## Introduction

The atmospheric partial pressure of CO2 (pCO2,air) has been increasing at a rate of about 1.8 parts per million by volume (ppmv) per year in recent decades as a result of human activities such as burning of fossil fuel, deforestation, and cement production1,2. Although substantial regional and decadal variability has been observed3,4, surface water pCO2 levels tended to have followed more or less those of the atmosphere, particularly in the open ocean5. This tracking trend is best shown by the data collected at regular intervals at a few ocean time series stations, which by now cover more than 30 years6. The close atmospheric tracking of surface water pCO2 is a consequence of the relatively long water residence time of the global surface ocean, with a time scale of more than a year7, which is longer than an air–sea CO2 exchange time scale of about 10 months7. However, it is not clear whether surface water pCO2 on continental shelves, defined here as shallow regions with depths between 20 and 200 m that exclude the very nearshore areas (see “Methods” section for details), also track the atmospheric pCO2 increase.

Our current understanding of the long-term trend in shelf pCO2 is very limited because it largely relies on observations from a few time series only with records much shorter than those in the open ocean. Furthermore, pCO2 in shelf regions is characterized by high temporal and spatial variability, making trend analyses more demanding8,9,10,11,12. The recent development of the community-driven global ocean pCO2 data product SOCAT (for Surface Ocean CO2 Atlas13) now offers a complementary approach to assess whether continental shelves show a change in the air–sea pCO2 gradient (ΔpCO2 = pCO2,airpCO2) over time. Although the data coverage remains sparse within SOCAT, it allows reconstructing the evolution in ΔpCO2 for 15 regions across the global shelves with a time span of at least a decade. We first aim to identify if the observed recent trends in ΔpCO2 support a strengthening or a weakening of the global CO2 uptake by shelf regions. Then, we investigate whether important regional differences emerge from the analysis, and if any global pattern can be discerned when combining all observational evidence. In what follows, we briefly review the current state of knowledge regarding shelf CO2 dynamics and then propose novel observational evidence of rates of change in the air–sea pCO2 gradient from the analysis of the SOCAT database.

Syntheses in the recent decade suggest that, globally, continental shelves currently absorb atmospheric CO2 at a rate of about 0.2 Pg C annually11,12,14,15,16,17,18. Despite great local variability, the data also suggest that mid- to high-latitude shelves are generally a sink of CO2, while warm tropical shelves are a moderate source of CO214,16,17. A broad consensus regarding the current strength of the global shelf CO2 sink and its large-scale spatial variability has thus recently emerged. In particular, continuous high-resolution pCO2 maps for continental shelf seas derived from the interpolation of experimental data19 clearly support this spatial trend in all oceanic basins. However, much less is known regarding decadal trends and associated variability in shelf CO2 sources and sinks across the globe.

The limited pCO2 time series obtained from coastal sites provide mixed evidence for the size of the decadal trends. Bates and co-authors6 reported for the coastal stations Mundia and Iceland Sea small long-term rates of increase in pCO2 (+1.3 μatm yr−1), i.e., rate that are lower than that of the atmosphere, while they show that the stations Irminger and CARIACO have rates as high as +2.4 and +2.9 μatm yr−1, respectively (Table 1). A shorter time series at the SEATS station in the South China Sea over the 1999–2003 period reveals an even faster increase in pCO2 with a rate of +4.2 μatm yr−1. While illustrative, such trends from a handful of locations do not allow drawing any conclusion regarding the overall change in the shelf air–sea pCO2 gradient over time.

Some data-driven regional analyses have also attempted to decipher the rate of pCO2 increase in continental shelf settings. Data from two large semi-enclosed shelf seas (North Sea and Baltic Sea) and from the Bering Sea suggest that continental shelves may exhibit a rapid increase in pCO220,21 toward atmospheric values, thus lowering the air–sea pCO2 gradient over time (Table 2). In contrast, another study in the North Sea22 and reports from the warm Caribbean Sea23 (mostly from areas deeper than the shelf depths as defined here), the coast of Japan24, West Antarctic Peninsula25, and the Scotia shelf26, showed that the sea surface pCO2 increase lags well behind that of the atmosphere, making the areas either an increased sink (Pacific coast of Japan, Coast West Antarctic Peninsula, and Puerto Rico) or a decreased source (Scotian shelf) for atmospheric CO2. However, a recent study27 suggests that the Japanese margin as a whole roughly tracks the atmospheric CO2 increase. Overall, these regional analyses highlight that trends in CO2 sources and sinks appear highly variable both within the same shelf and across different shelf systems.

