# Wind-Driven Control of Shelf-Sea CO2 Sinks

Jamie D. Shutler, Daniel J. Ford, Thomas Holding, Clement Ubelmann, Lucile Gaultier, Fabrice Collard, Bertrand Chapron, Marie-helene Rio, Callum Roberts, Craig Donlon

► To cite this version:

Jamie D. Shutler, Daniel J. Ford, Thomas Holding, Clement Ubelmann, Lucile Gaultier, et al., Wind-Driven Control of Shelf-Sea CO2 Sinks. Global Biogeochemical Cycles, 2025, 39 (9), e2024GB008461 (15p.). 10.1029/2024GB008461. hal-05314457

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Distributed under a Creative Commons Attribution 4.0 International License
# Global Biogeochemical Cycles®

## RESEARCH ARTICLE

10.1029/2024GB008461

Jamie D. Shutler, Daniel J. Ford, and
Thomas Holding joint first authors

**Key Points:**

* Wind-driven Ekman component of across shelf exchange is significantly related to long-term air-sea $pCO_2$ gradients in many shelf-seas

* Wintertime wind-driven across shelf exchange and air-sea $CO_2$ exchange describe 82% of the variance in the air-sea $pCO_2$ gradient

* Wind-driven exchanges help control shelf-sea $CO_2$ sinks; models assessing their carbonate state need to resolve these processes

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

J. D. Shutler,
j.d.shutler@exeter.ac.uk

**Citation:**

Shutler, J. D., Ford, D. J., Holding, T., Ubelmann, C., Gaultier, L., Collard, F., et al. (2025). Wind-driven control of shelf-sea $CO_2$ sinks. *Global Biogeochemical Cycles*, *39*, e2024GB008461. https://doi.org/10.1029/2024GB008461

Received 12 DEC 2024
Accepted 11 AUG 2025

**Author Contributions:**

**Conceptualization:** Jamie D. Shutler, Daniel J. Ford, Thomas Holding

**Data curation:** Clement Ubelmann, Lucile Gaultier, Fabrice Collard

**Formal analysis:** Jamie D. Shutler, Daniel J. Ford, Thomas Holding

**Funding acquisition:** Jamie D. Shutler

**Investigation:** Jamie D. Shutler, Daniel J. Ford

**Methodology:** Jamie D. Shutler, Daniel J. Ford, Thomas Holding, Clement Ubelmann, Lucile Gaultier, Fabrice Collard, Bertrand Chapron, Marie-Helene Rio, Craig Donlon

© 2025. The Author(s).
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

## Wind-Driven Control of Shelf-Sea $CO_2$ Sinks

<figure><img src="image_2.png" /></figure>

Jamie D. Shutler¹ ID, Daniel J. Ford¹ ID, Thomas Holding¹,² ID, Clement Ubelmann³, Lucile Gaultier⁴ ID, Fabrice Collard⁴ ID, Bertrand Chapron⁵ ID, Marie-Helene Rio⁶, Callum Roberts⁷, and Craig Donlon⁸

¹Centre for Geography and Environmental Sciences (CGES), University of Exeter, Penryn, UK, ²Now at Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany, ³Collecte Localisation Satellites (CLS), Brest, France, ⁴OceanDataLab (ODL), Brest, France, ⁵Ifremer, Laboratoire d'Oceanographie Physique et Spatiale (LOPS), IUEM, Brest, France, ⁶European Space Agency (ESA), Frascati, Italy, ⁷Centre for Ecology and Conservation, University of Exeter, Penryn, UK, ⁸European Space Agency (ESA), Noordwijk, The Netherlands

**Abstract** Continental shelf surface waters are considered a variable but increasing sink of atmospheric carbon dioxide ($CO_2$), but the mechanisms controlling these increasing sinks are unclear. We identify that the winter wind-driven surface atmosphere-ocean $CO_2$ gas exchange and wind-driven movement of water onto (or off of) shelf seas are consistent with the atmospheric $CO_2$ uptake tendency of many shelf seas. A 20-year observational-based analysis shows that geostrophic, wind and wave driven currents all contribute to the surface shelf break water velocities, but the dominance of each is location and season dependent. Analyzing these flows for fourteen shelf-seas based on their 20-year long-term gradient in air-sea partial pressure of carbon dioxide (their atmospheric $CO_2$ uptake tendency) identifies significant relationships between uptake tendency and winter ($r^2$ = 0.72 ± 0.03, *p* < 0.01, *n* = 14) and autumn ($r^2$ = 0.57 ± 0.05, *p* < 0.01, *n* = 14) wind-driven surface flows. These signals are most strong in winter, but the results are consistent at annual scales. Including the wintertime wind-driven air-sea $CO_2$ gas exchange further enhances this result, and collectively they describe 82% of the variance in the atmospheric $CO_2$ uptake tendency data ($r^2$ = 0.82 ± 0.06, *p* < 0.01, *n* = 14). These findings identify that long-term wind-driven water flow and surface gas exchange are key mechanisms for controlling their chemical evolution and their status as $CO_2$ sinks. This observational-based evidence highlights the need for these wind-driven processes to be resolved within methods used to predict or understand continental shelf-sea carbonate system state and ocean health.

**Plain Language Summary** Continental shelf seas are a variable but increasing carbon sink, having thought to have switched from a source of carbon to a sink in the last century. However, the processes that are driving this change and their increasing sink, is not known. Two possible mechanisms have been identified, one being the anthropogenic modification of the biological pump. For example, human activity on land causing more nutrient runoff which can promote increased phytoplankton growth in the shelf seas, in turn removing $CO_2$ from the water, enabling the water to absorb more from the atmosphere. The second mechanism being proposed are imbalances between water flows onto and leaving the shelf, which would lead to variations in the replenishment of water with the open ocean, which is low in dissolved carbon. But currently little evidence to support either mechanism exists. We provide the first observation-based evidence of a water flow control mechanism, suggesting that policies to reduce global emissions are critical to improve the health of continental shelf seas, as the increasing atmospheric emissions are the primary driver for the air to ocean absorption of carbon.

