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 A high-resolution marine proxy for atmospheric pCO2 is needed to clarify the phase lag between pCO2 and marine climate proxies and to provide a record of orbital-scale pCO2 variations before the oldest ice core measurement at 800 ka. Benthic δ13C data should record deep ocean carbon storage and, thus, atmospheric pCO2. This study finds that a modified δ13C gradient between the deep Pacific and intermediate North Atlantic (Δδ13CP−) correlates well with pCO2. Δδ13CP− reproduces characteristic differences between pCO2 and ice volume during Late Pleistocene glaciations and indicates that pCO2 usually leads terminations by 0.2–3.7 kyr but lags by 3–10 kyr during two “failed” terminations at 535 and 745 ka. Δδ13CP− gradually transitions from 41- to 100-kyr cyclicity from 1.3–0.7 Ma but has no secular trend in mean or amplitude since 1.5 Ma. The minimum pCO2 of the last 1.5 Myr is estimated to be 155 ppm at ∼920 ka.
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 Alkenone δ13C and boron-based proxies reconstruct pCO2 concentrations in the surface ocean, but currently these records lack orbital-scale resolution and have error bars of at least ±19 ppm [Hönisch et al., 2009; Tripati et al., 2009; Pagani et al., 2009; Seki et al., 2010]. Existing higher-resolution benthic δ13C records also have the potential to record changes in atmospheric pCO2 because glacial-interglacial changes in pCO2 are associated with changes in the ΣCO2 and δ13C of the deep ocean [Oppo and Fairbanks, 1990; Flower et al., 2000; Hodell et al., 2003; Köhler et al., 2010]. This study empirically evaluates several possible benthic δ13C-based proxies and uses the one best correlated with ice core pCO2 to evaluate the phase lag between pCO2 and benthic δ18O and to estimate pCO2 from 1.5–0.8 Ma.
 Decreased deep water ventilation and increased Southern Ocean productivity are thought to reduce glacial pCO2 by removing carbon from the surface and sequestering it in the deep ocean [e.g., Toggweiler, 1999; Brovkin et al., 2007; Martínez-Garcia et al., 2009]. These processes also decrease the δ13C value of deep waters as sinking low-δ13C organic carbon remineralizes at depth and glacial overturning is decreased [Toggweiler et al., 2006; Köhler et al., 2010]. Reduced terrestrial carbon storage is the only glacial process for which pCO2 and benthic δ13C changes are not positively correlated, increasing atmospheric pCO2 but decreasing mean ocean δ13C [Shackleton, 1977; Brovkin et al., 2007; Köhler et al., 2010]. A carbon cycle box model that includes all of these processes predicts a strong, linear relationship (r = 0.98) between pCO2 and deep Pacific δ13C, but the observed correlation is much weaker (r = 0.5) due to low-frequency (∼400-kyr) variations in δ13C not observed in pCO2 [Köhler et al., 2010].
 Here I evaluate Pacific δ13C, Δδ13CD−I and the average of the two as possible proxies for pCO2. The signal-to-noise ratio of δ13C signals is enhanced by averaging data from multiple cores within the same watermass to produce δ13C stacks for the deep Pacific, deep South Atlantic, and intermediate North Atlantic (Figure 1 and Table S1 of Text S1 of the auxiliary material) [Lisiecki, 2010]. The deep Pacific stack is used for the deep-intermediate gradient (Δδ13CP−NA) because watermass boundary movement provides an additional source of δ13C variability in the deep South Atlantic [Venz and Hodell, 2002] that does not affect the deep Pacific [Matsumoto et al., 2002; Lisiecki, 2010]. For further discussion see the auxiliary material. Although Pacific δ13C has approximately half the glacial-interglacial amplitude of South Atlantic δ13C, the following analysis is not highly sensitive to which deep water stack is used because Δδ13CP−NA and Δδ13CSA−NA are well correlated from 800–0 ka (r=0.79).
 Pacific δ13C and Δδ13CP−NA both correlate moderately well with pCO2, but their average Δδ13CP− produces the best correlation (Table 1 and Figure 1, bottom). Based on inter-core variability, Δδ13CP− has a 1-σ uncertainty of 0.11‰ from 0.8–0 Ma and 0.13‰ from 1.5–0.8 Ma (equivalent to 17.5 ppm and 19.2 ppm, respectively). When Δδ13CP− is scaled to the mean and standard deviation of ice core pCO2, it has a root mean square error (RMSE) relative to pCO2 of 17.5 ppm, whereas boron-based estimates have RMSE of 18.1 ppm [Hönisch et al., 2009] and 24.9 ppm [Tripati et al., 2009] (see auxiliary material).
 One possible physical explanation for the correlation between pCO2 and Δδ13CP− is that δ13C variability in the deep and intermediate Atlantic may be amplified relative to their Pacific and global mean counterparts, e.g., due to changes in temperature and/or deepwater formation processes in the Atlantic. Thus, Δδ13CP− corrects for differences in the amplitudes of variability between the Atlantic and Pacific. Alternatively, if Pacific δ13C and Δδ13CP−NA are influenced differently by additional climatic processes, the average of the two should amplify the pCO2 signal common to both.
