Quantifying the drivers of ocean‐atmosphere CO2 fluxes

A mechanistic framework for quantitatively mapping the regional drivers of air‐sea CO2 fluxes at a global scale is developed. The framework evaluates the interplay between (1) surface heat and freshwater fluxes that influence the potential saturated carbon concentration, which depends on changes in sea surface temperature, salinity and alkalinity, (2) a residual, disequilibrium flux influenced by upwelling and entrainment of remineralized carbon‐ and nutrient‐rich waters from the ocean interior, as well as rapid subduction of surface waters, (3) carbon uptake and export by biological activity as both soft tissue and carbonate, and (4) the effect on surface carbon concentrations due to freshwater precipitation or evaporation. In a steady state simulation of a coarse‐resolution ocean circulation and biogeochemistry model, the sum of the individually determined components is close to the known total flux of the simulation. The leading order balance, identified in different dynamical regimes, is between the CO2 fluxes driven by surface heat fluxes and a combination of biologically driven carbon uptake and disequilibrium‐driven carbon outgassing. The framework is still able to reconstruct simulated fluxes when evaluated using monthly averaged data and takes a form that can be applied consistently in models of different complexity and observations of the ocean. In this way, the framework may reveal differences in the balance of drivers acting across an ensemble of climate model simulations or be applied to an analysis and interpretation of the observed, real‐world air‐sea flux of CO2.


Introduction
The atmospheric inventory of carbon is regulated on interannual and longer timescales by the ocean carbon reservoir, mediated by the exchanges of carbon dioxide across the air-sea interface. This exchange (1) is proportional to the difference in ocean and atmosphere partial pressures of CO 2 , and its efficiency is a function of temperature, salinity, and wind speed, encapsulated in the gas transfer coefficient, K: In recent decades, coordinated observation campaigns and the compilation of local data sets have provided an unprecedented global view of the regional and seasonal changes in air-sea exchange of CO 2 (as illustrated in Figure 1a) based on measurements of atmospheric and surface ocean pCO 2 , along with estimates of K [Wanninkhof , 1992;Takahashi et al., 2002Takahashi et al., , 2009Wanninkhof et al., 2013]. This growing database provides a clear qualitative and quantitative view of the patterns and rates of the air-sea flux at regional and global scales.
Since atmospheric pCO 2 is globally mixed on timescales of a year or so, regional and seasonal variations reflect oceanic processes that drive surface pCO 2 levels away from equilibrium with the overlying atmosphere. These include changes in solubility due to surface heat fluxes and temperature variations, the biotic fixation of carbon, and the upwelling of carbon-rich deep waters [e.g., Murnane et al., 1999;Sarmiento et al., 2000;Takahashi et al., 2002Takahashi et al., , 2009Ito and Follows, 2013].
Though the total flux can be derived from information on the pCO 2 gradient, quantification of the relative contributions of each of these drivers of CO 2 flux is difficult at regional and global scales. At a few sites around the globe, notably the Hawaii Ocean Time-series (HOT) and the Bermuda Atlantic Time-series Station (BATS), comprehensive biogeochemical observations provide an explicit view of the contributions of physical and biological drivers to seasonal and annual air-sea carbon fluxes [Bates, 2001;Gruber et al., 2002;Bates et al., 2002;Dore et al., 2003Dore et al., , 2009Quay and Stutsman, 2003;Keeling et al., 2004]. Models can be tested and constrained Figure 1. Air-sea CO 2 fluxes (mol C m −2 s −1 ) for (a) the contemporary Takahashi et al. [2009] climatology (including anthropogenic carbon uptake) interpolated onto the same grid used by the model (approximately 3 ∘ × 3 ∘ ), (b) simulated MITgcm preindustrial CO 2 fluxes using (1), (c) zonally averaged fluxes for the Takahashi et al. [2009] climatology (blue) and the model simulated preindustrial CO 2 fluxes (red) with ±1 standard deviation bounds to illustrate zonal variations, and (d) zonally averaged fluxes for the simulated Massachusetts Institute of Technology general circulation model (MITgcm) preindustrial CO 2 fluxes (red) and two reconstructions using the framework detailed in (8) with "online" advective and diffusive fluxes averaged into monthly fields (blue) and "off-line" advective and diffusive fluxes calculated with monthly average velocity, diffusivity, and scalar fields (orange). Again, ±1 standard deviation bounds are shown to illustrate zonal variations. Positive values indicate oceanic uptake, while negative values indicate outgassing.
A common starting point is to consider the rate of change of the concentration of dissolved inorganic carbon (C T ) in the surface ocean, which can be described as the balance of physical and biological processes: Here the terms on the right-hand side describe the divergence of physical transport by advection and diffusion, including entrainment (terms one and two), biological sources and sinks of organic soft tissue and calcium carbonate (third and fourth terms), dilution by freshwater fluxes (fifth term), and, last but not least, the air-sea gas exchange of CO 2 . Symbols are defined in detail in Table 1.
In cases where atmospheric CO 2 can be assumed constant, averaging over the seasonal cycle, C T ∕ t approaches zero. Further integrating over the layer depth, h, we can rearrange (2) to explicitly relate the time-averaged air-sea exchange of CO 2 to the driving processes: The individual terms can be evaluated in numerical models, where complete four-dimensional diagnostic information is available [e.g., Lovenduski et al., 2013] (see also example in Appendix A). While such a breakdown provides an explicit quantification of each of the processes, its application is restricted to numerical  (3) to environmental fluxes and characteristics which are available in global climatologies and climate model diagnostics.
The purpose of this paper is to describe this extension and to test its validity and utility by diagnosing the drivers of CO 2 fluxes in a global numerical simulation.
Section 2 outlines the framework which links climatological physical forcing and ocean carbon reservoirs.
In section 3 we test the framework by interpreting the contributions of different forcing processes in a numerical model simulation (described in section 2.2). We quantify the errors introduced in the interpretation when input data are limited to monthly averaged values, as we might encounter in applications to climatological observations or model comparison databases. Finally, in section 4, we discuss the prospects for wider application of the framework.