Researchers have also attempted to use models to investigate the change in shelf air–water CO2 exchange. Using a box model, Mackenzie and co-workers were the first to suggest that shelves may have turned from a CO2 source in the preindustrial time to a sink at present and that the CO2 uptake rate would increase with time28. Consistent with these predictions, Bauer et al.8 and Cai14 also provided a conceptual model and suggested an increasing global shelf CO2 sink with time as a result of the atmospheric pCO2 increase. Recently, an eddy-resolving global model was used to simulate the flux of anthropogenic CO2 into the coastal ocean29. This latter model can be viewed as an open ocean model extended to the coast that lacks a few, but important processes in the nearshore environments. In particular, the global model lacks detailed sediment interactions, the handling of river fluxes, and shallow calcification processes, which were captured in the spatially and temporally crude box model, however28,30. Nonetheless, both approaches consistently show that the shelf water CO2 uptake increases with increasing atmospheric CO2 levels. However, no consensus emerges as to whether past and future decadal changes in shelf ΔpCO2 and, thus, CO2 absorption per unit area, will increase at a faster or slower rate compared with the global open ocean.

Two main mechanisms have been proposed to explain the evolution of the continental shelf CO2 sink. The first mechanism relies on the efficiency of the physical pump and more specifically on the different timescales for the air–water and shelf-open ocean exchanges of CO28,14. In the situations where the CO2 exchange rate across the shelf is faster than that with the atmosphere, the pCO2 increase in waters on the shelves may be slower than the atmospheric pCO2 increase, even if we assume that no change in biology and physics occurs over time8,14. In these margins, the accumulation of anthropogenic CO2 in shallow waters would be limited and would help maintain a significant air–water pCO2 gradient favouring an efficient uptake of anthropogenic CO2. In contrast, if the cross-shelf export is unable to keep up with the increasing air–sea flux of anthropogenic CO2, CO2 in shelf waters may accumulate and the pCO2 increase would follow the atmosphere due to this bottleneck in offshore transport29.

The second mechanism relies on the stimulation of the biological pump. Many continental shelves are seriously influenced by anthropogenic nutrient inputs and have higher biological production today than what they had in preindustrial time30,31. Thus, net ecosystem metabolism (NEM) on the shelves could have progressively shifted from net heterotrophy to net autotrophy and the change could have been sufficiently large to reverse the air–sea CO2 flux from a source during preindustrial times to a sink under present-day conditions. Net ecosystem calcification (NEC) also plays a significant role in the air–water CO2 exchange on the shelves, but the contribution of the carbonate pump to changes in air–water exchange fluxes over the historical period are likely not as large as the biological pump28.

Our aim here is to present the first observation-based analysis of decadal trends in global shelf pCO2. The results presented in our regional and global analysis are primarily derived from wintertime data when photosynthetic activity is generally the weakest, and when coastal ocean waters have the most intensive exchange with the open ocean, and consequently the strongest impact on the global ocean CO2 accumulation17,31. This results in trends that tend to be clearer. We check on these wintertime analyses also with results from an analysis using deseasonalized data for all seasons, confirming that our choice for wintertime only does not result in artefacts. However, this does not suggest that winter contributes more than other seasons to the overall annual trend.