 The correlation between marine proxies and pCO2 is not a perfect evaluation metric because it depends on the particular marine and ice core chronologies used; therefore, Δδ13CP− is also evaluated by whether it replicates features of the pCO2 record that are independent of age model. Here I focus on features that differ from the benthic δ18O record [Lisiecki and Raymo, 2005] of deep water temperature and global ice volume. pCO2 and northern hemisphere ice volume changes may differ if pCO2 is controlled by southern hemisphere processes that are only weakly coupled to northern hemisphere climate [Toggweiler, 2008].
 One notable difference between δ18O and pCO2 (Figure 2, top) is that pCO2 generally reaches its minimum early in each glaciation and then remains constant (e.g., Marine Isotope Stage (MIS) 6 and 12) or increases slightly (e.g., MIS 16) whereas benthic δ18O does not reach its glacial maximum until immediately before each termination, due to continuing ice sheet growth [Thompson and Goldstein, 2006; Lea et al., 2002]. Glacial trends in Δδ13CP− match those of pCO2, with Δδ13CP− reaching a minimum 30–40 kyr before the δ18O maximum during most glaciations (Figure 2, bottom). Additionally, Δδ13CP− correlates better with the magnitudes of glacial pCO2 minima than δ18O does. In Δδ13CP− and pCO2, MIS 12 is less extreme than MIS 8, 10, and 16, whereas in δ18O MIS 12 is similar to MIS 16 and more extreme than MIS 8 and 10. Thus, Δδ13CP− reproduces many pCO2 responses that are independent of age model uncertainty and differ from ice volume change.
4. Termination Lags Between pCO2 and δ18O
 Comparison of Δδ13CP− and the ice core pCO2 record provides an opportunity to link marine and ice core age models. Abrupt increases in pCO2 and Δδ13CP− have similar ages on their respective age models (Table S2), suggesting that the marine and ice core age models [Lisiecki and Raymo, 2005; Parrenin et al., 2007; Loulergue et al., 2007] are consistent to within 2.7 kyr during terminations. However, age model evaluation away from terminations is hampered by weaker correlation of the records' suborbital-scale variability.
 Climatic lags between pCO2 and ice volume during terminations are evaluated by comparing Δδ13CP− and benthic δ18O changes within marine sediments. During most terminations Δδ13CP− leads δ18O by 0.2–3.7 kyr, but Δδ13CP− lags δ18O by 9.8 and 3.5 kyr during Termination 6 (535 ka) and MIS 18 (745 ka), respectively (Table S3). These lags are also found between benthic δ18O and δ13C within individual Pacific cores (Figure S2). An anomalous phase relationship between ice volume and pCO2 may explain why these two warming events are weaker than most Late Pleistocene terminations. During both “failed” terminations, the initial δ18O change is approximately half the amplitude of most Late Pleistocene terminations; δ18O spends ∼20 kyr at intermediate values of 3.8–4.2‰ and then briefly returns to more glacial values before achieving full interglacial conditions ∼40 kyr after the initial warming. The Δδ13CP− lag during these two failed terminations suggests that full deglaciation requires an early pCO2 response.
 The initial trigger for terminations and the mechanistic link between pCO2 and northern hemisphere ice volume remain controversial [e.g., Huybers, 2009; Denton et al., 2010]. Variability in the phase between δ18O and Δδ13CP− supports the hypothesis of Toggweiler  that glacial changes in pCO2 are controlled by southern hemisphere processes only weakly linked to northern hemisphere insolation and ice volume. However, tighter coupling between the hemispheres appears to develop at ∼500 ka, as suggested by smaller phase differences between Δδ13CP− and δ18O (Table S3), an increase in pCO2 amplitude, and the phase lock between Antarctic temperature and northern hemisphere insolation during the last five terminations [Kawamura et al., 2007].
5. Estimates of pCO2 for 1.5–0.8 Ma
 Here Δδ13CP−-based estimates of pCO2 from 1.5–0.8 Ma are compared with several other paleoclimate records that may correlate with pCO2. A proxy for South Atlantic surface productivity (the logarithm of alkenone concentration at ODP Site 1090) [Martínez-Garcia et al., 2009] reproduces of the same glacial trends observed in pCO2 and Δδ13CP− (Figure 3, top) and has a similar correlation with pCO2 (Table 1). Although South Atlantic productivity change appears to explain only 40–50 ppm of Late Pleistocene pCO2 fluctuation, the proxy's correlation with pCO2 may be enhanced by sensitivity to climate changes correlated with pCO2, such as South American aridity and westerly wind strength [Martínez-Garcia et al., 2009]. Similarity between Δδ13CP− and the alkenone record from 1.1–0.8 Ma provides additional support for the reliability of both proxies, particularly because they are linked to pCO2 by different mechanisms.