### 1. Introduction

Despite only covering ~7% of the ocean surface, continental shelf seas play a critical role in the uptake of atmospheric carbon dioxide ($CO_2$), often called their carbon sink, and the re-distribution of this carbon in all of its forms through onward transport or processes including remineralization and biological activity. They are responsible for 10%–20% of this global ocean carbon uptake or sink (e.g., Chen et al., 2013; Laruelle et al., 2014), and are regions of intense biological activity. Ocean surface wind, currents and waves and their interactions play a major role in governing the exchange of heat, energy and carbon between the atmosphere and the ocean, and their onward transport. These global ocean currents are a combination of geostrophic currents ($C_G$) due to dynamic pressure gradients and the Coriolis effect (resulting in mesoscale and submesoscale dynamics), Ekman currents ($C_E$) due to wind stress on the surface water, and other ageostrophic components including tides, and the radial
**Project administration:** Jamie D. Shutler

**Resources:** Jamie D. Shutler,
Craig Donlon

**Software:** Daniel J. Ford, Thomas Holding

**Supervision:** Jamie D. Shutler

**Validation:** Daniel J. Ford,
Thomas Holding

**Writing – original draft:** Jamie

D. Shutler, Daniel J. Ford,
Thomas Holding

**Writing – review & editing:** Jamie

D. Shutler, Daniel J. Ford,
Thomas Holding, Clement Ubelmann,
Lucile Gaultier, Fabrice Collard,
Bertrand Chapron, Marie-Helene Rio,
Callum Roberts, Craig Donlon

motion of surface waves and swell systems (called Stokes drift). These currents span across multiple depths within the mixed layer and together characterize the net transport of water across the shelf break and into, or out of, shelf seas at the surface. Through the need for mass balance, surface water transport across the shelf break is balanced by a reciprocal and opposing flow at depth (Fewings et al., 2008; Graham et al., 2018; Holt et al., 2009; Mahjabin et al., 2019). In shelf seas where the net surface flow is onto the shelf, the opposing flow occurring at depth provides a conduit for the lateral transport of water rich in dissolved inorganic carbon from the shelf-sea to the interior deep ocean, a process referred to as the continental shelf-sea carbon pump (Bates, 2006; Painter et al., 2016; Tsunogai et al., 1999). Whereas, shelf seas that experience net transport of water leaving the shelf sea at the surface, a lateral transport of water that is poor in dissolved inorganic carbon, will have an opposing on-shelf transport at depth where water is upwelled to the surface (Fewings et al., 2008; Roughan & Middleton, 2004), which is rich in dissolved inorganic carbon and this commonly occurs within eastern boundary upwelling systems. In all shelf-seas, this transport of carbon via the slow replenishment of water across the whole shelf can take between months to multiple years to complete (Liu et al., 2019).

The transport of water onto or leaving shelf seas in the surface mixed layer can be determined using large scale observations of geostrophic conditions, wind speed measurements and water velocity measurements that capture wind, wave and current interactions. However, studies tend to be based on sparse in situ data and measurements, which provide valuable insights into shelf break transport, but the resulting assessments are coarse or incomplete in space and time for example, (Berden et al., 2020; Huthnance et al., 2009, 2022; Painter et al., 2016). In some cases, studies exploit satellite altimeter and wind observations or modeling approaches for example, (Lentz, 2008; Levin et al., 2018) resulting in increased spatial and temporal resolution, but these can overlook influences including eddies, filaments and waves (Levin et al., 2018; Yuan et al., 2017). Collectively, these approaches provide a good analysis for the region or time-period studied, but extrapolating their results to quantify global or longer-term conditions is problematic. A synoptic-scale observation-based approach that resolves mesoscale processes may provide the basis for a comprehensive approach.

One possibility for the long-term evolution of these shelf seas is that faster exchange of shelf-sea carbon with the ocean interior combined with biological activity within shelf-seas may have helped slow down the rate of increase in surface water partial pressure of CO₂ (pCO₂) (Laruelle et al., 2018). Two mechanisms have been proposed to explain this (Laruelle et al., 2018). The first is based on the efficiency of the physical pump, characterized by the atmosphere-ocean exchange of CO₂ at the water surface and its later export to the deep ocean either at the surface or depth. Imbalances in strength between these physical processes could modulate surface water atmospheric carbon uptake and its onward storage within shelf seas (Bauer et al., 2013; Cai, 2011). The second proposed mechanism is the modification of the biological pump due to anthropogenic activity, including for example elevated terrestrial riverine nutrient and carbon inputs and resuspension of organic carbon through seabed disturbance (e.g., Sala et al., 2021). These changes can result in a modification of the balance between heterotrophic (organism dependent on complex organic substances) and autotrophic (organisms that can synthesize their own food) conditions within the shelf sea, and storage of carbon within the shelf sea sediments (Laruelle et al., 2018). However, the export of carbon from the shelf sea added through atmospheric-ocean exchange or modified by anthropogenic pressures on the biological pump is likely coupled to the shelf break exchange at either the surface or depth (Bourgeois et al., 2016; Holt et al., 2009; Painter et al., 2016; Rogge et al., 2023); therefore, it is possible that a combination of the two mechanisms is occurring.

We are interested in characterizing the long-term currents that control the flows within the surface mixed layer onto or from global continental shelves and placing these into context for their long-term atmospheric CO₂ uptake tendency. The slow CO₂ equilibration times between the atmosphere and the ocean (of the order of 6 months to 1 year) combined with the relatively long residence time of carbon within shelf seas (of the order of >2 months to 3 years for these seas, Liu et al., 2019) suggest that investigating linkages between carbon processes and water flow requires the analysis of long-term data. A globally resolved observation-based ocean current re-analysis data set that includes geostrophic, and wind driven Ekman currents at two depths (Rio et al., 2014, 2016) and a wave model re-analysis of Stokes drift data allows a global assessment of the importance of these oceanographic features for driving shelf break flows. These long-term flows between 1995 and 2015 are then placed into context for 14 continental shelf-seas exhibiting differing long-term atmospheric CO₂ uptake tendency for the same 1995 to 2015 period (from Laruelle et al., 2018). Collectively, this work identifies that the wind-driven Ekman surface flow is an important component to describe differences in the atmospheric CO₂ uptake tendency within these shelf seas. Similarly, wind-driven air-sea CO₂ gas exchange further enhances this result and therefore driven wind-
process are likely playing a dominant role in controlling these shelf-sea air-sea CO₂ sinks and their long-term
carbonate state.

**2. Materials and Methods**

All analyses were performed on global data sets and three different types of data were used or calculated. These types are projected and gridded data at a 0.25° spatial resolution (stored as, or read from NetCDF files), shelf contour coordinate data for shallow and deep contours (Python pickle binary files), and a table containing a list of 0.25° grid cell data for all grid cells that interact with the shallow shelf contour (.csv file).

