The age of individual core samples has typically been estimated by linear interpolation between bio- and magnetostratigraphic datums which in turn have been calibrated relative to radiometrically dated rock samples. The accuracy of this method is generally < ± 10% [see Cande and Kent, 1992], but the precision of correlation among cores using this method is much better: correlation of individual datums has a precision generally < ± 0.1 Myr and interpolation between datums does not add significantly to that uncertainty. Orbital stratigraphy allows correlation among sections at a precision <0.02 Myr, but orbital stratigraphies are not available for most of the records in our compilation. The correlation with the New Jersey sea level (NJSL) record has a significantly greater uncertainty of ±0.5 Myr [Miller et al., 2005]. All records are shown relative to the GTS2004 timescale [Gradstein et al., 2004] although most of the underlying data sets were originally published relative to the timescale of Cande and Kent [1992, 1995] or earlier timescales. Adjustment to the GTS2004 timescale was made by linear interpolation between ages of magnetic polarity chron boundaries given by Ogg and Smith  and those in previous timescales.
 There is an inherent complication in combining time series that have been generated using different measurement techniques and pre-processed in different ways. The δ18Obf and Mg/Cabf trends used here were calculated using identical numerical techniques which should yield reconcilable records. However, we cannot rule out some artifactual differences especially at shorter wavelengths due to the higher sampling density of the underlying δ18Obf data set, the different processes that cause δ18Obf and Mg/Cabf to vary with temperature, and differing processes contributing to the noise in each measurement and reflected in the larger relative uncertainty associated with the Mg/Cabf trend estimate. The NJSL record is of substantially different character from the geochemical records: the record is not continuously sampled, having breaks at sequence boundaries so that sea level lowstand estimates are generally poorly constrained; as noted above, the precision of the underlying age models are generally not as good; and the numerical processing of the underlying data is completely different [see Kominz et al., 2008]. We have attempted to compensate for the differences in numerical processing by smoothing the sea level record with a LOESS filter similar to that used to calculate the δ18Obf and Mg/Cabf trends, which should yield a record with a similar frequency response. The effect is a low-pass filter that passes >80% of the amplitude for frequencies <0.5 Myr−1 (wavelength >2 Myr) ramping down to <20% of the amplitude for frequencies >1.25 Myr−1 (wavelength <0.8 Myr) [see Cramer et al., 2009].
 Cramer et al.  compiled δ18Obf records and calculated separate trends for the North Atlantic (including equatorial), South Atlantic and subantarctic Southern, high latitude Southern, and tropical Pacific oceans extending through the Cenozoic and into the Late Cretaceous (0–80 Ma), with a less well-constrained trend based on two sites extending through the Late Cretaceous (to ∼113 Ma). These records show that deep ocean δ18Obf was homogeneous among ocean basins during most of the Paleocene–Eocene (65–35 Ma), transitioning to heterogeneous deep ocean δ18Obf values in the Oligocene that reflect a thermal differentiation of northern and southern deepwater sources similar to the modern. On timescales greater than the mixing time of the ocean (∼1 kyr), the growth and decay of ice affect the δ18O of seawater on a global basis; variations in δ18Obf reflect these ice-driven changes as well as the mixing of water from temperature- and salinity-differentiated deep water source regions. Ice volume affects the global average δ18Osw, so we should ideally use a global average of foraminiferal δ18O measurements. Because the geographic and temporal distribution of data is too patchy for a meaningful global average δ18Obf value to be calculated, we use the Pacific record as the most representative monitor of deepwater conditions (black curve in Figure 1a). The Pacific basin has comprised the largest proportion of the global ocean volume throughout the Cenozoic, from ∼60% today to >80% of the global reservoir in the Late Cretaceous–early Paleogene.
Figure 1. Primary reconstructed proxy records used in this study: (a) δ18Obf, (b) NJSL, and (c) Mg/Cabf. Records we use are shown in black; prior and alternate versions of these records are shown for comparison. Note the much better correspondence of δ18Obf trends, as reconstructed by different studies spanning four decades, as compared with Mg/Cabf in studies spanning only one decade. This reflects the greater difficulty in reconciling Mg/Cabf, compared with δ18Obf analyses of different species and from geographic locations. For δ18Obf (Figure 1a) and Mg/Cabf (Figure 1c) the 90% confidence envelope is shown, calculated using a bootstrap approach [see Cramer et al., 2009]. For NJSL (Figure 1b) the uncertainty envelope from Kominz et al.  is shown, which takes into account the range of sea level estimates from individual core holes in New Jersey. Lowstand NJSL estimates are shown with dotted lines; these estimates are provided by Kominz et al.  and Miller et al. , but are poorly constrained by data.
