The MAB is commonly defined by boundaries at the coast, the shelf/slope front, and two imaginary lines across the shelf: one south of Nantucket Shoals and one east of Cape Hatteras (Mountain, 1991; Figure 1). The cruise data were collected throughout the entire MAB from March 1–10, 1996. The timing of the cruise was chosen to capture late winter conditions when shelf water temperatures are at their annual minimum (e.g., Mountain, 2003). The six transects (Figures 1A,B) sampled from north to south are the Nantucket Shoals (NS), Long Island (LI), New Jersey (NJ), Delaware (DE), Chesapeake Bay (CB), and Cape Hatteras (CH), and each transect traversed from the shelf to the upper slope, with the bottom depth reaching 1,000 m at the most offshore stations, except in the NS transect. However, water samples for inorganic carbon measurements were generally collected only in the upper 200 m to allow for high vertical sample resolution within the depth and density ranges of slope waters that could exchange directly with shelf waters. In addition, there is no significant exchange between the shelf water and the slope water below 200 m (Csanady and Hamilton, 1988; Supplementary Figure 1).

In the vicinity of the MAB, the main alongshore currents are an equatorward-flowing, cold, and fresh coastal current (Chapman and Beardsley, 1989) supplied by the Labrador Current, and the northward-flowing, warm, and salty Gulf Stream (Figure 1A). The Slope Sea separates the shelf waters from the Gulf Stream as far south as Cape Hatteras, with the western Slope Sea (within the MAB) being a closed cyclonic gyre, and the eastern Slope Sea having a more open cyclonic circulation. The Labrador Current flows out of the Canadian Arctic and mixes with the Gulf Stream and its extension, the North Atlantic Current, at the Grand Banks. Further south, the Labrador Current water exchanges with fresher water from the Gulf of St. Lawrence, and flows along the Scotian Shelf, and through the Gulf of Maine where mixing with a cross-isobath, onshore flow of warmer and saltier slope waters creates the characteristic shelf water mass of the MAB (Csanady and Hamilton, 1988; Chapman and Beardsley, 1989; Dong and Kelly, 2003; Townsend et al., 2006; Figure 1A). Within the MAB, there is additional local freshwater supply from rivers via several large bays, but the major freshwater sources for the MAB are the Chesapeake Bay, Labrador Current, and St. Lawrence River. A shelf-slope front that separates shelf waters from the Slope Sea has a variable location but lies typically over the 80-m isobath and is characterized by a salinity around ca. 34 and a sigma theta around 26.5 (Supplementary Figure 1).

The shipboard salinity and temperature data were collected with a Neil Brown Mark III (NBIS) conductivity temperature depth (CTD) device (Flagg et al., 2002). Nitrate (NO₃^–) and phosphate (PO₄^–) concentrations were determined by using a Technicon Autoanalyzer (Technicon AA-II, SEAL Analytical, Inc.) with spectrophotometric methods similar to those described in Wilson et al. (1989). The precision of these methods was around ± 2% (Atlas et al., 1971; Hager et al., 1972; Knap et al., 1996). The DIC concentrations were measured using a single operator multi-parameter metabolic analyzer (SOMMA) with a precision of ± 0.06% and an accuracy of ca. ± 2 μmol kg^–1, with values checked against Certified Reference Materials (CRM) (Dickson, 2010), and TA concentrations were determined with a Metrohm 665 Dosimat titrator and an Orion 720A pH meter with a ROSS glass pH electrode and an Orion double junction Ag, AgCl reference electrode through a nonlinear least squares approach with ±2 μmol kg^–1 precision and were corrected with the difference between the CRM stated and analyzed values (Johnson, 1992; Johnson et al., 1993; DOE, 1994; Jahnke and Verity, 1994; Knap et al., 1996). The apparent oxygen utilization (AOU) values were calculated from the difference between the theoretical oxygen (O₂) saturation values and O₂ concentrations determined by Winkler titrations (Chen, 1981; Garcia and Gordon, 1992); positive values of AOU represent O₂ undersaturation, and negative values reflect O₂ oversaturation. Most samples were analyzed on board during the cruise.

