Corresponding author: J. Tian, State Key Laboratory of Marine Geology, Tongji University, 1239 Siping Road, Shanghai 200092, China. (email@example.com)
 The Middle Miocene East Antarctic ice sheet expansion (EAIE), which is indicated by an abrupt ~1‰ increase in global benthic foraminiferal δ18O at ~13.8 Ma, marks the Middle Miocene climate transition (MMCT) and has been related to astronomically modulated changes in the global carbon cycle. Here, we present high resolution (3–4 kyr) benthic foraminiferal δ18O and δ13C records from IODP Site U1337 in the central equatorial Pacific, which spans the period 12.2–15.8 Ma. The isotopic records clearly demonstrate significant imprints from periodic variations in the Earth's orbital parameters, particularly the obliquity (40 kyr) and the long eccentricity (400 kyr) cycles. While the benthic δ18O and δ13C exhibit nearly identical amplitudes for glacial-interglacial cycles from 15.8 to 12.2 Ma, the long-term trends in the benthic δ18O and δ13C had started to reverse after the beginning of the EAIE. Within the 400-kyr band, the benthic −δ18O and δ13C displays a constant phase relationship between 15.8 and 12.2 Ma. At the 41-kyr band, however, a phase reversal reaching >180° between −δ18O and δ13C occurs from 13.8 Ma to 14.0 Ma during the period of the EAIE. A similar phase relationship of benthic foraminiferal −δ18O and δ13C at the 400-kyr band and the 41-kyr band is also observed at ODP Site 1146 from the northern South China Sea. This phase jump occurs when the long-term trends in δ18O and δ13C split, suggesting a decoupling of the global ice volume and ocean carbon reservoir changes during the Middle Miocene.
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 The Late Cenozoic global cooling has been highlighted by three major expansions of the polar ice sheets on Earth, namely the rapid appearance and growth of the southern hemisphere ice sheet on Antarctica at ~34 Ma [Kennett and Shackleton, 1976; Zachos et al., 2001a], the abrupt East Antarctic ice sheet expansion (EAIE) at ~13.8 Ma [Zachos et al., 2001b; Shevenell et al., 2004, 2008], and the onset of the northern hemisphere ice sheet at ~2.7 Ma [Haug et al., 1998, 2005; Tian et al., 2002, 2004, 2006].
 The Middle Miocene East Antarctic ice sheet expansion (EAIE) marks the Middle Miocene climatic transition (MMCT) 14.2 to 13.8 Ma, which is a major step in Earth's climate evolution during the Cenozoic [Miller et al., 1987; Zachos et al., 2001b]. Several significant climatic and paleoceanographic events are related to this event. The global sea level fluctuated with high amplitude during the Middle Miocene [Haq et al., 1987, Miller et al., 2005]. The estimated sea level drop associated with the EAIE [~60 m, John et al., 2011] is large enough that a large part of the East Antarctic Ice Sheet must have grown at this time.
 A pulse of evolutionary turnover in terrestrial and marine biota also happened during this period as evidenced by changes in planktonic and benthic foraminiferal assemblages [Wei and Kennett, 1986; Woodruff, 1985; Kurihara and Kennett, 1992]. Both surface and deep ocean circulation systems had changed or reorganized with southern component water production increasing during the MMCT [Kennett et al., 1985; Woodruff and Savin, 1989]. The locus of biogenic silica deposition transferred from the Atlantic Ocean to the North Pacific and the Antarctic oceans in the MMCT [Keller and Barron, 1983]. Also during this period, large sedimentary deposits of organic carbon and phosphatic deposits occurred in both the marginal seas and open oceans [Vincent and Berger, 1985; Compton et al., 1990]. The so-called “Monterey Carbon Excursion” events were composed of several δ13C maxima events from ~17 to ~13.5 Ma ago [Vincent and Berger, 1985; Woodruff and Savin, 1991]. These events reflecting episodic changes in organic carbon deposition relative to carbonate deposition ended after the MMCT. A stepwise sea surface cooling of 6° to 7°C [Shevenell et al., 2004] and a deep ocean cooling of 2° to 3°C [Billups and Schrag, 2002) was observed in the high-latitude southwest Pacific during the MMCT. The rapid cooling after the Early Miocene climatic optimum is the highlight of the MMCT. This abrupt cooling event is marked by a globally abrupt ~1‰ increase in benthic foraminifer δ18O at ~13.8 Ma [Shackleton and Kennett, 1975], of which 70% is interpreted to indicate the East Antarctic ice sheet expansion (EAIE) during the MMCT [Shevenell et al., 2008].
 The external insolation forcing controlled by Earth's orbital eccentricity, obliquity, and precession has played an important role in regulating global climate changes. Amplitude and phase are two important parameters to evaluate climatic responses imprinted in geological records by orbital forcing. Mathematical methods like spectral and continuous wavelet transform analyses are often used to identify the average or instantaneous strength of orbital cycles in climatic records. Other mathematical methods like cross-spectral and cross-continuous wavelet transform analyses are used to evaluate coherent or noncoherent relationships and phases between two climatic time series on a given orbital cycle. A few studies have revealed the astronomical imprints from the obliquity (40 kyr) and eccentricity (100 kyr and 400 kyr) cycles in the Middle Miocene global ice volume and ocean carbon reservoir changes as recorded in deep sea benthic foraminiferal δ18O and δ13C records, respectively [Shevenell et al., 2004; Holbourn et al., 2005]. Some modeling results also highlight the dominant long eccentricity (400 kyr) forcing on the Middle Miocene climate change [DeConto and Pollard, 2003; Ma et al., 2011]. These studies focus on the strength or amplitudes of the orbital cycles, but none probes the phase relationship of climate response to orbital forcing or among different climatic time series, which is more important to understand the forcing mechanism of the global climate change.