## Results

### Regional trends in ΔpCO2

Our analysis employing a narrow definition of the continental shelf corresponding to the 200 m isobaths and winter-only data provides decadal trends in ΔpCO2, i.e., dΔpCO2/dt values, for 825 cells with an average length of our time series of 18 years. Six hundred five of these 825 cells belong to 6 large regions each comprising at least 50 cells (Table 2). Another 190 cells belong to 9 smaller regions each comprising 10 cells or more. Together, these 15 regions account for 96 and 80% of the cells contained in our narrow and wide definitions of the shelf, respectively (see “Methods” section for details). Most regions display variable, but relatively consistent values of dΔpCO2/dt. Only the Baltic Sea and the Mid-Atlantic Bight show a significant but continuous spatial gradient in the trend within their respective domains. With the exception of the Labrador Sea, regional analyses of the air–sea CO2 exchange have been published for each of the areas presented here, but estimates of dΔpCO2/dt have only been reported for 9 out of the 15 regions (Table 3).

The highest positive dΔpCO2/dt, with an average rate of change of +2.9 ± 2.4 μatm yr−1, occurs in the Baltic Sea (Fig. 1a). This rate of increase in ΔpCO2 is higher than the atmospheric pCO2 increase rate and, therefore, surface water pCO2 actually decreases over time, most likely as a result of increased anthropogenic nutrient inputs and resultant increases in coastal productivity in this semi-isolated inland sea, which affect the biogeochemistry of the Baltic Sea all year long32. Our results are consistent with a recent study that the Baltic Sea is a decreasing source of CO2 to the atmosphere32. The North Sea (Fig. 1b), the Mid-Atlantic Bight (Fig. 1c), Southern Greenland, and Antarctic Peninsula (Fig. 1d) have dΔpCO2/dt values averaging close to +2 μatm yr−1 with σ of 1.2–1.5 μatm yr−1, except for the Mid-Atlantic Bight, which has more spatial heterogeneity (σ = 3.1 μatm yr−1). Therefore, their water pCO2 values do not increase with time or increase at a rate substantially lower than that of pCO2,air (Table 3). The results for the North Sea contrast sharply with an earlier report based on two sets of summertime data (2005 vs. 2001), which suggested that the North Sea pCO2 increased at a rate five times faster than the atmosphere20. A more recent study, however, also comparing summertime pCO2 between the years 2001, 2005, and 2008 revealed a large increase of 26 μatm between 2001 and 2005, but only a moderate increase of 4 μatm between 2005 and 200822. These disparate results support the idea that summertime pCO2 is more affected by the short-term imbalance of biological production and respiration, whereas wintertime reflects better the long-term trend in air–sea exchange due to reduced biological activities. The increase in the CO2 uptake by Greenland coastal waters reported here is in agreement with Yasunaka et al.33. Along the East coast of the United States, the Mid-Atlantic Bight is a typical western boundary current margin with intense exchange of water between the shelf and the deep ocean at a frequency of about once every 3 months and is also influenced by anthropogenic nutrient inputs and eutrophication31,34. A previous study suggested that the annual thermal cycle combined with high winds during wintertime dominates annual CO2 uptake in this region35. dΔpCO2/dt ranging from values >+5 μatm yr−1 in the north of the region to <−2 μatm yr−1 in the south could be a consequence of very different hydrodynamic characteristics along this coastal setting. The southern part of the region is under the influence of coastal currents and large estuaries (e.g., Chesapeake Bay) that effectively filter terrestrial organic carbon inputs36,37 while the northern part is characterized by significantly colder water from the Labrador Sea all year long38. The Antarctic margins, such as those along the Antarctic Peninsula, are dominated by an intense exchange with deep water masses and it appears that the rate of CO2 uptake is driven mainly by the strength of the upwelling and low-surface temperature39. The high dΔpCO2/dt along the West Antarctic Peninsula is consistent with another study25, which also suggested that winter is the season for which the rate of increase in ΔpCO2 is the fastest. Additionally, a general strengthening of the Southern Ocean CO2 sink has been recognized over the past decade39.

