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# Controls on surface water carbonate chemistry along North American ocean margins

## Abstract

Syntheses of carbonate chemistry spatial patterns are important for predicting ocean acidification impacts, but are lacking in coastal oceans. Here, we show that along the North American Atlantic and Gulf coasts the meridional distributions of dissolved inorganic carbon (DIC) and carbonate mineral saturation state (Ω) are controlled by partial equilibrium with the atmosphere resulting in relatively low DIC and high Ω in warm southern waters and the opposite in cold northern waters. However, pH and the partial pressure of CO2 (pCO2) do not exhibit a simple spatial pattern and are controlled by local physical and net biological processes which impede equilibrium with the atmosphere. Along the Pacific coast, upwelling brings subsurface waters with low Ω and pH to the surface where net biological production works to raise their values. Different temperature sensitivities of carbonate properties and different timescales of influencing processes lead to contrasting property distributions within and among margins.

## Introduction

Absorption of anthropogenic CO2 from the atmosphere has acidified the ocean, as indicated by increases in sea surface pCO2 and hydrogen ion concentration ([H+]) and decreases in pH, carbonate ion concentration ([$${\mathrm{CO}}_3^{2 - }$$]), and calcium carbonate (CaCO3) mineral saturation state1,2,3,4,5. The latter is a ratio of the ionic product, [Ca2+][$${\mathrm{CO}}_3^{2 - }$$], to its saturated value below which CaCO3 dissolution may occur (in this paper we only target the saturation state of aragonite, Ωarag, a mineral form that comprises the shells and hard parts of corals, mollusks, and many other marine organisms). More than a decade of ocean acidification research has improved our understanding of the mechanisms controlling the global spatial patterns and temporal variations of ocean carbonate chemistry5,6,7,8, and has begun to reveal how ocean chemistry (e.g., pH and Ωarag)9,10,11,12,13 and marine organisms14,15,16 are responding to anthropogenic CO2 uptake. In coastal regions, much of the ocean acidification research has focused on examining how anthropogenic CO2-induced acidification is mitigated or exacerbated by biological production (removing CO2) in surface waters and subsequent respiration (adding CO2) in subsurface waters as a result of natural nutrient enrichment or human-induced coastal eutrophication17,18,19,20. Attention has also been given to the effects of biological community composition and community metabolism on the potential to buffer or exacerbate ocean acidification21,22. There is, however, incomplete knowledge of large-scale patterns of carbonate chemistry and the mechanisms controlling its variability in coastal oceans, largely due to limited observations and the added complication of dynamic regional or local processes that can be large in magnitude.

Examples of local processes that influence surface water distributions of pCO2, pH, total alkalinity (TA), dissolved inorganic carbon (DIC), and Ωarag in ocean margins include river and wetland inputs, coastal circulation, vertical and lateral mixing, spatial and seasonal temperature variations, the balance of biological production and respiration, and anthropogenic CO2 uptake23,24,25,26,27,28,29,30. Rivers usually carry more acidified waters with a higher DIC/TA ratio than seawater, which may weaken the ability of coastal seas to withstand anthropogenic CO2-induced acidification29,31. Freshwater input can also suppress Ωarag by reducing [Ca2+]. However, increased nutrient input from rivers may lead to elevated biological CO2 removal or basification in surface waters32, whereas the respiration of this organic material back to CO2 in bottom waters may enhance acidification at depth17. Additionally, coastal upwelling can bring low pH and low Ωarag waters to shallow, nearshore regions and put coastal biological systems in stress27. Subsequent CO2 release to the atmosphere and biological production stimulated by the accompanying upwelled nutrients may increase pH and Ωarag33.

In addition to these driving processes, it is important to understand the influence of temperature on the spatial distributions of carbonate system properties. Coastal currents often bring waters from warm (or cold) locations to cold (or warm) locations, resulting in chemical equilibrium shifts and air–sea gas exchange, both of which are sensitive to temperature change:

$${\mathrm{CO}}_{\mathrm{2gas}}\mathop{\longleftrightarrow}\limits^{{K_0}}{\mathrm{CO}}_{\mathrm{2aq}},$$
(1)
$${\mathrm{CO}}_{\mathrm{2aq}} + {\mathrm{H}}_{2}{\mathrm{O}} + {\mathrm{CO}}_3^{2 - }\mathop{\longleftrightarrow}\limits^{{K_1/K_2}}2{\mathrm{HCO}}_3^ - .$$
(2)

Here K0 is the solubility constant, and K1/K2 is the ratio of the first and second dissociation constants of carbonic acid. When a water mass isolated from the atmosphere (referred to herein as a closed system) is cooled, the ratio, K1/K2, will increase (Fig. 1a), and the acid–base equilibrium will shift to the right to reduce dissolved CO2 (CO2aq) and $${\mathrm{CO}}_3^{2 - }$$ and increase $${\mathrm{HCO}}_3^ -$$ (Eq. 2). The gas solubility constant will also increase, further reducing pCO2 following Henry’s Law (pCO2 = [CO2aq]/K0) (Fig. 1a–c), as gas exchange is not allowed to compensate the cooling process in a closed system (Eq. 1). Although not explicitly shown in Eq. (2), cooling will also reduce [H+] and increase pH in a closed system because of the decrease in both acid dissociation constants (Fig. 1). Importantly, cooling can shift a water mass from being a source of CO2 to the atmosphere in warm, subtropical waters to a sink for CO2 in cold, mid-latitude waters when gas exchange occurs in an alongshore current. The process of cooling and gas exchange in an open-system increases CO2aq, a fraction of which combines with and reduces $${\mathrm{CO}}_3^{2 - }$$ and thus Ωarag.