 The phases between climate responses and orbital forcing at specific orbital frequencies have been variable through geological time [Clemens et al., 1996; Tian et al., 2011], and the phases for the periods beyond the Pliocene are uncertain [Shackleton et al., 1999]. When establishing an astronomically tuned timescale for time series beyond the Pliocene, researchers usually introduce a zero-phase lag of climatic index relative to orbital forcing at obliquity or precession bands. Therefore, probing the phases of climate response relative to orbital forcing during the Middle Miocene is neither feasible nor helpful in understanding the forcing mechanism of the MMCT. However, probing the phase relationship between two time series from the same core is feasible because they have the same age model. For example, the phase relationship between benthic δ18O and δ13C records from the same samples of the same core is of great significance in clarifying the forcing mechanism of the MMCT.
 In this study, we present high resolution (3–4 kyr) benthic foraminiferal δ18O and δ13C records spanning the period of 15.8–12.2 Ma from the Integrated Ocean Drilling Program (IODP) Site U1337 in the central equatorial Pacific (Figure 1) (Exp 320/321 scientific party, 2010 [Site U1337 chapter from proceedings]). We compare the benthic δ18O and δ13C records of IODP Site U1337 with those of ODP Sites 1146 and 1148 from the northern South China Sea (Figure 2), discussing the similarity and difference in the Middle Miocene isotopic records between the marginal sea and the open ocean and probing the potential causes. We further probe the Middle Miocene astronomical imprints in the benthic foraminiferal isotopic records and focus our discussions on the significance of the phase relationship between global ice volume and ocean carbon reservoir changes.
2 Materials and Methods
2.1 Site Selection and Stable Isotopic Analyses
 We picked benthic foraminifers from the deep sea sediments of IODP Site U1337 for stable oxygen (δ18O) and carbon (δ13C) isotopic analyses. Site U1337 is located in the eastern equatorial Pacific (3°50.009′N, 123°12.352′W; 4463 m water depth; Exp 320/321 scientific party, 2010 [Site U1337 chapter from proceedings]). Site U1337 has an essentially complete sedimentary section from 0 to >23 Ma. The spliced sedimentary section from U1337 is one of the two continuous Neogene sections retrieved during IODP Leg 321, both of which represent the only complete Neogene sections in the equatorial Pacific, possibly for all the tropics, that have high enough sedimentation rates to resolve orbitally forced sediment cycles. The sedimentation rate at Site U1337 is relatively low, varying from 17 m/myr for the Pliocene and Pleistocene to 21 m/myr for the Miocene. Sedimentation rates are sufficiently high to resolve the phase relationship of orbital frequencies between different climatic indices such as global ice volume changes and global carbon cycle, and because of the depth of Site U1337 at 15 Ma (~3900 m), the benthic isotopes should reflect changes in bottom water flowing into the abyssal Pacific.
 We present 944 paired benthic foraminiferal stable oxygen and carbon isotopic records from IODP Site U1337 in the depth interval 272.64–355.77 m (ccsf), with a depth resolution of ~8 cm. We used the revised composite depth scale of Site U1337 [Wilkens et al., 2012]. Bulk sediment samples were oven dried at 60°C and then soaked in water for 1–2 days, washed through a 63 µm sieve, redried, and then sieved to select benthic foraminifers Cibicidoides spp. from the >150 µm size fraction. The stable oxygen and carbon isotopes were measured at the State Key Laboratory of Marine Geology, Tongji University [Cheng et al., 2006; Tian et al., 2008]. Measurements were made using a Finnigan MAT252 isotope ratio mass spectrometer equipped with a Kiel III carbonate device. Analytical precision was monitored during the study (2010–2012) using the Chinese national carbonate standard, GBW04405. External reproducibility based on replicate analysis of benthic foraminifer samples is 0.07‰ and 0.04‰ for δ18O and δ13C, respectively. Conversion of measurements to the Vienna Peedee belemnite scale was performed using NBS-19 and NBS-18.
2.2 Age Model
 The age model for the depth interval 272.64–355.77 mcd (meters composite depth, or mcd using the ccsf-a method; Exp 320/321 shipboard scientific party, 2010) from the spliced section of Site U1337 was constructed by tuning the benthic δ18O to the obliquity of the astronomical solution of Laskar et al. . The astronomical tuning depends on an initial age model that constrains the time interval of the depth profile. The initial age model of Site U1337 is derived from a polynomial regression of the planktonic foraminiferal datum events, nannofossil datum events, radiolarian datum events, and magnetostratigraphic events [Exp 320/321 shipboard scientific party, 2010]. The polynomial initial age model indicates that the depth interval 272.64–355.77 m (mcd) roughly corresponds to the time interval 11–15 Ma. We further used the nannofossil datum, B Discoaster petaliformis, a standard biostratigraphic event used for the Miocene chronology, and the middle point of the sharp increase in the benthic δ18O (EAIE) to better constrain the ages of this depth interval. The middle point of the B D. petaliformis datum is at 352.82 m (mcd), with an age of 15.7 Ma [Exp 320/321 shipboard scientific party, 2010]. The EAIE event happened in less than 100,000 years and is globally comparative. In the Pacific Ocean, the middle point of this event roughly corresponds to an age of 13.86 Ma [Tian et al., 2009; Holbourn et al., 2005]. This event is found in the depths from 317.89 m (mcd) to 316.1 m (mcd) at Site U1337, and the middle points of this event is at the depth 316.93 m (mcd).