A second group of regions includes the shelves of Irminger Sea and the Labrador Sea, the Coast of Japan (Fig. 1e), the Cascadian shelf (Fig. 1f), and the South Atlantic Bight. These shelf regions have dΔpCO2/dt values ranging between +0.5 μatm yr−1 and +1.0 μatm yr−1. This range implies that their water pCO2 is increasing, but at a rate that is moderately slower than that of pCO2,air, implying a strengthening sink, or a weakening source. The South Atlantic Bight is a moderate sink of CO2 for the atmosphere40 because of its water residence time of a few months and rapid cross-shelf exchange with the open ocean in the winter41. Our estimate of +0.8 μatm yr−1 for the Pacific coast of Japan is also consistent with a survey24 that reports a slower increase of water pCO2 (+1.5 ± 0.3 μatm yr−1, Table 2) than that of pCO2,air (+2.0 ± 0.1 μatm yr−1) over the period of 1994–2008. Perhaps a bit counterintuitive, however, is the low-positive dΔpCO2/dt (+0.8 ± 1.7 µatm yr−1) along the Eastern Boundary current margins known for their strong upwelling off the U.S. West Coast (the California and Cascadian shelves). However, here upwelling source waters are not from the deeper Antarctic water as that in the Atlantic Ocean; rather, they are North Pacific surface water subducted only decades earlier, which thus carries with it the anthropogenic CO2 signal42,43,44. The enhanced upwelling strength in recent years may also have contributed to an increase in sea surface pCO245. The western shelves of North America especially the Cascadian shelves, however, are known for their strong spatial heterogeneity, suggesting that multiple processes drive their biogeochemical behavior46.

The third group of regions, which includes the English Channel (Fig. 1g), the Barents Sea, and the Tasmanian shelf, show a minimal or no increase in dΔpCO2/dt, meaning that their water pCO2 more or less tracks the pCO2,air increase (Table 3). The interannual dynamics of pCO2 in the English Channel is largely influenced by North Atlantic waters and thus partly constrained by the North Atlantic Oscillation47. While no long-term dΔpCO2/dt has been estimated for the English Channel itself, the increase of +1.7 μatm yr−1 for pCO2 calculated for adjacent Atlantic water1 is consistent with an increase following that of the atmosphere. In both the Barents Sea33 and Tasmanian shelf48, signs of a strengthening of the coastal CO2 sink have been reported and were partly attributed to decreases in sea surface temperature. While marginal (+0.1 μatm yr−1), the dΔpCO2/dt revealed by our calculations suggests an increase in the strength of CO2 sink in the Tasmanian shelf. Finally, the Patagonian continental shelf (−0.2 ± 0.4 μatm yr−1; Fig. 1h) and Bering Sea (−1.1 ± 0.7 μatm yr−1) are the only regions displaying a negative dΔpCO2/dt (meaning faster increase in water pCO2 than air pCO2). Thus, although they are still intense CO2 sinks17,49,50, these shelf systems have recently experienced a weakening in their capacity to absorb atmospheric CO2. While no long-term trend was reported for Patagonian shelf, it has been suggested that the CO2 uptake in the Bering Sea could be decreasing at a fast pace although these observations were based on a relatively short time series (1995–2001)51.

Overall, 13 of the 15 regions have positive dΔpCO2/dt values and 10 reveal values equal or greater than +0.5 μatm yr−1 (Table 3). Although these areas only account for a small fraction of the global coastal ocean, they show a consistent trend suggesting that winter sea surface pCO2 increases significantly slower than pCO2,air. Furthermore, in most regions, the variability around this trend is relatively limited. For instance, in 9 out of 15 regions, the standard deviation is less than 1 μatm yr−1. However, it remains difficult to identify the mechanisms responsible for these observed patterns in dΔpCO2/dt considering the diversity of morphological and hydrodynamical settings of the shelf regions covered by our analysis.

### Global shelf CO2 sink

Globally, our analysis of the 825 temporal trends in ΔpCO2 using winter-only data covers a shelf surface area of 1.4 × 106 km2, which represents ~6% of the global continental shelves. This includes data from the more isolated cells that were not considered in the previous section. While the coverage is relatively small, heterogeneous and somewhat skewed toward temperate latitudes in the northern hemisphere, it nevertheless covers most of the range of pCO2 and SST encountered in continental shelf waters (Supplementary Figures 1 and 2). Exceptions are the low latitudes, which are poorly represented in our data set. While we need to recognize this limitation, the broad coverage in terms of environmental conditions permits us to assemble all estimated trends and assume that they represent a sufficiently unbiased sample of the shelf trends across the globe.