To illustrate the temperature dependences of the marine carbonate system, we define two thermodynamic end members: the closed system, with no gas exchange, and the open system, with a complete CO2 gas exchange equilibrium between seawater and the atmosphere. Thus, our theoretical framework posits that the temperature-dependent change of a species or a property in an open system is the combined effect of gas exchange caused by the solubility change and the subsequent internal thermodynamic equilibrium shift in a closed system (Fig. 1). Importantly, these two temperature effects counteract each other for [CO2aq] (hereafter the subscript aq will be omitted), pCO2, [H+], and pH, whereas they work to enhance each other for [$${\mathrm{CO}}_3^{2 - }$$] and [$${\mathrm{HCO}}_3^ -$$] (or roughly DIC), with atmospheric equilibration playing the dominant role in an open system (Fig. 1). In summary, the combined result of the thermodynamic equilibrium shift and atmospheric equilibration during cooling is predicted to be an increase in [CO2] and DIC, essentially no change in [H+] and pH and, by definition, no change in pCO2, and a relatively large decrease in [$${\mathrm{CO}}_3^{2 - }$$] and Ωarag in surface waters (Fig. 1)7,8,34,35,36. Therefore, spatial variations in pH and pCO2 largely reflect air–sea disequilibrium caused by local physical and biological processes that act more rapidly than gas exchange.

Here we report results from large-scale, regional marine carbonate chemistry observing efforts on the Atlantic, Gulf, and Pacific coasts of North America. This synthesis reveals the domain-scale and local controls on carbonate properties driven by atmospheric CO2 exchange and physical, chemical, and biological ocean processes. Our comparative study of marine carbonate chemistry across physically and biologically dissimilar ocean margins provides new insight about the mechanisms controlling CO2 parameter distributions, timescales of variability, and responses to ocean warming and acidification.

## Results

### The Atlantic and Gulf coasts

The North American Atlantic and Gulf of Mexico (GOM) coastal regions are characterized by broad, shallow shelves influenced on the landward side by rivers and wetlands and on the seaward side by alongshore currents. Most notably, the northbound Gulf Stream Current system brings warm, high-salinity source waters from the tropics, while the southbound Labrador Current brings cold, low-salinity source waters from the Arctic and subarctic regions (Supplementary Fig. 1)37,38,39. While data presented here were collected during slightly different summer months on the Atlantic coast (Supplementary Table 1), the spatial patterns of all parameters are consistent for the cruises conducted in 2007, 2012, and 2015, each plotted with a shift in longitude for the purpose of illustration (Fig. 2, Supplementary Table 2).

Sea surface temperature (SST) (Fig. 2a) and salinity (SSS) (Fig. 2b) decrease from southwest to northeast. The surface TA distribution follows that of salinity, with the highest TA values in the GOM, a sharp south-to-north decrease along the Atlantic coast24,25, and nearshore modifications by major rivers40 (Fig. 2c). In contrast to the sharp meridional decline in TA, the DIC gradient is weak along the Atlantic coast, exhibiting smaller south-to-north decreases and some high values in the northern regions (Fig. 2d). Thus, the DIC/TA ratio increases sharply from south-to-north (Fig. 2f), which strongly correlates with SST (Supplementary Table 3). The DIC/TA ratio is a measure of the acid–base equilibrium point of seawater, with higher ratio indicating higher CO2 fraction in the DIC pool and more acidified, less buffered states41. Note, while the GOM has both high DIC and TA values, its DIC/TA ratio is the lowest, indicating the least acidified state of all the North American margins. In addition, elevated TA values in North America’s largest river, the Mississippi, cause the northern GOM to have one of the highest TA-to-salinity ratios (~75) in the world ocean (Fig. 2e)29,36,42,43.

Sea surface pCO2 and pH show more complex spatial patterns (Fig. 3a, c). These parameters exhibit no significant co-variation with SST and weak (or no) co-variation with DIC/TA and the percent saturation of dissolved oxygen (DO%) in surface waters, an indicator of biological activity (Supplementary Fig. 2 and Table 3). This is likely due to the influence of multiple competing processes along the Atlantic and GOM coasts. By normalizing the pCO2 and pH values to 25 °C (i.e., setting the thermodynamic constants to 25 °C in a closed-system calculation), a south-to-north pattern becomes apparent with high pCO2@25 °C and low pH@25 °C values in the cold northern regions. A comparison of pCO2 and pH distributions at in situ SST and at 25 °C not only reveals the important role of temperature in seawater carbonate system thermodynamic equilibrium, but, perhaps more importantly, also the role of gas exchange in eliminating the temperature-induced air–sea disequilibrium. In other words, high DIC/TA exists in cold northern waters mainly due to atmospheric CO2 uptake induced by low SST. In mid-latitude regions, low observed pCO2 and high observed pH appear in areas of high DO%, suggesting biological CO2 removal there (e.g., early summer in the Gulf of Maine, Fig. 3 and Supplementary Fig. 2)44.