**2.1. Determining the Shelf Break and Current Vectors Normal to the Shelf Break**

The General Bathymetric Chart of the Oceans (GEBCO) bathymetry data set (Weatherall et al., 2015) (version 2014) was re-sampled to 0.25° spatial resolution. Two shelf contour coordinate data sets were then produced from the re-sampled GEBCO data, one for the chosen shallow contour (500 m depth) and another for the deep contour (600 m depth). Each shelf coordinate data set was created by applying the marching squares algorithm (in SciPy, v1.2.3) to transit each path within the chosen contour and provide a list of coordinates for that contour (where a path is a discrete section of the contour). Small fragments and short paths (set at <150 points long from visually assessing the data) within the contour were removed as these represent islands or sea stacks. The number of line segments within each transited path provided by the marching squares algorithm was stored within each coordinate data set. This results in two shelf coordinate data sets (shallow and deep), which contain continuous coordinates for all paths for the contour (Figure S1a in Supporting Information S1), and the number of line segments that represent each path. Next, the cell data set for the shallow contour is created. Each path in the shallow contour coordinates data set was simplified into equal length straight-line segments (i.e., quantized) and the onto-shelf direction vector was determined as the line normal to each straight-line segment in the direction of the deeper contour (Figures S1b and S1c in Supporting Information S1). These were then aggregated into values for each 0.25° grid cell by first looping through each path in the shallow contour to identify every intercept between paths and grid cell boundaries (Figure S1d in Supporting Information S1). This results in co-ordinates of every cell that the shallow contour paths pass through, and the length of the shelf path within each of these grid cells was calculated. The shelf edge direction normal vector for each 0.25° grid cell in this list was then determined by identifying the nearest straight-line segment to each grid cell and assigning its normal vector to that grid cell (Figures S1b and S1c in Supporting Information S1). The cell data set now contains the length of each path of the shallow contour, and the onto shelf normal vectors for every grid cell along those paths (collectively referred to as $\overrightarrow{B_L}$). Figure S2 in Supporting Information S1 shows the content of the cell data set (which is also provided as a supplementary data set in Shutler et al., 2023) showing all of the resulting shallow shelf boundaries and their onto-shelf direction vectors. $\overrightarrow{B_L}$ is later used to allow current velocities to be calculated from the relevant ocean current data at each grid cell along the shelf boundary.

Larger values of the quantization of the contour lead to improved capability to follow complex shelf contours (e.g., compare Figures S1b to S1c in Supporting Information S1) but with increased computation time. The quantization was chosen so that there were 20 quantization steps within a 0.25° grid cell. The range in depth (from 500 to 600 m) was chosen to identify the shelf slope or transitions from shelf to open ocean, rather than simply identifying the edge of the shallow shelf (for which it is common to use a boundary at 200 m depth). To assess the sensitivity of the choice of shelf boundary depth, the cross-shelf currents were also calculated using shelf boundary depths of 300–800 m (in 100 m steps). In each case, the deep contour depth was selected to be 100 m deeper than the shallower shelf boundary depth.

**2.2. Indicator of Ekman Versus Geostrophic Dominance of the Shelf Break Flow**

Monthly mean geostrophic and Ekman current data (1995–2015 at 0.25° × 0.25°) were retrieved from the
GlobCurrent re-analysis product (CMEMS, 2023; Rio et al., 2014, 2016) (native global resolution of
0.25° × 0.25° and daily). These data are an observation-based assessment of ocean currents at the surface and
15 m depth, which resolves the spiral-like Ekman behavior with depth. These depth-resolved data and improved
retrieval of currents are achieved through the use three different types of global-coverage satellite measurements
(gravimetry, altimetry and sea surface temperature) and two types of globally distributed in situ sensors (surface
drifters and Argo floats). This combination of observations allows the currents to be resolved at the spatial scale of
0.25° (or ~28 km at the equator), which is greater than that achievable by using individual observation types (e.g., altimeters can typically only resolve spatial scales of ~125 km).

The wind-driven Ekman current ($\vec{C}_E$) both rotates and decreases in magnitude with depth, so $\vec{C}_E$ peaks at the surface. The net transport across the mixed layer due to the Ekman processes will be at ~90° to the direction of the wind. Rio et al. (2014) analyzed drifter data to determine the rotation angle of the surface current with respect to wind, and identified a 30.75° rotation of the surface current. Consequently, the magnitude of the surface component of $\vec{C}_E$ offset by 59.25° (i.e., 90°–30.75°) and normal to the shelf break provides an estimate of the upper range of the net Ekman current strength crossing the shelf break within the whole mixed layer. Multiplying this surface current component $\vec{C}_E$ at each grid cell by the length of the shelf boundary passing through that grid cell and the shelf edge normal vector (collectively given by $\vec{B}_L$) gives the net surface Ekman current that is normal and crossing the shelf boundary for each cell, which is denoted by $\vec{C}_{ES}$. The geostrophic current ($\vec{C}_G$) is comprised of barotropic and baroclinic components. The former are depth independent, and the latter are density dependent and so can vary with temperature and salinity, and thus depth. However, the density within the mixed layer will be approximately uniform, so the magnitude of the surface observed $\vec{C}_G$ which is normal to the shelf break should be a good proxy of the geostrophic current component crossing the shelf break at all depths within the mixed layer. Multiplying this current component $\vec{C}_G$ by the length of the boundary that passes through each grid cell and the shelf edge normal vector (collectively given by $\vec{B}_L$) gives the net surface geostrophic current crossing the shelf boundary at each cell, denoted by $\vec{C}_{GS}$. The ratio of $\vec{C}_{ES}$ to $\vec{C}_{GS}$ can then be used to indicate the geographic locations and temporal periods where either the geostrophic or Ekman current component likely dominates the cross-shelf flow within the mixed layer. So, the relative dominance (in terms of geostrophic vs. Ekman), $D_{GS}$, across the shelf break is then estimated using:

$$D_{GS} = \frac{|\vec{C}_{GS}|}{(|\vec{C}_{ES}| + |\vec{C}_{GS}|)} \qquad (1)$$

## 2.3. Indicator of Stokes Drift Influence On-Shelf Break Transport

The degree of turbulent flow at the surface (Reynolds stress term) is generally dominated by wind fluctuations and wind stress but can also encompass a wave (orbital motion)-induced transport. The gradient of this wave-induced transport leads to a surface drift, the Stokes drift. Its strength decreases exponentially with depth (depending on the surface wave characteristics) but can still be highly correlated with offshore transport (Woodson, 2013). The depth dependency means that the maximum influence will occur within shallow mixed layers that exist during low wind (weak Ekman) conditions. Following Woodson (2013), such conditions are defined as low along-shelf wind stress ($|\tau^{WY}| < 0.03 \text{ N m}^{-2}$) coincident with large significant wave heights ($H_s > 2 \text{ m}$), where wind stress is defined as $\tau = \rho_a \text{ Cd} (U_{10})^2$, $\rho_a$ is the density of air (assumed to be $1.225 \text{ kg m}^{-3}$), Cd is the drag coefficient (calculated following Smith (1980)) and $U_{10}$ is the 10 m wind speed. Regions and temporal periods where Stokes drift could be a significant controller of cross-shelf transport were identified using these condition constraints and a global coverage wave model re-analysis with the associated wind speed data set (Rascle & Arduuin, 2013; WAVEWATCH III Development Group, 2016). Multiplying the resulting Stokes current component at each grid cell by the length of the shelf boundary passing through that grid cell and the shelf edge normal vector (again using $\vec{B}_L$) gives the net surface Stokes current that is normal and crossing the shelf boundary for each cell, which is denoted by $\vec{C}_{SS}$. The dominance of the Stokes drift current ($D_{SS}$) across the shelf break with respect to the corresponding total surface current is then estimated as

$$D_{SS} = \frac{|\vec{C}_{SS}|}{(|\vec{C}_{SS}| + |\vec{C}_{ES}| + |\vec{C}_{GS}|)} \qquad (2)$$

where the denominator ($|\vec{C}_{SS}| + |\vec{C}_{ES}| + |\vec{C}_{GS}|$) is the estimate of the total current, $\vec{C}_{TS}$, crossing the shelf break.
2.4. Evaluating Correspondence of Currents With Atmospheric CO₂ Uptake Tendency