The bulk of our winter data consistently show trends that are dominantly in accordance with an increase in ΔpCO2 over time. Our narrow definition of the shelf yields a global average dΔpCO2/dt of +1.3 ± 1.9 μatm yr−1, while the wide definition for geographical extent leads to a smaller average value of +0.8 ± 1.8 μatm yr−1 (Fig. 2). Thus, our global-scale analysis of winter pCO2 data reveals that trends are more likely positive than not and support the idea that air–sea pCO2 gradients may have been increasing with time making continental shelves overall an increasing CO2 sink for the atmosphere. Nevertheless, as shown by the substantial standard deviations, large differences in dΔpCO2/dt can be observed across continental shelves. Within the 200 m water depth boundary, 653 cells (out of 825) display a positive dΔpCO2/dt, 76% of which are greater than +0.5 μatm yr−1 (i.e., 495 out of 653; Supplementary Table 1). For 66% of the latter cells (325 out of 495), the slope of the regression is considered statistically significant using an F-test with p < 0.05 and 71% with p < 0.1 (Fig. 2). On the other hand, for the 172 cells (out of 825) that display negative dΔpCO2/dt values, only 49% are more negative than −0.5 μatm yr−1 (84 out of 172). The trend is still observed when the boundary is relaxed to 500 m or 100 km from the coast. One thousand and sixty-six cells (out of 1364) display a positive dΔpCO2/dt, 64% of which is greater than +0.5 μatm yr−1 (i.e., 682 out of 1066) and only 149 out of the 298 non-positive cells having a negative dΔpCO2/dt are then characterized by rates more negative than −0.5 μatm yr−1 (Fig. 2). The use of the broader definition of the continental shelves not only decreases the average dΔpCO2/dt, but also increases the proportion of cells with dΔpCO2/dt between −0.5 and +0.5 μatm yr−1 (39% vs. 30%). Note that applying our method to all open ocean waters deeper than 500 m or further than 100 km from the coast yields a much smaller average dΔpCO2/dt of +0.2 ± 1.1 μatm yr−1, which is close to the open ocean observation1,2,3,4,5,6,52, further supporting the validity of our method.

The results from the analysis using data across the entire year generally confirm the results from the wintertime-only data as exemplified by the change in ΔpCO2 with time for all cells pertaining to the six largest regions used in the regional analysis (Fig. 3). For all regions, the range of ΔpCO2 values observed in winter (red) is largely less than that based on the entire year (black). Globally, calculations performed using deseasonalized data from the entire year allow deriving trends for 3721 cells (Supplementary Table 1). Although much noisier, the overall dΔpCO2/dt values using all seasonal data reveal qualitatively similar trends to those observed with data from the winter months only (Supplementary Table 1). The overall proportion of cells displaying statistically significant trends is much lower when all seasonal data are used (22%) than when winter data are retained (45%). Nevertheless, nearly three times more cells display significant trends for which d(ΔpCO2)/d> +0.5 μatm yr−1 (574) than for which d(ΔpCO2)/dt < −0.5 μatm yr−1 (201), a result in broad agreement with our analysis based on winter data only. Therefore, the analysis of deseasonalized data for all seasons also point toward a tendency for an enhanced shelf uptake of atmospheric CO2.

The rate of change in the air–sea CO2 gradient also has varied over time. Figure 4 presents the evolution from 1988 to 2007 of winter dΔpCO2/dt calculated for each year over a 15-year time period. Because the bulk of the data available in SOCAT are relatively recent, it is difficult to reconstruct trends earlier than the 1990s. The distribution of rates around the mean value is shown by the gray scale in Fig. 4 and the widening of the distribution can be observed as the number of data points increase but, for any given year, the bulk of the dΔpCO2/dt distribution remains constrained within the −0.5 to +2.0 μatm yr−1 range. While uncertainties are high in such an analysis, in particular because the trends from the investigated regions (about 6% of the total shelf area) might not hold for all the others, our results suggest that in addition to the dominance of positive dΔpCO2/dt, there is a good probability that the rate of change of the air–sea CO2 gradient has also increased over the past 15 years. Indeed, the average dΔpCO2/dt appears to remain below 1 μatm yr−1 before 1997 but above it since then.

