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 We reconstruct trends in ice volume and deep ocean temperature for the past 108 Myr, resolving variations on timescales of ∼2 Myr and longer. We use a sea level record as a proxy for ice volume, a benthic foraminiferal Mg/Cabf record as a proxy for temperature, and a benthic foraminiferal δ18Obf record as a proxy for both. This allows us to construct dual estimates of temperature and ice volume variations for the interval 10–60 Ma: extracting temperature from δ18Obf by using sea level as a proxy for ice volume to constrain the δ18Osw component, and extracting seawater δ18Osw (which reflects ice volume) from δ18Obf by using Mg/Cabf to constrain the temperature component. Each of these approaches requires numerous assumptions, but the range of plausible solutions are concordant on timescales >2 Myr and within an uncertainty of ±2°C temperature and ±0.4‰ δ18Osw. The agreement between the two approaches for the last 50 Myr provides empirical justification for the use of δ18Obf, Mg/Cabf, and sea level records as robust climate proxies. Our reconstructions indicate differences between deep ocean cooling and continental ice growth in the late Cenozoic: cooling occurred gradually in the middle–late Eocene and late Miocene–Pliocene while ice growth occurred rapidly in the earliest Oligocene, middle Miocene, and Plio-Pleistocene. These differences are consistent with climate models that imply that temperatures, set by the long-term CO2 equilibrium, should change only gradually on timescales >2 Myr, but growth of continental ice sheets may be rapid in response to climate thresholds due to feedbacks that are not yet fully understood.
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 Trends drawn through compilations of benthic foraminiferal oxygen isotope measurements (δ18Obf; see notation section at end of text for a glossary of abbreviated terminology) have long been used as a primary proxy for Cenozoic climate variations [Emiliani, 1954, 1961; Savin et al., 1975; Savin, 1977; Shackleton and Kennett, 1975; Miller et al., 1987; Zachos et al., 2001, 2008; Cramer et al., 2009]. These trends are robust estimators of variability on >1 Myr timescales, although they do not resolve the persistent orbitally driven climate cyclicity at <1 Myr timescales that is present in individual high resolution records. The δ18Obf trend is recognized as a proxy for a combination of two climate parameters: deep ocean temperatures that are presumed to reflect surface temperatures at high latitudes where most deep waters are formed, and the seawater δ18O value (δ18Osw) that reflects global ice volume (local evaporation/precipitation differences that affect surface water δ18Osw are damped in the deep sea). The interpretation of climate variations from δ18Obf trends is therefore ambiguous as to the separate variations in high latitude temperature and ice volume, especially during the late Paleogene–Neogene interval that is characterized by large variations in ice volume. Taking modern deep ocean temperatures as a minimal constraint on deep ocean temperatures in an ice-free world, Miller et al.  used the δ18Obf record to demonstrate the existence of large ice sheets since the earliest Oligocene. This was later confirmed by the finding of ice-rafted and grounded-ice debris in drill cores from the Antarctic continental shelf [Barrett, 1989; Hambrey et al., 1991] and from ice rafted material in the Southern Ocean [Zachos et al., 1992]. While it seems reasonable to assume that high latitude surface temperatures and global ice volume covary on long timescales [e.g., Crowley and Kim, 1995; Zachos et al., 2001; Hansen et al., 2008], that assumption is at odds with models indicating a nonlinear response of ice volume to temperature [e.g., DeConto and Pollard, 2003].
 Sequence stratigraphic records have been used to reconstruct sea level changes and confirm that specific δ18Obf increases in the Cenozoic and Late Cretaceous correspond with rapid (≪1 Myr) sea level falls caused by ice volume increases [Browning et al., 1996; Pekar and Miller, 1996; Miller et al., 1996, 1999, 2005, 2011]. On Myr timescales, sea level reconstructions generally provide only a minimum estimate of ice-volume changes because sea level lowstands are typically not recorded [e.g., Miller et al., 2005]. On 10–100 Myr timescales, sea level may also be affected by variations in the volume of the ocean basins due to changes in globally integrated seafloor spreading rates [e.g., Cogné et al., 2006; Müller et al., 2008; Rowley, 2002, 2008]. While the amplitudes of individual sea level falls have been compared with δ18Obf increases, the sea level record has not previously been used to constrain the ice volume component of a δ18Obf record prior to the Plio-Pleistocene.
 Because of the number of different assumptions that must be made in order to calculate temperature from Mg/Casw or δ18Osw from sea level (in order to subtract from δ18Obf) the uncertainty associated with using either of these approaches on its own is large (±10–15 m or ± 4°C) (K. G. Miller et al., The high tide of the warm Pliocene: Implications of global sea level for Antarctic deglaciation, submitted to Geology, 2011). However, we demonstrate that combining these three proxies (Mg/Cabf, δ18Obf and sea level) subject to the constraint of ice-free conditions in the early Eocene produces credible dual records of deep ocean temperature and ice volume variations since 50 Ma.
 In the next section of this paper we describe in detail the available constraints on parameters and equations necessary for the interpretation of δ18Obf (section 2.1), Mg/Cabf (section 2.2), and sea level (section 2.3) records. In section 3 we examine the results of calculations using the three proxy records, and the implications for parameters and equations that are poorly constrained. We give particular attention to the implications of the Cenozoic Mg/Cabf record for constraining the dependence of Mg/Cabf on temperature, Δ[CO3=], and Mg/Casw. In section 4 we discuss the potential implications of our results for understanding geologic processes and climate change through the Cenozoic. Reconstructions of variations in temperature and ice volume proxies (sea level, δ18Osw) from our calculations are available in the auxiliary material.
2. Primary Records: Characteristics and Limitations
 The primary records of the two geochemical proxies used in this study are analyses of sample series taken from ocean floor sediment cored by the Deep Sea Drilling Project, Ocean Drilling Program (http://odplegacy.org). These cores preserve records of climate change over millions of years at various locations in the ocean. The network of cores is not extensive enough to produce a complete oceanographic reconstruction for the Cenozoic; the records we use represent compilations of data representative of broad areas of the ocean. The paleo-water depth for each sample can be estimated using “backtracking” — applying an inverse model of tectonic subsidence to return the core location to its position at the time of deposition — and we use these estimates of paleo-water depth, calculated as described by Cramer et al. , to control for water depth-dependent variations in the geochemical proxies.
 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.
 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.
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,
 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.
3. Calculations and Reconciliation of the Records
 In this section, we examine the results from mathematical combination of the δ18Obf, Mg/Cabf, and NJSL records according to the various hypotheses, models, and constraints discussed in section 2. Some of these lead to implausible results indicating problems with those hypotheses and models. The quality of available data and knowledge of parameters necessary for the calculations are insufficient for determining a uniquely “correct” solution, but the range of results does place constraints on the variation in deep water temperature and ice volume over the last 113 Ma.
