Atmospheric p CO 2 sensitivity to the solubility pump: Role of the low-latitude ocean

[ 1 ] Previous research has shown that the atmospheric p CO 2 sensitivity to changes in low-latitude sea-surface chemistry (‘‘low-latitude sensitivity’’) depends on both the volume of the ocean ventilated from low latitudes and on the degree of air-sea disequilibrium at high latitudes. However, it is not clear which effect is more important. In this paper we present a diagnostic framework for quantifying the relative importance of low-latitude ventilation versus high-latitude air-sea disequilibrium in determining the low-latitude sensitivity of ocean carbon cycle models. The diagnostic uses a Green function that partitions the ocean’s carbon inventory on the basis of whether the carbon last interacted with the atmosphere in the low latitudes or in the high latitudes. The diagnostic is applied to a simple 3-box model, a box model with a ventilated thermocline, and a suite of OGCM runs meant to capture a range of possible ocean circulations for present and last-glacial-maximum conditions. The diagnostic shows unambiguously that the OGCM has a greater low-latitude sensitivity than the box models because of the greater amount of water ventilated from low latitudes in the OGCM. However, when applied to the suite of OGCM runs, the diagnostic also reveals that the effect of high-latitude air-sea disequilibrium can sometimes dominate the effect of low-latitude ventilation and is highly sensitive to the state of the ocean circulation. In particular, the magnitude of the high-latitude disequilibrium effect correlates strongly with the strength of the Atlantic meridional overturning circulation and the volume of water ventilated from northern high latitudes.


Introduction
[2] Ice core records show that during the glacial periods of the past 800,000 years, the partial pressure of atmospheric CO 2 (pCO 2 atm ) was 80 -100 matm lower than during the corresponding interglacial periods [Petit et al., 1999;Siegenthaler et al., 2005;Lüthi et al., 2008]. By increasing its store of carbon during glacial periods and decreasing it during interglacials, the ocean is believed to have played a dominant role in regulating these pCO 2 atm variations (see reviews by Sigman and Boyle [2000] and Archer et al. [2000a]). Variations in the ocean's carbon inventory are believed to be due to changes in the operation of the ocean's carbon pump [Volk and Hoffert, 1985]. The carbon pump is that suite of processes, both physical and biological, that enrich deep ocean waters in dissolved inorganic carbon (DIC) relative to surface waters. With a fixed amount of carbon in the ocean-atmosphere system, and assuming a constant ocean alkalinity, a stronger carbon pump translates to a decrease in the inventory of carbon in the surface ocean and also in the atmosphere which equilibrates with the surface ocean.
[3] Despite decades of research, the exact mechanism whereby the ocean regulates pCO 2 atm on glacial-interglacial timescales remains uncertain [see, e.g., LeGrand and Alverson, 2001]. One reason for this uncertainty is due to the fact that numerical models disagree on the degree to which changes in the chemistry of the low-latitude surface ocean can alter pCO 2 atm . Early box model studies [Knox and McElroy, 1984;Sarmiento and Toggweiler, 1984;Siegenthaler and Wenk, 1984] found that the relatively small area of the cold high-latitude ocean controlled the CO 2 content of the surface low-latitude ocean and of the atmosphere. Later studies pointed out that while pCO 2 atm in simple box models is relatively insensitive to changes in low-latitude sea-surface chemistry, three-dimensional dynamical ocean general circulation models (OGCMs) predict a much stronger sensitivity [Bacastow, 1996;Broecker et al., 1999]. Low-latitude sensitivity is important because of the large surface area of the low latitude as compared to the high-latitude oceans. As pointed out by Bacastow [1996], a strong low-latitude sensitivity implies that changes in the low-latitude sea-surface temperature could contribute significantly to the glacial-interglacial pCO 2 atm changes.
[4] Various mechanisms have been proposed to explain the discrepancy between the low-latitude sensitivity of box models and OGCMs. Archer et al. [2000b] suggested that diffusive mixing in OGCMs enhanced their low-latitude sensitivity, and showed that a 2-dimensional circulation model could be made to span the range of sensitivities of box models and OGCMs by adjusting the diffusive mixing in the model, with higher diffusivities producing higher low-latitude sensitivities. Follows et al. [2002] showed that simple box models were missing important circulation features, resulting in weak low-latitude sensitivities. By adding a box representing the ventilated thermocline to a 3-box model, Follows et al. [2002] showed that the sensitivity of the box model could be made to match that of an OGCM. On the other hand, Toggweiler et al. [2003] explained the same differences in sensitivity as being due to differences in the degree of air-sea disequilibrium at highlatitude ventilation sites. Toggweiler et al. [2003] showed that OGCMs support a greater air-sea disequilibrium than box models, and suggested that this was the ultimate reason for the higher low-latitude sensitivity of OGCMs as compared to box models.
[5] These studies showed that there are two effects that contribute to setting low-latitude sensitivity. The first is the amount of water ventilated from the low latitudes. The second is the degree of air-sea disequilibrium at highlatitude ventilation sites. Distinguishing between the two effects is important because, as pointed out by Toggweiler et al. [2003], the former affects nutrient cycling as well, whereas the latter does not, since nutrients do not exchange with the atmosphere. In this way atmospheric pCO 2 sensitivity to the solubility pump can be decoupled from sensitivity to the biological pump. Clearly, a method for quantifying the relative importance of air-sea disequilibrium and the size of the water mass ventilated from low latitudes would help us better understand the role of the low-latitude oceans in regulating atmospheric pCO 2 on glacial-interglacial timescales. In this article we develop a diagnostic formula that allows us to separate and quantify the effects of lowlatitude ventilation and high-latitude air-sea disequilibrium on the total low-latitude sensitivity of ocean carbon cycle models.