### Implications for the global carbon budget

Applying the mean rate of change in the winter air–sea CO2 gradient identified in Fig. 4 to a globally averaged winter ΔpCO2 of +28 µatm for the continental shelf seas in the reference year 200017, leads to an increase in water pCO2 that has consistently lagged behind the increase in atmospheric CO2. As noted in the previous section, dΔpCO2/dt also has increased in recent years (+1.2 μatm yr−1). The first records of shelf pCO2 date back from the early 1980s and it is thus impossible to reconstruct the earlier evolution of the air–sea exchange from direct observations. Although highly speculative, it is nevertheless interesting to extend the rate of change in the 1980s and early 1990s (+0.6 μatm yr−1) estimated here to the earlier decades. This approach allows comparing trends derived from observations alone with earlier modeling work and will stimulate further exploration of coastal CO2 trend28,30. Our calculations suggest that the magnitude of the average winter ΔpCO2 increased by 69% over the 1988–2007 period. By extrapolating this trend to earlier times, it can be speculated that the continental shelves might indeed have turned from a purported preindustrial source of CO2 into a sink for atmospheric CO2 as early as in the 1950s, at least during wintertime (Supplementary Figure 3). The occurrence of such a switch from source to sink in the mid-twentieth century would be consistent with previous model results28, although our data-based estimate may indicate that the switchover time could have occurred earlier than previously thought. Note that our assessment excludes the high pCO2 estuarine and very nearshore (proximal) zone that is believed to be a significant source of CO2 for the atmosphere at present12,16,53,54. A recent model hindcasts that the uptake rate of anthropogenic CO2 by continental shelves has increased rapidly since the 1950s29. Although this flux is much less than that modeled for the open ocean uptake29, it would imply an increase in the total CO2 uptake flux (natural plus anthropogenic) and an increase in the air–sea pCO2 gradient in the coastal ocean, assuming that the natural CO2 flux in their model does not change. Thus, the conjecture derived from our first global observation-based work is consistent with their model prediction. Nevertheless, this work also highlights the fact that the rate of increase of the air–sea pCO2 gradient in continental shelf waters and its importance in global ocean CO2 uptake is still poorly understood and deserve further study. In addition, if both observational evidence and model results support the idea that shelves are an increasing sink for the atmospheric CO2, we are far from quantitatively understanding the roles of the physical pump and biological pumps (NEM and NEC) in explaining this enhanced CO2 absorption and associated high variability globally. We suggest, however, that a faster exchange of shelf CO2 with the ocean interior and increased biological production due to anthropogenic nutrient inputs may have slowed down the rate of increase of surface ocean pCO2 in many shelf regions.

In principle, the slower pCO2 increase in shelf waters could increase the gradient and thus the uptake of atmospheric CO2 in the decades to come, although high spatial variability in air–sea fluxes is to be expected across shelf regions. The shift of shelf waters from releasing to absorbing CO2 between preindustrial time and the present day, as well as the possibility of shelves becoming a more important sink in the future, is a significant temporally changing term in the global carbon cycle and pathway of exchange for atmospheric CO2. It should thus be closely evaluated by further data collection and analysis and be considered in future global carbon cycle models and flux assessments6,31,35,39,52.