Methods: Diagnostic Framework and Testbed Simulation
Here we develop the extended diagnostic framework which quantitatively links physical and biological drivers to air-sea fluxes of CO 2 . We also describe the global ocean carbon cycle simulation used to test the new diagnostic framework and its robustness to some underlying assumptions.

Relating Air-Sea CO 2 Flux to Surface Drivers and Ocean Carbon Reservoirs
Expressions relating carbon fluxes and drivers (3) can be combined with parameterizations linking the individual terms to fluxes and state variables that are available in observed climatologies and standard climate model products. We also leverage on biogeochemical diagnostic approaches typically used to understand the controls on deep ocean carbon reservoirs (or carbon "pumps," [Brewer, 1978;Gruber et al., 1996;Ito and Follows, 2005;Williams and Follows, 2011]).
At the sea surface, the total dissolved inorganic carbon concentration, C T , can be separated into the saturated component, C sat , the concentration a water mass would have if at equilibrium with atmospheric pCO 2 , and a residual concentration, C res , reflecting the disequilibrium due to a variety of physical and biological processes [Ito and Follows, 2013]: C sat depends on atmospheric pCO 2 and sea surface temperature, salinity, and alkalinity. These relationships can be described assuming a linearization of carbonate chemistry [e.g., Williams and Follows, 2011]: where , S , and A T are solubility constants which reflect the close to linear relationships between C sat with temperature, salinity, and alkalinity. While the relationship with pCO 2 is highly nonlinear, for the purposes of this study we will be considering a fixed, uniform atmospheric pCO 2 , so pCO 2 = 0.
Substituting for C sat from (4) and (5) into (3), we express the drivers of F CO2 in terms of changes in environmental characteristics.
The first three terms on the right couch convergences of physical and biogeochemical characteristics as drivers of CO 2 fluxes. We can, in turn, relate these convergences in terms of air-sea fluxes of heat and freshwater. Consider, for example, the governing equation for surface temperature: Assuming steady state we can substitute −∇⋅(⃗ u )+∇⋅( ∇ ) = (F heat ∕ C p h) into (6). Similar substitutions can be made, including reframing biological sources and sinks in terms of the divergence of the nutrient transport (see Appendix B for a detailed derivation): CO 2 flux driver: Organic matter sources and sinks h Calcium carbonate sources and sinks We have now expressed the air-sea flux as a set of components related to fluxes that are either evaluated operationally (such as surface heat fluxes) or which can be derived from climatologies and ocean state estimates (such as nutrient transports). Each term in (8) quantifies a specific process that drives a proportion of the air-sea flux of CO 2 .
In (8), the first term on the right (first row) is the "potential" CO 2 flux due to heat fluxes [Murnane et al., 1999;Takahashi et al., 2002Takahashi et al., , 2009, which drive changes in C sat , the solubility of CO 2 . The second row of terms reflects the influence of surface evaporation and precipitation in three ways: the dilution of salinity and alkalinity, both affecting C sat , and the direct dilution of dissolved inorganic carbon, C T . Notice that the dilution of C T and alkalinity compensate: one acts to reduce pCO 2 solubility and the other to increase it. Both heat and freshwater fluxes, F heat and F W , are standard products of climate models and climatologies based on operational weather products [Kistler et al., 2001;Dee et al., 2011]. These drivers are quantified and reasonably well characterized.
The third row describes the production or remineralization of organic soft tissue with a carbon to phosphorus ratio R C∶P , integrated to depth h. Using the governing equation for phosphate (see Appendix B), we have linked biological sources and sinks to the divergence of the phosphate transport field. Advective and eddy-diffusive phosphate fluxes are easily obtained from ocean models and may be reconstructed offline (with some introduced error) if the flow field and phosphate concentration is known. Estimates may also be based on climatological distribution of phosphate (e.g., the World Ocean Atlas [Garcia et al., 2014]) with flow field and mixing parameters based on ocean state estimates [Wunsch and Heimbach, 2007;Forget, 2010;Forget et al., 2015]. We note that nitrate might equally well be the basis of the biological flux divergence estimate, depending on the currency of the model or data available. However, nitrogen fixation and denitrification make the interpretation of the flux divergences a little more uncertain.
The fourth row represents the production of calcium carbonate in the surface ocean linked simply to soft tissue production in the surface ocean by a simple constant rain ratio, R CaCO 3 , and integrated to depth h. This simple scaling holds in the upper ocean, although the full governing equation for alkalinity could be used (again, see Appendix B), to take into account the different dissolution profiles of organic and inorganic particles.
The fifth and final row describes the divergence of the transport of the disequilibrium carbon reservoir, C res , defined here as C res = C T − C sat . Below the surface mixed layer C res , as defined, includes contributions from regenerated organic matter, whereas, when modeling the carbon reservoirs in the deep ocean, the regenerated pool is explicitly diagnosed [Brewer, 1978;Gruber et al., 1996;Williams and Follows, 2011;Lauderdale et al., 2013]. Thus, here the divergence of C res transport includes three important effects: (i) the entrainment of subsurface waters rich in regenerated C T that will drive outgassing (ii) changes in surface fluxes of heat and freshwater that affect CO 2 solubility. For example, while cooling implies a positive change in the saturated carbon and therefore ocean CO 2 uptake, in a limited time period this potential flux is not achieved so the CO 2 flux due to C res is negative (outgassing) to compensate, and the time delay of air-sea carbon flux response which results in accumulation of significant disequilibrium and shifts the air-sea flux response downstream of the previous two influences.
C res can be diagnosed in models or from climatological data (the GLODAP atlas [Key et al., 2004]) by estimating C sat and subtracting it from C T . It is not currently possible to cleanly separate three factors that affect the C res fluxes. This component will also accumulate small errors associated with linearization of the carbonate chemistry in (5).
Each of the terms has a clear, mechanistic interpretation, and we suggest that (8) is more informative than (3). Additionally, all of the terms are formulated so that they can be quantitatively mapped from climatological databases and standard output from appropriate carbon cycle models.
As a proof of concept, we interpret the relative role of physical and biological drivers on patterns of air-sea carbon flux in a coarse-resolution ocean circulation and biogeochemistry model simulation. This provides a test bed where the air-sea flux of CO 2 is calculated prognostically at every time step by the model, using equation (1). We test the sensitivity of the framework to the input data density: climatological ocean data which might be used as inputs typically resolves monthly variations. Using the numerical simulations, we ask whether a useful diagnosis could be made with inputs at such temporal resolution.
In the next subsection we briefly describe the numerical simulation which forms the test bed. The application is discussed in section 3.