[6] The key new development which helps us to address the issue of low-latitude sensitivity is the introduction of a Green function which diagnoses the fraction of the ocean volume ventilated from any given patch on the ocean surface. We use the Green function to show that the sensitivity of pCO 2 atm to low-latitude solubility perturbations can be expressed as the sum of three terms: (1) a term that is dependent on the volume of the ocean ventilated from low latitudes and independent of air-sea disequilibrium, (2) a term that is dependent on both the volume of the ocean ventilated from high latitudes and the air-sea disequilibrium in high latitudes, and (3) a term that is dependent on the volume of the ocean ventilated from low latitudes and the air-sea disequilibrium in low latitudes. The magnitudes of these three effects can be diagnosed from a perturbation experiment without the need to rerun the model with fast air-sea gas exchange.
[7] The goals of this study are to quantify the magnitudes of the low-latitude ventilation and high-latitude air-sea disequilibrium effects in different types of models, to explore the sensitivity of each effect to the ocean circulation, and to clarify the mechanisms influencing their magnitudes. To make contact with previous work on the issue of low-latitude sensitivity, we revisit the question of why OGCMs are more low-latitude sensitive than box models. We compare the low-latitude sensitivities of the 3-box model of Toggweiler et al. [2003], the 5-box model with an explicit thermocline box of Follows et al. [2002], and a 3-dimensional abiotic carbon cycling model based on the OGCM of Primeau [2005]. Our diagnostic clearly shows that the difference between the low-latitude sensitivities of the three models is due to differences in the amount of water ventilated from the low latitudes.
[8] We also compare the low-latitude sensitivity of several different versions of the OGCM with different surface boundary conditions and different eddy diffusivity parameters. We find that low-latitude sensitivities in this suite of OGCM runs vary by more than a factor of 2, and depend critically on the state of the ocean circulation. Our diagnostic reveals that most of the variability in low-latitude sensitivity is due to variability in the effect of high-latitude air-sea disequilibrium. The disequilibrium effect is strengthened by increasing the strength of the meridional overturning circulation, and by the partitioning of more deepwater ventilation to the North Atlantic. Variability in low-latitude sensitivity is also caused by variability in the amount of water ventilated from low latitudes, which generally increases with higher wind stresses and higher diffusivities, and in the buffering capacity of the ocean, which increases with higher mean ocean temperature and with lower mean ocean pCO 2 .

Factors Influencing Low-Latitude Sensitivity
[9] To illustrate how the sensitivity of pCO 2 atm is related to the redistribution of carbon in the ocean-atmosphere system, Figure 1 shows the sense of the carbon flow between the atmospheric, surface, and deep ocean reservoirs as the system adjusts to a cooling perturbation at the surface of the low-latitude ocean. (Following Bacastow [1996], Broecker et al. [1999], andFollows et al. [2002], we use the example of a low-latitude cooling perturbation without taking into account its effect on the ocean circulation to illustrate the sensitivity of the solubility pump to lowlatitude perturbations.) A decrease in ocean temperature increases the solubility of CO 2 , causing a net flow of carbon from the atmosphere into the low-latitude surface ocean. Subduction and mixing processes transport the surface ocean carbon anomaly into the interior ocean. At the same time, the decreased atmospheric pCO 2 and the increased carbon in the ocean causes an anomalous outgassing of CO 2 at high latitudes. This flow of carbon from the high-latitude ocean to the atmosphere constitutes a negative feedback that tends to decrease the pCO 2 atm sensitivity to a low-latitude perturbation. As a result of this redistribution of carbon the system ultimately settles into a new equilibrium state. How far this new equilibrium is from the one before the perturbation was applied (i.e., the low-latitude sensitivity) depends on the amount of water that is ventilated directly from low latitudes, and also on the air-sea gas exchange rate and the surface residence time of waters in the high latitudes, which govern how much of the anomalous carbon is released back to the atmosphere.
[10] Both of these effects were originally discussed in a series of papers investigating the reason why OGCMs are more low-latitude sensitive than box models. As suggested by Broecker et al. [1999] and Archer et al. [2000b], and clearly demonstrated by Follows et al. [2002], the lowlatitude sensitivity of pCO 2 atm depends on the amount of water ventilated from the low-latitude surface ocean. This ventilation can in principle occur through diffusive mixing, as suggested by Archer et al. [2000b], but direct measurements of diffusivity in the tropical pycnocline [Ledwell et al., 1993] suggest that this method of ventilation is quite weak. Rather, the formation of a ventilated thermocline in the subtropical gyres, as demonstrated by Follows et al. [2002], is the dominant low-latitude mode of ventilation. For the case of a low-latitude cooling, ventilation processes carry the carbon rich surface anomaly into the interior ocean, sequestering carbon in the interior ocean and allowing surface waters to take up more carbon from the atmosphere. On the other hand, Toggweiler et al. [2003] highlighted the importance of air-sea disequilibrium in influencing low-latitude sensitivity. High-latitude air-sea disequilibrium increases low-latitude sensitivity because it tends to suppress the outgassing of anomalous carbon at high latitudes, thereby retaining a larger amount of carbon in the ocean.

Separating the Effects of Low-Latitude Ventilation and Air-Sea Disequilibrium on Low-Latitude Sensitivity
[11] In this section we derive a formula that allows us to quantify the relative impacts of air-sea disequilibrium and low-latitude ventilation on the low-latitude sensitivity of a model. Following Ito and Follows [2003], we consider the carbon mass balance for the ocean-atmosphere system, but instead of separating the ocean carbon inventory into upper and deep ocean pools we separate the ocean carbon inventory into high-latitude and low-latitude pools, where by highlatitude pool we mean the carbon that was last in contact with the atmosphere at high latitudes and by low-latitude pool we mean the carbon that was last in contact with the atmosphere at low latitudes. More precisely, where M a is the molar mass of the atmosphere and where DIC L and DIC H are the low-latitude and high-latitude dissolved inorganic carbon pools, respectively. Such a decomposition is made possible through the use of the volume integrated Green function G(r s ) [e.g., Primeau, 2005].