Carbonate chemistry calculations require any two of the four commonly measured parameters—TA, DIC, pH, and fCO₂ (fugacity of CO₂) or pCO₂ (partial pressure of carbon dioxide)—to determine the other two. The CO2SYS program (Lewis and Wallace, 1998; Pierrot et al., 2006) used measured DIC and TA concentrations to calculate values of pH on the total scale, using carbonic acid dissociation constants (K₁, K₂) of Lueker et al. (2000). Also calculated using the CO2SYS was the aragonite saturation, Ω_Arag, defined as [Ca²⁺][CO₃^2–]/K_Arag, where K_Arag is the solubility constant (Mucci, 1983), and the calcium concentration was determined from salinity (Millero, 1995). Finally, pH_{in situ} and Ω_Arag were calculated at in situ temperature and pressure.

Potential temperature–salinity (θ-S) diagrams (Figure 1C) are widely utilized to represent and quantify mixing of different water masses (Helland-Hansen, 1916; Mamayev, 1975). The geometry of the θ-S diagram, together with the assumption of no heat or gas exchange with the atmosphere, yields a set of closed system equations that allow quantitative water mass analysis (Tomczak, 1981). The source water types (known as endmembers) were identified for each transect in the MAB based on the bounding extremes and inflection points in the potential θ-S diagrams (Table 1 and Supplementary Figures 1, 2). The nearshore water endmembers were the points with the lowest salinity at each transect. The shelf water endmembers were the inflection points within the salinity range around 33–34, where the water column generally showed stratification. If there was another inflection point between the nearshore water and the shelf water, it would be identified as the nearshore water endmember 2, which reflects the mixing situation in shallow waters. The slope water was determined as the highest salinity point on the θ-S plot and was generally located around the isopycnal of 27 (Supplementary Figure 1). In the southern MAB, the Gulf Stream rather than the slope water served as the highest salinity endmembers for the CB and CH transects.

In this work, each transect was divided into two mixing regimes: a mixing between nearshore and shelf water, and a mixing between shelf and slope water (or the Gulf Stream for the two southern transects). The fraction of each water mass was estimated by a two-endmember mixing or a three-endmember mixing (when there were two nearshore water endmembers). The mass balance equations of a water sample (j) that is a mixture of various source water types (i) are:

where the subscript i refers to an individual seawater endmember or water type, and X_ij is the fractional contribution of the endmember (i) to a water sample (j). T_j and S_j are the temperatures and salinities of the samples, and T_i and S_i are the temperatures and salinities of the individual endmembers. Equation 1 is the mass balance of water and Equation 3 that of salt, both of which must be conserved. Salinity can vary due not only to mixing of different water types but also to precipitation and evaporation, but it is assumed that the latter processes have little influences on the water and salt masses during the sampling period. Strictly speaking, temperature (Equation 2) is not a conserved quantity, but it is nearly directly proportional to heat content, which is conserved. Water temperatures can also be affected by heat exchange with the atmosphere, but this is not considered in the mixing model. In the calculation of mixing model, the estimated salinities are consistent with corresponding data points, but temperature differences between estimated and measured values range from –1.3 to 0.9°C.

Theoretical mixing concentrations of biogeochemical parameters can be viewed as conservative and predicted based on the proportions and concentrations of different source water types as follows:

where A°_j refers to the theoretical, or conservative, mixing concentration in sample j, of a biogeochemical parameter such as AOU, phosphate, nitrate, or DIC, and A_i represents the concentrations of that biogeochemical parameter in the endmembers. The differences

between the observed sample concentrations A_j and theoretical concentrations predicted on the basis of conservative mixing reflect anomalies mainly resulting from biological processes such as production and remineralization.