## Methods

### Definition of the study area

For this work, we defined the continental shelf as all marine waters shallower than the 200 m isobath. This depth is commonly used in the literature as the depth at which the shelf breaks12,16,17,31,52. However, we also report results for a less restrictive definition, where the shelf limit is set at 500 m water depth or within 100 km from the shore (Supplementary Figure 4). This allows inclusion of the wide and deep shelves at high latitudes and of coastal processes that take place in deeper waters in regions where the shelf break is very close to the shore. With both definitions, coastal waters shallower than 20 m as well as internal waters, such as estuaries, fjords, lagoons, or tidal marshes, are excluded from this analysis. The pCO2 data selection was performed using water depths extracted from ETOPO2 and the distance to the coast was provided by SOCAT3. Our narrow and wide definitions of the continental shelf correspond to global surface areas of 22 × 106 km2 and 45 × 106 km2, respectively. These two values can be considered as lower and upper bounds as they comprise all reported surface areas obtained with other definitions of the continental shelf52.

### Data processing

Recently, numerous continental shelf pCO2 observational data have been quality controlled and included into the SOCAT database13. Version 3 released in 2015 comprises more than 14 × 106 measurements for the entire ocean, of which 3.4 × 106 and 5.2 × 106 are located within our narrow and wide shelf definitions, respectively. This unprecedented data coverage offers the opportunity to assess whether global shelf waters show a change in the direction and magnitude of the air–sea pCO2 gradient (ΔpCO2 = pCO2,airpCO2) over time (dΔpCO2/dt).

The coastal zone was divided into regular 0.5 × 0.5 degree cells and all the SOCAT measurements were allocated to a given cell according to their latitudes and longitudes. SOCAT fugacity data (fCO2) were converted into CO2 partial pressure (pCO2) in water using the following equation55.

$$\left( {p{\mathrm{CO}}_{2}} \right) = f{{\mathrm{CO}}_{2}}\left( {{1.00436} - {4.669\:10}^{ - 5}\,{\mathrm{SST}}} \right),$$
(1)

where SST is the sea surface temperature in degrees Celsius. For each month, an average ΔpCO2 was calculated within each cell. The winter data (defined as January, February, and March in the Northern Hemisphere and July, August, and September in the Southern Hemisphere) are not modified prior to calculating the linear regressions. The data from all seasons, however, are deseasonalized using monthly pCO2 climatological maps for continental shelves generated by artificial neuronal network interpolations19. This monthly pCO2 climatology allowed establishing an average seasonal pCO2 cycle for each grid cell. This signal was then removed from the raw data to perform a deseasonalization prior to calculate the linear regressions.

We found no significant trend in SST in the majority of the cells (i.e., the absolute rate of change in temperature only exceeds 0.1 °C yr−1 in less than 15% of the cells) and the average temperature change among all 825 cells used for the winter analysis using the narrow definition of the shelf is −0.0021 °C yr−1. In addition, warming should lead to a higher water pCO2 and, thus, should reduce dΔpCO2/dt.

For each data point, an atmospheric pCO2 was also calculated using:

$$\left( {p{\mathrm{CO}}_{2}} \right)_{\mathrm{air}} = {{\mathrm{XCO}}_{2}}\left( {P_{\mathrm{baro}} - P_{\mathrm{sw}}} \right),$$
(2)

where $$P_{\mathrm{baro}}$$ is the barometric pressure at sea surface and Psw is the water pressure at the temperature and salinity of the water within the mixed layer. XCO2 is the weekly mean CO2 concentration for dry air extracted from the GLOBALVIEW-CO2 database56. Psw was calculated assuming 100% humidity using sea surface temperature and salinity and Pbaro is the monthly mean barometric pressure at the sea surface from the NCEP/NCAR Reanalysis database57. All the data used were taken from the SOCAT files.