Testbed Numerical Simulation
The test bed simulation is a coarse resolution (2.8 ∘ ×2.8 ∘ , 15 vertical levels) version of the Massachusetts Institute of Technology general circulation model [MITgcm, Marshall et al., 1997] with online biogeochemistry Parekh et al., 2006]. The configuration is similar to the control experiment in Lauderdale et al. [2013], using the Gent and McWilliams [1990] scheme with a constant thickness diffusivity of 1000 m 2 s −1 but with the addition of the nonlocal K-Profile Parameterization (KPP) mixing scheme [Large et al., 1994] that a Coefficients were empirically diagnosed by calculating C sat over a range of values for temperature, salinity, or alkalinity while holding the others (including atmospheric CO 2 ) at surface mean values [Lewis and Wallace, 1998;Goodwin and Lenton, 2009;Ito and Follows, 2013] and finding the gradient by linear regression. enhances diapycnal mixing in regions where the water column is convectively unstable (above the constant value of 5 ×10 −5 m 2 s −1 ), including entrainment due to mixed layer deepening.
Biological transformations between carbon and nutrients are related using the fixed stoichiometric ratios of R C T ∶N∶P∶O = 117∶16∶1∶−170 [Anderson and Sarmiento, 1994] with a prescribed inorganic to organic rain ratio (R CaCO 3 ) of 7% [Yamanaka and Tajika, 1997]. Air-sea fluxes of CO 2 are calculated prognostically using (1) and are dependent on the square of local wind speed [Wanninkhof , 1992]. The annually averaged atmospheric CO 2 is 281 μatm, and the total ocean-atmosphere carbon inventory is conserved as there is no riverine carbon input, sediment carbon burial, nor external CO 2 emissions (hence, we neglect the accumulation of anthropogenic CO 2 at this stage). The simulations examined here have been integrated for 25,000 years, coming to a clear thermodynamic and biogeochemical steady state.
Advective and diffusive fluxes of all state variables, surface fluxes of heat, and freshwater, as well as biological production and losses of dissolved and particulate organic carbon and calcium carbonate were evaluated at each time step and saved as monthly averaged fields (see Appendix A). This provides a complete set of inputs for application and verification of the diagnostic framework. Furthermore, we use monthly averaged physical and biogeochemical scalars, velocity, and diffusivity fields mimicking the data density of typically available climatologies, to calculate oceanic fluxes in "off-line" mode and then apply the diagnostic framework to discover if a useful diagnosis could be made with inputs at such a low temporal resolution.