Consistent with regional circulation (see the Cruise description and regional hydrographic background section), surface temperature, salinity, nitrate, DIC, and TA in the MAB increase across the shelf from the shore to the Slope Sea (Figure 2). The lower temperatures occur in the most nearshore stations of NS, LI, and NJ because of the more important role of heat loss in shallow water to the atmosphere during winter, Labrador Current input, and coastal river inputs. The temperature of nearshore water also slightly increases with decreasing latitude due to the increased solar radiation and decreased influence of the Labrador Current. The highest temperature is at the most offshore station of CH due to the influence of the Gulf Stream (Figure 2A). The distribution of salinity is slightly different from that of temperature, with river discharge diminishing the salinity in the nearshore region, and more Labrador Current dominance leading to low salinity in the northern part of the shelf. The greatest onshore–offshore salinity contrast occurs in the CB and CH transects due to the large amount of freshwater input from the Chesapeake Bay and the greater influences of the Gulf Stream and slope water at the most offshore stations (Figure 2B).

In general, river discharges bring nitrate to the nearshore regions, as does mixing with slope water. However, in the MAB region, major river inputs are processed within large estuaries such as the Chesapeake and Delaware Bays with relatively long water residence times (Boynton et al., 1995; Kemp et al., 1997; Sharp et al., 2009). As a result, riverine nitrate and DIC are consumed, and pCO₂ is reduced in lower estuaries before reaching the shelf (Joesoef et al., 2015; Cai et al., 2017; Chen et al., 2020). Nutrients and DIC are also used for biological production in the MAB inner shelf, even during the late winter, as evidenced by relatively high Chlorophyll a (Chl-a) concentrations (Figures 2C–E). As river water is characterized by much lower DIC and TA concentrations than seawater, the surface DIC and TA distributions largely reflect the salinity distribution (Figures 2B,E,F). On the contrary, pH_{in situ} values decrease seaward with increasing salinity (Figure 2G). This pattern is a combined result of water mass mixing with an increasing temperature to the offshore direction and a stronger biological production (which increases pH) in nearshore waters. In the northern transects, it appears that strong biological activities play a more important role as pH normalized to 25°C has a similar pattern to the pH_{in situ} and as Chl-a values are clearly higher at nearshore stations (Figures 2G–I). In the southernmost transect (CH), however, once the temperature is scaled or normalized to a common temperature of 25°C, pH_25C increases toward the Gulf Stream endmember. Biological CO₂ could have a stronger impact in increasing pH in cold waters than in warm waters (Cai et al., 2020). The distribution of Ω_Arag is less consistent in the cross-shelf direction, decreasing seaward along the NS transect but increasing seaward in other transects.

Shallow inner shelf waters are vertically well mixed because of strong winds and cooling, as indicated by an overlap of symbols in the θ-S diagram from the same station (blue symbols in Figure 1C). The salinity maximum (S = 35.82) at offshore regions likely results from the subtropical subsurface water, reflecting the influence of the Gulf Stream (Gawarkiewicz et al., 1992; Marchese and Gordon, 1996), and this impact is particularly noticeable across the entire CH transect from coast to the shelf break (Figure 1C and Supplementary Figure 1), which is close to where the Gulf Stream leaves the coast. This vertical mixing results in a hook shape in the θ-S diagram for the CH transect at the highest salinity (S ≈ 34.5–35.8) and temperature (T ≈ 13.7–16.2°C), where the subtropical subsurface water mixes with coastal river plume water from the Chesapeake Bay (triangle symbols in Figure 1C). The most offshore stations (red symbols in Figure 1C) from the NS to the CB sections reflect the influence of the slope water (S ≈ 35.6), and the waters in the layer of σ_T ≈ 26.5–27 cluster in a small salinity and temperature range (Figure 1C). Excluding the lowest and highest salinity areas, the main trend shown in Figure 1C is nearly a linear relation between θ and S (S ≈ 33.0–35.6, T ≈ 4.7–12.2°C), reflecting the mixing between the low-salinity inner shelf water (S ≈ 32–33.5) and the higher-salinity slope water (S ≈ 35.6).