[12] G(r s ) can be interpreted as the volume of the ocean per unit surface area, that was last in contact with the atmosphere at the point r s on the surface of the ocean. A computationally efficient procedure for computing G(r s ) is presented in Text S1, but an intuitive understanding of how to compute it is all that is needed to understand our results. 1 To compute the value of G for a particular patch of  Marinov et al. [2006]. The upper (red) circulation is dominated by a clockwise rotating cell in which lowlatitude water flows northward at the surface and is returned southward at depth as North Atlantic Deep Water (NADW). The upper circulation sits on top of the deep (blue) circulation: a counter-clockwise rotating cell with northward flowing Antarctic Bottom Water (AABW) at depth. Antarctic Intermediate Water (AAIW) forms part of the upper ocean circulation as it is entrained into the thermocline. An eddy return flow transports low-latitude waters into the Southern Ocean [Gnanadesikan, 1999]. Subduction of mode waters ventilates the thermoclines of the subtropical gyres. In response to the cooling perturbation, CO 2 invades the ocean in the low latitudes. DIC is subducted downward into the thermocline (blue shading) and mixes into the interior ocean. Transport of DIC-enriched surface waters poleward causes anomalous outgassing in the high latitudes. This outgassing represents a negative feedback that tends to damp the atmospheric pCO 2 decrease. How much the atmospheric pCO 2 drops in response to the cooling (i.e., the low-latitude sensitivity) depends on how much of the ocean is ventilated directly from the low latitudes, and on how well the high-latitude surface waters equilibrate with the atmosphere. Lowlatitude sensitivity is enhanced by both an increase in the volume of low-latitude waters and by inhibited gas exchange in high-latitude regions.
the surface ocean, one can think of labeling (in a sense, ''coloring''), fluid elements as they enter the patch, and removing the color label as soon as a fluid element makes surface contact outside the patch. Taking the whole-ocean inventory, at steady-state, of colored fluid elements labeled in this way, yields the volume of the ocean ventilated through that particular patch. Performing this procedure for every grid point in the model, and dividing by the area of each grid box, yields the full spatial distribution G(r s ).
[13] Because G(r s ) has units of length, it can also be thought of as an ''effective thickness'' [Primeau, 2005], where the greatest effective thicknesses correspond to places that ventilate the largest part of the interior ocean. The integral of G(r s ) over the entire ocean surface W gives the total ocean volume, where in the second line we have partitioned the ocean volume into a volume V L that was last ventilated through a low-latitude surface patch W L , and a volume V H that was last ventilated through a high-latitude surface patch W H , with the union of the two regions covering the entire ocean surface. Figure 2 shows a plot of G(r s ) for one of the OGCM circulations analyzed in this paper, as well as the regions covered by W L and W H .
[14] The total ocean DIC inventory that cycles through the solubility pump is given by the convolution of G(r s ) and the surface DIC field, i.e., [15] To separate the effects of air-sea disequilibrium and low-latitude ventilation on the sensitivity of pCO 2 atm to lowlatitude perturbations, we relate the surface ocean DIC concentration to the atmospheric CO 2 content and a local air-sea disequilibrium function, where DpCO 2 pCO 2 atm À pCO 2 oce is the air-sea disequilibrium function and F represents the equilibrium CO 2 system for seawater. Note that in the limit of infinitely fast air-sea gas exchange DpCO 2 = 0 and pCO 2 atm = pCO 2 oce .
[16] We now consider a perturbation to low-latitude temperature that causes a redistribution of carbon between the atmosphere and ocean. (We should note that while we develop our theory in the context of a temperature perturbation, our results apply equally well to any perturbation to low-latitude sea-surface chemistry. One must simply replace the derivatives with respect to temperature with those with respect to alkalinity, salinity, or DIC.) Taking the derivative of (1) with respect to temperature we obtain M a dpCO atm [17] As already mentioned we neglect the change in the ocean circulation due to the temperature perturbation so that dG(r s )/dT = 0. In this case, the derivative of DIC L with respect to a low-latitude temperature perturbation can be expanded into the following expression where in the second line we have dropped the spatial dependencies in G, DpCO 2 , and F for notational convenience, a convention we retain in the equations that follow. The expression for dDIC H /dT is similar, except that the integral is taken over W H , Figure 2. Plot of the Green function G(r s ) for OGCM run S1. Note the logarithmic scale. W L is defined on the ocean surface between 45°N and 45°S. W H is defined on the ocean surface outside W L . The plot shows mode waters forming in some areas of the low latitudes, while the major ventilation sites (red) lie in the North Atlantic and Southern Ocean regions. The units of meters result from dividing the volume of the ocean ventilated at each grid point r s by the surface area of each grid point.
[18] In the above expressions, the partial derivative of F with respect to T represents the change in DIC, holding pCO 2 oce fixed, due to the temperature dependence of the solubility coefficient and of the equilibrium constants in the seawater CO 2 system. The partial derivative of F with respect to pCO 2 oce represents the change in DIC, holding temperature fixed, due to the change in the sea-surface partial pressure of CO 2 .
[19] Substituting (6) and (7) into (5), solving for dpCO 2 atm /dT and multiplying through by dT (which is 0 on W H since the temperature perturbation is confined to the low latitudes) yields where [20] Equation (8) is a diagnostic that quantifies the effects discussed in section 2.1. The first term on the right-hand side quantifies the direct effect of low-latitude ventilation in carrying the carbon perturbation into the deep ocean. We call this the ''low-latitude ventilation effect''. This is the effect that Follows et al. [2002] showed to be an important factor in determining the greater low-latitude sensitivity of OGCMs as compared to box models. OGCMs ventilate more of the interior ocean through the low latitudes, because of the downward Ekman pumping and the formation of a ventilated thermocline, so that G(r s ) is bigger in low latitudes and thus for a given temperature change there is a larger perturbation in pCO 2 atm . The second term on the right-hand side quantifies how high-latitude ventilation interacts with the air-sea disequilibrium in high latitudes to affect pCO 2 atm . It captures the effect that Toggweiler et al. [2003] had in mind when they suggested that differences in the high-latitude air-sea disequilibrium between box models and OGCMs could explain their different low-latitude sensitivities. The greater the high-latitude air-sea disequilibrium, the more important this effect becomes. The last term on the right-hand side quantifies how low-latitude ventilation interacts with the air-sea disequilibrium in low latitudes to affect pCO 2 atm . This term is generally small enough to be negligible. Note that with infinitely fast airsea gas exchange both DpCO 2 and dDpCO 2 /dT vanish so that the last two terms cannot contribute to low-latitude sensitivity.