Simulated air-Sea Flux of CO 2
The global simulation qualitatively and quantitatively captures the magnitude and variation of the climatological, observed air-sea flux of CO 2 [Takahashi et al., 2009, Figure 1a-c]. Some differences are expected since the climatology reflects the current, transient state of the carbon cycle (in the reference year 2000, atmospheric CO 2 was around 350 μatm), while the simulation is for the natural, preindustrial state (∼280 μatm). In the climatology, uptake of anthropogenic carbon by the ocean is evident in the stronger, more widespread fluxes at high latitudes, relative to the simulation, as well as the slightly weaker outgassing at the equator. The simulation provides a plausible, self-consistent system for which all fluxes and state variables can be accurately quantified. In the following section, we infer the drivers of the simulated pattern using the framework outlined in (8).

Inferred CO 2 Flux and Drivers
We evaluated each of the terms in equation (8) in the numerical simulation using fluxes from each time step and averaged into monthly fields. Heat and freshwater fluxes were obtained from the model's physical boundary conditions. The saturated and disequilibrium components were evaluated following standard procedures [Williams and Follows, 2011] using C T , , S, and A T in the upper ocean, as well as the atmospheric pCO 2 of 281 μatm from the simulation. The solubility coefficients ( , S , and A T ) were determined (Table 2) by calculating C sat over a range of values for temperature, salinity, or alkalinity while holding the others (including atmospheric CO 2 ) at model surface mean values [Lewis and Wallace, 1998;Goodwin and Lenton, 2009;Ito and Follows, 2013].
We integrated the terms in (8) over the upper 50 m, in order to map the individual driver distributions in terms of an air-sea carbon flux. The framework reveals that surface heat forcing (Figure 2a), the dilution of , (c) changes in alkalinity driven by freshwater , (d) changes in carbon driven by freshwater fluxes , (e) divergence of total C res , and (f ) biological activity (soft tissue and carbonate terms, from divergence of nutrient concentration). Positive values indicate oceanic uptake from the atmosphere, while negative values indicate outgassing from the ocean. alkalinity ( Figure 2c) and C T (Figure 2d), the divergent transport of C res (Figure 2e), and biological sources and sinks (Figure 2f ) are all of similar magnitude though with different patterns. The forcing due to dilution of salinity ( Figure 2b) is much less significant. We also note that the dilution of alkalinity and C T are strongly compensatory, as anticipated.
We can simplify the diagnostics, showing the leading order aggregated terms in Figure 3. The total reconstructed flux, F CO2 (Figure 3a), is largely accounted for by heat flux forcing of solubility ( Figure 3b) and the sum of direct biological forcing and the divergence of C res (Figure 3c). The compensation between C res fluxes and biological forcing (Figures 2e and 2f ) that lead us to group the drivers in this way is, in part, because biological carbon uptake is supported by the entrainment of regenerated nutrients, which simultaneously supplies regenerated carbon from the ocean interior to drive C res outgassing [Ito and Follows, 2013]. The biogenic-C res compensation is far from complete on the local scale due to inefficiencies in biological activity, which may be restricted from full potential in some regions such as the Southern Ocean, limited by light and/or micronutrient concentrations . Nevertheless, unutilized nutrients subducted from these regions may fuel a biological activity in other parts of the ocean through entrainment into the surface layer [Sarmiento et al., 2004]. This is the case in most regions (Figure 2f ), although, again, the C res component is also affected by changes in solubility, particularly the cooling and rapid subduction of water masses from the surface. This would reinforce C res outgassing at high latitudes because the potential saturated carbon uptake determined by the heat forcing is not achieved in the limited time at the surface, so that C res is negative to compensate. Conversely, there are a few regions of C res -driven uptake that correlate with patches of intense heat fluxes (warming, leading to outgassing in Figure 2a), which suggests that again, these surface waters are being rapidly advected downstream before local equilibration to the potential saturated concentration, determined by the heat forcing. There is a negligible contribution from the sum of CO 2 fluxes driven by the hydrological cycle, that is, changes in salinity and alkalinity, which affect C sat , and changes in the C T concentration (Figure 3d).
We note that the total flux evaluated as the sum of the individually quantified components accurately reflects F CO2 as calculated in the forward simulation (compare the maps in Figures 1b and 3a or the zonal average in Figure 1d). This is pleasing, indicating that no key processes have been overlooked (compared to the numerical simulation).
The global, annual average model-reconstruction difference is very small: −8 × 10 −10 mol C m −2 s −1 , less than 1% of typical average fluxes locally and of the order of 0.1 PgC yr −1 integrated globally over 1 year (Table 3). Over this time frame, most of the components go to zero, which would be expected at steady state. Outgassing driven by C res is closely compensated by the uptake driven by biological forcing, with a small residual probably representing a proportion of C res linked to errors in linearization of the C sat equation (5). a The regions are divided by whether they are a net source or a net sink of CO 2 or neutral with respect to the zero contour of the simulated net air-sea CO 2 flux (see Figure 1b). Positive values indicate oceanic uptake of CO 2 from the atmosphere, while negative values indicate oceanic outgassing of CO 2 to the atmosphere.
When we use fluxes calculated offline using monthly averaged physical transports along with monthly averages of physical and biogeochemical concentrations to imitate climatological databases (Figure 1d), we find a degree of error is introduced, particularly leading to overestimation of equatorial outgassing and Southern Ocean uptake. Partly, there is an offset at midlatitudes (around 40 ∘ N/S) where the CO 2 flux framework slightly overestimates oceanic carbon uptake in the swift Gulf Stream, Kuroshio and Antarctic Circumpolar currents. This is not surprising since such regions will be prone to errors in the estimated flux divergence of C res due to swift current and sharp gradients. Furthermore, uncertainty in vertical mixing of carbon and nutrients as a result of smoothing vertical concentration gradients leads to errors in the biological and disequilibrium terms. Nevertheless, the framework is still able to reconstruct the net air-sea CO 2 fluxes and their variation to a reasonable degree, which gives us confidence that careful application of (8) to climatological data and observations could warrant merit.