Laruelle et al. (2018) identified that the mean temporal rate of increase in surface water pCO₂ with respect to the atmospheric value varies for different shelf-seas. Using a long-term wintertime in situ data set, they identified 15 shelf regions where these temporal trends were significant, implying the tendency for these seas to have enhanced uptake of atmospheric CO₂. The increasing tendency does not necessarily indicate an increasing CO₂ sink, as it could also represent a decreasing CO₂ source. Both of the mechanisms that they proposed to explain the evolution of these shelf-sea air-sea CO₂ sinks will be reliant on the exchange of water (and the carbon within it) at either the surface or depth. Therefore, it is possible that a relationship could be observed between the long-term CO₂ uptake tendency and the long-term average shelf break currents, indicating a link with either export at the surface (i.e., off-shelf flow at the surface) or at depth (on-shelf flow at the surface). Similarly, a relationship between the long-term CO₂ uptake tendency and the long-term average air-sea CO₂ gas exchange (i.e., surface turbulence driving exchange of CO₂ at the air-sea interface) could be observed, as this will promote ocean uptake of CO₂ from the atmosphere (and a subsequent increase in inorganic carbon). The majority of the in situ data used within Laruelle et al. (2018) are from 1995 to 2015 (e.g., see Figure 3 of Laruelle et al., 2018), which is consistent with the data distribution within the underlying in situ data set (Bakker et al., 2016). Therefore, all analyses were performed for the period 1995–2015. The mean aggregated Laruelle et al. (2018) determined CO₂ uptake tendency data, dΔpCO₂/dt (where ΔpCO₂ = air minus water pCO₂, t is time) for each shelf sea (i.e., shelf wide dΔpCO₂/dt values presented in Laurelle et al. (2018, Table 3) were regressed against the equivalent shelf sea hemisphere specific season mean and absolute mean current components (for 1995 to 2015) across the adjacent shelf break (C<sub>SS</sub>, C<sub>ES</sub>, C<sub>GS</sub>, C<sub>TS</sub>). All seasons were assessed as it can take up to 1 year for CO₂ to equilibrate across the air-sea interface, so testing all seasons could identify a lagged response. We also investigated via regression any relationship between the long-term mean wind-driven air-sea CO₂ gas transfer across the entire shelf sea region and dΔpCO₂/dt values. The air-sea CO₂ gas transfer velocity was calculated using a wind speed gas transfer parameterization (Nightingale et al., 2000) and the wind speed data (from the current data set), and a sea surface temperature climate data record (Merchant et al., 2019) for 1995 to 2015. Similarly, the sea surface temperature and dΔpCO₂/dt were regressed against each other as a significant relationship could indicate a changing Revelle factor. The regressions took the form of linear and non-linear regressions in Python using SciPy v1.2.3, and additionally generalized additive models (GAM; pyGAM v0.9.1), and the most significant and strongest regression result (lowest *p*-value, and highest *r*²) for each current and dΔpCO₂/dt pairing were retained. The GAM was used to test the potential of combining the surface current data with the wind-driven air-sea gas transfer data when regressing against the dΔpCO₂/dt values. All results are presented, but only those with *p*-value (*p*) < 0.05 are discussed and the main conclusions focus on results with *p* < 0.01. Each current component was sampled at the highest frequency possible within a spatially consistent region to that of the Laruelle et al. (2018) data, before being aggregated to determine the 1995 to 2015 shelf sea signals and regressed against the equivalent 1995 to 2015 dΔpCO₂/dt signal. The Baltic Sea is not fully covered within the ocean current re-analysis data set, so 14 shelf seas were analyzed (in comparison to the 15 analyzed by Laruelle et al., 2018). The sensitivity of each regression result to potential “outliers” was tested using a statistical bootstrapping approach. For this part of the analysis, two different data points (shelf seas) were systematically removed, and the respective regression was recalculated to produce a new *r*². The removed data points were then replaced, and a different pair removed, the *r*² recalculated and the data points replaced. This process was repeated across all possible data-point pairings. The variance of the *r*² values across this ensemble of results from all of the regression pairings is then provided as the estimate of the robustness to outliers of each full data set regression result. The GAM was constructed using the dΔpCO₂/dt as the response, and the seasonal Ekman current flows and gas transfer coefficient as the predictors. The GAM fits the predictors to the response function using an identity link function. None of the data were transformed before input into the GAM and were assumed to be normally distributed. The pyGAM fits spline functions to the model terms such that the model takes the form; G = *s*(current) + *s*(gas transfer); where G is the output and *s*() represents the spline function for each input data set. The spline fits were penalized to prevent overfitting using a second derivative with a weighting of 0.6 (which is the default value for pyGAM). We note that even with this step to prevent overfitting, the low number of samples (*n* = 14) in this study means that the results will still likely be sensitive to the structure of the GAM. The existence of any long-term temporal trends in the shelf sea currents was also evaluated. These temporal trends were calculated using the slope of a linear regression after each parameter data set had been split into seasonal values and were calculated on individual 0.25° regions before being aggregated for each shelf.
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Mean total shelf break current for all continental shelf sea boundaries for 1995 to 2015, with shelf-seas of interest labeled during (a) northern hemisphere winter (January, February and March) and (b) northern hemisphere summer (July, August and September). Positive values indicate on-shelf currents, and negative values indicate off-shelf currents. The black boxes are the shelf-seas studied by Laruelle et al. (2018).</figcaption></figure>

# 3. Results

## 3.1. Total Cross Shelf Flows

Overall, the method identifies shelf break current velocities valid for the mixed layer and calculated across years 1995–2015 that appear consistent with the understanding of shelf break flows globally (Figure 1). For example, eastern boundary upwelling systems show off-shelf currents at the surface (i.e., the Benguela and Cascadian shelf systems), on-shelf currents along the Northern European shelf including the North Sea (Huthnance et al., 2022; Painter et al., 2016), and an on-shelf flow in the Mid Atlantic Bight with an off-shelf flow in the South Atlantic Bight (Levin et al., 2018). Seasonal changes in these shelf break flows are also consistent with our understanding, such as stronger off-shelf currents observed along the Benguela shelf during the upwelling season (September to March; Figure 1a) compared to the non-upwelling season (Figure 1b) (Strub et al., 1998), and a switch from on-shelf (Figure 1a) to off-shelf (Figure 1b) flows along the Oman-Somali coastline in response to the Monsoon (Schott & McCreary, 2001). These results remain consistent with the chosen shelf boundary depth (examples of Figure 1a in Figure S3 in Supporting Information S1 for shelf boundaries between 300 and 800 m).
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Relative strength indicator results for the geostrophic versus Ekman transport across all continental shelf sea boundaries for 1995 to 2015, with shelf-seas of interest labeled during (a) northern hemisphere winter (January, February, and March) and (b) northern hemisphere summer (July, August, and September). A value of 0.0 indicates transport dominated using Ekman processes, whereas a value of 1.0 indicates transport dominated by geostrophic components. The black boxes are the shelf-seas studied by Laruelle et al. (2018).</figcaption></figure>