A moving spatial window of 1.5 degrees of width (i.e., three cells) was used to increase the data pool and minimize the effect of anomalous single measurements on our calculations. Effectively, this means that, for a given grid cell, all data located in the surrounding eight cells are also taken into account in the regression calculation58. Then, within each 0.5 degree cell, the slope of the linear regression of ΔpCO2 vs. time using the bi-square method was calculated to evaluate dΔpCO2/dt. Additionally, to reduce the influence of interannual variations in ΔpCO2, we limited the analysis to cells for which we could extract at least ten data points from five or more different years spanning a period of at least 10 years between the first and last measurement. These operations are performed in similar fashion for winter-only and all-year deseasonalized data. Although the minimum period is short compared to any decadal variability that might be present in the trend, it was chosen to keep a sufficiently large pool of cells in the statistical analysis. Linear regressions were then calculated using the bi-square method. The slope of the linear regression provides the rate of change in ΔpCO2, which is defined as

$${\mathrm{d}}(\Delta p{\mathrm{CO}}_{2})/{\mathrm{d}}t = \left( {\Delta p{{\mathrm{CO}}_{2}}\left( {t}_{2} \right)-\Delta p{{\mathrm{CO}}_{2}}\left( {t}_{1} \right)} \right)/({t}_{2}-{t}_{1})$$
(3)

where t2t1 defines the period for which winter data are available for a given cell.

Finally, the cells for which dΔpCO2/dt could be calculated are clustered into relatively broad regions consisting of groups larger than 50 connected cells and smaller regions consisting of groups larger than 10 connected cells following our narrow definition of the shelf (Supplementary Figure 5). These groups are used as a basis for the regional analysis and allows, for the first time, to analyze consistently temporal trends in winter ΔpCO2 over the global continental shelves in a similar fashion.

### Statistics

Prior to calculating the linear regressions, several statistical tests were performed for each cell. First, the normality of the distribution of the residuals was evaluated using a Kolmogorov and Smirnov test and >95% of the time series do not exhibit significant deviations from a normal distribution (Supplementary Figure 6a). Then, the existence of autocorrelation within the time series has been diagnosed using a Durbin–Watson’s test. Results yield values clustered around 2, revealing no significant autocorrelation (Supplementary Figure 6b). The consistency of the variance of the residuals over time was assessed using White’s test and significant heteroscedasticity was detected in about half of the times series. As a consequence, the linear regressions were calculated using the bi-square method rather than the simple least square method, which is less robust when the residual is not consistent throughout the entire data set.

These statistical tests were also used to determine the minimum required length of the time series (i.e., data spanning at least 10 years, more than 10 individual data, at least 5 different years with data). Using this set of criteria, the average length of our time series is 18 years. Finally, to assess the statistical significance of the regressions, an F-test was performed in each cell (Supplementary Table 1).

### Temporal evolution of ΔpCO2

To investigate how the rate of change in air–sea CO2 gradient, d(ΔpCO2)/dt, has varied globally over time, the entire SOCAT data set was used to produce 20 subsets, each covering a period of 15 years (from 1980 to 1994, then 1981 to 1995 and so on until 2001 to 2015) and used to calculate the rate of change for the central year of each period. For instance, d(ΔpCO2)/dt for year 1988 is calculated using data ranging from 1981 to 1995. This method provides estimates for years 1988 to 2006. For each period, d(ΔpCO2)/dt were calculated for each cell following the procedure described above. The average rate of change in ΔpCO2 for a given period was then calculated as the average of all the rates calculated for each cell for which observations were available (Fig. 4).

A global estimate for the coastal ocean carbon sink for winter of 0.26 Pg C yr−1,17 was used over a surface area of 30 106 km2 in conjunction with the gas transfer velocity of 9.0 cm h−1 to estimate an average global ΔpCO2 of 28 µatm for the continental shelf seas in the reference year 2000. Year 2000 was selected as the estimate of Laruelle et al.17 represents an average over the 1990–2011 period. From this reference value, the ΔpCO2 in previous and following years (period 1988–2006) was calculated by adding or subtracting the average d(ΔpCO2)/dt calculated using the 20 data subsets described above. Earlier than 1988, d(ΔpCO2)/dt was assumed to be the average over the 1988–1993 period. Using annually averaged atmospheric pCO2 values from Mauna Loa and these d(ΔpCO2)/dt, estimates of the water pCO2 are then calculated for each year (Supplementary Figure 3). Results show that shelf water pCO2 could have been lower than atmospheric pCO2 as early as 1950.

### Data availability

The data that support the findings of this study are available from the corresponding author on reasonable request.