[21] M oa measures the total inertia of the oceanatmosphere system, and is closely tied to the buffering capacity of the ocean. M oa can be related to the total ''buffered carbon'' inventory of the ocean-atmosphere system, defined by Goodwin et al. [2007Goodwin et al. [ , 2008 as where DIC is the globally averaged DIC concentration and R global is the globally averaged Revelle buffer factor defined [Goodwin et al., 2007] Combining (9) and (10) and using the fact that we obtain the relation M oa can also be thought of as an inverse sensitivity, where sensitivity S measures the change in atmospheric pCO 2 due to a change in the (nonbuffered) ocean carbon inventory [Marinov et al., 2008b], [22] The relationships (12) and (13) show that sensitivity is directly proportional to pCO 2 , as shown by Marinov et al. [2008bMarinov et al. [ , 2008a, and inversely proportional to the buffered carbon inventory I B , as shown by Goodwin et al. [2009].
[23] In section 3 we will introduce the models used in this study. For each model we will use the diagnostic formula (8) to determine the relative contribution of low-latitude ventilation and high-latitude air-sea disequilibrium to the total low-latitude sensitivity of the model.

Model Design
[24] For the 3-box model calculations we use the so-called ''Harvardton Bear'' model [Bacastow, 1996;Knox and McElroy, 1984;Sarmiento and Toggweiler, 1984;Siegenthaler and Wenk, 1984]. It consists of three ocean boxes coupled to a well-mixed atmospheric box (Figure 3a). Model parameters not given in the caption to Figure 3 are the same as those used by Toggweiler et al. [2003]. No biology is included in the model.
[25] For the 5-box model calculations we used the thermocline box model of Follows et al. [2002]. The lowlatitude surface ocean is split into two boxes representing the tropical and subtropical ocean (Figure 3b). The interior ocean is partitioned into a deep box and thermocline box, with the thermocline box ventilated through the subtropical ocean.
[26] For the OGCM calculations we use the same circulation model used by Primeau [2005], Primeau and Holzer [2006], and Primeau [2006, 2008], coupled to a well-mixed atmospheric box. The ocean model uses the time-averaged flow field from a coarse-resolution threedimensional dynamical ocean circulation model forced with seasonally varying climatological winds, sea-surface temperatures, and sea-surface salinities, as described by Primeau [2005]. The equilibrium solution to the abiotic OGCM was found using Newton's method as described by Kwon and Primeau [2006].
[27] We also obtained 12 new circulations with our OGCM by restoring the model to different sea-surface temperature and salinity climatologies, and by using different zonal wind stress forcings and different background diffusivities. Each model was spun up for 3000 years and the steady-state advective-diffusive flow was extracted as described by Primeau [2005]. The different combinations of surface boundary conditions and diffusivities for each run are described in Table 1.
[28] To facilitate comparison among all of the models we made some minor modifications to the original model formulations. First, we used the equilibrium constants for the CO 2 system recommended by Zeebe and Wolf-Gladrow [2001] in all models. Second, we did not include virtual fluxes of carbon due to evaporation and precipitation. Third, we used a uniform piston velocity of 5.5 Â 10 À5 m/s to drive air-sea gas exchange, as by Follows et al. [2002]. Finally, when computing the ocean pCO 2 we used a uniform salinity of 34.7 psu and a uniform alkalinity of 2341 mmol/kg, following the formula given by Follows et al. [1996].

Sensitivity Experiments
[29] With each model we performed two runs to diagnose the low-latitude sensitivity: [30] 1. A control run in which the total carbon inventory is adjusted so that pCO 2 atm is 278 matm. The same total carbon inventory was kept for run 2.
[31] 2. A temperature perturbation run in which we simulated a cooling of the low-latitude sea surface by reducing the temperature at which the equilibrium constants of the CO 2 system are computed by 6°C, as by Bacastow [1996]. For the 3-box model, the low-latitude sea surface is the interface between box L and the atmosphere. For the 5-box model, the low-latitude sea surface is the interface between boxes T and ST and the atmosphere. For the OGCM, we picked the low-latitude sea-surface to be between 45°S and 45°N, in accord with Follows et al. [2002]. In all the runs, the physical transport model was ''offline'' and did not respond dynamically to the imposed temperature perturbation.
[32] Our metric for determining the low-latitude sensitivity of each model is simply the change in pCO 2 atm induced by a change of À6°C in the low-latitude temperature (i.e., the difference in pCO 2 atm between runs 1 and 2).
[33] For the experiments in which we compared the box models and the OGCM, we also ran analogues of runs 1 and 2 under conditions of ''fast gas exchange''. In these runs the air-sea gas exchange piston velocity was increased uniformly so that the pCO 2 of the surface ocean was nowhere more than 1 matm greater or less than that of the atmosphere, as by Toggweiler et al. [2003]. The piston velocity in the box models was increased by 100 times, and that in the OGCM by 500 times, relative to the control run to achieve this condition. The total carbon inventory was kept the same as The 3-box model consists of three ocean boxes H, L, and D, representing the high-latitude, low-latitude, and deep oceans, respectively, coupled to an atmospheric box A. The overturning circulation T is set to 20 Sv, and the high-latitude mixing term f hd is set to 60 Sv. The gas exchange coefficient k ge for the H and L boxes is proportional to the CO 2 solubility and surface area with a piston velocity of 5.5 Â 10 À5 m/s. Box H has a depth of 250 m and covers 15% of the sea surface, while box L has a depth of 100 m and covers 85% of the sea surface. (b) The 5-box model is modified from the 3-box model to include both tropical (T) and subtropical (S) surface ocean boxes. The cold (blue) overturning T c is set to 20 Sv, while the warm (red) overturning T w , which ventilates the thermocline, is set to 5 Sv. The thickness of box H is 1000 m, and the thickness of the thermocline box (M) is 900 m. Box T has a temperature of 25°C and box S has a temperature of 17°C. Boxes S and T each cover 42.5% of the ocean surface area. All other model parameters are the same as in the 3-box model. in runs 1 and 2. The fast gas exchange sensitivities provide a check to ensure that (8) correctly diagnoses the effects of air-sea disequilibrium from runs 1 and 2, without having to run the fast gas exchange models.