 For the Miocene–Oligocene periods, the time series of δ18O from benthic foraminifers is a widely accepted tuning material [Pälike et al., 2006]. The astronomical solution of Laskar et al.  was used for the tuning target. The spectral analysis of the δ18O record on the polynomial initial age model reveals strong cycles of 100 kyr (eccentricity) and 41 kyr (obliquity) but weak cycle of 21 kyr (precession).
 We followed a common tuning strategy similar to Shackleton et al. . The tuning of δ18O data to the Earth's orbital solution of Laskar et al.  was done by aligning the data time series to that of the target at the obliquity frequency (41-kyr period). We did not constrain the tuning by the 100-kyr amplitude modulation of precession by eccentricity because the precession cycle is very weak in the δ18O record. The peak δ18O minimum was related to peak obliquity maximum. As explained in Holbourn et al. , relatively warm summers during high obliquity would promote ice-sheet melting in Antarctica, whereas cool summers during low obliquity would favor ice-sheet growth, and a low summer insolation gradient between low and high latitudes during high obliquity would decrease poleward moisture transport, inhibiting ice-sheet buildup.
 The tuning was done with the “Linage” module from the software Analyseries 1.2 [Paillard et al., 1996]. The sedimentation rate was controlled between 0.015 m/kyr and 0.045 m/kyr (Figure 1d). After tuning, the depth interval 272.64–355.77 m (ccsf) from IODP Site U1337 corresponds to the time interval 12.23–15.89 Ma. The tuned isotopic records still show significant obliquity and long eccentricity cycles, strong short eccentricity cycles and weak precession cycles (Figure 3) as in the unturned isotopic records. The power of the obliquity (41 kyr) cycles in both the δ18O and δ13C records increases relative to that in the un-tuned isotopic records, particularly in the δ18O record. However, tuning will not change the coherent or phase relationship between the δ18O and δ13C records at the specific orbital cycles.
3.1 Benthic Foraminiferal δ18O and δ13C of Site U1337
 The benthic δ18O record of Site U1337 from 15.89 Ma to 12.23 Ma is marked by a sharp increase of ~1‰ in less than 100 kyr, beginning at ~13.9 Ma. The δ18O increase marks the East Antarctic Ice Sheet Expansion (EAIE, Figure 1). Between ~13.8 Ma and ~13.65 Ma, δ18O of Site U1337 is characterized by relatively heavy values and stable glacial/interglacial cycles with small amplitudes less than 0.3‰ (Figure 1). The average δ18O of Site U1337 before the EAIE event is much lighter than that after this event, and after 13.9 Ma amplitudes of glacial/interglacial cycles are big, generally larger than 0.5‰ and some nearly reaching 1‰. Generally, the δ18O of Site U1337 is much lighter between ~13.9 and 15.89 Ma, indicating a climate optimum during the Middle Miocene. The δ18O of Site U1337 after ~13.65 Ma is characterized by a gradually increasing trend in values and a decreasing trend in amplitudes of glacial/interglacial cycles. A series of Middle Miocene stepwise glaciation events such as Mi3 and Mi4 are clearly identified in the δ18O record of Site U1337 (Figure 1a), as globally recognized [Miller et al., 1991]. The Mi4 event at Site U1337 can be divided into two cooling events, Mi4a and Mi4b, with a time interval between them of ~400 kyr [Holbourn et al., 2007].
 The benthic δ13C record of Site U1337 is characterized by a series of globally recognized CM events (carbon maximum, Vincent and Berger, ; Woodruff and Savin, ) during the period of the Monterrey Carbon Isotope Excursion (16.5–13.5 Ma). Five CM events from CM4a to CM6 are identified in the δ13C record (Figure 1), which recur every 400 kyr. The CM6 event is the most significant among all the CM events, with a positive excursion of ~1‰. It commenced and ended synchronously with two Middle Miocene glaciation events, the EAIE event and the Mi3 event, respectively. After the CM6 event, the δ13C of Site U1337 shows a gradually decreasing trend in secular change, being opposite to the gradually increasing trend in the δ18O after the glaciation event Mi3.
 The long-term (30% weighted) trends of both the benthic δ18O and δ13C are nearly parallel before the EAIE but trend opposite each other afterward (Figure 1). After subtracting the long-term trends from the original records, the detrended δ18O and δ13C show similar glacial/interglacial cycles in both amplitude and timing (Figure 1).
3.2 Comparison of Benthic δ18O and δ13C Between Site U1337 and Site 1146
 High resolution (<5 kyr) benthic δ18O and δ13C records during the Middle Miocene period are sparse in the tropical Pacific Ocean. Two published high resolution (3–4 kyr) records are from ODP Site 1146 (water depth 2092 m) located in the northern South China Sea in the western Pacific and ODP Site 1237 (water depth 3212 m) located on the Nazca Ridge off Peru in the eastern Pacific [Holbourn et al., 2007].
