the pCO2 are also visible in the merged pCO2 product (Fig. 10a). A notable exception is the Korean Straight, where observations suggest a lower pCO2 than reconstructed. The strong variability in the observed pCO2 reflects the complex carbon dynamics in the Sea of Japan , which is also reflected in the larger mismatch between products and towards the SOCAT observations (Fig. 10d–f). The disagreement may indicate that the global-scale NNopen and NNcoast products are not particularly skilled in representing the strong regional dynamics of marginal sea. A better agreement between the neural network reconstructions and observations is found in the Pacific Ocean east of the Japanese islands, where the merged estimate also reveals a better agreement between NNopen and NNcoast (Fig. 10d) and low biases in the range of 5 µatm towards SOCAT observations (Fig. 10e and f).

Some of the best monitored regions spanning both coastal and nearshore open ocean can be found along the US coast . Indeed all 1×1∘ open ocean and almost all 0.25∘×0.25∘ coastal pixels are filled with raw observations off the eastern US coastline. While the mean of all observed pCO2 values from SOCAT (Fig. 11b and c) suggests substantial regional variability, the merged estimate (Fig. 11a) is, as a result of the neural network interpolation algorithm, substantially smoother. In particular, the lower latitudes (25–35∘ N, Fig. 11e and f) are well reconstructed by the neural network algorithms in both open- and coastal-ocean domains. Larger discrepancies however exist in the higher latitudes (35–45∘ N, Fig. 11e and f). attributed a larger mismatch to the complex biogeochemical dynamics of the Gulf Stream region, where the measured pCO2 is underestimated by both the open and coastal products. The strong mesoscale dynamics and the influence of the cold Labrador current in this region are not well represented in the rather coarse 0.25∘ NNcoast and 1∘ NNopen products. The smooth transition between coastal and open ocean in Fig. 11a indeed suggests that the intensively surveyed US east coast aquatic continuum can be well reconstructed by combining the open-ocean and coastal-ocean pCO2 datasets.

Similarly well monitored to the US east coast is the US west coast upwelling system, not the least because its variability is tightly linked to El Niño–Southern Oscillation (ENSO) see, e.g.,. Here, we find an overall good agreement between NNcoast and NNopen. The agreement in the overlap area of the merged product (Fig. 12d) is among the best reported globally. Interestingly, nearshore, the merged estimate (Fig. 12a) reveals a lower mean pCO2 than suggested from both the open-ocean and coastal-ocean SOCAT datasets (Fig. 12b and c). The small error compared to the SOCAT observations suggests that this is not the result of the two products being in disagreement but might relate to changes in upwelling as a result of interannual variability linked to ENSO events that are not well captured by the merged product.

Finally, we investigate the spatial structure of the reconstructed pCO2 from a region typically dominated by the freshwater outflow of a large river mouth, i.e., the Amazon outflow in the tropical Atlantic Ocean (Fig. 13). Studies linking circulation with the local CO2 dynamics are sparse . Very few observations exist, particularly in the nearshore region (Fig. 13b–c). Nevertheless, studies suggest that the Amazon river outflow becomes a significant CO2 sink when it mixes with ocean waters . The strong variance in observed pCO2 provides a challenge for any algorithm to reconstruct the full pCO2 field in such a region. Nevertheless, both coastal and oceanic data products are in good agreement (Fig. 13d) with the exception of the area under direct influence of Amazon river outflow. This difference potentially stems from the NNopen being unable to associate the pCO2 variability observed in this area with the strong salinity gradients, which is better represented in the coastal-ocean pCO2 product. Both products show differences of similar magnitude when compared to the SOCAT observations (Fig. 13e–f) and similar error structures as both products overestimate the pCO2 in the northern and underestimate the pCO2 in the southern sections of the overlap area.