[34] As already mentioned, we did not include the dynamical effects of the low-latitude temperature change in our experiments. One reason for ignoring the sensitivity of the ocean circulation to low-latitude temperature perturbations is to obtain consistency with previous studies [Bacastow, 1996;Broecker et al., 1999;Follows et al., 2002]. Another reason is that the circulation change induced by a cooling confined to low latitudes would be an ad hoc representation of the true ocean response to surface cooling such as occurred during glacial periods, since the actual cooling is likely to have been applied unevenly across the entire ocean surface, including the high latitudes. Rather than guess the right temperature perturbation to apply in the high-latitude regions in the OGCM, we chose to run the OGCM under the different boundary conditions shown in Table 1 to simulate a range of possible ocean circulation states, and then to compare the low-latitude sensitivities of the different model runs using the procedure described above. These runs give a sense of how changes in ocean circulation can affect the low-latitude sensitivity.

Comparison of Box Models and an OGCM
[35] Both the amount of water ventilated from low latitudes [Follows et al., 2002] and the air-sea disequilibrium in high latitudes [Toggweiler et al., 2003] have been implicated in enhancing the low-latitude sensitivity of OGCMs as compared to box models. One of the goals of this study is to present a quantitative assessment of the relative importance of each mechanism. Table 2 shows the low-latitude sensitivity of the box models and our standard OGCM, separated according to equation (8) into a low-latitude ventilation effect, a high-latitude air-sea disequilibrium effect, and a low-latitude disequilibrium effect. The pCO 2 atm sensitivity of the OGCM to the low-latitude perturbation is more than twice that of the 3-box model, and about 70% greater than that of the 5-box model. Our diagnostic shows that Also shown are changes in pCO 2 atm partitioned according to the change due to the low-latitude ventilation effect and the high-latitude and low-latitude disequilibrium effects. The low-latitude ventilation effect and high-latitude and low-latitude disequilibrium effect quantities correspond to the three terms on the right-hand side of equation (8), divided by the inertia M oa . Values in parentheses are results from the fast gas exchange runs. Units are matm. The ''Modern'' runs simulate a range of circulations using modern temperature and salinity forcing. The control (C) temperature and salinity is the climatology used by Primeau [2005], while WOA05 indicates the World Ocean Atlas 2005 objectively analyzed monthly mean sea-surface temperature  and salinity  averaged over the top 50 m of the ocean. Perturbations from each of the basic states are obtained by increasing or decreasing the zonal wind stress or the background vertical diffusivity. ''LGM'' runs present two possible glacial circulation states obtained using the GLAMAP last glacial maximum temperature and salinity reconstructions described by Paul and Schafer-Neth [2003]. We used the ''core'' version of the data set available at ftp://ftp.ncdc.noaa.gov/pub/data/paleo/paleocean/by_contributor/paul2003. PSN+1 adds a 1 psu salinity anomaly in the Weddell Sea as suggested by Paul and Schafer-Neth [2003], while PSN omits this anomaly. The units of K v are cm 2 /s. the low-latitude ventilation effect is much stronger in the OGCM than in either of the box models. The high-latitude disequilibrium effect is slightly greater in the OGCM than in the box models, and the low-latitude disequilibrium effect is nearly negligible in all of the models.
[36] Our results show that the OGCM has a higher lowlatitude sensitivity than the box models because the OGCM ventilates more water from low latitudes. This is in accord with Follows et al. [2002] who showed that the presence of a ventilated thermocline enhances low-latitude sensitivity. Nevertheless, air-sea disequilibrium is an important contributor to low-latitude sensitivity in all three models. The high-latitude disequilibrium effect accounts for most of the low-latitude sensitivity of the 3-box model, 1/2 the sensitivity of the 5-box model, and more than 1/3 of the sensitivity of the standard OGCM. As we will show in section 4.2, the magnitude of the high-latitude disequilibrium effect is highly sensitive to wind stress forcing, diffusivity, and the partitioning of deep ocean ventilation between northern and southern sources. In fact, the high-latitude disequilibrium effect can be greater than the low-latitude ventilation effect.
[37] Table 2 also shows the low-latitude sensitivity of the fast gas exchange models (numbers in parentheses). In the fast gas exchange runs, the pCO 2 of the surface ocean is nowhere more than 1 matm different from pCO 2 atm , so that there is almost perfect air-sea equilibration. The results are as expected. The air-sea disequilibrium effects approach zero, and only the low-latitude ventilation effect remains. The magnitude of the low-latitude ventilation effect is nearly the same as in the standard sensitivity runs. The slightly larger low-latitude sensitivity in the fast gas exchange models is due to a reduction in the inertia M oa which occurs because of a reduction in the buffered carbon inventory. These results indicate that it is not necessary to run additional experiments with fast gas exchange in order to separate the effects of low-latitude ventilation from those of air-sea disequilibrium. It is sufficient to compute the three terms in equation (8) for the standard sensitivity experiments (runs 1 and 2) in order to know the magnitudes of these effects. For this reason, we will not show results of the fast gas exchange models for the remaining experiments.