In northern GOM coastal waters, low pCO2 and high pH values (at both SST and 25 °C, Fig. 3a–d) strongly correlate with the low salinity, high DO%, and low DIC/TA ratios in the nutrient-rich Mississippi River plume-influenced region, revealing the importance of local biological CO2 removal driven by riverine nutrients (Supplementary Table 3). The rest of the GOM has relatively high pCO2 and low pH, reflecting the warm climate and low biological production in offshore waters42. Carbonate precipitation is another process that could be contributing to the relatively high pCO2 and low pH conditions. This is supported by a slightly lower TA/SSS ratio (Fig. 2e) and a higher DIC/TA ratio (Fig. 2f, Supplementary Fig. 4) in southern GOM, indicating more TA removal than DIC removal. Precipitation likely occurs in waters above CaCO3-rich banks at the Florida Keys and Yucatan peninsula, but can also happen in other areas45.

Most strikingly, along the entire Atlantic and GOM coasts, the large-scale spatial distribution of Ωarag, an important metric for ocean acidification stress on organisms, bears little resemblance to the distributions of pCO2 and pH (Fig. 3). Rather, the Ωarag distribution is similar to SST and is inversely correlated with the DIC/TA ratio (r = −0.996, p < 0.001 in the Atlantic, see Supplementary Table 3 for other margins). Thus, similar to the strong DIC/TA and temperature gradients, there is a strong south-to-north decline in Ωarag. Interestingly, Ωarag and its associated parameters (e.g., [$${\mathrm{CO}}_3^{2 - }$$], Supplementary Fig. 3), but not pCO2 and pH, change abruptly at Cape Hatteras, where the Gulf Stream moves offshore and the influence of the Labrador Current increases in coastal waters. The highest Ωarag appears in the GOM, which is consistent with the existence of the highest SST and TA and lowest DIC/TA ratio there. Strong biological CO2 removal in the Mississippi River plume also contributes to low DIC/TA ratio and high Ωarag values in local surface waters42. Finally, distinct from pCO2 and pH, temperature-normalizing Ωarag does not alter the south-to-north spatial pattern in the Atlantic and GOM coasts (Fig. 3f).

### The California Current System

The California Current System (CCS) extends from roughly the US-Canadian border to Baja California and is characterized by narrow shelves with strong, cold equatorward alongshore currents, and wind-driven upwelling events from late spring to early fall (Supplementary Fig. 1)46,47,48. While upwelling strength may vary, the observed carbonate chemical patterns are largely consistent (2007 and 2016 data were collected in late spring, while 2011, 2012, and 2013 data were collected in late summer) (Figs. 2 and 3). Here, similar to SSS, TA shows a weak south-to-north-decreasing gradient (Supplementary Table 3), while DIC has only a slightly stronger south-to-north-decreasing gradient46. As a result, there is no coherent meridional gradient in the DIC/TA ratio, reflecting different mechanisms at play from those along the Atlantic and Gulf coasts. However, higher pCO2 and lower pH values are generally observed in the south.

As reported previously, pCO2 is high and pH is low near coastal upwelling centers in the CCS (Fig. 3)27,49. These hot spots are caused by the strong upwelling of subsurface waters with high DIC/TA ratios and low O2, pH, and Ωarag values caused by biological respiration and anthropogenic CO2 (Supplementary Fig. 5 and Table 3)27,47. An interesting characteristic of the CCS, offshore of the immediate upwelling centers, is that pCO2 is generally lower and pH is higher relative to the Atlantic and GOM coasts at similar latitudes. This is mainly a result of the strong biological compensation following upwelling and incomplete compensation by air-sea gas exchange in the CCS as shown by field observations49 and a numerical model47. However, once the temperature is normalized to 25 °C, such CCS vs. Atlantic contrasts largely disappear (Fig. 3). This reflects the important role of low SST values in keeping pCO2 low and pH high via thermodynamic equilibrium shift and in maintaining a significant air–sea disequilibrium. In contrast, Ωarag is almost ubiquitously low along the entire CCS coast relative to the GOM and southern Atlantic margins. It is particularly notable that, distinct from pCO2 and pH, normalization to 25 °C does not alter this Ωarag contrast between the West and East Coasts. Low SST in the CCS allows more CO2 to be retained in the CO2-rich upwelling waters due to a greater gas solubility, which keeps [$${\mathrm{CO}}_3^{2 - }$$] low (Eq. 1). Thus, the seemingly paradoxical co-existence of relatively high pH and low Ωarag in the CCS reflects the distinct sensitivities of these parameters to thermodynamic constants, gas exchange, mixing, and biological processes.

### Other Pacific coastal regions

The Gulf of Alaska has the widest continental shelves on the Pacific coast and is characterized by poleward winds and downwelling surface circulation during summer months50. Sea surface pCO2 is low and pH is high in these relatively high-latitude, cold waters (Fig. 3), while Ωarag is ubiquitously low. In Mexican Pacific coastal waters, south of the Gulf of California, SST is particularly high, while SSS and TA are similar to its northern neighbor (the CCS)51. Here, pCO2 and pH values generally align with the weak south-to-north trends of Pacific coastal waters; however, DIC and DIC/TA are notably lower and Ωarag is much higher than the waters to the north (Figs. 2 and 3).

### The Revelle factor distributions

The capacity of seawater to resist a change in its acid–base properties in response to a DIC perturbation caused by CO2 uptake from the atmosphere, or other processes, is important when considering the impacts of ocean acidification9,10,52,53. The characteristics of how each carbonate system species will respond to such a disturbance can be described with a set of buffer factors41,54,55. Among them, the Revelle factor (RF) is most often used,

$${\mathrm{RF}} = \frac{{\Delta p{\mathrm{CO}}_{2}}}{{p{\mathrm{CO}}_{2}}}/\frac{{\Delta \mathrm{DIC}}}{{\mathrm{DIC}}},$$
(3)

which is the fractional change of the CO2 species to a fractional DIC change at constant SST, SSS, and TA. A lower RF indicates a greater buffer capacity and a lower sensitivity of seawater pCO2 to changes in DIC.