 Comparison of the δ18O records between Site U1337 and Site 1146 shows that the two benthic δ18O records are highly similar to each other in both the long-term trend and the glacial-interglacial cycles including the amplitude and timing (Figures 2a and 2b). The other low resolution (~10 kyr) δ18O record of ODP Site 1148 (water depth 3294 m) from the northern South China Sea also shows great similarity to the δ18O records of Sites U1237 and 1146 [Tian et al., 2008, 2009]. The most marked Middle Miocene glaciation event, the East Antarctic Ice Sheet Expansion (EAIE in Figures 1 and 2) are synchronous in the three sites, displaying the same ~1‰ increase in the benthic δ18O.
 The high resolution δ13C records of Site U1337 and Site 1146 also display great similarities (Figures 2c and 2d). The most significant CM6 event, which is synchronous with the EAIE event in the δ18O, shows nearly identical amplitude and duration at both Site U1337 and Site 1146. The other CM events 3b through 5b also display similar amplitude and duration in the two δ13C records, recurring at a pace of nearly 400 kyr. The two δ13C records also show the same long-term decreasing trend after the CM6 event. Besides great similarities, discrepancies exist in the δ13C records of Sites U1337 and 1146 (Figure 2c and 2d). In the two δ13C records, the peak values of δ13C for the CM events 3b through 5b are not synchronous at Site U1337 and Site 1146. For example, the peak value of the CM5b event in the δ13C record of Site U1337 precedes that of Site 1146 by ~100 kyr (Figures 2c and 2d). The most significant discrepancy between the central equatorial Pacific and the northern South China Sea is the lack of the CM6 event in the δ13C record of the deeper South China Sea Site 1148. While the benthic δ13C of both Site U1337 and Site 1146 increases after the EAIE event, the benthic δ13C of Site 1148 decreases gradually until the end of the CM6 event (Figure 2d) [Tian et al., 2009]. The lack of CM6 event at ODP Site 1148 causes an abrupt ~1‰ increase of the δ13C gradient between the intermediate water (Site 1146) and the deep water (Site 1148) in the South China Sea from 13.9 to 13.8 Ma (Figure 2e).
3.3 Astronomical Cycles in δ18O and δ13C
 We performed cross-spectral analyses between the δ18O and δ13C records of Site U1337 and Site 1146 in the two time intervals (Figure 3), 13.9–12.3 Ma and 15.8–14.2 Ma for Site U1337, 13.9–12.8 Ma and 16.4–13.9 Ma for Site 1146, respectively, by using the “ARAND” software package [Howell et al., 2006].
3.3.1 Site U1337
 At Site U1337, for the δ18O record, as shown in Figure 3, the standard 41-kyr obliquity cycle and the 400-kyr long eccentricity cycle are very strong in the two time intervals. The 100-kyr short eccentricity cycle is only recognized in the period of 13.9–12.3 Ma. However, this cycle is absent in the period of 15.8–14.2 Ma in which a non-Milankovitch cycle of 150 kyr is found in the spectrum. The precession cycles from 18 kyr to 27 kyr are recognized in the spectrums on logarithmic scales in the two time intervals but they are actually very weak. Some other non-Milankovitch cycles such as 51 kyr, 60 kyr, and 150 kyr are also found to be meaningful in the spectrum of the δ18O.
 The 400-kyr cycle is also very strong in the spectrums of the δ13C record in both of the time intervals, with the same power density as that of the 400-kyr cycle in the δ18O record (Figure 3). The 41-kyr cycle is strong in both intervals in the δ18O record and is weaker but present in the spectrums of the δ13C record. The weak precession cycles are also identified in the spectrums on logarithmic coordinates in the two time intervals. However, these precession cycles in the δ13C record are not stable, varying from 18 kyr to 27 kyr as those in the δ18O record, which might be caused by relatively low sampling (4 kyr) and perhaps age model uncertainties because the basic tuning cycle is 41 kyr. The same non-Milankovitch cycles as seen in the spectrum of the δ18O record, such as 51 kyr, 60 kyr, and 150 kyr, also exist in the spectrum of the δ13C record.
 Generally, the 400-kyr long eccentricity and the 41-kyr obliquity cycles dominate the Middle Miocene benthic foraminiferal δ18O and δ13C records from the eastern equatorial Pacific Site U1337. The 21-kyr precession cycle is weak in both of the isotopic records. The 100-kyr short eccentricity cycle is also not as significant as the 400-kyr and the 41-kyr cycles. The spectrums of the Middle Miocene δ18O and δ13C records are disturbed by noise from the non-Milankovitch cycles.
 The continuous wavelet transform (CWT) analysis was used to uncover the time-frequency characteristics of the δ18O and δ13C records of Site U1337 through time, which display the instantaneous density of the periodic changes in the isotopic records [Torrence and Compo, 1998] (Figures 4a and 4b). Additionally, it also measures the instantaneous phases between the δ18O and δ13C records. By decomposing the δ18O and δ13C into time-frequency space, we are able to determine both the dominant modes of variability and how those modes vary in time. The spectral features revealed by cross-spectral analyses by ARAND are also reflected in the continuous wave transform analyses in the δ18O and δ13C records (Figures 4a and 4b).