 We begin the discussion of our results by obtaining our best estimate of ice volume from the NJSL curve, one proxy for ice volume (section 3.1 and Figure 3). We then use this estimate to extract the ice volume component from the Pacific δ18Obf compilation to yield a deep-sea temperature curve (section 3.2 and Figure 4). We obtain an independent temperature curve from our Mg/Cabf compilation and use this in combination with the δ18Obf compilation to extract a δ18Osw record, an independent proxy for ice volume (section 3.3 and Figure 5). These are compared on a single summary diagram (Figure 6) showing mutual support for some features in the reconstructed temperature and ice volume histories, and we note problems with the underlying data sets that may explain intervals in which the results differ (section 3.4). Special attention is given to the potential implications of this comparison for the temperature and Mg/Casw sensitivities of Mg/Cabf records (section 3.5).
 Applying equations (8a) and (8b) to NJSL effectively treats uncorrected NJSL as the best estimate of SLice for the late Paleogene–Neogene (<∼40 Ma) (Figure 3). This is an interval over which crustal production reconstructions are reasonably well constrained [Rowley, 2008] and most studies agree that changes in crustal production were small [Rowley, 2002; Müller et al., 2008] (but see Cogné and Humler ). Our analysis requires a 50–90 m correction during a discreet interval of the early–middle Eocene (55–40 Ma), due to either higher SLbasin or tectonic lowering of NJ, or both. The required correction is lower (15–40 m) in the Cretaceous–Paleocene (Figure 3b).
 Because we smooth the SLice record to approximate the smoothing reflected in the δ18Obf and Mg/Cabf records the result is significantly affected by the absence of a NJSL estimate at sequence boundaries. We fill the data gaps using the poorly constrained lowstand estimates provided by Kominz et al.  as a minimum estimate, linear interpolation as a maximum estimate, and the midpoint between these as the best estimate. The uncertainty envelope for NJSL from Kominz et al.  with lowstands filled in this way is applied to the SLice record in the interval <40 Ma; for the interval >40 Ma the uncertainty envelope is defined by the different SLice records resulting from equations (8a) and (8b) (Figure 3c). The black curve, with uncertainty envelope, in Figure 3c is used as a reconstruction of SLice in the discussion below.
 In addition to affecting the magnitude of the required adjustment to NJSL, equations (8a) and (8b) lead to substantially different estimates of the magnitude of Myr-scale changes in SLice. For equation (8a) the magnitude of Myr-scale variations is equivalent to that measured by NJSL. For equation (8b), it is assumed that the whole ocean crust isostatically responds to water loading and consequently the magnitude of Myr-scale variations in NJSL is only 2/3 the magnitude of SLice changes (SLice reflects changes in water thickness rather than global sea level). The magnitude of Myr-scale SLice variations calculated by equation (8b) is 50% larger than those calculated by equation (8a), and would require 50% larger ice sheets. During the Cretaceous–Eocene, that would require accommodating ice sheets as large as 80% of modern, rather than only ∼50%, and it would require accommodating ice sheets in the early Oligocene substantially larger than modern rather than roughly equivalent to modern. We find the results and implications of equation (8a) to be more reasonable, reducing the size of ice sheets that would have to be reconciled with Paleogene warm climates. This suggests that the assumption of a whole ocean adjustment to Airy loading is incorrect [see also Peltier and Fairbanks, 2006].
 Scaling the NJSL-based SLice record to δ18Osw (equation (9)) allows a comparison to the Pacific δ18Obf record and the calculation of deep water temperature via equation (1) (Figure 4). On 10 Myr timescales, the resulting temperature curve shows three warm intervals (early–middle Miocene, early–middle Eocene, and Cenomanian–Campanian) superimposed on a 100 Myr-timescale ∼12°C cooling trend from the Late Cretaceous to the Neogene. While the Miocene temperature peak (8 ± 1°C) is clearly cooler than the Eocene (14 ± 2°C), the degree to which high temperatures of the Eocene are cooler than those of the Late Cretaceous is dependent on assumptions about the long-term evolution of δ18Osw and ocean pH. We treat these two variables independently to delineate extremes for reconstruction of the temperature curve (the two have opposite effects on the calculated temperature, so combination of the two would result in calculated temperatures falling between these extremes). Correcting for the potential pH effect on δ18Obf (−0.7‰/100 Myr; see section 2.1) implies Late Cretaceous peak temperatures (∼20°C; red curve in Figure 4c) substantially higher than Eocene, while correcting for the potential change in δ18Osw due to cycling of seawater through the crust (+1‰/100 Myr; see section 2.1) results in Late Cretaceous peak temperatures (∼13°C; blue curve in Figure 4c) only slightly higher than Eocene. It should be noted that minimal Late Cretaceous δ18Obf values (peak temperatures) are constrained by analyses from only two sites (DSDP Sites 511 and 258); although there is no reason to suspect that these records are severely biased it is possible that a Pacific δ18Obf record from this interval would show higher values (lower temperatures). In any case, it is not likely that peak Late Cretaceous temperatures were cooler than those of the Eocene, though they may not have been significantly warmer.
 Combining different assumptions about the various parameters needed to transform Mg/Cabf into a temperature record allows for a large number of different interpretations. The various resulting temperature records can be used in conjunction with δ18Obf to produce various δ18Osw records. Ice volume constraints on δ18Osw rule out some of these scenarios, but the uncertainty regarding seawater pH and crustal cycling effects on δ18Obf means that a wide variety of possibilities are still plausible. We discuss end-member scenarios constrained by treating the seawater pH and crustal cycling effects independently (Figure 5), as we did for interpreting δ18Obf above. We calculate an uncertainty envelope for the temperature trends using the 90% confidence interval for the Mg/Cabf trend; in the calculation of δ18Osw the uncertainty envelope also takes into account the 90% confidence interval for the δ18Obf trend and either a crustal cycling or pH effect on δ18Obf for maximum and minimum temperature boundaries, respectively.
 As noted above, the two temperature equations we consider require different assumptions about the sensitivity of Mg/Cabf to variations in Mg/Casw. The Mg/Casw sensitivity required for equation (7b) (H = 0.70 in equation (4)) is similar to values determined for shallow water benthic foraminifera [Segev and Erez, 2006], while equation (7a) requires Mg/Cabf to be essentially insensitive to Mg/Casw (H = 0.03). The Mg/Casw sensitivity implied by equation (7b) is therefore more plausible in the context of Mg/Casw sensitivity in other calcareous marine organisms [Hasiuk and Lohmann, 2010], but Stanley et al.  showed that one species of coccolithophore, Coccolithus neohelis, precipitates coccoliths with Mg/Ca independent of Mg/Casw (H = 0), so it is possible that benthic foraminifera are characterized by the low Mg/Casw sensitivity implied by equation (7a).