## 3.2. Dominance of Geostrophic, Wind, and Wave Driven Flows Varies by Location and Season

Figure 2 identifies where geostrophic currents normal to the shelf break likely dominate exchange over Ekman currents (i.e., the results from applying Equation 1 of the methods) for the northern hemisphere winter (Figure 2a) and summer (Figure 2b). Some regions are clearly dominated by shelf break geostrophic currents (e.g., The North Sea in Figures 2a, 3a, and 3b), whereas in many regions the cross-shelf currents are a mixture of both geostrophic and Ekman (e.g., English Channel in Figures 3, 4a, and 4b). Some regions also exhibit distinct changes in hydrodynamic regimes along the shelf (e.g., the Mid and South Atlantic Bights in Figures 2, 3c, and 3d).

Figure S4 in Supporting Information S1 identifies the regions and periods where Stokes driven currents could become important for cross-shelf exchange (the results from applying Equation 2). Generally, Stokes drift contributes a smaller influence on the shelf break currents than geostrophic or Ekman components (Figure S4 in Supporting Information S1), but its contribution can still equal (e.g., Californian Coast non-upwelling period or
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Contributions to the currents within the mixed layer and normal to the shelf break due to Ekman (green) and geostrophic (blue) currents during northern hemisphere winter (January to March, left column) and summer (July to September, right column) for 1995 to 2015. The equivalent Stokes component normal to the shelf break where $|rW_y| < 0.03 \text{ N m}^{-2}$ and $H_s > 2 \text{ m}$ is shown in orange. Shaded areas are ±1 standard deviation. Regions are (a) and (b) the European shelf sea comprising the North Sea and English Channel, and (c) and (d) the Mid-Atlantic Bight. Labeled red lines denote the shelf break that occurs within the Laruelle et al. (2018) region definition in Figure 1. Note the different y-axis limits between all plots.</figcaption></figure>

Chilean coast; Figure S4 in Supporting Information S1) or exceed that of Ekman (year round on parts of the European shelf, Figures 3a and 3b, Figure S4 in Supporting Information S1).

Overall, pressure driven geostrophic, wind driven Ekman and wave driven Stokes drift currents are all important for driving the shelf break currents and therefore the cross-shelf surface transport within the mixed layer. But globally and regionally the relationship between the different current components (geostrophic, Ekman and Stokes) and their strength can be highly variable in space and between seasons. Collectively, this highlights the difficulty in using isolated in situ studies to characterize the wider shelf regions, and the need to characterize geostrophic and ageostrophic components, as otherwise important hydrodynamic variability can be easily missed.

Figure S3 shows the impact of varying the depth definition of the shelf break. The depth definition of the shelf break may modify the location of the shelf break and direction of the normal vector in locations of low gradients
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Regression of mean Ekman shelf break surface flows between 1995 and 2015 against the long-term gradient in gaseous CO₂ (dΔpCO₂/dt, the atmospheric CO₂ uptake tendency) from Laruelle et al. (2018) (a) mean winter time shelf break Ekman current to dΔpCO₂/dt from Laruelle et al. (2018) showing a significant relationship (*p* < 0.01). All shelf seas are labeled and the black dashed line is the non-linear regression line. In plot statistics are coefficient of determination (r²) and their variance from the bootstrapping exercise, p-value and number of samples (*n* shelf seas). Panel (b) same as (a) but for mean autumn time shelf break Ekman current showing a significant relationship (*p* < 0.01). Fourteen datapoints are plotted (in comparison to Laruelle et al. (2018) who show 15) as no ocean current data were available for the Baltic Sea.</figcaption></figure>

between the shelf and the deep oceans. This may become an issue in some small regions but appears to be insignificant when assessed globally, as Figure S3 in Supporting Information S1 shows no discernible differences.

The $\vec{C}_{ES}$ result is used to provide an indicator of the upper bounds of $\vec{C}_E$ across the mixed layer. This approach likely overestimates the contribution of $\vec{C}_E$, as it does not take account of the exponential decrease of $\vec{C}_E$ with depth, however there are clearly instances within the results where Ekman processes do not dominate so this issue is not considered significant for the conclusions presented here. Similarly, Stokes drift is not necessarily aligned with the wind stress and can be modified (to a limited extent) by non-local swell systems. The Stokes drift can affect the surface mixed layer, and thus the vertical diffusion to impact the final Ekman spiral. For example, Ardhuin et al. (2009) identified that Stokes drift can cause the deflection angle in the Ekman layer to increase into the range of 45-70°. But as a practical first evaluation this analysis has ignored interactions between the different current components, focusing instead on identifying where each component is likely to dominate or influence. The published near zero bias values for the geostrophic, Ekman and Stokes current data sets indicate that no single data set will dominate the ratios (i.e., Equations 1 and 2) within this 20-year global time series analysis. The analysis presented here has ignored the impact of tidal flows and currents, as none of the data sets used include tidal oscillations or their influences; therefore, there was no way of including these tidal components. We do note though that the net tidal influence over a whole tidal cycle will generally be small at the surface (Huthnance et al., 2009) but could be important for shelf exchange in some regions (Graham et al., 2018; Ricker & Stevnev, 2020; Wang et al., 2013). Within this study, the resolution of the analysis was constrained by the available data resolution of the depth resolved observation-based current data. However, the representation of the across-shelf flows is likely to be dependent on the spatial resolution of the underlying current data and the onto shelf direction vector. In theory, higher spatial resolutions would capture the smaller scale variability in the onto shelf direction vector, and those from the underlying current data. The potential impact of this issue was evaluated using the native resolution of an ocean reanalysis data set designed for forecasting (at 0.083°; Jean-Michel et al., 2021) and by creating the bathymetry data to the same resolution. Figure S6 in Supporting Information S1 shows visually how a subsampled lower resolution analysis (0.25°) appears to capture the variability in the across shelf current compared to the native resolution (0.083°), but as expected some small differences are apparent (see description in Text S1 in Supporting Information S1). Repeating the mean across shelf current flow analysis using 0.083° (bathymetry and currents) instead of 0.25° results in zero bias (between the two results, 0.25° vs. 0.083°) with a small root mean squared difference (RMSD) of 0.07 m s⁻¹ (Figure S7 in Supporting Information S1) in representing the flows within each 0.25° region. This means that performing the analysis at a spatial resolution of 0.25° has maintained the accuracy of the mean flows; therefore, the choice of spatial resolution has not biased the results. The precision of the mean currents (indicated by the RMSD) has been
marginally altered. These small differences suggest that the chosen resolution of the bathymetry and current data used in the main analysis has no major impact on our overall results, as they will not be biased by the change in spatial resolution. We note however, that regional biases can be large in some geographic locations (e.g., in the Agulhas region, Figure S7 in Supporting Information S1).