3.3.2 Site 1146
 The spectrums of the δ13C and δ18O records of Site 1146 differ from those of Site U1337, although they also bear many similarities (Figures 3c and 3d). At Site 1146, the δ13C and δ18O records in both time intervals have strong power in the cyclic changes at the long eccentricity cycle (400 kyr). The obliquity cycle (41 kyr) is strong in both the δ13C and δ18O records of Site 1146 before 13.9 Ma, but it becomes very weak in the δ13C record while remaining strong in the δ18O record after 13.9 Ma. Both δ13C and δ18O records of Site 1146 show strong density at the precession cycles (23 kyr and 19 kyr) before 13.9 Ma but weak density after 13.9 Ma. The eccentricity cycle (100 kyr and 126 kyr) is marked in both the δ13C and δ18O records for the two time intervals.
 In summary, the obliquity (41 kyr) and long eccentricity (400 kyr) cycles dominate the δ13C and δ18O records of both sites. The eccentricity (100 kyr) cycle is consistently strong in the δ13C and δ18O records of Site 1146, and its spectral density becomes stronger in the time interval after 13.9 Ma than before 13.9 Ma. However, the eccentricity cycle in the δ13C and δ18O records of Site U1337 is only distinct in the time interval after 13.9 Ma. Both the δ13C and δ18O records of the two sites exhibit the same transition from high amplitude obliquity cycle to high amplitude eccentricity cycle at ~13.9 Ma, being consistent with a similar analysis in Holbourn et al. .
3.4 Coherencies Between δ18O and δ13C
3.4.1 Site U1337
 Coherence is a measure of the linear correlation between two time series over a given frequency when the phase difference is set to zero (Figure 3). For the time interval 13.9–12.3 Ma, the benthic δ18O is highly coherent (Figure 3a) with the δ13C at the 400 kyr band, with the coherence exceeding 95% statistical confidence level. The two isotopic records are also highly coherent at the 41-kyr and the 100-kyr bands, with the coherence exceeding 90% statistical confidence level. Coherent relationship is also found between the δ18O and δ13C records at the precession bands though their spectral density is low.
 For the time interval 15.8–14.2 Ma (Figure 3b), the δ18O and δ13C records are also highly coherent at the 400-kyr and the 41-kyr bands, with coherence exceeding 95% statistical confidence level. The δ18O and δ13C records of Site U1337 are also highly coherent with each other at the non-Milankovitch cycles of 150 kyr and 60 kyr.
 The continuous wavelet coherency analyses (CWC) [Grinsted et al., 2004] indicates that the wavelet coherence between the δ18O and δ13C records at the 400-kyr band has been continuously high from 15.8 to 12.2 Ma (Figure 4c). Significant wavelet coherence between the two isotopic records is also found at the 41-kyr band and the 100-kyr band, although the coherence is not continuously high over the entire interval. Wavelet coherence at the 100-kyr band only occurs after ~14 Ma, similar to the cross-spectral analysis. High wavelet coherence at the 41-kyr band occurs only intermittently from 15.8 Ma to 12.2 Ma.
3.4.2 Site 1146
 In the time interval before 13.9 Ma, the benthic δ18O and δ13C records of Site 1146 are coherent with each other at all the major orbital cycles including long eccentricity, eccentricity, obliquity, and precession (Figure 3d). This spectral feature differs from that of Site U1337 at which the δ18O and δ13C records are only coherent with each other at the obliquity and long eccentricity cycles and at a non-Milankovitch cycle (150 kyr). In the time interval after 13.9 Ma, the benthic δ18O and δ13C records of Site 1146 are coherent with each other at the long eccentricity (400 kyr) and eccentricity (100 kyr) cycles, but are not coherent at the obliquity and precession cycles. In a perspective of the phase relationship and spectral density at the orbital cycles, influence of the 100-kyr eccentricity forcing in the benthic δ18O and δ13C increases after 13.9 Ma whereas that of the 41-kyr obliquity forcing decreases after this time. This feature is also distinctively reflected in the continuous wavelet transform and continuous wavelet coherency analyses for the δ18O and δ13C records of both sites (Figure 4). Of particular interest is that the wavelet coherence between the δ18O and δ13C records of Sites U1337 and 1146 at the 400-kyr band has been continuously high from 16.4 to 12.8 Ma (Figures 4c and 4f).
4.1 Internal Factors Controlling the MMCT
 The East Antarctic Ice Sheet Expansion (EAIE), as indicated by the abrupt ~1‰ increase in the benthic foraminiferal δ18O, marks the Middle Miocene Climate Transition (MMCT) [Miller et al., 1987; Zachos et al., 2001b]. EAIE is synchronous with the beginning of the Monterey Carbon Excursion event 6 (CM6) (Figures 2a–2d). CM6 corresponds to a period of low values of the orbital forcing (ETP, as explained in the figure caption, Figure 2g). Causes of the MMCT have usually been ascribed to two groups of internal factors. One group relates to changes in atmospheric pCO2 and global carbon cycling [Vincent and Berger, 1985; Raymo and Ruddiman, 1992; Pagani et al., 1999; Kürschner et al., 2008], while the other relates to changes in meridional heat and moisture flux associated with reorganizations of intermediate and deep ocean circulation [Woodruff and Savin, 1991; Flower and Kennett, 1994; Shevenell et al., 2004].