 The calculated temperature histories show Paleocene temperatures of 12–20°C gradually cooling to 8–12°C in the middle Eocene (Figure 6). The results from equations (7a) and (7b) diverge beginning in the late middle Eocene, with equation (7a) resulting in a ∼4°C cooling to 4–7°C in the early Oligocene and equation (7b) resulting in a smaller ∼2°C cooling to 6–9°C. Equation (7a) indicates a slight warming to 7–9°C in the early Miocene while equation (7b) indicates a slight cooling to 6–8°C. Results from equation (7a) indicate a cooling by ∼2°C in the middle Miocene followed by a ∼1°C warming in the late Miocene; the cooling is of smaller magnitude for equation (7b) (∼1°C) and subsequent warming is negligible. Cooling during the late Miocene–Pliocene leads to Pleistocene temperatures of ∼0°C, with a larger uncertainty for equation (7a) (−1–2°C) than for equation (7b) (0–1°C). The discrepancy between the results for equations (7a) and (7b) in the middle Eocene–early Miocene reflects the different temperature and Mg/Casw sensitivities. Temperature decreases more gradually with Mg/Cabf in equation (7b) than in equation (7a), so the middle Eocene cooling is of smaller magnitude; equation (7a) requires low Mg/Casw sensitivity so that less of the Oligocene–middle Miocene Mg/Cabf increase is attributed to the coincident Mg/Casw increase.
 When combined with δ18Obf, results from both equations (7a) and (7b) indicate ice volume decreasing from ∼200% of modern in the Paleocene to ∼10% in the early Eocene; large ∼2 Myr oscillations in this interval would require accumulation and melting of the equivalent of the modern Antarctic ice sheet. We know of no evidence for continent-scale Antarctic ice sheets during the early Paleogene, so we consider the Paleocene results and the amplitude of oscillations in the early Eocene to be unreasonable. The large 2–5 Myr oscillations in Mg/Cabf in the Paleocene–early Eocene are most likely a consequence of aliasing higher frequency variability: the transition from high amplitude to more subdued oscillations is coincident with a change from low- to high-resolution sampling for the Site 1209 record (Figure S1). Following an increase in ice volume to ∼50% of modern in the middle Eocene, results for the two equations diverge: equation (7b) indicates a decrease to 0% modern ice volume in the late Eocene and an abrupt increase at the Eocene/Oligocene boundary to ∼140% of modern ice volume; results from equation (7a) indicate a decrease to negative ice volume (clearly unreasonable) in the late Eocene followed by an abrupt increase at the E/O boundary to ∼100% of modern ice volume. Increasing ice volume during the Oligocene for equation (7a) and a late Oligocene decrease in ice volume for equation (7b) leads to a crossover of the results: results from equation (7a) indicate greater ice volume in the early Miocene (∼140%) than results from equation (7b) (∼120%). The results indicate a decrease in ice volume from the early to middle Miocene (to ∼100% for equation (7a) and ∼60% for equation (7b)), and increase from the middle to late Miocene (to ∼200% for equation (7a) and ∼160% for equation (7b)). Gradually decreasing ice volume for equation (7a) (overprinted by 2–5 Myr oscillations) and a late Pliocene increase in ice volume for equation (7b) leads to convergence of the results at ∼190% of modern ice volume in the Pleistocene. The mean Pleistocene ice volume is expected to be between interglacial and glacial extremes. Considering that the ∼120 m sea level lowering at the last glacial maximum [Peltier and Fairbanks, 2006] indicates ice volume ∼280% of modern, ∼190% is reasonable for the mean Pleistocene state.
 In summary, the ice volume results suggest that our Mg/Cabf-based temperature reconstruction yields temperatures that are too high in the Paleocene, that the amplitude of variability in the early Eocene is too large, and that the late Eocene temperatures for equation (7a) are too low. Results from equation (7b) show the expected increase in ice volume in the late Pliocene–Pleistocene. Results from equation (7a) instead indicate greater ice volume in the late Miocene than in the Pleistocene, implying that the Mg/Cabf-based temperature results from equation (7a) are too high in the late Miocene.
3.4. Comparison of Results
 The calculations above provide two largely independent approaches to deriving deep water temperature and ice volume: one using ice volume approximated from sea level to extract temperature from δ18Obf, and another using temperature calculated from Mg/Cabf to extract ice volume from δ18Obf (Figure 6) (for brevity in the subsequent discussion we use subscripts as a shorthand describing the underlying data used for the different approaches: IVSL/Tδ−SL and IVδ−Mg/Ca/TMg/Ca). The two approaches, as implemented here, are not fully independent: because of uncertainties about the necessary parameters we have forced all the records calculated here to produce essentially ice-free conditions in the early Eocene. That constraint in the early Eocene should not affect the timing of cooling and ice sheet growth through the late Paleogene and Neogene, and we consider the concordance of results from the two approaches over this interval as supporting evidence that the underlying models are sound. Variability at timescales >3 Myr is well correlated between results from the two approaches; the correlation is less good at timescales <3 Myr, but is statistically significant at >95% confidence for both temperature and ice volume reconstructions at all timescales >1 Myr (Figure S5).
 We stress that our observations are not applicable to Myr-scale variations, which have been filtered out of these records. For instance, a number of studies have addressed the apparent incompatibility of sea level, δ18Obf, and Mg/Cabf records in the earliest Oligocene [Lear et al., 2000, 2004, 2008; Billups and Schrag, 2003; Coxall et al., 2005; Katz et al., 2008]. Our results indicate that the long-term shift in the mean cryosphere state that occurred near the Eocene/Oligocene boundary was not accompanied by a similarly abrupt shift in the long term mean deep ocean temperature, but that has very little relevance to the relative contribution of ice growth and temperature change during the much larger (>1.0‰), transient (<300 kyr) δ18Obf event in the earliest Oligocene (Oi-1).
 Our reconstructions indicate a gradual decline in temperature during the Eocene, from 14 ± 3°C in the early Eocene to 6 ± 2°C in the late Eocene. The δ18Obf–sea level approach (Tδ−SL) (black line and gray shaded area in Figure 6a) indicates a further ∼2°C cooling during the Oligocene followed by a ∼3°C warming in the late Oligocene–early Miocene, while the Mg/Cabf approach (TMg/Ca) (orange and blue lines and hatched areas in Figure 6a) indicates either a slight warming or essentially stable temperatures through this interval, depending on the value of H. The magnitude of the cooling during the middle Miocene is larger for Tδ−SL (∼4°C) than for TMg/Ca (2–3°C).