### 3.3. Placing the Surface Flows Into Context for Atmospheric CO₂ Uptake Tendency

Table 1 shows the long-term $d\Delta pCO_2/dt$ rates ($\Delta pCO_2$ = air minus water $pCO_2$, $t$ is time) and groupings from Laruelle et al. (2018) along with the corresponding long-term winter-time currents valid for the mixed layer, and the long-term winter-time shelf-region atmosphere-ocean (air-sea) $CO_2$ gas exchange rates.

The wintertime $d\Delta pCO_2/dt$ were regressed against both seasonal and annual means of total shelf break currents, the geostrophic, Ekman and Stokes shelf break current components, the proportions of these components to the total shelf break current and the respective air-sea $CO_2$ gas exchange values (see Figure S5 in Supporting Information S1 for all regression results). The annual mean total shelf break current, annual mean absolute total shelf break, and air-sea gas exchange regressions showed no clear relationships to $d\Delta pCO_2/dt$ (Figure S5 in Supporting Information S1). Splitting the total current into the individual components (i.e., geostrophic, Ekman and Stokes) identifies a significant relationship between $d\Delta pCO_2/dt$ and the wintertime Ekman component of the flow (Figure 4a; $r^2$ = 0.72 ± 0.03, $p$ < 0.01, $n$ = 14). With a similar but weaker significant relationship during autumn (Figure 4b; $r^2$ = 0.57 ± 0.05, $p$ < 0.01, $n$ = 14). A significant relationship to the annual Ekman is also evident but explains less of the variance (Figure S5a in Supporting Information S1; $r^2$ = 0.35 ± 0.1, $p$ = 0.03, $n$ = 14). The bell shaped (or curved) regressions in Figure 4 allow the on- or off-shelf surface currents across the different shelf seas to be seen, visually showing how the different seas are behaving. However, these significant results are also reflected in the equivalent annual, wintertime and autumn time mean absolute Ekman component regression results, except the removal of the flow direction (due to using the absolute Ekman current) has reduced the strength of the results as a lower amount of the data variance is captured (i.e., $p$-value is still significant but with a lower $r^2$, Figures S5b, S5m, and S5at in Supporting Information S1). No significant relationship was identified between sea surface temperature and $d\Delta pCO_2/dt$ (Figure S5 in Supporting Information S1).

The potential for the air-sea $CO_2$ gas exchange to provide additional predictive power (as discussed in the introduction) is indicated in Figure S5 in Supporting Information S1, which shows the nonlinear regression between $d\Delta pCO_2/dt$ and the wintertime mean wind-driven gas exchange. These wintertime and autumn time regression results are not significant on their own at the $p$ = 0.01 level (Figure S5r in Supporting Information S1, wintertime, shows $r^2$ = 0.16 ± 0.07, $p$ = 0.16, $n$ = 14; Figure S5ay in Supporting Information S1, autumn time, shows $r^2$ = 0.02 ± 0.03, $p$ = 0.62, $n$ = 14). However, combining the Ekman wintertime data with the wintertime mean wind-driven air-sea $CO_2$ gas exchange data using a GAM gives $r^2$ = 0.82 ± 0.06, $p$ < 0.01, $n$ = 14 (Table 2), whereas using the autumn equivalent pair gives no real improvement in autumn time $r^2$ or significance ($p$-value). So the combination of the two processes, long-term wintertime Ekman currents at the shelf break and the long-term mean wintertime wind-driven air-sea $CO_2$ gas exchange across each shelf-sea collectively explains 82% of the variance in the shelf wide $d\Delta pCO_2/dt$ data for all 14 shelf seas. From the temporal trend analysis, a weak but significant relationship between $d\Delta pCO_2/dt$ and the long-term trend in the autumn cross-shelf Ekman current signal was observed ($r^2$ = 0.35 ± 0.11, $p$ = 0.02, $n$ = 14; Figure S8 in Supporting Information S1). Similarly, a weak but significant relationship was identified between $d\Delta pCO_2/dt$ and the long-term trend in the winter cross-shelf Stokes current signal ($r^2$ = 0.37 ± 0.11, $p$ = 0.02, $n$ = 14; Figure S8 in Supporting Information S1).

### 4. Discussion

These results identify that shelf seas with strong Ekman components either onto or leaving the shelf at the surface have strong positive $d\Delta pCO_2/dt$ trends. This suggests that their tendency (or potential) to act as an air-sea $CO_2$ sink is increasing as the Ekman accelerated rate of transport of carbon from the shelf appears to be exceeding the rate of downward mixing of carbon or its utilization by biology. This apparent strong influence of the Ekman signal poses the question of how would the Ekman component be modifying the atmospheric $CO_2$ uptake tendency of the shelf seas studied by Laruelle et al. (2018). Of the three flows studied, the wave driven stokes drift is relatively small and limited to the very surface, and less likely to influence the whole mixer layer. Despite the geostrophic current flows sometimes being large within the proximity of the shelf seas, much of the geostrophic flow will align with the shelf edge, so its ability to push water on (or off of) the shelf at the surface and the
<table><caption>**Table 1**