Regional Variations in the Drivers of Air-Sea CO 2 Fluxes
Having demonstrated that the diagnostic framework is able to capture the magnitude and regional variations in CO 2 fluxes, we now illustrate the application of the framework by quantifying the relative significance of different CO 2 flux drivers over several distinct regions of the simulated ocean. The results are summarized in Table 3.
We chose the aggregated regions according to whether they are a net source or sink or neutral with respect to atmospheric CO 2 (see the zero contour of the simulated net air-sea CO 2 flux in Figure 1b and the shaded regions in Figure 4). The regions are (i) the uptake region of the North Atlantic and North Pacific basins, the outgassing region of the tropics and subtropics, the region of uptake in the Southern Ocean midlatitudes (north of ∼60 ∘ S to the zero CO 2 contour), and finally, the relatively neutral polar Southern Ocean, south of ∼60 ∘ S.
A further decomposition also reveals some significant longitudinal patterns and is illustrated in Table 4 and Figure 4.

Northern Hemisphere (Oceanic Uptake)
In the North Pacific and North Atlantic the net CO 2 flux is into the ocean, as a result of solubility-driven uptake in the poleward flowing Gulf Stream and Kuroshio western boundary currents, which cool, and due to biological uptake. Disequilibrium-driven outgassing is large, which is a combination of strong convective mixing, particularly around southern Greenland, bringing remineralized carbon (and nutrients) to the surface, as well as subduction of surface waters into the ocean interior before coming to equilibrium with the atmosphere.
There are three different patterns governing zonal variation of CO 2 fluxes in the Northern Hemisphere ( Figure 4a and Table 4): . Area-integrated air-sea CO 2 fluxes (red) broken down into the CO 2 flux due to heat fluxes (yellow), biological activity (grey), the residual, C res , component (light blue), and the total effect of freshwater fluxes (dark blue, the sum of salinity, alkalinity, and C T changes) all in PgC yr −1 . Positive values indicate ocean uptake, while negative values indicate outgassing. The regions are primarily divided by whether they are a net source or a net sink of CO 2 as in Table 3, with ocean uptake of CO 2 occurring in the crosshatched regions, and further by the grey shaded areas of (a) the Northwest and Northeast regions of the Atlantic and Pacific, (b) the equatorial and subtropical Indian ocean, and the west and east regions of the Atlantic and Pacific, (c) the Indian, Pacific, and Atlantic midlatitude sectors of the Southern Ocean (north of ∼60 ∘ S), and (d) the East Antarctic, Ross Sea, and Weddell Sea regions (south of ∼60 ∘ S). a The regions are divided by whether they are a net source or a net sink of CO 2 or neutral with respect to the zero contour of the simulated net air-sea CO 2 flux and then by longitude (see shaded regions in Figure 4). Positive values indicate oceanic uptake of CO 2 from the atmosphere, while negative values indicate oceanic outgassing of CO 2 to the atmosphere.
1. In the western boundary current-dominated Northwest Pacific and Northwest Atlantic as mentioned above, the swift northward boundary current flow produces rapid cooling that is partially compensated by the subduction of mode waters that are incompletely equilibrated with the atmosphere causing negative C res component fluxes. As a result, the absolute values of the disequilibrium fluxes are significantly larger than the opposing biologically driven fluxes. 2. In the Northeast Atlantic and high-latitude Northern Atlantic, the cooling of surface waters and deep water formation mostly drives the CO 2 uptake. This deep convective mixing, meanwhile, brings nutrient-rich waters to the surface that drives biological CO 2 uptake but also subducts deep waters from the surface before they have fully equilibrated with the atmosphere, again leading to outgassing disequilibrium fluxes. 3. In the more quiescent Northeast Pacific, CO 2 uptake is dominated by biological activity which is partially offset by the residual fluxes, with little influence of heat fluxes.