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 The δ18Obf trends of Cramer et al.  were calculated using δ18O values measured on various species of benthic foraminifera corrected to the genus Cibicidoides (for the Neogene and Oligocene only analyses of Cibicidoides were used). It is common practice in the paleoceanographic literature, following Shackleton , to assume that tests of the genus Uvigerina are precipitated at equilibrium with seawater and to use paleotemperature equations calibrated to δ18O values for Uvigerina. More recently, it has become clear that the temperature-dependent oxygen isotopic fractionation between water and inorganic calcite determined by Kim and O'Neil  is more consistent with δ18Obf values for Cibicidoides rather than Uvigerina (Figure 2a) [Bemis et al., 1998; Lynch-Stieglitz et al., 1999; Costa et al., 2006; Fontanier et al., 2006; Bryan and Marchitto, 2008]. Moreover, as noted by Bemis et al. , the elevated pH in pore waters should be expected to affect the δ18O values of the infaunal Uvigerina [Spero et al., 1997; Zeebe, 1999], while there is no obvious reason to expect the epifaunal Cibicidoides to precipitate tests out of equilibrium with seawater. We use the relationship determined from core top measurements of Cibicidoides δ18Obf over the temperature range 4.1–25.6°C by Lynch-Stieglitz et al. :
In this equation and throughout this paper, δ18Obf values are expressed relative to VPDB and δ18Osw values are expressed relative to VSMOW; the −0.27‰ adjustment in the equation reflects a combination of the difference between the two scales and the difference in isotopic value obtained from equilibration with water and acid reaction of carbonate [see Hut, 1987]. The difference between temperatures calculated using equation (1) and temperatures calculated following Shackleton  is small at high δ18O (low temperature) but larger at low δ18O (high temperature; Figure 2a), resulting in warmer temperatures calculated for the early Cenozoic in this study compared with previous studies.
 Two other factors should be considered in interpreting variations in δ18Obf over long timescales (≫10 Myr). First, δ18Osw may vary as a consequence of cycling of water through the lower oceanic crust [Veizer et al., 1999; Wallmann, 2001]. Over the last 100 Myr, this process has potentially resulted in an increase in δ18Osw of 1 ‰ [Veizer et al., 1999; Wallmann, 2001, 2004; Jaffrés et al., 2007], although this interpretation is controversial (see discussion by Jaffrés et al. ). Second, δ18O of planktonic foraminifera has been shown to reflect ocean pH as well as temperature and δ18Osw [Spero et al., 1997] due to construction of foraminiferal tests from dissolved inorganic carbon (DIC), fractionation of oxygen isotopes among the different species of DIC (H2CO3, HCO3−, and H2CO3=), and variation in the equilibrium concentrations of these as a buffer to seawater pH [Zeebe, 1999]. Because the pH effect on δ18O of calcite has a thermodynamic basis, the relationship can be theoretically constrained as a 1.42‰ reduction in δ18O of calcite for every 1 unit increase in pH [Zeebe, 2001]. The actual relationship has been shown to vary among different planktonic foraminiferal species [Spero et al., 1999]. Because of the thermodynamic basis of the pH effect, it is likely to affect all marine carbonates, although this has not been empirically demonstrated in benthic foraminifera [Zeebe, 2001]. The deep ocean pH in the past is essentially unconstrained, but assuming the potential for a ∼0.5 unit increase in pH since the Cretaceous from modeling results [Wallmann, 2004] and that the theoretical relation holds for benthic foraminifera, it is possible that the pH effect has resulted in a ∼0.7 ‰ decrease in δ18Obf since 100 Ma. To the extent that both processes have affected δ18Obf since the Cretaceous, the pH effect has likely counteracted the effect of water cycling through the crust.