Spatial distributions of RF (Fig. 4a) show clear meridional gradients along the Atlantic margin, but no such pattern in the CCS. This suggests that the most buffered waters are in the GOM, southern US East Coast, and Mexican Pacific coast. The least buffered waters, which may be most sensitive to increasing ocean carbon content, are in the CCS upwelling centers and the mid to northern Atlantic waters of our study domain. In other words, the change in pCO2, pH, and Ωarag per unit DIC increase will be larger in the upwelling-dominated CCS waters and northern Atlantic waters than in other coastal waters of the North American margin. However, next to upwelled waters with characteristically high RF in the CCS, strong biological removal of CO2 substantially increases the buffer capacity as indicated by the low RF values associated with high DO% and low nitrate at around 12 °C in Fig. 4c, d.

The spatial patterns of RF are similar and closely correlated to [$${\mathrm{CO}}_3^{2 - }$$] and Ωarag (Figs. 3e, 4a, b and Supplementary Fig. 3 and Table 3), supporting the notion that the $${\mathrm{CO}}_3^{2 - }$$ concentration plays a critical role in the ability to resist acidification as added anthropogenic or respiratory CO2 is largely neutralized by $${\mathrm{CO}}_3^{2 - }$$ to form $${\mathrm{HCO}}_3^ -$$ (Eq. 2). Thus, [$${\mathrm{CO}}_3^{2 - }$$], Ωarag and inversely the DIC/TA ratio (Fig. 2f) are good proxies or easy-to-understand surrogates for seawater buffer capacity. In all North American margin waters, the DIC/TA ratio is inversely correlated with [$${\mathrm{CO}}_3^{2 - }$$] and Ωarag (Supplementary Table 3). In seawater, the point at which DIC/TA ≈ 1 (or DIC ≈ TA) represents the most sensitive state of the system to CO2 addition because, at this point, [CO2] ≈ [$${\mathrm{CO}}_3^{2 - }$$] and pH = −0.5 log(K1K2) − 0.5 log([CO2]/[$${\mathrm{CO}}_3^{2 - }$$]) changes the fastest17. Also note that this point (pH ≈ −0.5 log(K1K2)) occurs at a higher pH in cold waters (7.71 at 3 °C and 7.60 at 10 °C) than in warm waters (7.35 at 30 °C) (Supplementary Fig. 6), making cold waters more sensitive to CO2 addition56. The cold waters of the northeastern margins, Alaskan shelf, and the CCS upwelling centers are approaching this point and are thus most vulnerable to ocean acidification.

### Continental-scale pattern vs. local variability

To explore the first-order controlling mechanisms on large-scale spatial patterns of carbonate chemistry parameters on contrasting margins, we first compare field-observed DIC, pCO2, pH, and Ωarag distributions with those predicted from gas equilibrium with atmospheric CO2. We do this by calculating each of these parameters from SST, SSS, and TA under the assumption of sea surface CO2 gas equilibrium with the atmosphere. Over a large latitudinal range involving multiple water masses along the North American Atlantic and GOM coasts, DIC and Ωarag generally follow air–sea gas equilibrium-based predictions on a seasonal timescale (months) (Fig. 5a, b, e, f). This atmospheric CO2 equilibrium control mechanism would dictate a relatively high DIC and low Ωarag in cold northern waters, where CO2 solubility is high and the acid–base equilibrium favors the neutralization of CO2 and $${\mathrm{CO}}_3^{2 - }$$ to $${\mathrm{HCO}}_3^ -$$ (Eqs. 1 and 2; Fig. 1a). In contrast, relatively low DIC and high Ωarag conditions would occur in warmer southern waters, where CO2 solubility and K1/K2 are lower, favoring $${\mathrm{HCO}}_3^ -$$ dissociation to CO2 and $${\mathrm{CO}}_3^{2 - }$$ with CO2 degassing to the atmosphere. Such distribution patterns are known in global open-ocean basins5,6,7,36,57 but have not been reported before in more dynamic coastal oceans. The fact that the DIC/TA ratio is lowest in the GOM and highest in northern Atlantic coastal waters reflects the temperature-regulated gas equilibrium and acid–base equilibrium shift. The observations of particularly low DIC/TA ratio and high Ωarag in the Mexican Pacific margin (Figs. 2f and 3e) further support the argument made here that air–sea gas equilibrium largely controls DIC and Ωarag in surface waters. This is true even in the region that is located right above the North Eastern Tropical Pacific (15–20°N, 100–110°W) oxygen minimum zone with elevated DIC concentrations of 2200 μmol kg−1 at a depth of only 50 m (ref. 51). To the north in the Gulf of Alaska, however, slightly lower DIC and higher Ωarag than predicted from atmospheric equilibration are likely due to legacy effects of strong biological CO2 removal in late spring and early summer (Fig. 5c)50.

Along the CCS, however, while atmospheric equilibrium still exerts strong control on DIC, upwelling and subsequent biological utilization of CO2 have greatly modified the DIC concentrations in coastal waters. These processes have variable timescales of days to weeks46,47,49 and are much less than the timescales of gas equilibration (one to a few months). The association of a positive DIC deviation with low temperature and high nutrients, a sign of upwelling (Fig. 5c, d), confirms that the source of DIC is from CO2-rich subsurface waters that have been upwelled in the CCS. The impact of upwelling and biology becomes greater for Ωarag, which deviates substantially from the atmospheric equilibrium-based prediction in the CCS (Fig. 5g, h).