 The evidence from the South China Sea relates the MMCT to significant ocean circulation reorganization. As shown in Figures 2d and 2e, the abrupt ~1‰ increase of the δ13C gradient between the intermediate water (Site 1146) and the deep water (Site 1148) in the South China Sea happened from 13.9 to 13.8 Ma, which is just within the EAIE. The abrupt increase in the δ13C gradient in the South China Sea was interpreted to be caused by an increase in production and northward flux of intermediate and deep Southern Component Water at ~13.8 Ma [Tian et al., 2009]. As suggested earlier, this ocean circulation reorganization related to the expansion of the Antarctic cryosphere and resulted in a concurrent increase in the southward flux of waters from the North Pacific [Wei and Kennett, 1986; Flower and Kennett, 1994; Shevenell et al., 2004].
 Recently, a new pCO2 record was reconstructed from the planktonic δ11B of two deep ocean sites between 16.6 and 11.8 Ma (Figure 2f) [Foster et al., 2012]. Although this record has no ability to demonstrate changes of the pCO2 on orbital cycles due to its low time resolution (~300 kyr), it depicts a gradually decreasing trend of the pCO2 during the MMCT. The MMCT is marked by a series of Middle Miocene glaciation events such as EAIE, Mi3, Mi4a, and Mi4b (Figure 1a), and thus it is an important period of the Antarctic ice sheet development. An insignificant decline rather than a big and abrupt drop is observed at ~13.9 Ma in this pCO2 record (Figure 2f), being inconsistent with the abrupt 1‰ increase in the benthic δ18O. But the gradual decrease of the pCO2 from ~400 ppm to ~200 ppm during the MMCT indicates a linear relationship of atmospheric CO2 forcing on the Middle Miocene global ice volume change.
 It seems that internal factors including ocean circulation reorganization and atmospheric CO2 are believed to play a significant role in modulating the polar ice sheet growth and climate transition during the Middle Miocene.
4.2 External Orbital Forcing on the MMCT
4.2.1 Long Eccentricity (400 kyr) Forcing
 As revealed above, the strong 400-kyr long eccentricity cycles have been found to be continuously dominant in the Middle Miocene records of benthic δ18O and δ13C. Also, the benthic δ18O and δ13C have been continuously coherent with each other at the 400 kyr band during the Middle Miocene. Benthic foraminiferal δ18O and δ13C have been widely used as proxies of global ice volume and ocean carbon reservoir [Shackleton, 1967], respectively. As indicated in benthic δ18O and δ13C records, the Oligocene has recorded the most pronounced 400-kyr cycles in global ice volume and ocean carbon reservoir changes, which act as the heartbeat of the Oligocene climate system [Pälike et al., 2006]. Marked 400-kyr cycles have also been found in the continuous benthic δ18O and δ13C records from ODP Site 1148 in the northern South China Sea for the Neogene period [Tian et al., 2008]. However, this 400-kyr long eccentricity cycle is not evident in the Pleistocene Ice Ages, neither in the δ18O nor in the δ13C records. It is apparent in some sediment records covering the early Pliocene and the Miocene [Clemens and Tiedemann, 1997; Zachos et al., 2001a]. As discussed above (Figures 2, 3, and 4), the high resolution (<5 kyr) benthic δ18O and δ13C records of Site 1146 from the marginal seas of the west Pacific and Site 1237 near the Peru margin in the east Pacific reveal prominent 400-kyr cycles in the Middle Miocene (12–16 Ma) [Holbourn et al., 2007]. Our high resolution (<4 kyr) benthic δ18O and δ13C records of Site U1337, which is located in the deep central equatorial Pacific and should be representative of a major flow of AABW, reveal that the 400-kyr long eccentricity cycle is a pervasively dominant climate cycle in global ice volume and ocean carbon reservoir changes for the Middle Miocene.
 The eccentricity's 400-kyr cycle originates from the amplitude variation of the eccentricity which affects global climate change by amplitude modulation of the precession cycles. Because the direct contribution to insolation by changes in eccentricity is smaller than 0.1% [Berger et al., 2005], strong and even dominant eccentricity cycles (400 kyr and 100 kyr) in climate records can only be explained by a nonlinear mechanism. The 100 kyr short eccentricity cycle is particularly significant in the Late Pleistocene global benthic foraminiferal δ18O records characterized by a sawtooth shape. As summarized by Berger et al. , most of the interpretations of the 100-kyr climate cycle relate to changes of one of the astronomical parameters, such as a nonlinear response to precession (1/19–1/23 ~ 1/100) [Wigley, 1976], the first derivative of eccentricity [Rial, 1995], the frequency variations of obliquity [Liu, 1992), and the inclination of the Earth's orbital plane on the invariable plane [Muller and MacDonald, 1995]. Similarly, the 400-kyr climate cycle is not a linear but a nonlinear response to solar forcing. The Pliocene benthic δ18O record possesses pronounced 400-kyr cycles, which have been interpreted to be a nonlinear response from global ice volume change to the truncated (warm portion) summer insolation forcing from the high northern latitudes that displays very strong 400-kyr cycles [Clemens and Tiedemann, 1997; Tian et al., 2011]. The Oligocene benthic δ13C record also exhibits a dominant 400-kyr cycle. A box model simulation reveals that the Oligocene 400-kyr cycle in the ocean carbon reservoir can be produced by an interaction of carbon cycle and solar forcing which modulates the deep ocean acidity, production, and burial of global biomass [Pälike et al., 2006]. Another box model simulated the 400-kyr cycles in the deep and surface ocean waters for the Miocene Climatic Optimum period [17–14 Ma; Ma et al., 2011]. The results reveal that carbon input by orbitally forced changes in weathering will change the burial ratio of carbonates to organic carbon and result in periodic changes in the oceanic δ13C. Consistent with the geologic record, model eccentricity maxima lead to minima of δ13C by enhancing weathering intensity and nutrient supply, while eccentricity minima do the inverse. The box model results support the idea that the prominent 400-kyr cycle in ocean carbon reservoir change is likely caused by a long memory of the carbon cycle in the ocean.