The cross-shelf sections of temperature, salinity, nitrate, Chl-a, DIC, TA, pH_{in situ}, and Ω_Arag for each transect are presented in Figures 3, 4. Cold and freshwater occupies the shelf, whereas warm and salty water sits over the slope, with the boundary between these two water masses marked by the persistent shelf-break front (green area in Figures 3A–F, yellow area in Figures 3G–L). The colder and fresher shelf water extends seaward in the upper layer, while the warmer and saltier slope water onwells shoreward in the bottom layer from the NS to the CB transects (Figures 3A–L). In the alongshore direction, the northern MAB region (NS-NJ) is colder, fresher, and has a larger extent of vertical mixing on the shelf than in the southern region (DE–CH), reflecting a north-to-south change in the volume of the shelf water (Mountain, 1991). At the nearshore end of CB transect, the water from the Chesapeake Bay greatly reduces both salinity and temperature. The highest temperature and salinity waters occupy the shelf break edge of the CH transect (Figures 3F,L), consistent with its proximity to the Gulf Stream, which turns northeastward around Cape Hatteras (Rossby and Benway, 2000).

As noted in the Surface distributions of current, physical, chemical, and biological parameters section, inner shelf waters tend to have low nitrate concentrations, which increase seaward due to wintertime mixing with deeper, subsurface waters with high nutrient concentrations that occur in the Slope Sea (Figures 3M–R). However, nitrate concentrations are also high inside the shelf-break at about the 50-m depth in the CB transect due to bottom recycling driven by high biological production in the surface water (Figure 3Q; Fisher et al., 1988). Generally, concentrations of Chl-a are high along the coastal shelf and decrease with distance from shore, and at some shallow stations, (e.g., those <50 m, Figure 3S) concentrations are highest near the bottom due to either wind-enhanced mixing or bottom shoreward nutrient supply (Figures 3S–X; Makinen and Moisan, 2012).

Dissolved inorganic carbon and TA values on the shelf are between 1,850 and 2,050 and 2,050 and 2,250 μmol kg^–1, respectively, whereas the slope water is characterized by DIC and TA that are higher than 2,100 and 2,300 μmol kg^–1, respectively (Figures 4A–L). The lowest DIC and TA are found at the most nearshore station in the CB transect (Figures 4E,K), consistent with the lowest salinity found there because of river plume water influences (Figure 3K). The highest DIC and TA originate from the subsurface water of the Slope Sea that partially onwells to the edge of the shelf (Figures 4A–L). Similar to the surface distributions, pH_{in situ} values are consistently higher in the nearshore water columns and decrease seaward (Figures 4M–R), whereas Ω_Arag distributions are variable (Figures 4S–X). The lower pH_{in situ} values are also present near the bottom or in the subsurface water.