 Both empirical proxies indicate that pCO2 generally varies between 180–260 ppm from 1.1–0.8 Ma, except for a large oscillation at 950–900 ka (Figure 3, top). Both suggest a pCO2 minimum at 920 ka of ∼155 ppm, i.e., less than the ice core pCO2 minimum of 172 ppm at 668 ka. Many other paleoclimate records also contain evidence for extreme climatic conditions at ∼900 ka, including anomalously low sea surface temperatures (SST), ocean circulation change, and increased Asian aridity [Clark et al., 2006].
 The increase in glacial benthic δ18O values across the mid-Pleistocene transition (MPT) from 1.3–0.6 Ma is often attributed to decreasing glacial pCO2 values [e.g., Raymo, 1997; Herbert et al., 2010]. Although Δδ13CP− gradually shifts from 41-kyr to 100-kyr cyclicity from 1.3–0.7 Ma (Figure S3), it does not match the secular trend or amplitude increase observed in benthic δ18O from 1.3–0.6 Ma. Boron-based measurements suggest that glacial pCO2 minima decrease at ∼800 ka [Hönisch et al., 2009; Tripati et al., 2009], but these sparse measurements may not reliably sample glacial minima (Figure 3, top). The Δδ13CP− and alkenone proxies, which show no change in glacial pCO2 minima, actually agree with the low-resolution pCO2 estimates of Hönisch et al.  and Seki et al.  from 1.5–0.8 Ma to within uncertainty (including age uncertainty). Also, the results of a carbon cycle box model suggest that a change in glacial pCO2 minima during the MPT cannot be reconciled with the amplitude of Pacific δ13C variability [Köhler and Bintanja, 2008].
 Additionally, SST change at some tropical sites unaffected by upwelling is thought to be driven by changes in radiative forcing [Medina-Elizalde and Lea, 2005; Herbert et al., 2010]. An SST record from the Western Equatorial Pacific (WEP) warm pool shows no significant trend from 1.35–0.5 Ma [Medina-Elizalde and Lea, 2005], consistent with the results of the Δδ13CP− and alkenone proxies. A recent tropical SST stack that includes both upwelling and non-upwelling sites shows a slight cooling trend [Herbert et al., 2010], but if its long-term trend is adjusted to match the SST trend of the WEP and other non-upwelling sites, the SST stack agrees well with Δδ13CP− from 1.25–0.2 Ma (Figure 3 (bottom) and auxiliary material). Thus, only the pCO2 estimates of Tripati et al.  are inconsistent with steady glacial pCO2 minima since 1.25 Ma.
 However, before 1.25 Ma glacial temperatures in the trend-adjusted stack are ≥1°C warmer than would be expected based on Δδ13CP−. The SST stack could be affected by possible upwelling change at 1.25 Ma, such as thermocline shoaling or cooling at source water formation sites. However, a change in the relationship between Δδ13CP− and pCO2 is also possible, perhaps as the result of circulation or whole-ocean ΣCO2 change. Additional high-resolution proxies are needed to improve confidence in glacial pCO2 estimates, especially before 1.25 Ma.
 In conclusion, Δδ13CP− correlates well with ice core pCO2 from 800–0 ka and reproduces many features of the pCO2 record. Comparison of Δδ13CP− and pCO2 suggests that marine and ice core age models [Lisiecki and Raymo, 2005; Parrenin et al., 2007; Loulergue et al., 2007] differ by ≤2.7 kyr at terminations. Within the marine sedimentary record Δδ13CP− usually leads δ18O by 0.2–3.7 kyr at terminations but lags by 3–10 kyr during “failed” terminations at 535 and 745 ka. Thus, an early pCO2 response appears necessary for complete deglaciation, and pCO2 appears less tightly coupled to northern hemisphere ice volume before 500 ka.
 Several proxies that correlate with pCO2 (Δδ13CP−, South Atlantic productivity [Martínez-Garcia et al., 2009], and WEP SST [Medina-Elizalde and Lea, 2005]) and a carbon cycle box model [Köhler and Bintanja, 2008] suggest that glacial pCO2 minima do not decrease during the MPT. Moreover, the minimum pCO2 concentration of the last 1.5 Myr is estimated to occur at 920 ka. Δδ13CP− gradually shifts from 41-kyr cycles to 100-kyr cycles from 1.3–0.7 Ma but shows no secular trend in mean or amplitude over the last 1.5 Myr, whereas tropical SST records suggest warmer glacial maxima before 1.3 Ma [Herbert et al., 2010]. This likely indicates that at least one of these proxies is affected by factors other than pCO2 before 1.3 Ma; thus, additional high-resolution proxies are needed.
 I thank D. Lea, D. Raynaud, T. Herbert, M. Raymo and two anonymous reviewers for useful suggestions and discussions. Support provided by NSF-MGG 0926735.