 Both approaches indicate an abrupt increase in ice volume at the Eocene/Oligocene boundary (Figure 6b); the magnitude of this shift is greater for the δ18Obf–Mg/Cabf approach (IVδ−Mg/Ca) than for the NJSL approach (IVSL) (change equivalent to ∼110% vs ∼60% of modern ice volume). During the Oligocene–early Miocene all results indicate ice volume in the range 60–140% of modern, although results differ in showing a gradual increase in ice volume through this interval (IVSL and equation (7a) IVδ−Mg/Ca) or a late Oligocene–early Miocene decrease (equation (7b) IVδ−Mg/Ca). It is worth noting that topographic reconstruction of the Antarctic landscape for 34 Ma indicates that land area was 10–20% greater than has been assumed [Wilson and Luyendyk, 2009] (updated to 18–24% greater by Wilson et al. ), and hence could accommodate a substantially larger ice sheet.
 The largest discrepancy between the two approaches occurs in the Paleocene–early Eocene, with lesser discrepancies in the late Miocene and late Eocene (Figure 6). In section 4.1 we examine the potential implications of the discrepancies for geologically interesting parameters: Mg/Casw, δ18Oice, and Δ[CO3=]. However, the discrepancies may instead simply reflect problems with the underlying data that we discuss here.
 The Paleocene–early Eocene Mg/Cabf record is primarily constrained by a single record, from ODP Site 1209 (Shatsky Rise, western Pacific [Dutton et al., 2004, 2005]), with data from ODP Site 689 (Weddell Sea, Southern Ocean [Lear et al., 2000; Billups and Schrag, 2003]) in only a short interval ∼55 Ma. Moreover, the ODP Site 1209 record is constrained almost exclusively by analyses of Nuttalides truempyi in the interval >53 Ma; the Mg/Ca for the single O. umbonatus analysis in this interval (∼58 Ma) is low relative to the corrected N. truempyi measurements and consistent with the lower temperature indicated by the Tδ−SL reconstruction. N. truempyi may have a different sensitivity to Mg/Casw than O. umbonatus; alternatively, N. truempyi is an infaunal species and may not have a consistent offset relative to O. umbonatus due to changes in pore water chemistry. In their discussion, Dutton et al.  provide good arguments against potential explanations for the discrepancy between this record and δ18Obf variations: diagenesis, variable Mg/Casw, ice volume, seawater pH, and interbasinal δ18Osw variations. We explore the potential for Mg/Casw changes in section 4.1, but stress that the Paleocene–early Eocene Mg/Cabf trend needs to be confirmed before concluding that one, or some combination, of these unlikely scenarios must be true. There is some support for the trend we show from a tropical Pacific planktonic foraminiferal Mg/Ca record that similarly indicates stable Mg/Ca values during this interval of increasing δ18O, although those values may be explained by diagenetic recalcification of planktonic foraminifera [Tripati et al., 2003].
 In the middle Miocene, both approaches indicate a temperature decrease and ice volume increase, but the Tδ−SL decrease is larger than in TMg/Ca and the IVSL increase is smaller than in IVδ−Mg/Ca. There are reasons to question both the Mg/Cabf and the NJSL record in this interval. The bias in NJSL toward interglacial sea level highstands is expected to increase as the amplitude of ice volume changes increases. Offshore drilling by IODP Expedition 313 [Expedition 313 Scientists, 2010] has targeted lower-middle Miocene lowstand deposits that are not represented onshore and it is clear that the early middle Miocene eustatic estimates from onshore NJ are strongly biased to highstands [Miller et al., 2005; Kominz et al., 2008]. For example, on the Marion Plateau, eustatic falls during late middle Miocene were backstripped as ∼55 m, versus ∼40 m in New Jersey at this time [John et al., 2004]. The Mg/Cabf record suffers from lack of continuous records through this interval (Figure S2a). The constraint on the early Miocene Mg/Cabf peak is limited to a record from Site ODP 747; the trend for ODP 747 in the middle Miocene–Pleistocene does not match any of the other records but we include the late Oligocene–early Miocene portion because no other records are available (Figure S1). The middle Miocene Mg/Cabf minimum occurs at the young end of the record from ODP Site 1171 (Pacific sector Southern Ocean) and the old end of the record from ODP Site 806 (western Equatorial Pacific); the record from ODP Site 926 (western Equatorial Atlantic) is continuous through this interval, but we have excised the late Miocene interval of this record because it shows a warming not present in the Pacific (Figure S2a) [see Billups and Scheiderich, 2010].
3.5. Mg/Cabf Sensitivity to Temperature and Mg/Casw
 There is a clear linear correlation between Mg/Cacorr (equation (4)) and Tδ−SL, if we ignore the interval >53 Ma that is constrained only by Site 1209 N. truempyi analyses (Figure 7). It is possible that an exponential temperature dependency could explain the data >57 Ma, which would then leave the data 45–57 Ma as anomalously low in Mg/Cacorr, but we believe it is more plausible that the Paleocene N. truempyi Mg/Cabf data are anomalously high. Clearly, the exponential fit to core top O. umbonatus data of Rathmann et al.  cannot explain the correlation we observe with or without the data >57 Ma (compare Figures 2 and 7).
 Because temperature decreases and Mg/Casw increases through the Cenozoic, there is a tradeoff in this data between the temperature sensitivity and Mg/Casw sensitivity of Mg/Cabf: assuming high (low) temperature sensitivity requires high (low) Mg/Casw sensitivity and vice versa. The Cenozoic record conforms well to the high temperature sensitivity of the Rathmann et al.  core top O. umbonatus data if a high Mg/Casw sensitivity (H = 0.70 in equation (4)) is assumed, but it also conforms well to the low temperature sensitivity of the Lear et al.  O. umbonatus data and the Marchitto et al.  C. pachyderma data if a low Mg/Casw sensitivity is assumed (H = 0.03 in equation (4)) (Figure 7). As noted above, a high Mg/Casw sensitivity for benthic foraminifera is consistent with most of the marine organisms for which the sensitivity is known [Hasiuk and Lohmann, 2010]; our results show that a high Mg/Casw sensitivity is inconsistent with data indicating a low temperature sensitivity for modern benthic foraminifera [Marchitto et al., 2007; Bryan and Marchitto, 2008].