Ω_Arag increases from north to south with the increase in TA/DIC ratio and temperature (Figure 2). This trend is largely determined by the temperature dependences of CO₂ solubility, the solubility of aragonite, and the dissociation constants of carbonic acid (Millero et al., 2006; Cai et al., 2020). Jiang et al. (2015) have derived a regional empirical formula based on the data collected from 1970 to 2010 to predict the surface water Ω_Arag in the Atlantic Ocean from sea surface temperature (SST) and concluded that the tight correlation between Ω_Arag and temperature is mainly a result of the different air–sea CO₂ exchange fluxes induced by the north–south temperature gradient rather than a direct thermodynamic effect of temperature. In other words, more CO₂ is taken up by cold water in the north, thus, converting more CO₃^2– to HCO₃^– and leading to a higher DIC and a lower TA/DIC ratio than in the warmer water in the south (Takahashi et al., 2014; Xu et al., 2017; Cai et al., 2020). A similar correlation exists for the MAB shelf water (the dotted line in Figure 5), likely for the same reason, even though TA and environmental conditions change greatly and are often patchy in these coastal waters. The average Ω_Arag in the MAB surface waters is generally lower than the value predicted using Jiang’s formula because the TA/DIC ratio in nearshore water is generally lower than the open ocean surface waters (note that the TA/DIC ratio is ≤ 1.0 in most rivers and typically near 1.15 in open ocean waters). Such latitudinal pattern does not exist in the surface pH_{in situ} distribution as it is more controlled by the local biological activities. The closely linked, but somewhat different, responses of pH_{in situ} and Ω_Arag to temperature, mixing, and biological production observed here are consistent with those reported in Cai et al. (2020) at a large, though less fine, spatial scale in the waters off the northern American eastern coast.

Property–property plots such as those presented in Figure 6 can reveal whether associated variables follow the same physical mixing process or are altered by biological processes. Here, we have categorized data into two groups: (i) mixture of shelf water with slope water or Gulf Stream water (gray circles) and (ii) mixture of nearshore water with shelf water (black cross symbols). For DIC-TA plot, the slope of the black symbols, located near the shore, is consistent with linear mixing (two black solid lines) between seawater and riverine (nearshore) endmembers based on the riverine TA data from the United States Geological Survey (USGS) for the same period and assuming TA ≈ DIC (Cai et al., 2010). As noted earlier, as riverine concentrations of DIC are subject to modification by net biological production in large estuaries and low-salinity inner shelf waters (Figure 6A), it may therefore be more appropriate to use nearshore endmembers instead of river endmembers to examine mixing and biological effects. The black crosses with high DIC concentrations (a few symbols above the solid lines) on the northern shelf indicate another low-salinity endmember (Figure 6A; Table 1).

Graphs of DIC vs phosphate, nitrate vs phosphate, and AOU vs DIC, are shown in Figures 6B–D, respectively. Overall, most of the slopes in these plots differ from the stoichiometry given by the Redfield ratios (Redfield, 1958), which are expected from biological processing alone (C:P = 106:1; N:P = 16:1; O:C = 138:106), due to the mentioned physical mixing. For biological activities, the low nitrate makes nitrogen, rather than phosphate, the limiting nutrient (black cross symbols in Figure 6C), and similar distributions also exists in Georges Bank and the Gulf of Maine (Townsend and Thomas, 2002). In most of the inner shelf water (black cross in Figure 6C), nitrate falls below the expected Redfield ratio and may be the result of a more rapid regeneration for phosphate than nitrate (Paytan and McLaughlin, 2007). Denitrification and gas exchange can also affect the relations (see discussion in the Separation of water mixing and biological effects section). Because of a combination of complex mixing and biological activities operating in different regions of the MAB, a simple interpretation of water column processes based on observed property–property relations is unlikely, and a more rigorous treatment of mixing is needed to elucidate the influences of biological processes on nutrient and inorganic carbon distributions.

In order to distinguish biological effects from water mass mixing on the property distributions and to examine stoichiometric ratios during biological processes, we use the mixing model to separate the effects of these two processes. We first use the results of linear programming optimization (Goodarzi et al., 2014)—that is, Equations 1–3—to calculate the fractions of various water masses that contribute at each location. Then, the estimated fractions of identified water masses are used to calculate the theoretical concentrations of biochemical parameters. Finally, the difference between the observed property and the mixing predicted value is defined as the anomaly, which is attributed to non-conservative biological processes (atmospheric exchange is neglected here). The source water types are determined from the θ-S diagram as detailed earlier (Figure 1C), and nutrient and DIC concentrations are then used to distinguish the water masses with similar θ-S values (Table 1). Although the identified endmembers may vary both spatially and temporally, the concept and procedure proposed here, nonetheless, allow us to effectively separate biological processes from physical mixing. However, it must be noted that this approach does not provide a measure on the biological activities in the endmembers, such as that in the highly productive nearshore waters.