Comparison of OGCM Runs With Different Circulations
[38] The results from section 4.1 show that in a realistic ocean circulation model both the low-latitude ventilation effect and the high-latitude disequilibrium effect play a significant role in determining the ocean's low-latitude sensitivity. It is thus worthwhile to explore what mechanisms might influence the magnitudes of each of these effects in the real ocean, as well as the uncertainty in the magnitudes of each effect. To this end we performed the alternate OGCM runs with the boundary conditions and eddy diffusivity parameters given in Table 1. Each of the runs produces a new circulation and temperature field. We have also included two runs in which last glacial maximum (LGM) temperature and salinity reconstructions from Paul and Schafer-Neth [2003] are used as boundary conditions in the model. These runs are not meant to produce definitive versions of the actual ocean circulation at the LGM, but are added to help constrain the uncertainty in low-latitude sensitivities by expressing different circulation regimes that could have occurred during the LGM. In all, the alternate OGCM runs are meant to span a reasonable range of uncertainty in the state of the ocean circulation, so that we can gain a sense of how low-latitude sensitivity depends on the state of the ocean circulation.
[39] Table 3 shows the low-latitude sensitivity of the 13 different versions of our OGCM. The drop in atmospheric pCO 2 following low-latitude cooling ranges from 11.30 matm in run WL2, to 24.66 matm in run LGM1. In all runs both the low-latitude ventilation effect and the highlatitude disequilibrium effect contribute significantly to the total low-latitude sensitivity. The low-latitude disequilibrium effect remains negligible and will be ignored in our discussion. Our theory and model results will reveal two simple scaling relationships which show that lowlatitude sensitivity depends most critically on three factors: the volume of low-latitude waters, the strength of the meridional overturning circulation, and the volume of northern high-latitude waters.
[40] We first consider what mechanisms influence the magnitude of the low-latitude ventilation effect. Under conditions of complete air-sea CO 2 equilibration, we can Run S1 is the OGCM analyzed in Table 2. Only results from models with normal gas exchange are shown. All units are matm.

GB4020
DEVRIES AND PRIMEAU: LOW-LATITUDE SENSITIVITY write the atmospheric pCO 2 sensitivity to a low-latitude temperature perturbation as which is simply the first term in (8). From (14) we see that if the state of the CO 2 system chemical equilibria is approximately constant across all the models (i.e., M oa and dF/dT are approximately the same), then to a good approximation the magnitude of the low-latitude ventilation effect should scale directly with the volume V L of water ventilated from low latitudes, since [41] This is precisely the relationship intuited by Broecker et al. [1999] and shown clearly in the model comparison study of Follows et al. [2002].
[42] Figure 4a shows that the magnitude of the lowlatitude ventilation effect does scale linearly with the volume of the ocean ventilated from low latitudes. The scatter in the plot is due to variations in the inertia M oa (Table 4), which depends on the buffering capacity of the ocean. Accounting for this effect by dividing V L by M oa eliminates the scatter, as shown in the inset plot in Figure 4a. (A perfect correlation is guaranteed by (14) as long as @F/@T is the same in all runs.) Since the initial atmospheric pCO 2 was kept at 278 matm for all runs, (12) shows that variations in M oa are due to variations in the buffered carbon inventory. The buffered carbon inventory is sensitive to the ocean circulation through the influence of the ocean circulation on the mean ocean chemistry. In general the buffered carbon inventory increases with higher mean ocean temperature and with lower mean ocean CO 2 concentration.
[43] Our results show that the magnitude of the lowlatitude ventilation effect is relatively constant across a wide range of ocean circulations. Figure 4a shows that increasing the background vertical diffusivity or the surface wind stress (red symbols) from the standard cases (S1 and S2) both increase the volume of low-latitude water and enhance low-latitude sensitivity, while decreasing either of these two factors (blue symbols) reduces low-latitude sensitivity. On the other hand, reducing vertical diffusivity in a high wind stress regime increases the volume of lowlatitude waters (run WHKL). However, the differences are relatively small in all cases. From these results it appears that the magnitude of the low-latitude ventilation effect is well constrained, and that the solubility effects of lowlatitude cooling cannot explain a significant portion of the glacial-interglacial pCO 2 atm variability without taking into account the effect of high-latitude air-sea disequilibrium.
[44] The high-latitude air-sea disequilibrium effect is generally smaller than the low-latitude ventilation effect in our runs, but there is more variability across our suite of runs implying a greater uncertainty about its importance in explaining glacial-interglacial pCO 2 atm variability. Ignoring the low-latitude ventilation and disequilibrium terms, we can write the atmospheric pCO 2 sensitivity to a low-latitude temperature perturbation as Figure 4. (a) The magnitude of the low-latitude ventilation effect scales linearly with the amount of water ventilated from low latitudes, expressed in this plot as the fraction of the total ocean volume ventilated from low latitudes. Higher low-latitude sensitivities are associated with larger volumes of low-latitude water. The scatter in the plot is due to the fact that the inertia M oa , which depends on the buffering capacity of the ocean, is not constant across all model runs: accounting for this effect eliminates the scatter (inset plot). (b) The magnitude of the air-sea disequilibrium effect in the northern high latitudes scales linearly with the product of the strength of the Atlantic meridional overturning circulation (AMOC) and the fraction of the ocean ventilated from the northern high latitudes, in agreement with the relationship (19) derived in section 4.2 and Appendix A. The magnitude of the disequilibrium effect in the Southern Ocean is generally smaller and less variable in our OGCM runs than that in the northern high latitudes (inset plot).
which is just the second term on the right-hand side of (8).
Assuming that the state of the CO 2 system equilibria is approximately constant across all runs (i.e., M oa and @F/@pCO 2 are constant), then differences in the high-latitude disequilibrium effect across the runs should scale with the volume of water ventilated from the high latitudes and the disequilibrium anomaly in high latitudes produced by the low-latitude cooling, [45] To rid (17) of the convolution integral, we make the simplifying assumption that the disequilibrium anomaly is uniform at both the northern and southern high-latitude ventilation sites. Under these conditions, (17) reduces to where V S and V N are the volumes of water ventilated from the southern and northern high latitudes, respectively.
[46] Equation (18) shows that the magnitude of the highlatitude disequilibrium effect is influenced by the magnitude of the disequilibrium anomalies in the southern and northern high latitudes, as well as the partitioning of deep ocean ventilation between southern and northern sources. Our results show that disequilibrium driven through the northern high latitudes is generally larger than that driven through the Southern Ocean, and is also more sensitive to the state of the ocean circulation. For this reason we will focus on mechanisms influencing the disequilibrium anomaly in the northern high latitudes.