Continental Shelf Seas Groups With Identified Atmospheric CO₂ Uptake Tendency (Significant Decadal Trends in ΔpCO₂) and Their Controls of Shelf Break Currents and Strengths of Atmosphere-Ocean (Air-Sea) Gas Exchange</caption><thead><tr><th>Shelf seas from Laruelle et al. (2018)</th><th>dΔpCO<sub>2</sub>/dt groups from Laruelle et al. (2018)</th><th>dΔpCO<sub>2</sub>/dt from Laruelle et al. (2018) (μatm yr<sup>-1</sup>)</th><th>Implied pH</th><th>Winter time shelf total current (μ ± σ, ms<sup>-1</sup>)</th><th>Winter time shelf break exchange via Ekman component (μ ± σ, ms<sup>-1</sup>)</th><th>Winter time air-sea exchange (μ ± σ, cm hr<sup>-1</sup>)</th><th>Implied conditions</th></tr></thead><tbody><tr><td>Mid Atlantic Bight</td><td>High rate of increase</td><td>1.92 ± 0.36</td><td>Decreasing slower than would be expected due to rise in pCO<sub>2(ann)</sub></td><td>-0.04 ± 0.02</td><td>-0.03 ± 0.001</td><td>22.8 ± 0.5</td><td>Carbon is rapidly exported from the shelf either at the surface, or depth, due to Ekman driven exchange, or the carbon is rapidly utilized by biological growth.</td></tr><tr><td>North Sea</td><td></td><td>1.81 ± 0.10</td><td></td><td>0.18 ± 0.01</td><td>0.04 ± 0.003</td><td>34.5 ± 0.3</td><td>Carbon is unable to accumulate within the water of the shelf, largely reducing the expected increase in pCO<sub>2(ann)</sub> due to increase in pCO<sub>2(ann)</sub> (ΔpCO<sub>2(ann)</sub> increasing).</td></tr><tr><td>Southern Greenland</td><td></td><td>1.73 ± 0.15</td><td></td><td>-0.21 ± 0.01</td><td>0.04 ± 0.002</td><td>42.2 ± 1.0</td><td></td></tr><tr><td>Antarctic Peninsula</td><td></td><td>1.57 ± 0.13</td><td></td><td>0.00 ± 0.01</td><td>-0.02 ± 0.004</td><td>21.4 ± 0.2</td><td></td></tr><tr><td>Cascadian Shelf</td><td>Moderate rate of increase</td><td>0.97 ± 0.18</td><td>Decreasing slower than would be expected due to rise in pCO<sub>2(ann)</sub></td><td>-0.08 ± 0.01</td><td>-0.02 ± 0.003</td><td>22.2 ± 0.3</td><td></td></tr><tr><td>Labrador Sea</td><td></td><td>0.71 ± 0.06</td><td></td><td>0.06 ± 0.01</td><td>-0.02 ± 0.001</td><td>33.9 ± 1.0</td><td></td></tr><tr><td>South Atlantic Bight</td><td></td><td>0.7 ± 0.14</td><td></td><td>-0.46 ± 0.08</td><td>-0.02 ± 0.003</td><td>13.8 ± 0.6</td><td></td></tr><tr><td>Iminger Sea</td><td></td><td>0.47 ± 0.06</td><td></td><td>-0.02 ± 0.01</td><td>-0.01 ± 0.001</td><td>27.8 ± 0.1</td><td></td></tr><tr><td>Barents Sea</td><td>Nominal or no rate of change</td><td>0.31 ± 0.06</td><td>Decreasing at a rate consistent with rising pCO<sub>2(ann)</sub></td><td>0.26 ± 0.02</td><td>0.03 ± 0.001</td><td>28.5 ± 0.4</td><td>Carbon is not rapidly exported from the shelf at the surface or depth due to Ekman driven exchange, or carbon is not rapidly utilized by biology, and is therefore able to accumulate within the shelf waters.</td></tr><tr><td>Coast of Japan</td><td></td><td>0.22 ± 0.05</td><td></td><td>0.01 ± 0.01</td><td>-0.00 ± 0.003</td><td>21.1 ± -0.4</td><td>pCO<sub>2(ann)</sub> therefore largely follows the increasing pCO<sub>2(ann)</sub> (ΔpCO<sub>2(ann)</sub> does not change).</td></tr><tr><td>Tasmanian Shelf</td><td></td><td>0.15 ± 0.04</td><td></td><td>0.05 ± 0.01</td><td>0.02 ± 0.005</td><td>24.4 ± 0.6</td><td></td></tr><tr><td>English Channel</td><td></td><td>-0.03 ± 0.04</td><td></td><td>-0.02 ± 0.01</td><td>-0.01 ± 0.001</td><td>28.6 ± 0.3</td><td></td></tr><tr><td>Patagonian Shelf</td><td></td><td>-0.11 ± 0.06</td><td></td><td>-0.23 ± 0.04</td><td>0.02 ± 0.005</td><td>34.0 ± 0.9</td><td></td></tr><tr><td>Bering Sea</td><td>Moderate rate of decrease</td><td>-1.44 ± 0.14</td><td>Decreasing faster than would be expected due to rise in pCO<sub>2(ann)</sub></td><td>0.04 ± 0.01</td><td>0.01 ± 0.001</td><td>24.8 ± 0.3</td><td>Carbon is not efficiently exported or utilized by biology from the shelf and is able to accumulate within the water.</td></tr></tbody></table>

Note. dΔpCO₂/dt rates and region names are from Laruelle et al. (2018) using the wide shelf definition. An increase in dΔpCO₂/dt implies a strengthening sink of CO₂, nominal or no increase implies a temporally constant sink, whereas a decrease implies a weakening sink. The Baltic Sea is not included as no ocean current data were available for this sea. μ indicates the mean, and σ indicates the standard error of the variable. The term “rapidly utilized” refers to biological uptake of carbon which removes it from its dissolved state in the water.
<caption>**Table 2**</caption>

Generalized Additive Models (GAM) Applied to Regress $d\Delta pCO_2/dt$ With the Annual and Seasonal Ekman Current and Air-Sea $CO_2$ Gas Transfer Data

<table><thead><tr><th>Season</th><th>GAM Ekman current + air-sea CO<sub>2</sub> gas transfer r<sup>2</sup></th><th>GAM Ekman current + air-sea CO<sub>2</sub> gas transfer p-value</th></tr></thead><tbody><tr><td>Annual</td><td>0.51 ± 0.29</td><td>&lt;0.01</td></tr><tr><td>Winter</td><td>0.82 ± 0.06</td><td>&lt;0.01</td></tr><tr><td>Spring</td><td>0.13 ± 0.12</td><td>0.20</td></tr><tr><td>Summer</td><td>0.05 ± 0.04</td><td>0.42</td></tr><tr><td>Autumn</td><td>0.67 ± 0.10</td><td>&lt;0.01</td></tr></tbody></table>

Note. Coefficient of determination ($r^2$) and their (±) variance are derived from the bootstrapping exercise.

reciprocal flow at depth is diminished. Therefore, the geostrophic component of the across shelf flow results from intrusions of currents (i.e., slope current or a western boundary current) (Graham et al., 2018; Levin et al., 2018; Malan et al., 2022; Roughan & Middleton, 2004) or the presence of deep ocean eddies traveling along the shelf break (Cherian & Brink, 2016; Malan et al., 2020; Waite et al., 2016; Zhang & Gawarkiewicz, 2015). These geostrophic surface currents across the shelf break could be large but will affect a relatively small area of the shelf. Although geostrophic processes are important for shelf-ocean mixing (Cherian & Brink, 2016; Malan et al., 2020; Waite et al., 2016), they appear unlikely to generate the on-shelf surface currents capable of significantly driving off-shelf carbon export, a conclusion which is consistent with our results. The Ekman flow occurring in the vicinity of a shelf edge will likely be orthogonal to the shelf edge, enabling a greater ability to push water across the shelf edge. The wind driven Ekman component of the flow onto the shelf is therefore unlikely to act solely at the shelf break and can influence the entire shelf (Cherian & Brink, 2016; Malan et al., 2022). If the Ekman shelf break flow is onto the shelf, there is likely to be flow across the whole shelf toward the land, downwelling of water near the coast, and off-shelf transport at depth (Holt et al., 2009; Mahjabin et al., 2019). Previous work supports the idea that the export of carbon from the shelf sea added through atmospheric-ocean exchange or modified by anthropogenic pressures on the biological pump are likely coupled to the shelf break exchange at either the surface or depth (Bourgeois et al., 2016; Holt et al., 2009; Painter et al., 2016; Rogge et al., 2023), so a combination of the physical and biological processes likely controls the carbon export. The high variance described by the regressions (Figure 4) supports the conclusion that the wind-driven flows are the primary linkage to the $d\Delta pCO_2/dt$ with air-sea exchange also being important. This supports the conclusion that the efficiency of the physical pump, characterized by wind-driven imbalances in strength and timing between across shelf water flows and on shelf air-sea interactions, is the primary way shelf sea carbon accumulation is controlled (Table 1, see the column labeled 'implied conditions').