The adopted endmember values differ between different transects (Table 1). The phosphate concentration of nearshore water at the CB transect is zero, consistent with reports that phosphate is limited in the Chesapeake Bay during winter (Prasad et al., 2010). The low nitrate concentration of nearshore waters at the NS transect may result from the near-zero nitrate of the Gulf of Maine surface water (Townsend et al., 2010). The AOU of nearshore water increases from the NJ to the CH transect, and the DIC concentration either decreases or remains nearly constant. It is worth noting that nearshore or coastal river plume water is most heterogeneous and variable, and can be divided into two sub-types (nearshore water-1 and nearshore water-2) in the northern transects (NS-NJ), where nearshore water-1 is slightly colder and fresher than nearshore water-2. Surface cooling and vertical mixing in nearshore areas may contribute to the lower temperature there, and cause the winter-only mid-shelf front in the northern MAB (Ullman and Cornillon, 2001). The nitrate concentration of shelf water in the NS and LI are similar to the reported values for the Georges Bank (Table 1; Townsend and Thomas, 2001; Bisagni, 2003). For the shelf water endmember, the nutrient and DIC concentrations decrease southward from the NS to the CB, but the salinity increases consistent with the water flow direction, showing a reduced Labrador Current influence (Table 1).

Using the water mass endmembers identified above and the mixing model presented in the Water mass mixing model section, we are able to separate the effects of biological processes from the water mass mixing using correlations among the biogeochemical anomalies, dDIC, dP, dN, and dAOU presented in Figure 7, calculated using Equations 1–5. Each plot is divided into four quadrants based on the sign of the anomalies, with positive and negative values representing addition to or removal from the theoretical mixing values, respectively. In particular, the anomalies in quadrant I denote the addition of DIC and inorganic nutrients and consumption of O₂ due to organic matter decomposition, and those in quadrant III represents removal of DIC and inorganic nutrients and production of O₂ by biological production and other processes (see discussion below).

Most anomalies from the mid and outer shelves (gray circles in Figure 7) occur in quadrants I and III, and those on the inner shelf (black crosses in Figure 7) cluster near the origin. dDIC, dP, dN, and dAOU anomalies in the mixed shelf and slope (Gulf Stream) waters (gray circles in Figure 7) are negative in quadrant III, meaning that these concentrations are removed by biogeochemical activities. Thus, the MAB ecosystem tends to be autotrophic during late winter, a result consistent with a recent numerical model study (Friedrichs et al., 2019). In the mixed nearshore-shelf waters, most of the dissolved oxygen is oversaturated (black crosses in Figure 7D, AOU < 0 in Figure 6D), and the excess oxygen escapes to the atmosphere (dAOU ∼ 0), while the DIC is consumed by phytoplankton (dDIC < 0). While both O₂ supersaturation and CO₂ deficit are compensated by gas exchange in the surface or shallow waters, the impacts on the dAOU and dDIC are different. This is because air–sea exchange is more rapid for O₂ than for CO₂, and more importantly, the impact of the carbonate buffering system, i.e., the gas exchange-induced changes in aquatic CO₂ are buffered by a much larger carbon pool of HCO₃^–-CO₃^2– (Wallace and Wirick, 1992; DeGrandpre et al., 1998; Carrillo et al., 2004; Zhai et al., 2009).