 It is likely that different species of benthic foraminifera have different sensitivities to Mg/Casw. Segev and Erez  determined different sensitivities for two different species of the shallow water genus Amphistegina (H = 0.7 for A. lessonii and H = 0.8 for A. lobifera) while Stanley et al.  demonstrated that different genera of coccolithophores can have extremely different Mg/Casw sensitivities (H = 0.9 for Pleurochrysis carterae, H = 1.5 for Ochrosphaera neopolitana, and H = 0.0 for Coccolithus neohelis; values calculated by Hasiuk and Lohmann ). If the Mg/Cabf differences among species in part reflects different sensitivities to Mg/Casw then the offsets among species should not be expected to be constant through the Cenozoic. The large difference between analyses of Nuttalides and those of Oridorsalis and Cibicidoides (Figure S2) may reflect a large difference in Mg/Casw sensitivity, which could contribute to the discrepancy between the TMg/Ca and Tδ−SL reconstructions in the Paleocene. There is supporting evidence for a difference in Mg/Casw sensitivity between Nuttalides and Oridorsalis in a much larger difference between N. umbonifera and O. umbonatus analyses observed in the early Oligocene (DSDP Site 522) compared to the Neogene (Sites DSDP 573 and ODP 926). We do not observe a variation in the offset among O. umbonatus, C. mundulus, and C. wuellerstorfi Mg/Cabf during the Neogene, when Mg/Casw changes are large, so these species most likely have similar Mg/Casw sensitivities (a more robust data set of paired analyses would be required to entirely rule out differences in Mg/Casw sensitivity among these species). The problem is further complicated by the need to correct Mg/Cabf measurements for Δ[CO3=] variations and the potential that different species respond differently to Δ[CO3=].
 Reconstructing Cenozoic temperatures using Mg/Cabf requires knowing not only the Cenozoic variation in Mg/Casw but also the Mg/Cabf sensitivity to Mg/Casw. The difficulty of culturing deep sea benthic foraminifera may prevent laboratory determination of the Mg/Casw sensitivity for most species [see, e.g., Filipsson et al., 2010]. With adequate constraint on the temperature sensitivity and Mg/Casw, the correlation between corrected Mg/Cabf and Tδ−SL demonstrated here can provide some constraint on Mg/Casw sensitivities.
 We undertook the analysis presented here with the intention of testing the hypothesis that NJSL and Mg/Cabf are robust climate proxy records for long-timescale variations in global ice volume and deep ocean temperature, respectively. By combining these two proxies with δ18Obf, which reflects a combination of ice volume and temperature effects, we have generated separate records of deep ocean temperature and δ18Osw that overlap from the Paleocene–Miocene. Except at the ends of this overlapping interval, the separate records are consistent within ±2°C temperature, a difference that is similar in magnitude to the uncertainty in the Mg/Cabf trend calculation (equivalently, the consistency can be stated as ±0.4‰ δ18O, ±60% modern ice volume, or ±35 m sea level). Variability in the separate reconstructions is correlated over all timescales >1 Myr (confidence >95%; Figure S5), confirming that the visually apparent concordance is not a consequence of the imposed temperature decrease since the early Eocene. Our analysis, therefore provides significant support to the use of these records as proxies for climate change through the Cenozoic, and we argue that these reconstructions provide fundamental insight into the >5 Myr variability in deep ocean temperature and ice volume through the Cenozoic.
 There are also obvious discrepancies between the derived temperature and ice volume records. As discussed in the previous section, there are potential problems with the underlying data that may account for these discrepancies, but it is also possible that these discrepancies reflect variations in parameters that are more interesting from a geologic perspective. In the following sections we explore the potential implications of interpreting the discrepancies as reflecting variations in Mg/Casw, δ18Oice, or Δ[CO3=], and then discuss how these records may change our view of Cenozoic cooling.
4.1. Mg/Casw, δ18Oice, and Δ[CO3=]
 The difference between temperature reconstructions (Tδ−SL and TMg/Ca) or between ice volume reconstructions (IVSL and IVδ−Mg/Ca) can be used to reconstruct variations in Mg/Casw, δ18Oice, or Δ[CO3=] (Figure 8); we assume the CCD-based correction for Δ[CO3=] when calculating Mg/Casw and δ18Oice, the Farkaš et al.  reconstruction of Mg/Casw when calculating Δ[CO3=] and δ18Oice, and a constant δ18Oice of ∼−40‰ (k = −0.011 in equation (10)) when calculating Mg/Casw and Δ[CO3=]. For Mg/Casw,
where 3700 m is the mean depth of the ocean, −1.17 and 64 are the δ18Osw and SLice with no ice, and δ18Osw is calculated using Mg/Cabf to constrain temperature (equations (7a) and (7b)) and solving equation (1) for δ18Osw. For Δ[CO3=],
Equations (13a) and (13b) correspond with temperature equations (7a) and (7b) respectively. We make these calculations using curves filtered to remove variations at <5 Myr wavelength. Variations in δ18Oice and Δ[CO3=] may contribute to the lack of coherence among the records at shorter wavelength, but we do not have sufficient confidence in the available records to attempt to interpret these variations (see section 3.4 and Figure S5). The Mg/Casw reconstruction is further smoothed because Mg/Casw is not expected to vary rapidly due to the long residence time for Mg in the ocean. Rendering the differences between reconstructions in these ways (Figure 8) is perhaps most useful in indicating intervals in which other factors must be involved, such as the data problems discussed in section 3.4. We evaluate these by comparing the Mg/Casw reconstruction with estimates from fluid inclusions and with crustal production reconstructions, by comparing the δ18Oice reconstruction with the modern end-member values for the East Antarctic ice sheet (−57 ‰) and the Greenland ice sheet (−34 ‰ [Lhomme et al., 2005]), and by comparing the Δ[CO3=] reconstruction with changes in the CCD. The values of all these reconstructions can be shifted by assuming different values for the Mg/Cabf sensitivity to Mg/Casw (H in equation (4)); these reconstructions may therefore provide some insight whether equation (7a) or (7b) is more realistic.