 In summary, both the 400-kyr and 100-kyr cycles in the Middle Miocene global ice volume change likely originate from a nonlinear response to orbital forcing, but the 400-kyr cycle in the Middle Miocene ocean carbon reservoir change probably comes from an internal feedback of the Earth's climate system.
4.2.2 Obliquity (41 kyr) Forcing
 The Middle Miocene benthic δ18O and δ13C records of Site 1146 from the marginal sea of the west Pacific show a striking transition of the dominant cycle from 41 kyr to 100 kyr around the EAIE as revealed in Figures 3c and 3d. Particularly, in the δ13C record, the 41-kyr cycle becomes very weak and nearly negligible after the EAIE, whereas the 41-kyr cycle in the δ18O record is still notable though much weaker than the 100-kyr cycle. For Site U1337 from the central equatorial Pacific, however, the spectral and continuous wavelet transform analyses on the benthic δ18O and δ13C records (Figures 1, 2, and 3) demonstrate that the 41-kyr obliquity cycle dominates the Middle Miocene global ice volume and ocean carbon reservoir changes. In the δ18O record, the 41-kyr cycle is always stronger than the 100-kyr cycle for the entire interval from 15.8 to 12.2 Ma. In the δ13C record, the 41-kyr cycles have similar power to that of the 100-kyr cycles after the EAIE and appear as recognizable cycles before the EAIE, although they are much weaker than the 150 and 400-kyr cycles. In both the δ18O and δ13C records of Site U1337, the 100-kyr short eccentricity cycle has never been the dominant cycle during the Middle Miocene. This new finding in the open equatorial Pacific Ocean greatly differs from that in the marginal South China Sea, which shows a striking transition of the dominant cycle from 41 kyr to 100 kyr in the Middle Miocene benthic δ18O and δ13C records around the EAIE (Figures 3c and 3d).
 As revealed from short (<400 kyr) climatic time series of Imbrie et al. , the 41-kyr (obliquity) and 21-kyr (precession) cycles of glaciation are continuous, linear responses to orbitally driven changes in the Arctic radiation budget. However, the Milankovitch theory stresses summer insolation from the high northern latitudes as a driver of global climate change which is dominated by the 21-kyr precession cycle [Milankovitch, 1930]. But, as more long climatic records extending beyond the Late Pleistocene have been reconstructed from deep-sea sediments, the 41-kyr obliquity cycle has been found to be the dominant cycle of climate change. Popular and convincing explanations of the 41-kyr climatic cycles during the Pliocene and the Pleistocene still relate to the external insolation forcing. However, researchers give more attention to the insolation gradient along latitudes [Raymo and Nisancioglu, 2003] or the integrated summer insolation [Huybers, 2006] or the annual mean insolation [Ma et al., 2010]. If the 41-kyr cycle in climate change is still believed to be a linear response to the insolation forcing, the integrated seasonal insolation or insolation gradient along latitudes, rather than the seasonal or monthly mean daily insolation, is a reasonable direct forcing because the dominant cycle of their changes is 41 kyr rather than 23 kyr or 19 kyr. The same forcing mechanism should also apply to the dominant 41-kyr cycles in the Miocene and even in the Oligocene climate, ice volume, and ocean carbon reservoir changes.
4.2.3 Coherency and Phase Relationship
 The cross-spectral and CWT as well as CWC analyses on the δ18O and δ13C records of Site U1337 and Site 1146 (Figures 3 and 4) indicate that global ice volume change is largely coherent with ocean carbon reservoir change on an orbital timescale during the Middle Miocene. We also did evolutive cross-spectral analyses between −δ18O and δ13C for the two sites to evaluate the phase relationship of global ice volume with the ocean carbon reservoir on orbital cycles (Figure 5). Positive phase indicates a leading of δ18O minimum relative to δ13C maximum. Particularly, at the 400-kyr long eccentricity band, as revealed by continuous wavelet coherency analyses on the isotopic records of both sites (Figures 4c and 4f), the highly coherent relationship between global ice volume and ocean carbon reservoir changes is very stable from 16.4 to 12.2 Ma, implying continuously stable long eccentricity forcing. The phase between them is also constant at the 400-kyr band, as revealed by evolutive cross-spectral analyses (Figure 5e) and Gauss band-pass filtering analyses (Figure 5d) between the benthic δ18O and δ13C records of Site U1337. The constant phases at the 400-kyr band are also found between the δ18O and δ13C records of Site 1146 (Figures 5a and 5b). The high coherency and constant phase indicate that there should be an internal factor or one process that controls the 400-kyr nonlinear responses of both global ice volume and ocean carbon reservoir to the external eccentricity forcing. Model results suggest that weathering induced carbon input as well as the long residence time of carbon in the oceans probably produce the 400-kyr cycles in ocean carbon reservoir changes [Pälike et al., 2006; Ma et al., 2010]. As revealed before, the coherent relationship between the global ice volume and ocean carbon reservoir changes at the 400-kyr band does not exist for all of the past 23 Myr [Tian et al., 2008] nor for the past 5 Myr [Wang et al., 2010]. The continuously coherent relationship of global ice volume with the ocean carbon reservoir has also been found in the Early Miocene and Oligocene [Zachos et al., 2001a; Coxall et al., 2005; Pälike et al., 2006]. The constant phase at the 400-kyr band between ice volume and the ocean carbon reservoir changes is probably a specific case for the Middle Miocene. The interaction between global ice volume and the ocean carbon cycle is an important clue to unraveling the forcing mechanism of global climate change. For example, the Late Pleistocene ice volume change was found to lag the air CO2 concentration, air temperature, and bottom water temperature change at the 100-kyr eccentricity band [Shackleton, 2000]. The global ice volume is also highly coherent with the ocean carbon reservoir at the 41-kyr band, as revealed by cross-spectral analyses between the δ18O and δ13C records of Site U1337 and Site 1146 (Figure 3). As noted above, the coherency at this band is lower than that at the 400-kyr band and the continuous wavelet coherency at this band is also not as continuous as that at the 400-kyr band (Figures 4c and 4f).