 We have updated the compilation of Mg/Cabf measurements shown by Katz et al.  and recalculated the Cenozoic trend using different species offsets (see below) (Figures 1 and S1–S3; data compilation and calculated trend are available in the auxiliary material, and published single site records are archived at http://paleoceanDB.net). There are insufficient data from any single ocean basin to calculate basin-specific Mg/Cabf trends. We use all data that are visually consistent with the available Pacific records in calculating the Mg/Cabf trend (Figure S1). Significant interbasinal δ18Obf differences occur only in the Oligocene and Miocene, and primarily with respect to the high latitude Southern Ocean [Cramer et al., 2009], and it should be expected that temperature differences reflected in Mg/Cabf show the same pattern. For further reassurance, we have calculated a δ18Obf trend for a selection of individual records equivalent to that used to construct the Mg/Cabf trend, indicating that there is minimal difference relative to the Pacific basinal trend (Figure S4).
 It has been documented that Mg/Cabf offsets occur among different genera of benthic foraminifera as well as among different species of Cibicidoides. Our compilation includes Mg/Cabf measured on samples of C. wuellerstorfi, C. mundulus, mixed Cibicidoides, Oridorsalis umbonatus, Nuttallides umbonifera, and N. truempyi [ear et al., 2000, 2003, 2004, 2010; Billups and Schrag, 2002, 2003; Dutton et al., 2005; Shevenell et al., 2008; Sosdian and Rosenthal, 2009; Billups and Scheiderich, 2010; Dawber and Tripati, 2011]. There are insufficient data from paired analyses of separate species picked from the same core sample to produce robust fitted calibrations among these different species. Oridorsalis umbonatus analyses are present throughout the time span of the compilation, and we infer offsets between analyses of other species and those of O. umbonatus based on data trends for individual species (Figure S2). Although species offsets in Mg/Cabf have often been treated as additive, including multiplicative offsets provides a better fit (Figure S2). Published linear temperature calibrations indicate different slopes for the temperature-Mg/Cabf relationship in different species [e.g., Elderfield et al., 2006; Bryan and Marchitto, 2008], which implies that interspecies correction factors should have a multiplicative as well as an additive component.
 The influence of Mg/Casw variations on Mg/Cabf ratios is not as straightforward as the relation between δ18Osw and δ18Obf. Modeled Mg/Casw [Farkaš et al., 2007] is consistent with reconstructions from analyses of fluid inclusions in marine evaporites [Lowenstein et al., 2001; Horita et al., 2002], but indicates somewhat higher Mg/Casw than analyses of mid ocean ridge flank carbonate veins [Coggon et al., 2010] and fossil echinoderms [Dickson, 2002, 2004] (Figure 5b). The model of Farkaš et al.  differs from previous models for Mg/Casw [Wilkinson and Algeo, 1989; Hardie, 1996; Stanley and Hardie, 1998; Demicco et al., 2005] in that it uses the marine 87Sr/86Sr record as an input rather than tectonic reconstructions of seafloor spreading rates. Recent reconstructions of seafloor spreading rates [Rowley, 2002; Cogné and Humler, 2006; Müller et al., 2008] bear no resemblance to that of Gaffin  that has been used as input for Mg/Casw reconstructions, and it is questionable whether seafloor spreading rates can be reliably estimated from the spreading history of existing oceanic crust [Rowley, 2008].
 Studies of Mg/Ca ratios in various calcareous organisms [Ries, 2004; Segev and Erez, 2006; Hasiuk and Lohmann, 2010] indicate that the dependence on Mg/Casw generally conforms to the equation
Previous studies of Mg/Cabf have followed Lear et al.  in multiplying Mg/Cabf by the ratio of modern Mg/Casw to Mg/Casw at the time of deposition, effectively assuming H = 1 in equation (2), but to our knowledge this has not been calibrated for deep ocean benthic foraminifera. Segev and Erez  cultured shallow water symbiont-bearing benthic foraminifera (Amphistegina lobifera and A. lessonii) and determined values of 0.8 and 0.7 for H, and Hasiuk and Lohmann  calculated H = 0.42 for the planktonic foraminifera Globigerinoides sacculifer using data from Delaney et al. . As we show below, it is necessary to assume different values for H depending on the assumed temperature sensitivity for Mg/Cabf. We ignore uncertainty in the modeled Mg/Casw of Farkaš et al.  and in the analytical reconstructions of Mg/Casw [Lowenstein et al., 2001; Horita et al., 2002; Dickson, 2002, 2004; Coggon et al., 2010] because it is not separable at the scale of this study from the uncertainty in the exponent, H, in equation (2).