Despite the strong role of air–sea gas exchange, observed pH and pCO2 values can deviate greatly from those at atmospheric equilibrium even in the Atlantic and GOM coasts (Fig. 5i, j, m, n). This is particularly true in the CCS where strong upwelling (high nutrient) or biological production (low nutrient) lead to extreme pH and pCO2 values, whereas the expected pH and pCO2 from the atmospheric equilibrium are nearly invariable (Fig. 5k, l, o, p). Deviations of DIC, Ωarag, and pH from gas equilibration are highly correlated with positive or negative deviations of seawater pCO2 from atmospheric pCO2 on all margins (Supplementary Fig. 7). In the CCS, the positive deviation in DIC and negative deviations in Ωarag and pH are associated with CO2 supersaturation induced by the upwelling of CO2-rich subsurface waters, while the opposite conditions (CO2 undersaturation) are associated with the subsequent stimulation of biological production27,47. In the GOM, such deviations are controlled by biological CO2 removal in the low-salinity river plume and net respiration and CaCO3 precipitation in the high-salinity waters. On the Atlantic coast, a combination of temperature changes associated with physical transport by large-scale alongshore currents, biological CO2 removal, and local terrestrial exports are all at play (Supplementary Fig. 7).

### Sensitivity of carbonate chemistry to perturbations

A fundamental question to ask is why do DIC and Ωarag generally follow air–sea gas equilibrium-based predictions in the Atlantic and Gulf coasts, while pH and pCO2 distributions are decoupled from the atmospheric equilibrium and are most sensitive to local physical and biological modifications? We contend that this is mainly the result of two factors. First and most importantly, the temperature effect on carbonate chemistry has two components, one is the internal effect on the thermodynamic equilibrium constants, including the acid–base dissociation constants K1 and K2 and the solubility constant K0 under no gas exchange conditions, while the other is the external effect related to DIC concentration changes caused by gas exchange. As shown in Fig. 1, in an open system these two temperature effects tend to cancel each other out completely for pH and pCO2 and partially for [CO2], but have an additive effect for [$${\mathrm{CO}}_3^{2 - }$$], DIC, and Ωarag, with the gas equilibrium playing the dominant role. Thus, moderate carbonate system perturbations caused by local physical and biological processes are essentially overshadowed for DIC and Ωarag due to their large latitudinal gradients along the Atlantic and GOM margins associated with the south-to-north temperature gradient, but are apparent for pH and pCO2, which have no clear meridional trends. The contrasting temperature effects are also compounded by the fact that physical and biological addition and removal of DIC act linearly, while their impacts on pCO2 changes are non-linear. Second, while the internal temperature effect and upwelling of high DIC subsurface waters are essentially instantaneous or of short timescale, air–sea gas exchange compensates carbonate chemistry changes over monthly timescales. As a result, slow-acting surface processes such as cooling in poleward-moving currents along the Atlantic coast are largely compensated and appear to have relatively small impacts on surface seawater carbonate chemistry. The processes that contribute most visibly to carbonate chemistry, in particular pCO2 and pH variability, are those that act much faster than the timescales of gas equilibrium (e.g., upwelling, river input, and primary production, which lack SST-related meridional trends)36.

These factors also contribute to the observed sensitivity differences of pH and Ωarag to anthropogenic, physical, and biological processes in the CCS upwelling waters. In these waters, excess CO2 relative to CO2 expected from equilibration with a preindustrial atmosphere comes from both subsurface organic carbon respiration and anthropogenic CO2 obtained when subsurface water masses were previously in contact with the atmosphere. These sources can combine to create seawater that greatly exceeds even the anthropogenically elevated modern atmospheric pCO2 and cause pH and Ωarag in the newly upwelled waters to be much lower than they would be at atmospheric equilibrium (Supplementary Fig. 7). Subsequent CO2 degassing and biological blooms can reduce CO2 and increase pH and Ωarag. A very strong correlation between DO and Ωarag in the CCS (Supplementary Table 3a) suggests that biological drawdown of DIC and upwelling of waters rich in respired DIC together overpower the influence of the small latitudinal SST-gradient in this region. However, generally lower temperatures in the CCS (compared to the GOM and south Atlantic regions) and incomplete compensation by gas exchange allow these waters to simultaneously have relatively high pH but low Ωarag because the effects of low temperature outweigh the impacts of biological CO2 removal for Ωarag but not for pH (Supplementary Fig. 8). The same discussion applies to high-latitude waters in the Labrador Sea in the Atlantic and Gulf of Alaska in the Pacific all have high pH but low Ωarag, although in these places, the main driver for a low Ωarag is the high CO2 solubility at low SSTs and the main driver for a high pH is the biological CO2 removal.

### Timescales of coastal ocean processes

To support the conclusions derived from the field data and first principle-based analysis and to further explore the different responses of carbonate parameters to atmospheric forcing and local physical and biological processes, we simulated seasonal changes in carbonate chemistry using a time-variable box model for the Atlantic coast. The model simulates carbonate parameter changes and the associated gas exchange flux in an idealized surface mixed layer following prescribed time series of salinity, temperature, wind, biological production, and vertical exchange with the subsurface water (see details in the “Methods” section). In the northeastern margin, SST follows a typical seasonal cycle, while SSS is high in winter and decreases to a minimum in summer as a result of changing river discharge and meltwater supply37 (Fig. 6a). As expected, surface water pCO2 increases and pH decreases from spring to summer following the seasonal warming and display opposite behavior from summer to fall following cooling (Fig. 6b). This thermal seasonality is enhanced by high riverine CO2 export and reduced by spring biological blooms35. The pCO2 decrease and pH increase in the summer to fall cooling period are also enhanced by biological blooms and decreased river discharge. In the meantime, in contrast, DIC increases toward winter and decreases toward summer, whereas Ωarag decreases toward winter and increases toward summer (Fig. 6c).