Equatorial-Subtropical Region (Oceanic Outgassing)
The equatorial-subtropical region generally outgases CO 2 to the atmosphere. Thermally driven outgassing is countered by net biologically driven CO 2 uptake, since individually, the residual component flux is completely counteracted by biological activity, although only partial equilibrium after heating may reduce the C res -driven flux. Furthermore, assuming that all the nutrients required to drive the biological uptake are supplied by the equatorial upwelling, then suggests that these waters had outgased CO 2 when they were last in contact with the atmosphere. If this were not the case, the C res -driven outgassing flux would closely balance the biologically driven uptake flux.
There are also longitudinal gradients in the regional drivers of the air-sea CO 2 flux at low latitudes, particularly in the west and east equatorial Pacific (Figure 4b and Table 4). The strongest upwelling of cool waters occurs in the east Pacific, associated with the sea surface temperature gradient and shoaling of the thermocline, with subsequently greater outgassing through warming due to heat fluxes. This is the region of strongest CO 2 outgassing, and its variability in the real ocean is heavily influenced by El Niño-La Niña conditions, associated with weakening (strengthening) of the longitudinal thermocline gradient and reduced (increased) upwelling of cool waters and residual carbon.

Southern Ocean Midlatitudes (Oceanic Uptake)
In southern midlatitudes, net uptake of CO 2 by the ocean occurs in all three basins (Table 3). Over the entire region, biologically driven CO 2 uptake is completely compensated by the C res -driven outgassing, which are mechanistically linked, leaving CO 2 uptake driven by cooling to dominate the net flux.

10.1002/2016GB005400
Considering the zonal variation ( Figure 4c and Table 4), the cooling flux is dominated by the Indian sector of the Southern Ocean where there is strong heat loss at the boundary between subtropical waters and the Antarctic Circumpolar Current, falling to one third of the size in the Pacific sector of the Southern Ocean. However, in the Indian Ocean sector the significant excess of C res -driven outgassing compared to biologically driven uptake suggests that the cooling waters are incompletely equilibrated before subduction. Compare this to the Pacific sector, where biological activity closely compensates the residual flux.
The South Atlantic region as a whole displays a different pattern, with small heat flux-driven CO 2 fluxes (that actually suggest outgassing), leaving biological drivers to dominate the overall CO 2 uptake, incompletely compensated by C res -driven outgassing. A patch of outgassing in the South Atlantic at 40 ∘ S (Figures 1b and  3a), which does not appear in the climatology (Figures 1a), may be a model artifact associated with the incorrect positioning of the subtropical front where the Antarctic Circumpolar Current (ACC) detaches from the coast of Argentina. Anomalously cold waters of the ACC would induce strong surface temperature relaxation in the model, which is seen in the heat flux-driven CO 2 flux component ( Figure 3b). However, there is also a strong uptake flux associated with the C res component (Figure 2e), suggesting that the swift current advects the surface waters into a neighboring cooling region before the warming effect is fully achieved. When integrated over the entire south Atlantic region, where cooling is also occurring in common with the rest of the Southern Ocean midlatitudes, the final result is that these opposing heat fluxes closely compensate in this region. Furthermore, the pattern of outgassing (due to upwelling of regenerated carbon) and uptake (due to incomplete equilibration to the saturated concentration determined by the heat forcing) in the disequilibrium component results in a comparatively small C res -driven flux.

Southern Ocean South of 60 ∘ S (Neutral)
Finally, in the highest southern latitudes, south of roughly 60 ∘ S, the average flux is around zero ( Table 3) although many of the individual components are significantly larger, indicating considerable compensation and interplay. Cooling of waters adjacent to Antarctica induces a positive CO 2 flux associated with the saturated carbon pool. The largest individual flux in this region comes from the residual, disequilibrium component driven by upwelling of deep waters rich in regenerated carbon and nutrients. While biological activity partly compensates, the net effect is negative (leading to outgassing) because the upwelled nutrients are incompletely utilized and biological activity is restricted from its full potential, limited by light and/or micronutrient concentrations. Additionally, cooling with incomplete equilibration may result in C res -driven outgassing with the atmosphere before subduction into the deep ocean. In the Weddell Sea of this model in particular, there is a relatively strong CO 2 uptake associated with cooling due to heat fluxes, twice that of the East Antarctica and the Ross Sea regions, which is partly compensated by outgassing associated with the residual flux, suggesting the bottom waters formed here are incompletely equilibrated.