While global errors between the data products and observations remain low (see Table 1), Figs. 7–13 show that, at the regional scale, larger differences emerge. We therefore expend our standard error statistics as presented in Table 2 for the selected regions. Overall, we find at the regional level that the inter-product mismatch, represented by the bias, is substantially larger than in the global analysis but does not exceed ∼8 µatm with one prominent exception: the Peruvian upwelling system where the mismatch reaches 14.8 µatm. Here, the substantial disagreement between the two products results from the underestimation of the coastal observations in the overlap domain by the coastal-ocean pCO2 product already shown by .

We find that the bias between NNopen and NNcoast in the overlap area is larger where they are not co-located to observations (Table 2). The error spread between NNopen and NNcoast, represented by the RMSE, is likewise larger in areas where fewer observations exist (contrast column 1 and 2 in Table 2). Exceptions include the US east coast and the west coast of Australia possibly linked to the larger mismatch of the individual products towards the respective SOCAT observations at these locations. Results from both products in the Amazon outflow region, in the US east coast for NNcoast and in the west coast of Australia for NNopen, show a larger bias towards the SOCAT observations than the respective inter-model bias, illustrating that both methods generalize well. This further suggests that the estimates are locally constrained by information outside the investigated domain, which is possible considering the spatial distributions of the biogeochemical provinces generated by the SOM.

A further analysis in the selected regions aims to investigate the seasonal differences in pCO2 between the original data products, the merged product and observations (Fig. 14). In particular, we investigate the extent to which the mean biases reported above can be explained by seasonal differences in pCO2 among the different products. To this end, we average all months from 1998 through 2015 to create a seasonal climatology from our pCO2 products, without correction to a nominal reference year. We repeat this procedure for the SOCAT datasets, likewise without any corrections but being aware that this could lead to a sampling bias in the observed climatology. This approach is justified because we lack knowledge about the short-term variability in the observed carbon cycle, and it is thus unclear on how such a correction would improve the representation of the observed pCO2 field.

In spite of the lack of seasonal sampling bias corrections, our analysis displays, for most regions, a close correspondence within a few microatmospheres (µatm) between open-ocean and coastal-ocean pCO2 data from SOCAT within the overlap area (blues and yellow bars in Fig. 14) with deviations mostly arising in the Peruvian upwelling system and the Amazon outflow regions where monthly differences can exceed 10 µatm. The good correspondence is expected to some degree because both datasets share a large fraction of the data. The analysis shows that the seasonality of the neural network-based on NNopen and NNcoast satisfactorily reproduces the seasonal fluctuations obtained directly from the raw data, highlighting that the reconstructed seasonal cycle is well constrained by the existing observations. Monthly deviations between the products largely stay within 10 µatm. An exception is the Sea of Japan in boreal winter, where NNopen overestimates the surface ocean pCO2 values recorded in the SOCAT data. All but three of the selected regions have full seasonal data coverage. The three regions without full coverage are the west coast of Australia, the Amazon outflow region and the Peruvian upwelling system. Despite the lack of seasonal observations along the west coast of Australia, both products agree well with regards to the seasonal cycle and differences stay within of 8–10 µatm between the different products. Likewise, the otherwise good agreement between coastal-ocean and open-ocean estimate breaks down in the boreal summer in the Amazon outflow region, despite the lack of strong seasonality in the tropical latitudes.

The largest mismatch between data products and observations exists along the Peruvian upwelling system, where monthly differences between open-ocean and coastal-ocean estimates exceed 40 µatm. Both estimates however show similar seasonal variability. The seasonal analysis further reveals that from all investigated regions, the Peruvian upwelling system shows the largest monthly differences between open-ocean and coastal-ocean SOCAT observations, with, for example, mean differences in March exceeding 30 µatm between the open-ocean and coastal-ocean SOCAT datasets . Furthermore, the largest observed partial pressures in NNopen appear in August where no data are available in the coastal-ocean SOCAT dataset, highlighting that NNopen draws information from observations further away from shore during this month.