 There is abundant evidence that foraminiferal Mg/Ca reflects the seawater Δ[CO3=] as well as temperature and Mg/Casw [Martin et al., 2002; Rosenthal et al., 2006; Elderfield et al., 2006; Yu and Elderfield, 2008]. Yu and Elderfield  calibrated the effect as ∼0.009 mmol mol−1 Mg/Cabf/μmol kg−1 Δ[CO3=] for C. wuellerstorfi, which is consistent with the inferred relationship from other studies [Elderfield et al., 2006; Healey et al., 2008; Raitzsch et al., 2008]. Multiproxy methods for simultaneous reconstruction of temperature and Δ[CO3=] are being developed [Bryan and Marchitto, 2008; Lear et al., 2010], but published multiproxy data are not available for most of the records in our compilation. We apply a correction for the Δ[CO3=] effect based on the observed decrease in Δ[CO3=] with water depth in the modern ocean. The residual values between Mg/Cabf data from individual sites and the overall trend show a decrease with paleodepth that is consistent with Δ[CO3=] data from the modern ocean, in contrast with residual δ18Obf values that show no trend with paleodepth (Figure S3). This provides supporting evidence for a Δ[CO3=] effect on Mg/Cabf of ∼0.009 mmol mol−1/μmol kg−1 and we adjust the Mg/Cabf data based on a scaled logarithmic fit to the modern Δ[CO3=] data:
where d is the paleodepth for the sample. There may be a threshold Δ[CO3=] value above which there is little to no effect on Mg/Cabf, although there is not yet definitive evidence for this in calcareous benthic foraminifera. The offset applied in equation (3) to align Pacific Mg/Cabf with the global Δ[CO3=] regression (Figure S3) is reminiscent of the threshold value of 25 μmol/kg proposed by Yu and Elderfield . Although much of the deep ocean is characterized by Δ[CO3=] < 35 μmol/mol, we note that our data compilation shows systematic offsets between ocean basins even at shallow depths (where Δ[CO3=] > 35 μmol) that are most easily explained as reflecting interbasinal differences in Δ[CO3=]. We correct all of our data, regardless of paleodepth, using equation (3). We do not correct the Mg/Cabf values for interbasinal differences in Δ[CO3=], but when calculating temperatures from Mg/Cabf we use the CCD reconstruction for the Pacific of Van Andel  as a proxy for Δ[CO3=] changes through time.
 Prior to calculating temperature, the Mg/Cabf trend must be corrected for the effects of Mg/Casw and Δ[CO3=] variations through time. We combine equations (2) and (3) to define the corrected Mg/Ca ratio:
In our calculations the exponent, H, is set so that when the Mg/Cabf temperature is used to solve equation (1) for δ18Osw the result is consistent with minimal ice in the early Eocene. We calculate that melting of all modern ice would lower δ18Osw from the modern value of 0‰ to −0.89‰ (VSMOW). This is based on the present mass of ocean water (1.39 × 1021 kg; calculated from Charette and Smith ), the mass of Antarctic and Greenland ice (2.26 × 1019 kg and 2.66 × 1018 kg; calculated from Lemke et al. ), and the mean δ18Oice for Antarctic and Greenland ice (−52‰ and −34.2‰; Lhomme et al. ). The uncertainty in the magnitude of the δ18Osw decrease with melting of all ice is ∼± 0.02‰ (1σ), based on propagating conservative estimates of uncertainty in each of the masses and δ18O values above, and is therefore negligible in comparison with the other uncertainties involved in our calculations.