Summary and Outlook
We have developed diagnostic framework for interpreting the regional drivers of the air-sea flux of CO 2 which can be expressed succinctly and generally as Drivers of the air-sea CO 2 flux are (1) The effect of heat and freshwater fluxes on the saturated ocean carbon concentration, which depends on surface temperature, salinity, and alkalinity at steady state atmospheric pCO 2 ; (2) the direct effect of freshwater dilution on surface C T concentrations; and (3) carbon uptake and export by biological activity (as both soft tissue and carbonate) through nutrient utilization, and atmosphereocean disequilibrium, which is influenced by upwelling and entrainment of remineralized carbon-and nutrient-rich waters from the ocean interior as well as rapid subduction of surface waters before reaching full equilibrium.
Here in order to cleanly illustrate the framework, we have diagnosed the relative importance of air-sea flux drivers from a numerical model simulation. We demonstrated that the sum of the individually determined components is close to the known total flux of the simulation. In breaking down the contributions in the simulation, we find a dominant role for the air-sea heat flux forcing, as has been suggested by sensitivity experiments [Follows et al., 1996;Murnane et al., 1999;Sarmiento et al., 2000;Takahashi et al., 2002Takahashi et al., , 2009].
However, the analysis reveals that this is not universal, with a dominant role for biological-and air-sea disequilibrium-driven fluxes. In the upwelling regions of the Southern Ocean, the combined effect of biological activity and disequilibrium opposes the heat flux-driven CO 2 uptake. Here biological activity is limited from its maximum efficiency and so the upwelling of regenerated carbon is not completely compensated. Subduction of cooling waters before equilibrium also reinforces the C res outgassing. In the equatorial upwelling regions, biological CO 2 uptake is generally larger than the disequilibrium-driven fluxes, offsetting the warming-driven outgassing.
Going beyond this proof-of-concept analysis of a single simulation, we believe that this diagnostic approach has potential for interesting applications. The approach could be applied offline with simulation data from climate models to reveal differences in the balance of drivers acting across an ensemble of simulations. Potentially more interesting still is the application to observed climatologies and the real-world air-sea flux of CO 2 . Using monthly averaged fluxes calculated offline, the framework is still able to successfully reconstruct air-sea fluxes of CO 2 compared to the model simulation, albeit with a degree of error introduced into the biological activity and disequilibrium terms. Finally, there is also the prospect of extending the approach to include a time-varying atmospheric pCO 2 . This is clearly challenging but should be explored.
In summary, we have developed and presented a new framework for analyzing the relative contributions of different physical and biogeochemical drivers to the air-sea flux of CO 2 . Using numerical model simulations, where the correct solution is known, we have demonstrated that the method can work given appropriate input data. We suggest that applications to ensembles of model simulations and, in particular, climatological observations may be fruitful.

Appendix A: The Upper Ocean Carbon Budget
Taking the model surface layer of uniformly 50 m depth over which (2) is integrated, the carbon budget can be partitioned into six components, combining the effects of soft tissue and order of magnitude smaller carbonate biogenic activity ( Figure A1). Divergence of the horizontal and vertical advective fluxes (including parameterized eddy bolus advection) taken separately is an order of magnitude larger than the sum ( Figure A1a) and therefore show a large degree of compensation. For example, upwelling of carbon in the equatorial regions and the Southern Ocean is largely, but incompletely, redistributed by the horizontal gyre circulation leading to small, but significant, accumulation of carbon. Similarly, in the subtropical gyres there is convergence of C T due to horizontal advection but this is counteracted by downwelling and deepened pycnoclines leading to net decrease in C T .
Divergence of horizontal and vertical diffusive fluxes of C T ( Figure A1b) is almost entirely due to vertical diffusion, increasing C T concentrations everywhere, but particularly elevated in the eastern equatorial Pacific, parts of the Southern Ocean and western boundary current regions where vertical gradients are large and convective mixing is important.
Upwelling of carbon to the surface is also accompanied by dissolved nutrients that drive widespread decrease in surface C T concentrations due to biological fixation of carbon at the surface and vertical export to depth as sinking particles ( Figure A1c). The rate of carbon concentration change here is prognostically calculated by the biogeochemical model as the net effect of biological productivity depending on the availability of light and nutrients, export fluxes, and remineralization of dissolved and particulate organic and inorganic matter. Biological activity particularly occurs in the equatorial and high-latitude oceans where nutrients are abundant in the model, although in some places limited by availability of light and micronutrients [e.g., Dutkiewicz et al., 2006], with low biological drawdown in the oligotrophic subtropical gyres.
Net surface freshwater fluxes can induce changes in surface carbon concentration ( Figure A1d). Regions where precipitation dominates (including relaxation to surface salinity climatology) such as low latitudes under the Intertropical convergence zone the C T concentration is decreased through dilution, whereas in the subtropical regions where evaporation is the dominant process, C T concentration increases by roughly the same amounts.
Accumulating the effects of advection, diffusion, biological activity, and freshwater fluxes leads to regions of net C T accumulation or reduction at the surface, which drive oceanic pCO 2 variations and ultimately air-sea fluxes of CO 2 . The CO 2 fluxes in Figure A1e (redrawn from Figure 1b) are computed by the biogeochemistry model using (1) and show outgassing in the equatorial-subtropical regions and uptake at the midlatitudes.

Appendix B: Development of the Carbon Flux Diagnostic Framework
This section lays out the specifics of the new, mechanistic carbon flux framework (8). Terms are defined and described in Table 1.