[47] In the Atlantic Ocean, the meridional overturning circulation (AMOC) transports low-latitude water northward where it is transformed into NADW (Figure 1). It is intuitively clear that speeding up the AMOC enhances airsea disequilibrium in the high latitudes by reducing the surface residence time of poleward flowing water parcels. Slowing down the AMOC has the opposite effect. Although the exact relationship between the strength of the AMOC and the air-sea disequilibrium in high latitudes is complicated by diffusive mixing, we show in Appendix A that for purely advective flow and relatively small perturbations to the MOC strength, dDpCO 2 scales linearly with the strength of the AMOC. The linear relationship holds as long as the surface residence time is long compared to the air-sea equilibration timescale (see equation (A10)). If these conditions are met, then we can use (18) to write where we have focussed only on the component of disequilibrium driven through the northern high latitudes, as indicated by the N superscript.
[48] Figure 4b shows that the relationship (19) holds remarkably well in our OGCM. In the main plot we have shown only that portion of the high-latitude disequilibrium effect that is due to ventilation from areas north of 45°N (obtained by evaluating the integral (16) on W H north of 45°N). The disequilibrium effect is highly sensitive to the state of the ocean circulation through the dependence of the AMOC strength and the volume of northern-source waters on wind stress and vertical diffusivity. Table 4 shows that increasing wind stress in our model both strengthens the AMOC and partitions more ventilation to the north Atlantic, which increases the magnitude of the northern high-latitude disequilibrium effect according to the simple theory (19). Changing the vertical diffusivity k v produces two competing effects. On one hand, increasing k v increases the strength of the AMOC (Table 4), which tends to increase dpCO 2 atm j diseq N . This scaling of MOC strength with diffusivity in coarseresolution OGCMs is a well-known effect [Bryan, 1987;Gnanadesikan, 1999]. On the other hand, reducing k v partitions more of the deep ocean ventilation to the north Atlantic, which also increases the northern high-latitude disequilibrium effect. In most of the runs the two effects nearly cancel, but run KL1 partitions so much more ventilation to the North Atlantic that there is a significant increase (compared to run S1) in the magnitude of the northern high-latitude disequilibrium effect, as well as the high-latitude disequilibrium effect as a whole. When both vertical diffusivity is decreased and wind stress is increased  45°N), and V N is the volume of the ocean ventilated from the northern high latitudes (north of 45°N). V is the total ocean volume. AMOC is the maximum strength of the Atlantic meridional overturning circulation north of 45°S. M* oa is a unitless inertia defined M* oa M oa /(M a + f 0 R Gd 2 r s ), where f 0 = 1024.5 mol/m 3 .

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DEVRIES AND PRIMEAU: LOW-LATITUDE SENSITIVITY (run WHKL) the AMOC strengthens, more water is ventilated from the North Atlantic, and the high-latitude disequilibrium effect is enhanced.
[49] The inset plot in Figure 4b shows the weaker and less variable disequilibrium effect that is driven through ventilation in the Southern Ocean, as a function of the fraction of the ocean ventilated south of 45°S. The Southern Ocean disequilibrium effect shows some clear trends if one focusses solely on the effects of changing one parameter. For example increasing wind stress increases the air-sea disequilibrium effect in the Southern Ocean, perhaps due to stronger Ekman pumping associated with stronger westerly winds, while weaker vertical diffusivities reduce the magnitude of the disequilibrium effect in the Southern Ocean by partitioning more ventilation to the north Atlantic. Overall though we could find no clear relationship to explain the variation across all runs. Exchange of low-latitude waters with the Southern Ocean does not follow the simple MOC pattern of the north Atlantic, and is most likely driven by mesoscale eddy transport [Gnanadesikan, 1999].
[50] Run LGM1 is a particularly interesting case, because the high-latitude disequilibrium effect is actually larger than the low-latitude ventilation effect. This run highlights the potentially large impact of northern hemisphere air-sea disequilibrium on low-latitude sensitivity. This large impact occurs because the circulation state of LGM1 produces relatively rapid overturning circulation and large volumes NADW. The low-latitude ventilation effect in run LGM1 is comparable in magnitude to the rest of the runs. This emphasizes the point that the low-latitude ventilation effect and the high-latitude disequilibrium effect are two separate effects which are not necessarily correlated.

Summary and Conclusions
[51] In this article we developed a diagnostic formula to quantitatively assess the relative importance of both lowlatitude ventilation and high-latitude air-sea disequilibrium in setting the low-latitude sensitivity of abiotic ocean carbon cycle models. We applied the formula to sensitivity experiments in which we simulated cooling of the low-latitude surface ocean in two box models and a suite of OGCMs. Our goals were to quantify the magnitudes of the lowlatitude ventilation and high-latitude air-sea disequilibrium effects, to explore the sensitivity of each effect to different ocean circulations, and to clarify the mechanisms influencing the magnitude of each effect.
[52] Our main theoretical result is summarized by equation (8), which in conjunction with our experiments tells us the following: [53] 1. In the limit of infinitely fast gas exchange (i.e., DpCO 2 = 0), low-latitude sensitivity depends directly on the volume V L of the ocean ventilated from low latitudes, that is, on the value of G on W L . As shown clearly by Follows et al. [2002], low-latitude sensitivity is weaker in simple box models without a representation of the ventilated thermocline than in OGCMs. Our diagnostic confirms that the weak low-latitude sensitivity of simple box models is due to the smaller volume of low-latitude water in box models compared to OGCMs, rather than to differences in high-latitude air-sea disequilibrium. A suite of experiments with a coarse-resolution OGCM further confirms the direct correlation between the amount of water V L ventilated from low latitudes and the low-latitude sensitivity. Increasing the background vertical diffusivity or the surface wind stress from their basic states, increases V L and enhances lowlatitude sensitivity. Small deviations from a direct correlation between V L and low-latitude sensitivity are found to be due to variations in the buffering capacity of the ocean across model runs.