 As noted above, it is not possible to calculate Mg/Casw using results from equation (7a). The results from equation (7b) indicate Mg/Casw values similar to that modeled by Farkaš et al.  except in the Paleocene, late Oligocene, and late Miocene (Figure 8b). High Mg/Casw reconstructed in the late Miocene and late Oligocene is not compatible with either the Farkaš et al.  model or data from fluid inclusions [Lowenstein et al., 2001; Horita et al., 2002]. High Mg/Casw values in the Paleocene, gradually decreasing to the early Eocene, are also not compatible with the Farkaš et al.  model, but there are no analytical data to compare with in this interval. Crustal production reconstructions [Rowley, 2002; Müller et al., 2008] show an increase in the late Paleocene that might account for such a decrease in Mg/Casw. Likewise, the increase in NJSL to anomalously high levels in this interval could be accounted for by a significant increase in crustal production rates affecting SLbasin (Figure 3). We note a slight similarity between the equation (7b) Mg/Casw reconstruction and the crustal production reconstruction of Müller et al. : Mg/Casw minima at ∼16 Ma, ∼36 Ma, and ∼50 Ma lag crustal production maxima, as would be expected due to the long residence time for Mg.
 We attempt to interpret reconstructions of δ18Oice only for the Oligocene–Miocene; in the Paleocene–Eocene the δ18Oice reconstructions are erratic due to low ice volume (i.e., the denominator in equation (12) is near 0; Figure 8). Results from equation (7a) indicate δ18Oice in the range of the modern Antarctic ice sheet in the Oligocene–middle Miocene; results from equation (7b) indicate an increase in the δ18Oice from values slightly lower than the modern East Antarctic ice sheet in the early Oligocene to values slightly higher than the modern Greenland ice sheet in the middle Miocene. The equation (7a)δ18Oice reconstruction is consistent with an expectation that the dynamic Oligocene ice sheet [Naish et al., 2001; Barrett, 2007] had composition varying between that of the modern polar East Antarctic ice sheet and the more temperate modern West Antarctic ice sheet and LGM northern hemisphere ice sheet. The equation (7b) reconstruction instead implies that the ice sheet composition was similar to the modern East Antarctic ice sheet in the early Oligocene, shifting toward the modern Greenland composition in the early–middle Miocene. This is possibly consistent with measurements indicating lower δ18O in precipitation during the greenhouse climate of the Cretaceous [White et al., 2001], and would make it easier to explain the magnitude of the early Oligocene δ18O increase (Oi-1 [see Katz et al., 2008]). Both equations (7a) and (7b) indicate a decrease in δ18Oice during the middle Miocene, consistent with the transition to a stable, cold ice sheet at this time [Lewis et al., 2007, 2008; Bertler and Barrett, 2010], but the increase is of larger magnitude than can be explained by the range between modern Greenland and Antarctic ice sheet δ18Oice (equation (7a) indicates late Miocene δ18Oice lower than that of the modern Antarctic ice sheet while equation (7b) indicates middle Miocene δ18Oice higher than that of the modern Greenland ice sheet).
 The Δ[CO3=] reconstructions show an increase in the late Eocene–early Oligocene more than twice as large as the increase we assumed based on the Pacific CCD reconstruction of Van Andel . The reconstruction based on equation (7a) continues to increase gradually through the early Miocene; the reconstruction based on equation (7b) instead shows a decrease from the late Oligocene–early Miocene that is more consistent with the Van Andel  reconstruction of the CCD for the Atlantic basin, although again of much larger magnitude (note that the shallowing of the Atlantic CCD in this interval is very poorly constrained [Berger and von Rad, 1972]). The increase in Δ[CO3=] during the middle Miocene is consistent with the results of Lear et al.  based on paired Li/Ca and Mg/Ca analyses from the Indian Ocean (Site 761), but the Lear et al.  reconstruction indicates a peak at ∼14 Ma with a subsequent decrease while our calculations indicate continued increase into the late Miocene. Billups and Scheiderich  attributed the late Miocene Mg/Cabf increase present in Atlantic records in part to increased Δ[CO3=] due to changes in circulation patterns, as reflected in increased carbonate preservation in the Atlantic at the expense of the Pacific. That hypothesis would lead to the expectation of reduced Δ[CO3=] reflected in Pacific records, which is the opposite of what our Δ[CO3=] reconstruction shows.
 Reconstructions from equations (7a) and (7b) both show an increase and subsequent decrease (for equation (7a)) in Δ[CO3=] during the middle Eocene that could be viewed as supporting evidence for a deepening of the CCD in this interval [Tripati et al., 2005; Lyle et al., 2006]. The high Paleocene Δ[CO3=], and decrease during the early Eocene, is consistent with the suggestion by Hancock et al.  that the CCD was deep (>4000 m) for an interval of the late Paleocene–early Eocene, although the implied whole-ocean saturation with respect to CaCO3 is extreme.
 The analysis above supports the conclusion that the Mg/Cabf, δ18Obf, and NJSL records are easily reconcilable in the Oligocene–early Miocene. In this interval the records have potentially interesting implications for the evolution of ice sheets and ocean carbonate chemistry, but there is inadequate constraint on the Mg/Cabf sensitivity to temperature and Mg/Casw to draw firm conclusions. Calculations based on equation (7a) broadly support our assumption of constant δ18Oice (although at a lower value) and CCD-based Δ[CO3=] changes for the Oligocene–early Miocene; for the same interval, the calculations based on equation (7b) support the Farkaš et al.  reconstruction of Mg/Casw, but are at odds with the assumption of constant δ18Oice and the Pacific CCD reconstruction. Better constraint on the Mg/Cabf sensitivities would allow more robust conclusions; in the case of high Mg/Casw sensitivity the first order (>10 Myr) variations could be reconciled with small changes in the Mg/Casw model.
 The records in the middle–late Miocene are more difficult to reconcile. While a decrease in δ18Oice in conjunction with growth and stabilization of the East Antarctic ice sheet conforms to our expectation, the magnitude of the implied increase is larger than expected. If further research confirms the NJSL and Mg/Cabf trends in this interval, then reconciling this with δ18Obf most likely requires a combination of Mg/Casw, δ18Oice, and Δ[CO3=] variations.
 The Paleocene–Eocene records are not easily reconciled, requiring extreme variations in δ18Oice, Δ[CO3=], or Mg/Casw. The Paleocene records can only be reasonably explained by changing Mg/Casw, assuming a high Mg/Cabf sensitivity; it is most likely that the Mg/Cabf record in this interval is inaccurate (see section 3.4). The discrepancy among records in the Eocene may be explainable by a combination of Δ[CO3=], δ18Oice, and Mg/Casw variations, but more robust records are needed to confirm the second-order (5–10 Myr) variations in Mg/Cabf. The discrepancy in this interval also highlights the anomalously high NJSL in the early–middle Eocene; we assume ice free conditions at warm intervals throughout the Paleocene–early Eocene, with growth and decay of temporary glaciers during cold intervals, but we cannot rule out the possibility of growth of permanent ice sheets in the Paleocene and middle Eocene.