The extent to which biological processes determine the anomalies of various parameters can be examined by comparing ratios of the anomalies to the Redfield ratios, as noted above. The dDIC/dP ratio of 96.8 ± 4.8 is slightly lower than the Redfield ratio of C:P = 106, likely because of the decrease of processes that compensate dDIC, such as an increase due to absorbing atmospheric CO₂ (Figure 7A). The surface seawater in the MAB was a moderately strong atmospheric CO₂ sink during late winter in 1996 (DeGrandpre et al., 2002; Signorini et al., 2013). The air–sea CO₂ flux will tend to compensate biological DIC removal or addition; that is, to reduce dDIC in the third quadrant and to reduce oversaturated CO₂ in the first quadrant (Figure 7A). Another reason for the dDIC/dP ratio being lower than the Redfield ratio is that it does not adequately account for recycled phosphate. The dDIC/dN ratio of 5.85 ± 0.21 is similar to the Redfield ratio C:N = 6.625 and to that reported by Hedges et al. (2002), C:N = 6.23 (Figure 7B), yet lower than that reported by Chen et al. (1996), C:N = 7.69. Denitrification will also diminish nitrate, and substantial denitrification may occur on the seafloor (Seitzinger and Giblin, 1996; Fennel, 2010). However, as the dN/dP ratio of 16.96 ± 0.42 is similar to the Redfield ratio of N:P = 16 (Figure 7C), we conclude that the impact of benthic denitrification on water column N is quite limited in winter, probably because of the diminished denitrification under low temperature (Brin et al., 2014) and high oxygen concentration due to a well-mixed condition during wintertime. Finally, the dAOU/dDIC ratio of 1.44 ± 0.01 is also similar to the Redfield ratio for these quantities, O:C = 1.30, as well as with those reported by Chen et al. (1996), O:C = 1.27, and Hedges et al. (2002), O:C = 1.45 (Figure 7D). Slight differences in ratios may be actual differences across sampled areas or may result from deviations in endmembers. Overall, the results capture biological effects well and support the validity of a water mass mixing approach.

As suggested in the Surface distributions of current, physical, chemical, and biological parameters section, pH_{in situ} indicates a biological control mechanism. After removing the influence of physical mixing, strong correlations remain between positive dpH_{in situ} and negative dAOU, dDIC, dP, and dN (Figures 8A,C,E,G), indicating that the increase in pH_{in situ} and the decreases in AOU, DIC, and nutrient concentrations are controlled by the same biological process. The same strong correlation occurs between positive dΩ_Arag and negative dAOU, dDIC, dP, and dN (Figures 8B,D,F,H). Biological production releases oxygen (negative AOU) and consumes DIC, hydrogen ions (increases pH), and nutrient concentrations, which are represented by anomalies in the second quadrant of Figure 8 (corresponding to quadrant III in Figure 7). In contrast, the anomalies in the fourth quadrant of Figure 8 result from organic matter decomposition (corresponding to quadrant I in Figure 7), which increases the AOU, DIC, hydrogen ions (decreases pH), and nutrient anomalies. Regression lines of dDIC, dpH_{in situ}, dN, dP, and dΩ_Arag all pass through the origin, indicating that these quantities are influenced by the same biological processes, and supporting the overall validity of the mixing and mass balance model and our choices of the endmember values (circles in Figures 7, 8).

In contrast, consistently in all anomaly plots, at dDIC = 0 or dpH = 0 or dΩ_Arag = 0, dAOU values scatter from –20 to 0 μmol kg^–1 in the mixed shelf-slope waters (gray circles in Figures 7D, 8A,B). While we have no independent supporting evidence (for example, information from an inert gas such as argon), we suggest this negative shift in dAOU is caused by air bubble-induced O₂ supersaturation (Craig and Hayward, 1987; Wallace and Wirick, 1992; Cassar et al., 2009; Emerson and Bushinsky, 2016). During wintertime, strong winds and deep mixed layer depth could facilitate increased O₂ solubility at high hydrological pressure in the offshore water. A changing O₂ gas solubility due to bubbling effect is a physical process that is not considered in our water mass mixing model and is, thus, a non-conservative term as far as the mixing is concerned, although it is non-biological either. This process would have little effect on the CO₂ system as it is buffered by the HCO₃^– and CO₃^2–.