 Of the most interest is the abrupt phase shift of the 41-kyr band between the −δ18O and δ13C records of both Site U1337 and Site 1146 across the EAIE (Figures 5c and 5f), which corresponds to the separation of the long-term trends of the benthic foraminiferal δ18O and δ13C records (Figures 1a and 1b). At Site U1337, the phases of the 41-kyr band keep constant between ~15.0 and ~14.3 Ma and then gradually decline from positive to negative until ~14.1 Ma. They then keep relatively constant until ~13.85 Ma and finally shift from ~ −90° to 125° between ~13.85 to ~13.75 Ma. This abrupt phase shift occurs just within the time interval of the EAIE. At Site 1146, the phases of the 41-kyr band are constant before ~14.0 Ma and after ~13.9 Ma, but an abrupt phase shift of more than 90° happens between ~14.0 and 13.9 Ma, just within the time interval of the EAIE. Although both sites show the same abrupt phase shift between global ice volume and ocean carbon reservoir at the obliquity band across the EAIE, the direction of their shifts are opposite. At Site 1146 from the marginal sea of the West Pacific, the phase shifts toward a more negative value which indicates an expansion of the lag relationship of the global ice volume minimum relative to the ocean carbon reservoir maximum in the obliquity band. At Site U1337, from the central equatorial Pacific however, the phase shifts from a negative value to a positive value that implies a reversal from a lag to a lead relationship between the global ice volume minimum relative to the ocean carbon reservoir maximum in the obliquity band. The effect of global ice volume explains >70% of the change in the benthic foraminiferal δ18O (Billups et al., 2002), and this effect is the same in the South China Sea and the central equatorial Pacific. Factors influencing the benthic foraminiferal δ13C are more complicated than those influencing the δ18O, and more complex in the marginal seas than in the open oceans due to terrestrial fluxes. Other factors such as ocean circulation and the regional carbonate pump also affect the deep ocean δ13C and thus the benthic foraminiferal δ13C in specific locations. Thus, it is hard to explain in the South China Sea and the central equatorial Pacific why the phase at the obliquity band between the benthic δ18O and δ13C is different and why it shifts in the opposite direction across the EAIE. However, the abrupt phase shift at the obliquity band decisively suggests that there probably were some unknown climate or paleoceanographic changes that happened during the time interval of the EAIE which altered the phase relationship of the global ice volume relative to the ocean carbon reservoir. The phase shift indicates the importance of the solar radiation-albedo feedback in amplifying the complicated climate system in the 41-kyr obliquity cycle. The phase shift may also be caused by, or related to, changes in atmospheric pCO2. A simply way to test this hypothesis is to evaluate the phases by making evolutive cross-spectral analyses between pCO2 and benthic foraminiferal δ18O or δ13C when high resolution (<5 kyr) pCO2 data are available for the Middle Miocene.
5 Concluding Remarks
 The isotopic records of IODP Site U1337 and ODP Site 1146 [Holbourn et al., 2007] clearly demonstrate the obliquity (41 kyr) and the long eccentricity (400 kyr) forcing on the Middle Miocene global ice volume and ocean carbon reservoir changes. The abrupt shift of the phases at the 41-kyr band between the benthic δ18O and δ13C of the two sites across the EAIE corresponds to the reversal of the long-term trends in δ18O and δ13C, suggesting a decoupling of the global ice volume and ocean carbon reservoir changes during the Middle Miocene. For a better understanding of the forcing mechanism of global climate change and global carbon cycle during the Middle Miocene on orbital timescale, a systematic and detailed model study such as the intermediate complexity 3-D models should be considered.
 This research used samples provided by the Integrated Ocean Drilling Program (IODP). Funding for this research was provided by the NSFC (Grant No. 40976024, Grant No. 91128208). This research was also sponsored by Shanghai Shuguang Program (11SG24), Fok Ying Tong Education Foundation (111016), and program for New Century Excellent Talents in University (NCET-08-0401). Lyle and Shackford were supported by NSF grant OCE-0962184.