Recent work identified that winter-time turbulent air-sea $CO_2$ exchange and lower water temperatures are the dominant controllers of annual (i.e., short-term) atmosphere-ocean uptake of $CO_2$ within European shelf seas (Kitidis et al., 2019) when assessing against the biological control (which in comparison was small). This is consistent with the results identified here where long-term winter-time cross-shelf exchange and turbulent air-sea $CO_2$ gas exchange account for 82% of the variance in the $d\Delta pCO_2/dt$ data (an indicator of the tendency of the shelf-sea atmospheric $CO_2$ sink). Collectively, these findings suggest that annual surface uptake and the long-term uptake tendency of shelf seas are mostly governed by winter-time wind-driven ocean physics.

We propose that those seas that fall close to the regression lines between $d\Delta pCO_2/dt$ and the Ekman component of shelf break flow (Figure 4) are primarily controlled by shelf-break exchange and this control is further enhanced by wintertime air-sea $CO_2$ gas exchange. Shelf seas further away from the regression line are likely to have stronger secondary controls, which could include the biological pump contributions, alterations of the biology through anthropogenic pressures including nutrient inputs and carbon resuspension, non-wind driven $CO_2$ gas exchange controls, limitations on the water buffering capacity, localized warming, or other processes (Yuan et al., 2017).

The evidence provided here supports the hypothesis that shelf-seas with strong wintertime shelf break Ekman components could continue to uptake atmospheric $CO_2$ and maintain their status as air-sea $CO_2$ sinks. Shelf seas with weak shelf break Ekman components could continue to track atmospheric $CO_2$ and accumulate carbon. But, how these conditions change or evolve will be linked to any changes in surface winds that control the Ekman
processes, the buffer capacity of the seas and changes in the other secondary controls including biology and disturbance. The analysis in this paper has taken a long-term assessment of each current component and analyzed them with respect to the long-term $d\Delta pCO_2/dt$ toward identifying what is driving the observed $d\Delta pCO_2/dt$. This does not assume that the currents are temporally stable, only that their long-term signal has influenced the long-term $d\Delta pCO_2/dt$. The global wind fields have been observed to be increasing due to anthropogenic climate change, with the increase in mean wind speeds and swell generation (e.g., Reguero et al., 2019), which likely impact the respective currents. The existence of temporal trend in the current components was confirmed within the analysis and these long term current trends could be related to $d\Delta pCO_2/dt$, as weak ($r^2$ = 0.34 to 0.35; $p$ < 0.03) but significant relationships were identified between $d\Delta pCO_2/dt$ and the long-term trend in the autumn cross-shelf Ekman current signal and the winter Stokes current signal (Figure S8 in Supporting Information S1). This suggests that the fingerprint of the anthropogenically driven changes in wind fields and its impact on shelf chemistry are evident within this analysis, which means that changes in global winds and storm systems driven by climate change could influence shelf sea carbon. Therefore, it would appear important for models used to assess the evolving shelf sea $CO_2$ uptake to resolve wind-driven shelf break currents and flows along with wind-driven air-sea $CO_2$ gas exchange. New satellite observation methods that hope to directly observe wind and current fields at resolutions relevant to shelf-seas could prove invaluable for supporting these modeling efforts or for identifying changes in cross-shelf flows (e.g., Ardhuin et al., 2019; Torres et al., 2023).

## 5. Conclusions

Previous studies have been unable to consider the global perspective of deep-ocean to coastal-ocean exchange. Here we have taken a pragmatic approach to identify the relative importance of the different ocean current components in influencing global cross-shelf surface transport, which in turn, through the need for mass balance, is a dominant control of the export of water from the shelves. Analyzing fourteen shelf-seas across a 20 year time series identifies that the atmospheric $CO_2$ uptake tendency within shelf seas is significantly controlled by winter and autumn wind-driven flows and surface air-sea exchange. This suggests that shelf-seas with strong shelf break wind-driven Ekman surface currents could continue to uptake atmospheric carbon, and their status as $CO_2$ sinks could continue. Future changes in shelf break currents could significantly influence shelf sea atmospheric $CO_2$ uptake and the size of the continental shelf-sea carbon pump. Any efforts to monitor, predict or understand the carbonate system health of these continental shelf seas, from annual to decadal-scale, require approaches that can resolve shelf-break wind-driven currents and shelf-region wind-driven air-sea $CO_2$ exchange.

## Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

## Data Availability Statement

The software code for this analysis is available at https://doi.org/10.5281/zenodo.10255325 (Shutler et al., 2023). The bathymetry data are available at Weatherall et al. (2015). The Globcurrent ocean geostrophic, Ekman currents are available from the Copernicus Marine Data Store (CMEMS, 2023; https://doi.org/10.48670/mds-00327) and Stokes current data are available from the Ifremer FTP server (ftp.ifremer.fr; download scripts are provided in the accompanying software). The shelf sea $pCO_2$ trend values used are available from Laruelle et al. (2018).

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## Acknowledgments

The authors acknowledge funding through the European Space Agency (ESA) Sea surface KInematics Multiscale monitoring (SKIM) Mission Science study (contract 4000124734/18/NL/CT/gp), the ESA SKIM Scientific Performance Evaluation study (contract 4000124521/18/NL/CT/gp), and from the Convex Seascape Survey (https://convexseascapesurvey.com/). We thank Fabrice Ardhuin for useful comments on the manuscript. The Surface Ocean $CO_2$ Atlas (SOCAT) is an international effort endorsed by the International Ocean Carbon Coordination Project (IOCCP), the Surface Ocean Lower Atmosphere Study (SOLAS) and the Integrated Marine Biosphere Research (IMBeR) program to deliver a uniformly quality-controlled surface ocean $CO_2$ database. The many researchers and funding agencies responsible for the collection of data and quality control are thanked for their contributions to SOCAT, which was the origin of the main data set within the work of Laruelle et al. (2018).
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