B1. Estimating the Effect of Biological Processes
Considering (3), the most difficult terms to infer are the effects of biological activity, S bio and S CaCO 3 , on the surface flux of CO 2 . A similar equilibrium relationship to (2) can be written considering the steady state phosphate concentration (B1), from which the S bio component can be obtained from the advective and diffusive fluxes of nutrients (B2). Nitrate could also be used here instead.
Rearranging the steady state budget of alkalinity (A T , B3) could yield a similar expression for the S CaCO 3 component from the advective and diffusive fluxes of alkalinity, the consumption of charged nutrients, and dilution or concentration of A T by surface freshwater fluxes (B4).
For simplicity, however, S CaCO 3 can also be estimated by assuming an organic carbon to inorganic carbonate production/remineralization ratio (R CaCO 3 ), in which case

B2. Saturated and Disequilibrium Carbon Reservoirs
The advective and diffusive fluxes of C T in the carbon budget (3) can be further broken down into several different constituents, linking surface carbon fluxes to interior carbon reservoirs [Brewer, 1978;Gruber et al., 1996;Ito and Follows, 2005;Williams and Follows, 2011]. In turn, this allows atmosphere-ocean carbon fluxes to be linked to physical forcing of the ocean.
At the sea surface, a parcel of water in chemical equilibrium with the atmosphere will have a dissolved carbon concentration equal to the saturated concentration, C sat (B6). However, since CO 2 gas exchange is not instantaneous, having a timescale of the order of 1 year [Ito et al., 2004], there will be a residual disequilibrium concentration, C res , which results from other processes that drive the surface C T concentration away from the "potential" chemical equilibrium concentration. This measure of incomplete air-sea gas exchange is largely influenced by the upwelling of regenerated carbon of biogenic origin from the deep ocean [Ito and Follows, 2013] and rapid subduction of waters from the surface before equilibration with the atmosphere. In some regions, outside the surface layer, there may also be a contribution to C T from the remineralization of sinking soft tissue (C soft ) and carbonate (C carb ) particles of biogenic origin, however these reservoirs are zero by definition in the surface ocean.
The concentration of C sat in the surface ocean depends on atmospheric pCO 2 and the surface temperature, salinity and alkalinity. Again, away from the surface ocean there is a contribution to the alkalinity from remineralization of calcium carbonate particles and addition of charged nutrients (A T = A pre + A reg ); however, these reservoirs are zero by definition in the surface ocean.
It is possible to separate the individual effects of the latter three terms by linearizing the buffering capacity of seawater at constant pCO 2 such that perturbations of C sat can be evaluated from surface changes in , S, and A T (B7).
The solubility coefficients ( , S , and A T ) that represent the tight linear relationships between equilibrium carbon concentrations and forcing can be determined by calculating C sat over a range of values for temperature, salinity, or alkalinity while holding the others (including atmospheric CO 2 ) at surface mean values [Lewis and Wallace, 1998;Goodwin and Lenton, 2009;Ito and Follows, 2013] ( Table 2).
The relationship between C sat and pCO 2 is nonlinear due to the buffering capacity of seawater, and an expression involving the Revelle buffer factor, B, is required [Ito and Follows, 2005;Goodwin et al., 2007] to correctly diagnose changes in the saturated carbon associated with changes in atmospheric CO 2 (B8); however, we do not develop this part of the framework, keeping atmospheric CO 2 at a constant value in (5) neglecting anthropogenic carbon emissions.
Thus, the concentration of C sat can be diagnosed for other data sources as will be described in the next section; however, knowledge of C T is still needed to determine C res using (B6).

B3. Evaluating Individual Components of the Saturated Carbon Flux
Individual contributions from , S, and A T (B7) to the potential equilibrium air-sea CO 2 flux can be calculated from the steady state budgets for temperature (B9), salinity (B10), and alkalinity (B11). Note that the biological formation of calcium carbonate is not included in the alkalinity equation because the dominant balance at steady state is between the fluxes of alkalinity due to ocean circulation and air-sea freshwater fluxes. Biological fluxes are an order-of-magnitude smaller. The dominance of freshwater at the surface produces a close linear relationship between surface concentrations of alkalinity and salinity. This does not suggest that we totally disregard the small contribution of calcium carbonate cycling in the surface layer, but by the definition of (B6), we have instead partitioned it into the C res pool. This is consistent with the treatment of the biological fixation of soft tissue carbon, which is also accounted for in the disequilibrium pool since increased productivity drives undersaturation of C T , making the concentration of C res more negative, which leads to CO 2 uptake.
At steady state, setting ∕ t, S∕ t, and A T ∕ t to zero, the changes in saturated carbon ( , S, and A T ) and the residual carbon concentrations can be inferred directly from surface heat and freshwater fluxes and substituted in (2) and (3) for the advective and diffusive fluxes of C T (B12).
Again, note that the contributions to the saturated carbon exchange due to temperature, salinity, and alkalinity are potential fluxes that are only fully realized at chemical equilibrium. In reality, the individual temperature, salinity, and alkalinity fluxes will only be partially fulfilled, with the remainder collected in the residual, disequilibrium flux (C res ).
Drawing together these different components into (3) with the additional parameters from (B2), (B5), (B6), and (B12) substituted for the soft tissue and carbonate components of biological activity, saturated carbon advection, diffusion from temperature, salinity, and alkalinity surface forcing, and finally C res , which results from other processes such as upwelling into the surface layer that drive the surface C T concentration away from equilibrium, gives a new quantitative, mechanistic framework to diagnose regional drivers of the global air-sea CO 2 fluxes (8).