[54] 2. For finite gas exchange, air-sea disequilibrium in the high latitudes increases low-latitude sensitivity, as suggested by Toggweiler et al. [2003]. The magnitude of this ''high-latitude disequilibrium effect'' depends directly on the degree of high-latitude air-sea disequilibrium and on the volume of the ocean ventilated from high latitudes. Models in which air-sea gas exchange is restricted in the high latitudes where deep waters form will have large lowlatitude sensitivities, as claimed by Toggweiler et al. [2003].
Our suite of OGCM experiments shows that the magnitude of the high-latitude disequilibrium effect is highly sensitive to the state of the ocean circulation and can approach or exceed that of the low-latitude ventilation effect. Much of the variation in the disequilibrium effect across our suite of OGCM runs can be explained by considering flow from the low latitudes to the high latitudes to be purely advective. This leads to a model which predicts that the magnitude of the high-latitude disequilibrium effect scales directly with the strength of the meridional overturning circulation (MOC). We showed that this relationship holds very well for the water masses forming in the northern high latitudes. Variations in surface wind stress and vertical diffusivity produce highly variable low-latitude sensitivities by varying the MOC strength and by modifying the partitioning of deep ocean ventilation between southern and northern sources.
[55] On the whole, our results do not support a very large role for low-latitude solubility perturbations in explaining glacial-interglacial pCO 2 atm variations. Based on the experiments presented in this paper, we believe that the part of the low-latitude sensitivity which is driven by direct ventilation of the interior ocean from the low latitudes is fairly well constrained, and probably not a significant source of glacialinterglacial pCO 2 atm variability. However, we have identified some intriguing uncertainty in the degree to which highlatitude disequilibrium can affect the low-latitude sensitivity. Under conditions of rapid meridional overturning and large volumes of water ventilating from the North Atlantic, low-latitude sensitivity can be significantly enhanced. The effect may be even greater with extensive sea ice inhibiting gas exchange. The state of the ocean circulation at the LGM remains highly uncertain [Wunsch, 2003;Gebbie and Huybers, 2006;Huybers et al., 2007]. Because of this, until the LGM ocean circulation can be better constrained we cannot rule out the possibility of low-latitude solubility perturbations contributing in some significant way to the glacial-interglacial pCO 2 atm variability.
[56] A final point we would like to make is to caution against applying the results in this paper to the biological pump. For example, it would be untrue to claim that pCO 2 atm sensitivity to perturbations to low-latitude biological productivity is related to the sensitivity to low-latitude solubility perturbations. The diagnostic presented here, and our analysis, is applicable only to the solubility pump. The component critical to the biological pump that we have not included in our framework is the pool of regenerated carbon in the ocean. The physics governing the transport of regenerated carbon are different from those governing the transport of DIC. Therefore, the response of the oceanatmosphere system to perturbations in the biological pump could be very different from the response to perturbations in the solubility pump. Green functions analogous to the one presented in this paper can be defined for the regenerated carbon transport pathways, allowing for a framework similar to the one presented here to be developed for the biological pump. We plan to address this issue in a future paper.
Appendix A: High-Latitude Air-Sea Disequilibrium Response to a Low-Latitude Solubility Perturbation [57] In this section we derive an analytic expression for the air-sea disequilibrium in high latitudes, and show how the anomalous air-sea disequilibrium in high latitudes due to a low-latitude temperature perturbation scales with the strength of the meridional overturning circulation. The expressions are derived for a simple 3-box model without mixing, but as shown in section 4.2 the relationships also apply well to results from the OGCM.
[58] Consider the simple case where the ocean surface is divided into two regions: a low-latitude region and a highlatitude region. Advection transports water from the low latitudes to the high latitudes, as in the 3-box model (Figure 3a). At steady-state in the high-latitude region, there exists a distribution of fluid elements with different residence times in that region. The air-sea disequilibrium is given by the mass-weighted integral of the air-sea disequilibrium of all fluid parcels, i.e., where Q(t) is the residence-time PDF and DpCO 2 (t) is the air-sea disequilibrium of water parcels with residence time t. Q(t) has the functional form where t c V/M is a mean surface residence time defined by the volume V of the high-latitude box and the strength M of the overturning circulation.
[59] The air-sea disequilibrium as a function of residence time t can be derived from the differential equation governing the equilibration of DIC between the atmosphere and ocean, where v is the piston velocity in m/yr, A is the surface area of the high-latitude region in m 2 , a is the solubility of CO 2 in mol/kg/atm, and k = vAa/V. Since DIC is a function of pCO 2 we can write and substitute this equation into (A3) and integrate to obtain where t g (1/k)(@DIC/@pCO 2 ) is the gas exchange timescale.
[60] Combining (A1), (A2), and (A5) yields, which can be integrated to obtain an expression for the steady-state air-sea disequilibrium as a function of the initial disequilibrium and two timescales: the gas exchange timescale and the surface residence timescale, [61] The initial air-sea disequilibrium in the high latitudes depends on the air-sea disequilibrium in the low latitudes as well as the temperature gradient between the low-latitude and high-latitude surface oceans, i.e., [62] Assuming nonlinearities in the CO 2 system equilibrium are small enough so that t g is the same both before and after the low-latitude temperature perturbation dT L , the change in the high-latitude air-sea disequilibrium is given by [63] In the experiments that we performed the magnitude of the temperature perturbation dT L was a constant 6°C. Additionally, the air-sea disequilibrium in the low latitudes is always small so that to a good approximation dDpCO 2 L is a constant. Thus the change in the high-latitude air-sea disequilibrium is proportional to the ratio of the gas exchange and surface residence timescales, where the constant K is negative for a negative temperature perturbation in the low latitudes.
[64] Equation (A10) predicts that the change in highlatitude air-sea disequilibrium after a perturbation to lowlatitude temperature should be sensitive to the surface residence timescale t c , which depends on the strength of the meridional overturning circulation M. The sensitivity of