For comparison with the box model simulation, we also calculate carbonate system parameters while assuming instantaneous equilibrium between sea surface pCO2 and the atmosphere (open system conditions). The full-model Atlantic margin pCO2 and pH values completely decouple from the values expected from atmospheric equilibrium, but track water mass property changes associated with seasonal temperature variations and short-term local physical and biological processes. Note that the equilibrium values exhibit a much smaller range of pCO2 and pH variability due to cancellation of the two temperature effects under the imposed conditions where gas exchange is instantaneous (Fig. 1 and Fig. 6b, d, e). In contrast, the modeled DIC and Ωarag values approximately track those predicted by instantaneous equilibrium with atmospheric CO2, although with a time lag of 1–2 months. Here a seasonal DIC maximum and Ωarag minimum occur during winter when CO2 solubility is the highest with opposing results found during summer (Fig. 6c, f, g). These model-derived behaviors are consistent with the field observations and our mechanistic interpretation of them; although seasonal SST variations are used to illustrate the carbonate chemistry behaviors in the simple box model, latitudinal SST variations are reflected in the summertime observations along the Atlantic and Gulf coasts.

Interestingly, modeled pCO2 and pH values also show the high-frequency signals of SST and SSS variations caused by local short-term processes reflected in SST and SSS changes. In contrast, the impacts of high-frequency local processes are largely absent in the modeled DIC and greatly dampened in modeled Ωarag values (Fig. 6). When a disturbance (vertical mixing with high DIC subsurface water) is introduced (with a sudden increase of DIC), with all other conditions unchanged, the e-folding time of CO2 system restoration (that is the disturbance is reduced to 1/e or 37% of the initial value) due to degassing varies from 10 days at very high gas exchange rates (to mimic an instantaneous gas equilibration) to more than 100 days at low gas exchange rates (approaching a closed system) with ~1 month at an average wind condition and typical mixed-layer depths (Supplementary Fig. 9). In general, two to three e-folding intervals are needed for a disturbed signal to be completely erased. Increases in the associated nutrient input, and thus net biological production, will have an opposite effect and speed up the restoration (not shown). Thus the very different carbonate chemistry behaviors reported in this work reflect timescales of physical, chemical, and biological processes differ from instantaneous thermodynamic equilibrium, including rapid local physical processes (upwelling, mixing, etc.) acting on timescales of days to weeks, biological production (weeks), alongshore current transport (months), gas exchange processes (months to seasonal), and the seasonal thermal cycle.

## Discussion

Our study illustrates that, as in the open ocean, the large-scale meridional gradient in surface water temperature regulates CO2 gas equilibration with the atmosphere and plays a first-order role in determining the spatial distributions of DIC and Ωarag on seasonal timescales in non-upwelling-dominated ocean margins. In contrast, pCO2 and pH variations are more reflective of short-term, local modifications by coastal ocean physical and biological processes. In upwelling-dominated regions along eastern boundary current ocean margins, however, the atmospheric CO2 equilibrium mechanism is perturbed much more than that along other ocean margins and in the open ocean5,6,8,36,58. This is because dynamic coastal conditions further accentuate the contrasts between longer timescale air–sea equilibrium in slowly moving coastal currents and modifications by short-term, local physical and biological processes. As such, the two commonly used ocean acidification metrics, pH and Ωarag, can vary quite differently in upwelling vs. non-upwelling-dominated systems and in warm southern vs. cold northern waters. As organisms respond to pH and Ωarag differently (both during development and calcification)14, our findings emphasize the importance of examining multiple aspects of organismal and ecosystem responses to ocean acidification with respect to pCO2, pH, Ωarag, and DIC changes under warmer and higher CO2 future ocean conditions.

Recently, contrasting seasonal cycle responses of Ωarag, [H+], pH, and pCO2 to DIC increases throughout the global surface ocean have been shown with observations10 and models9,11,13,59. These findings, in addition to a more localized, estuarine study60, suggest that seasonal (and higher-frequency) variability may intensify more rapidly on upwelling-dominated and cold high-latitude margins due to their naturally lower buffering capacity and higher sensitivity to increasing CO2 content in the ocean. However, the absolute rates of Ωarag decrease are faster in warm and high Ωarag tropical and subtropical waters26. Our work further shows that there are substantial spatial differences in buffering capacities across the North American ocean margins and these differences imply a natural disparity in regional sensitivities to ocean acidification. In particular, the RF distribution clearly draws our attention to ecosystems—including the CCS and northern-latitude coastal regions, such as the Gulf of Maine (Atlantic) and the Gulf of Alaska (Pacific)—as being particularly sensitive and vulnerable to anthropogenic CO2 forcing.