 Consideration of the thermodynamic effect on the distribution coefficient leads to the expectation of an exponential relationship between Mg/Cabf and temperature,
but it has long been recognized that Mg/Cabf does not conform to this expectation and therefore that the temperature dependence must be mainly due to physiological processes (see discussion by Rosenthal et al. ). Many investigators have noted that the Mg/Cabf-temperature relationship is equally well fit by a linear equation,
[e.g., Lear et al., 2002; Elderfield et al., 2006; Marchitto et al., 2007] and that the linear form gives more believable results when extrapolated to low temperatures [Marchitto et al., 2007]. Early calibration studies [Rosenthal et al., 1997; Martin et al., 2002; Lear et al., 2002] were compromised by analytical bias and likely by high-Mg overgrowths (see discussion by Marchitto et al. ) and it is questionable whether equations defined only by low-temperature (<5°C) data [e.g., Yu and Elderfield, 2008; Healey et al., 2008] can be extended to the higher temperatures that characterize most of the Cenozoic. There is a well-constrained temperature calibration for Cibicidoides pachyderma, with data spanning temperatures of 5.8–18.6°C [Marchitto et al., 2007; Curry and Marchitto, 2008], but there are no C. pachyderma measurements in our compilation.
2.3. Sea Level
 The New Jersey sea level (NJSL) record has been developed using water depth estimates for a network of cored sections from onshore New Jersey [Miller et al., 1998, 2004, 2005]. The most recent update [Kominz et al., 2008] provides an estimate of sea level changes for 10–108 Ma with an error generally ±20 m in less constrained intervals (e.g., the early Miocene) and ±10 m or better in well-constrained intervals (e.g., the Oligocene) and a temporal resolution of ±0.5 Myr to as fine as ±0.1 Myr in some intervals, although gaps (up to ∼2.5 Myr) occur at sea level low-stands. In addition to the analytical error, NJSL as a measure of the change in water thickness attributable to ice sheet growth and decay (SLice) is subject to systematic uncertainty related to changes in the volume of the global ocean basin (SLbasin).
 One approach to extracting the SLice signal would be to independently constrain SLbasin and the tectonic history of New Jersey and subtract those components from NJSL. Changes in SLbasin can be inferred from ocean crustal production rates (the spreading history of the ocean crust and occurrence of submarine large igneous provinces), but there are major disagreements on the history of global ocean crust production rates and even the sense of SLbasin change over the past 100 Myr [see Rowley, 2002; Demicco, 2004; Cogné and Humler, 2006; Conrad and Lithgow-Bertelloni, 2007; Müller et al., 2008]. The absence of older crust due to subduction leads to large uncertainties in the SLbasin reconstruction for the Paleogene and earlier, and therefore large differences between results from different models. Rowley  has argued persuasively that spreading rate histories for no-longer-existing oceanic ridge systems are entirely dependent on model assumptions rather than data. As such, highstands in the NJSL record may provide the best available constraint on SLbasin for time periods when continental ice was minimal, although unconstrained tectonic changes in the elevation of New Jersey may be a significant factor [e.g., Müller et al., 2008].
 SLice would reach a maximum of ∼64 m with the melting of all modern ice sheets. This takes into account recent estimates for the volume of grounded ice on Antarctica and Greenland [Lythe et al., 2001; Bamber et al., 2001] (see Lemke et al.  for summary), but it does not account for isostatic rebound or alteration of the geoid surface. According to a long-standing assumption, the ∼64 m of extra water thickness would lead to only ∼42 m eustatic sea level rise (i.e., as measured by the NJSL record) due to isostatic compensation involving subsidence of the ocean crust into the mantle under the additional water weight (“Airy” loading; see for instance Pekar et al.  and Miller et al. ). Considering that growth and decay of large ice sheets involves the transfer of mass between continent-scale land area and the global ocean, the actual crustal response is probably not adequately constrained by a simple Airy loading model. Studies of sea level change since the last glacial maximum (LGM), in response to melting of northern hemisphere ice sheets, imply that whole ocean loading is a minimal effect due to global deformation of the geoid and mantle adjustment, with the result that sea level change during the deglaciation as measured in different locations is widely variable [Peltier, 1998; Peltier and Fairbanks, 2006; Raymo et al., 2011]. Without a similarly complex model for the far-field effects of Antarctic glaciation, we treat the Airy loading model (42 m) and no loading (64 m) as end-member scenarios constraining the contribution to NJSL change from the growth of ice sheets to modern size.