 From these observations, we conclude that, while it is possible that IVδ−Mg/Ca reconstructions are an accurate reflection of ice sheet history, it is more likely that the large ice volumes implied by these reconstructions are artifacts of the constant δ18Oice and simplistic Δ[CO3=] history imposed in our calculations. Intervals with negative IVδ−Mg/Ca must reflect either these artifacts or incompatibility of the δ18Obf and Mg/Cabf records. The same conclusion is not warranted for the TMg/Ca reconstructions: these could be reconciled with reasonable ice volumes by assuming variable δ18Oice. In the case of Tδ−SL and IVSL, any artifacts from assuming constant δ18Oice are reflected in the temperature rather than ice volume reconstruction.
 The lack of sea level records comparable with NJSL and continuous through the late Miocene–Pleistocene (<9 Ma) means that we are only able to calculate IVδ−Mg/Ca in this interval, and we have concluded that these reconstructions are not reliable. Miller et al. [2005, 2011, also submitted manuscript, 2011] provide a sea level reconstruction for this interval based solely on δ18Obf, constrained by well-founded assumptions about the relative contribution of temperature and ice volume in glacial-interglacial cycles and the magnitude and timing of cooling since the late Miocene. The resulting sea levels in the late Miocene are similar to NJSL [Miller et al., 2005, 2011] and are consistent with well-constrained sea level records in the late Pliocene (Miller et al., submitted manuscript, 2011). We have calculated temperature based on this sea level reconstruction using equation (1), and refer to these records when relevant in the discussion below (Figures 9 and S7).
4.2. Cenozoic Changes in Temperature and Ice Volume
 The transition from the early Cenozoic greenhouse to the late Cenozoic icehouse climate has long been inferred from δ18Obf records as a gradual cooling through the Eocene followed by three steps: the Eocene/Oligocene transition, middle Miocene, and Plio–Pleistocene [e.g., Shackleton and Kennett, 1975; Miller et al., 1987; Zachos et al., 2001; Cramer et al., 2009] (see Figure 1). The default assumption has been that each of these steps represents a combination of temperature and ice-volume changes [e.g., Crowley and Kim, 1995; Zachos et al., 2001; Hansen et al., 2008]. That view has received some support from models involving ice sheet dynamics [Oerlemans, 2004], but can be questioned in light of models indicating strong threshold effects in the growth of continent-scale ice sheets [DeConto and Pollard, 2003]. We consider as an appropriate null hypothesis that on >5 Myr timescales temperatures change only gradually, but ice sheets may respond abruptly to climate thresholds. The expectation that long-term temperature should change only gradually is based on an assumption that changes in the equilibrium atmospheric pCO2 drive global temperature changes over these timescales [e.g., Royer et al., 2004] and recognition that the balance between addition of CO2 through volcanic and tectonic processes and removal of CO2 by weathering sets the equilibrium pCO2 level [e.g., Walker et al., 1981; Toggweiler, 2008]. If the weathering sensitivity to atmospheric pCO2 also responds primarily to tectonic processes, such as mountain building and the latitudinal distribution of continents, then the rate of change in pCO2 is limited to slow tectonic rates. Our analysis is consistent with this null hypothesis, though still with considerable uncertainty.
 We find that the second-order (∼10 Myr timescale; e.g., Figure 9) features of the Cenozoic cooling of the deep ocean and growth of continental ice volume are largely uncorrelated. Statistical analysis of variability in the ice volume and temperature reconstructions confirms our qualitative observations: the correlation between ice volume and temperature variability at 2–22 Myr timescales is not in general significantly different from the expectation for uncorrelated random processes (Figure S6). Qualitatively, we find that ice sheets remained small as deep-ocean temperatures cooled through the Eocene, while the large, abrupt increase in ice volume near the Eocene/Oligocene boundary occurred when cooling either slowed (according to Tδ−SL) or ceased (TMg/Ca; Figures 6, 9, and S8). Importantly, both Tδ−SL and TMg/Ca indicate that deep ocean temperatures during the early Miocene were equivalent to those during the late Eocene, although ice volume was significantly different. Cooling during the middle Miocene was accompanied by some increase in ice volume, but ice growth continued with temperatures stable or warming in the late Miocene (Figures 6, 9, and S7).
 The relationship between cooling and ice sheet growth in the late Miocene–Pleistocene is not clear from our analysis. Increasing amplitude of glacial-interglacial cycles in δ18Obf records in the late Pliocene (2.5–2.8 Ma) and Pleistocene (0.6–1.1 Ma) requires increasing northern hemisphere ice volume during glacial periods, implying increases in the long term mean ice volume. Our TMg/Ca reconstructions show overall cooling from the late Miocene–Pleistocene (<8 Ma) with an early Pliocene inflection to more rapid cooling (<4.5 Ma; Figures 6 and S7). We hesitate to interpret higher frequency variability (see Figures S5 and S6), but there is no obvious change in cooling rate associated with the late Pliocene and Pleistocene increases in glacial-interglacial amplitude, resulting in increases in IVδ−Mg/Ca at these times. Miller et al. (submitted manuscript, 2011) assumed that cooling occurred mainly in a ∼2 Myr interval prior to the late Pliocene increase in glacial-interglacial amplitude; this results in temperature and ice volume trends similar to our TMg/Ca and IVδ−Mg/Ca results, but beginning at lower temperature and ice volume consistent with our late Miocene Tδ−SL and IVSL results (Figures 9, S7, and S9). These three reconstructions agree in showing early Pliocene cooling associated with ice volume decrease, with no obvious change in rate of cooling associated with late Pliocene–early Pleistocene ice volume increase.
 It is worth noting the caveat that deep ocean temperature variations may be decoupled from surface temperatures, although it is common to use the oversimplification that deep ocean temperature changes reflect (latitudinally consistent) high-latitude surface temperatures [e.g., Zachos et al., 2001; Cramer et al., 2009] and have also been used as a proxy for mean surface temperatures [e.g., Crowley and Kim, 1995; Hansen et al., 2008]. Deep ocean temperatures reflect the surface/intermediate ocean temperatures at deep-water source regions, and the relative strengths and latitudinal position of those source regions should be expected to vary through time. The homogeneity of δ18Obf from different ocean basins during the Eocene implies that there was little differentiation with respect to temperature among deep water source regions [Cramer et al., 2009]. This contrasts with large δ18Obf gradients between ocean basins beginning in the Oligocene [Cramer et al., 2009] and the ∼2°C difference between NADW and AABW in the modern ocean. The differentiation between temperatures in Northern and Southern Hemisphere deep-water source regions is primarily the result of the development of the Antarctic circumpolar current [Toggweiler and Samuels, 1995; Toggweiler and Bjornsson, 2000; Cramer et al., 2009]. This resulted in a physical separation of the Southern Hemisphere deep water source regions around Antarctica from warmer midlatitude surface waters, a net transport of heat from the Southern to the Northern Hemisphere, and increased deep water production in the Northern Hemisphere. Under at least one model parameterization, the net result is a warming in most of the deep ocean (compare Figures 3–6 in the work by Toggweiler and Bjornsson ), concomitant with cooling and thermal isolation of Antarctica that favors ice sheet growth. In addition, changes in the depth of the sills around Iceland have been implicated in changes in the strength of deep water production in the North Atlantic during the Neogene [Wright and Miller, 1996; Poore et al., 2006] and in the early Oligocene [Abelson et al., 2008] With a shallow sill, any deep water production would presumably be sourced from warmer surface waters south of Iceland, whereas a deep sill would allow deep water formation at colder, more northern latitudes.