## Methods

### Description of the field program

Starting in 2007, under the auspices of National Oceanic and Atmospheric Administration (NOAA)’s Climate Program Office and, since its inception in 2010, Ocean Acidification Program, NOAA Pacific Marine Environmental Laboratory and NOAA Atlantic Oceanographic and Meteorological Laboratory, in collaboration with academic partners and international collaborators, have conducted multiple surveys of the North American ocean margins. The most recent quality-controlled survey data are from the East Coast Ocean Acidification (ECOA) and Gulf of Alaska cruises in summer 2015, the West Coast Ocean Acidification (WCOA) cruise in late spring 2016, and the GOM Ecosystem and Carbon Cycle (GOMECC) cruise in summer 2017. Results from these cruises are presented in Fig. 2 and 3 along the coastlines of the North American continent and associated ocean margins, while previous cruises in the same regions (West Coast: late spring 2007 and late summer 2011, 2012, and 2013; GOM and Atlantic: summer 2007 and 2012). In addition, data from the Scotian Shelf and Labrador Sea as well as the Mexico Pacific coast, although limited, are included to extend the geographic coverage. Supplementary Table 2 summarizes the relevant cruise information.

In this work, all DIC samples were measured at sea by coulometric titration using a modified Single-Operator Multi-Metabolic Analyzer system, and TA was measured by acidimetric titration using the open cell method61,62. Both DIC and TA measurements were calibrated daily using Certified Reference Materials from Dr. Andrew Dickson’s laboratory at Scripps Institution of Oceanography. The overall uncertainty of each of these two measurements is ±2 µmol kg−1. DO was measured by a Winkler titration technique. Detailed descriptions are available at, for ECOA 2015, [https://www.nodc.noaa.gov/oads/data/0159428.xml] or [https://doi.org/10.7289/v5vt1q40], for WCOA 2016, [https://www.nodc.noaa.gov/oads/data/0169412.xml] or [https://doi.org/10.7289/v5v40shg], for GOMECC 2017, [https://www.nodc.noaa.gov/oads/data/0188978.xml] or [https://doi.org/10.25921/yy5k-dw60], and for AZMP, [https://www.dfo-mpo.gc.ca/science/data-donnees/biochem/index-eng.html].

For the purpose of examining spatial distributions, pH, pCO2, and Ωarag were calculated from DIC and TA together with nutrient concentrations using the CO2SYS program63 applying the carbonic acid dissociation constants of Mehrbach et al.64 as refitted by Dickson and Millero65. We use the DIC–TA pair because both parameters are available and were measured at high quality during all cruises. Good internal consistency among multiple parameters was observed and potential issues were identified in an earlier study66. pH is expressed on the total proton concentration scale67. Ωarag is defined as the concentration product of dissolved calcium and carbonate ions divided by the aragonite mineral solubility product68.

### DIC, Ωarag, pH, and pCO2 at equilibrium with atmospheric pCO2

The values at equilibrium are calculated assuming that seawater pCO2 is in equilibrium with annual mean atmospheric pCO2. In this case, the input pair to CO2SYS is pCO2 and TA. The atmospheric CO2 data, as a dry air mole fraction, was obtained from the Mauna Loa Observatory, Hawaii.

### Box-model simulation

To study the relationships that control surface-ocean carbonate parameters and air–sea CO2 fluxes, we use a box model to simulate an idealized mixed layer. The box model simulates the carbonate systems as a homogeneous surface-ocean water mass located either in the North-West Atlantic (NWA, 40.1–42.5°N, 69.2–67.5°W) and South Atlantic Bight (SAB, 28.3°N–29.7°N, 77.6°W–79.2°W). The model is driven by realistic temperatures and salinities from the Mercator 1/12° data-assimilated General Circulation Model with a daily resolution in time69.

The carbonate system is defined from DIC and TA and re-adjusted to changes in temperature and salinity at each time step using the CO2SYS package63. Throughout the model simulation, TA is calculated from prescribed salinity61,69. The model is initiated with the carbonate system defined by pCO2 in equilibrium with atmospheric values and TA (TAt0) defined by initial salinity70. DIC is calculated from pCO2(aq), TAt0, temperature, and salinity at t = 0. The model is spun up for 180 days using prescribed physical and biological conditions as described above. pCO2_t(aq) is calculated using CO2SYS as well. ΔDICBio and ΔDICVertical are prescribed (see below), while ΔpCO2_air–sea is calculated at each time step using the relationship ΔpCO2_air–sea = 0.24 × k × K0 × (pCO2_t(aq) − (pCO2_(atm)). K0 is the CO2 gas solubility71 and k is defined as k = 0.251 × W2 × (Sc/660)−0.5, where W is wind speed in m s−1 and Sc is the Schmidt number72,73.

Biological production is assessed from weekly averages of daily changes in satellite-derived chlorophyll (Chl) for the year 2015 using the daily MODIS aqua 4-km level 3 product74. We extract daily time series for each grid cell that falls within the NWA and SAB model regions, identify all pairs of consecutive days with valid data, and convert changes in Chl to a carbon flux by using a fixed C:Chl ratio of 60 (ref. 75). The resulting weekly averages are interpolated to daily time series. The resulting change in DIC due to biological production is significantly smaller than other sources and sinks in the current study. The highest net community production (NCP) values we get are on the order of 0.1 mmol C day−1 m−3. This corresponds to ~50 mg C m−2 day−1. Satellite-derived net primary production (NPP) is on the order of 400 mg C m−2 day−1 and with an expected NCP to NPP ratio of ~10%; thus, our biological production parameters are reasonable.