 In intervals where NJSL exceeds these bounds we assume that either SLbasin was higher or that the elevation of NJ was tectonically lower than at present. This is the case in the interval older than 34 Ma. A minimal correction would reduce highstands in this interval to 64 m (assuming no isostatic loading effect in NJ) or 42 m (assuming Airy loading in NJ). Such a correction implicitly assumes ice-free conditions during early–middle Eocene highstands, which is a reasonable assumption given that recent paleoclimate model-data integration indicates high latitude surface temperatures >25°C [Huber, 2008]. While there is definite evidence for large-scale glaciation of Antarctica starting in the earliest Oligocene (ca. 34 Ma), there is no physical evidence for continent scale ice sheets older than 34 Ma and it is likely from isotopic evidence that essentially ice-free conditions occurred during warm “interglacial” intervals of the Late Cretaceous to Eocene (see discussion by Miller et al. ).
 We extract SLice from NJSL by imposing an upper bound on sea level highstands:
where max0.8 indicates the maximum of the values over a 0.8 Myr interval and LOESS10 indicates the locally weighted quadratic regression filter originally described by Cleveland  as implemented in the software IGOR Pro 6.1 (www.wavemetrics.com) with 10 Myr width. The two forms of the equation are for different treatments of whole-ocean isostatic response: equation (8a) assumes no isostatic subsidence of the ocean floor in response to shifting water from continental ice sheets to the ocean, while equation (8b) assumes water loading leads to isostatic subsidence equivalent to 1/3 of the added water thickness. The LOESS filter is applied so that only variability on long timescales (i.e., the timescales of tectonic processes) is removed, leaving short timescale variability that is most likely attributable to ice-volume changes. Taking the maximum value of NJSL over a 0.8 Myr interval ensures that the correction is adequate to reduce sea level maxima below the 64 m cap (otherwise, the LOESS filter would project a trend through the middle of the data rather than through the highstands we assume are ice-free).
 The backstripped NJSL is consistent with other recent sea level records (e.g., Marion Plateau [John et al., 2004, 2011]). Although it is ∼1/3 of the amplitude and differs in detail from the frequently cited Exxon Production Research Company estimates of Haq et al. , reviews of new evidence by Miller et al. [2005, 2008, 2011] show why the Haq et al. estimates were unrealistically high. The NJSL estimate presented here is also consistent with constraints placed by the size of potential ice-volume budgets. For example, the ∼55 m sea level fall in the earliest Oligocene is consistent with development of an Antarctic ice sheet that is equivalent to the East Antarctic ice sheet today (∼57 m), with the record of Antarctic glaciation [Zachos et al., 1992; Barrett, 1999], and with detailed records from the U.S. Gulf coast [Katz et al., 2008; Miller et al., 2008].
 The purpose of extracting SLice from NJSL is to use it to constrain the δ18Osw component in δ18Obf, thereby allowing the calculation of deep ocean temperature (see equation (1)). There is a linear relation between changing sea level and δ18Osw:
where k is in units of ‰/m and Δδ18Osw and ΔSLice are the change in mean isotopic composition of seawater and mean sea level during accumulation or melting of continental ice. Alternatively, k is also related to the mean δ18O value of continental ice:
where Msw and Mice are the mass of seawater and mass of ice and 3700 is taken to be the mean depth of the ocean. (The approximation is valid when ∣δ18Osw∣ ≪ ∣δ18Oice∣, ΔSLice ≪ 3700 m, and the change in the surface area of the ocean and density of seawater due to accumulation/melting of continental ice is negligible.) A commonly used value for k is −0.011‰/m (corresponding to δ18Oice ≈ −40‰), derived by calibrating the glacial-interglacial sea level and δ18O amplitude in late Pleistocene coral [Fairbanks and Matthews, 1978; Fairbanks, 1989], although other constraints on glacial-interglacial δ18Osw amplitude imply a value closer to −0.008‰/m (δ18Oice ≈ −30‰) [Schrag et al., 1995; Waelbroeck et al., 2002]. Melting of the present-day East Antarctic, West Antarctic, and Greenland ice sheets (mean δ18Oice of −56.5‰, −41.1‰, and −34.2‰ [Lhomme et al., 2005]) would yield k of −0.015‰/m, −0.011‰/m, and −0.009‰/m, respectively. These differing values result from varying degrees of fractionation of water during evaporation, transport, precipitation, and incorporation into the ice sheet. Clearly, k should not actually be expected to remain constant through time, but modeling variations in δ18Oice are beyond the scope of this paper. We use the value −0.011‰/m in our calculations, and return to the topic in the discussion of our results.