 We therefore cannot rule out an abrupt shift to cooler mean surface temperatures coincident with the abrupt shift to larger ice volume in the earliest Oligocene. It is plausible that the lack of such a cooling in our reconstructions reflects a decoupling of deep ocean and mean surface temperatures at this time, or that a cooling of mean deep ocean temperatures is not reflected in our reconstructions. Cramer et al.  showed that a ∼0.5‰ difference in δ18Obf between the Southern Ocean and Pacific developed near the Eocene/Oligocene boundary, in conjunction with the large increase in ice volume shown here. If we assume that difference is entirely due to temperature, then an abrupt but persistent ∼2°C cooling occurred in the Southern Ocean coincident with the abrupt and persistent increase in ice volume. The lack of a significant increase in the rate of cooling at this time in the Pacific Tδ−SL reconstruction may be due to increased influence of warmer North Atlantic sourced deep water and lesser influence of colder Southern Ocean sourced deep water, or it may reflect lack of cooling in a possible North Pacific deep water source region. It is also possible that the different δ18Obf trends at this time reflect different variations in local (non-ice volume) δ18Osw rather than temperature; large variations in δ18Osw in the Atlantic basins could be offset by much smaller δ18Osw changes in the Pacific due to its much larger volume. It should be noted that in the modern ocean δ18Obf is a poor indicator of deep ocean inhomogeneity with respect to temperature and δ18Osw because the δ18Osw difference between AABW and NADW is largely offset by the temperature difference when incorporated into δ18Obf. There is evidence that the earliest Oligocene glaciation was accompanied by a sharp decrease in surface temperature [Lear et al., 2008; Katz et al., 2008; Eldrett et al., 2009; Liu et al., 2009] and decrease in pCO2 [Pearson et al., 2009], although it is not clear that this decrease entails a permanent shift to cooler temperatures rather than a temporary perturbation.
 We have demonstrated that available δ18Obf, Mg/Cabf and sea level curves are reconcilable under reasonable assumptions. Mg/Cabf can be used to constrain temperature, and combined with δ18Obf to constrain ice volume (Figure 5); sea level can be used to constrain ice volume (Figure 3), and combined with δ18Obf to constrain temperature (Figure 4). The resulting records of temperature and ice volume are largely independently constructed, other than sharing the requirement of ice-free conditions in the early–middle Eocene. Most importantly, the temporal pattern of temperature change and ice volume increase from Eocene to Miocene times is mutually consistent between the two approaches (Figures 6, 9, and S5). The reconstructions of these second-order patterns are fully independent, and the coherence of the independent records can be used as evidence for the use of these parameters as robust climate proxies.
 We have identified a complementarity between the assumed Mg/Cabf sensitivities to temperature and Mg/Casw. In the context of Cenozoic climate and Mg/Casw changes we demonstrate that Mg/Cabf must either have high sensitivity to both temperature and Mg/Casw or low sensitivity to both (Figure 7). This provides a framework for interpreting the Cenozoic Mg/Cabf record, but a robust calibration is needed for Mg/Cabf offsets between species analyzed from the geologic record and species used for temperature calibrations. The calibration of these species offsets is more complicated for Mg/Cabf than for δ18Obf, because of the possibility that different species have different sensitivities to Mg/Casw and Δ[CO3=]. We believe that our analysis indicates this problem is surmountable, and that the calibration of species offsets will allow use of Mg/Cabf as a robust climate proxy.
 Our calculations challenge the commonly used assumption that ice volume and temperature are proportionally represented throughout the late Cenozoic δ18Obf record. Instead, our results indicate that the correlation of temperature decrease and ice volume increase is not significantly different from random (Figure S6). Qualitatively, the Cenozoic increase in ice volume occurred primarily in two steps, in the earliest Oligocene and near the middle/late Miocene boundary, whereas the Cenozoic deep ocean cooling occurred in two prolonged intervals: the middle–late Eocene and the late Miocene–Pleistocene (Figures 6 and 9). The more detailed evolution of temperature and ice volume through the Cenozoic would be subject to greater uncertainty due to inadequate constraint on Mg/Cabf and sea level and the parameters needed to interpret these records. Despite these shortcomings, our analysis provides the best available synthesis of long-term temperature and ice-volume changes since the Late Cretaceous.
benthic foraminiferal δ18O relative to VPDB standard (‰).
seawater δ18O, relative to VSMOW (‰).
δ18O of continental ice sheets, relative to VSMOW (‰).
sea level as measured using cores from the New Jersey coastal plain (m).
change in sea level due to growth and decay of continental ice sheets (m).
sea level contribution from variations in the volume of the ocean basins (m).
change in δ18Osw per unit change in SLice; see equation (9) (‰/m).
benthic foraminiferal Mg/Ca ratio (mmol/mol).
seawater Mg/Ca ratio (mol/mol).
Mg/Cabf corrected for variations in Δ[CO3=] and Mg/Casw (mmol/mol).
partition exponent for Mg/Casw in Mg/Cabf see equation (2) (unitless).
carbonate ion saturation state for CaCO3 ([CO3=]seawater – [CO3=]saturation) (μmol/mol).
calcite compensation depth; CaCO3-rich to CaCO3-poor sediment boundary (km).
ocean temperature calculated from Mg/Cabf (°C).
ocean temperature calculated from δ18Obf using SLice to constrain δ18Osw (°C).
ice volume calculated from δ18Obf using Mg/Cabf to constrain temperature (%).
ice volume calculated from SLice (%).
 We are very grateful to two anonymous reviewers, whose comments led to major changes in our analysis and forced us to deal with the full complexity of the Mg/Cabf proxy. This research was funded in part by NSF grant OCE-0927663 to B.S. Cramer.