Winds are prescribed to 7 m s−1 in the summer and 10.5 m s−1 in the winter, to be consistent with representative wind data from the NOAA/Seawinds blended wind data set69. Winter mixing in NWA is simulated by adding 0.1 mmol m−3 DIC daily from October to February (over 155 days). The value is based on a scaling analysis of vertical DIC gradients and diffusivity estimates in the region based on observational in 2015 in the NWA region. Literature values of physical vertical diffusion combined with vertical profiles of DIC from the ECOA 2015 cruise suggests that diffusive transports of DIC is negligible during summer. We use constant winds to minimize noise and to isolate the effect by changes in solubility on the carbonate system. Atmospheric pCO2 is set to 395 μatm.

Specifically, the forward iteration from time t_n to t_n + 1 is performed by the following steps:

DICt + 1 = DICt + ΔpCO2_air–sea + ΔDICBio + ΔDICVertical.

1. 1.

Calculate the carbonate system defined by temperature, salinity, DIC, and TA at t_n.

2. 2.

Apply changes to the DIC concentration at t_n + 1 by biological processes, vertical mixing and air–sea exchange (based on pCO2 values at t_n).

3. 3.

Recalculate the carbonate system using temperature, salinity, and TA at t_n, and DIC at t_n + 1.

4. 4.

Record pH, pCO2, and Ωarag at t_n + 1.

The reason to use temperature, salinity, and TA at t_n when performing step 3 is to make sure that all carbon parameters are calculated using the same physical conditions. All the details are given inside the coding: https://doi.org/10.5281/zenodo.3833678.

We also calculate DICeq, a property that is based on the same TA, salinity, and temperature as the model but with pCO2(aq) relaxed to pCO2(atm), which can be interpreted as the air–sea exchange being infinitely fast. Here for simplicity, we assume pCO2(atm) equals the dry CO2 mole fraction.

### Statistical information

We used the built-in Matlab function (corrcoef) to compute the correlation coefficients (https://www.mathworks.com/help/matlab/ref/corrcoef.htl).

## Data availability

Discrete bottle data from all NOAA ocean acidification regional research cruises are available at NOAA’s National Centers for Environmental Information. For ECOA 2015, [https://www.nodc.noaa.gov/oads/data/0159428.xml] or [https://doi.org/10.7289/v5vt1q40]; for WCOA 2016, [https://www.nodc.noaa.gov/oads/data/0169412.xml] or [https://doi.org/10.7289/v5v40shg]; for GOMECC 2017, [https://www.nodc.noaa.gov/oads/data/0188978.xml] or [https://doi.org/10.25921/yy5k-dw60], and for AZMP, [https://www.dfo-mpo.gc.ca/science/data-donnees/biochem/index-eng.html]. Atmospheric CO2 data are available at https://www.esrl.noaa.gov/gmd/ccgg/trends/data.html.

## Code availability

The box model was written in python and the code can be found at https://doi.org/10.5281/zenodo.3833678.

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## Acknowledgements

Data reported in this work were collected under the auspices of the National Oceanic and Atmospheric Administration (NOAA)’s Global Carbon Cycle (GCC) and Ocean Acidification Programs (OAP). We thank captains and crew of all vessels involved in collecting the data at sea and the outstanding technical staff, students, postdocs, and PIs at NOAA and partner labs for their collaboration on the first decade of NOAA ocean acidification cruises. The Canadian data were collected with support from NSF and Department of Fisheries and Oceans (DFO) Aquatic Climate Change Adaptation Services Program (ACCASP). We are grateful to the governments of Canada and the United Mexican States for fishing licenses and research permission allowing us to conduct our research within their Exclusive Economic Zones during all cruises (PPFE/DGOPA-072/16, PPFE/DGOPA-137/17, EG0082017, EG00032016, No. 343609, and IDR-1279). W.-J. C was also supported by NSF (grant no OCE-1559279).  B.J. was supported by Simons Foundation via grant no 549947 (SS). This is contribution number 4853 from the NOAA Pacific Marine Environmental Laboratory.

## Author information

Authors

### Contributions

R.A.F. and S.R.A. are responsible for the design of the West Coast Ocean Acidification (WCOA) cruises. J.C. is responsible for the design of the Gulf of Alaska Coast Ocean Acidification cruises. J.E.S., W.-J.C., and R.W. are responsible for the design of the East Coast Ocean Acidification (ECOA) cruises. R.W. and L.B. are responsible for the design of the Gulf of Mexico Ecosystem and Carbon Cycle (GOMECC) cruises. K.A.-S. and P.P. are responsible for the Davis Strait work. J.M.H.-A. is response for the Mexican Pacific coastal data. L.-Q.J. compiled the initial list of cruise data. J.J.R., B.C., N.H., Q.L. and C.L. contributed to data collection efforts. Y.-Y.X. and W.-J.C. analyzed data. W.-J.C. prepared the paper. B.J. did the box-model simulation. L.X. and W.-J.C. did the temperature effect model. A.J.F., S.R.A., B.R.C., R.W., R.A.F., B.J., A.J.S., C.-T.A.C., and D.K.G. edited the paper. All authors contributed to the discussion and writing.

### Corresponding author

Correspondence to Wei-Jun Cai.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communication thanks Marta Álvarez, Adam Subhas, and other, anonymous, reviewers for their contributions to the peer review of this work. Peer review reports are available.

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Cai, WJ., Xu, YY., Feely, R.A. et al. Controls on surface water carbonate chemistry along North American ocean margins. Nat Commun 11, 2691 (2020). https://doi.org/10.1038/s41467-020-16530-z

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• , Janet Reimer
•  & Baoshan Chen

Journal of Geophysical Research: Oceans (2020)