δ¹⁸O and SST signal decomposition and dynamic of the Pliocene-Pleistocene climate system: new insights on orbital nonlinear behavior vs. long-term trend

Abstract

The global LR04 δ¹⁸O, the tropical ODP Site 846 sea surface temperature (SST), and the global ΔSST stack records were investigated using the advanced method for time-series decomposition singular spectrum analysis to outline the quantitative role of orbital forcings and to investigate the nonlinear dynamics of the Pliocene and Pleistocene climate system. For the first time, a detailed quantitative evaluation is provided of the δ¹⁸O and SST variance paced by long-period orbital modulation, short eccentricity, obliquity, precession, and half-precession cycles. New insights into the nonlinear dynamic of the orbital components suggest considering astronomical signals as composite feedback lagged responses paced by orbitals and damped (Early Pliocene) or amplified (Mid-Late Pleistocene) in a range of − 100 to + 400% the forcing. The Early Pliocene asymptotic decay of the δ¹⁸O and SST response sensitivity up to − 100% observed for the first time in all orbital responses is interpreted as damping effect of a wide global forest cover along with a possible high ocean primary productivity, through the CO₂-related negative feedbacks during time of global greenhouse. An anomalous post-Mid-Pleistocene Transition (MPT) sharply declines to near-zero in obliquity response sensitivity observed in both global δ¹⁸O and tropical SST, suggesting an attenuation mechanism of the obliquity driving force and a reduction of the related feedback amplification processes. It is hypothesized the post-MPT obliquity damping has contributed to the strengthening of the short eccentricity response by mitigating the obliquity “ice killing”, favoring a long-life ice sheet sensitive to a synergistic ~ 100-kyr amplification of positive feedback processes during the time of a global icy state. The global δ¹⁸O, the tropical SST, and the global ΔSST trend components, all explaining ~ 76% of the Plio-Pleistocene variance and significantly modifying the mean climate state, appear to be related to the long-term pCO₂ proxies, supposedly controlled by plate tectonics through the global carbon cycle (CO₂ outgassing, explosive volcanism, orography and erosion, paleogeography, oceanic paleocirculation, and ocean fertilization). Finally, singular spectrum analysis provides a valuable tool in cyclostratigraphy with the remarkable advantage of separating full-resolution time series by variance strength.

Introduction

The Milankovitch theory elegantly describes the collective effects of changes in the Earth’s movements on its climate. Such orbital changes (eccentricity, obliquity, and precession) alter the amount and the distribution of solar radiation reaching the Earth. However, despite the studies of Kominz and Pisias (1979) and Wunsch (2004), in some textbooks or papers, there is still the misleading notion that the insolation changes are a major element controlling climate. A lot of studies have analyzed a variety of records finding the Milankovitch frequencies, but few have quantitatively investigated the hypothesis that most of the energy conveyed in paleoclimate records is not related to orbital forcing (Kominz and Pisias 1979; Raymo 1994; Wunsch 2004; Mudelsee and Raymo 2005; Hansen et al. 2013). This study applies a novel nested analytical approach based on the advanced method for signal decomposition singular spectrum analysis (SSA) with the aim of separating full-resolution time series by signal variance, the latter a useful “proxy” of the energy conveyed in paleoclimate records. SSA is a relatively new and powerful technique to processing time-series data, applicable to broad areas such as climatology, marine science, geophysics, engineering, image processing, and medicine (Vautard and Ghil 1989; Elsner and Tsonis 1996; Ghil et al. 2002; Hassani 2007). However, the SSA approach is little used in the study of paleoclimate records compared to conventional Fourier analysis, despite its capability to estimate frequencies with higher resolution than Fourier approach and to detect signal structural changes, as highlighted in the present study. Plio-Pleistocene long-term climatic cooling and the increasing glacial cycle amplitude towards the Late Pleistocene are evidence of significant changes in the climate system dynamic described in the literature, but the cause of these features remains poorly understood. The aim of this study is to investigate these topics by decomposing two selected δ¹⁸O and sea surface temperature (SST) records to outline the quantitative role of astronomical forcings and the nonlinear behavior in the orbital responses and to assess the Earth’s long-term controlling factors as a “stand-alone” climate system and its interaction with the astronomical one. Through the SSA, it provides for the first time a detailed quantitative evaluation of the δ¹⁸O and SST signal variance in a wide spectrum of orbital components from long-period orbital modulation cycles to the half-precession, both unidentified in the previous studies of the original records. The nonlinear dynamic of the astronomical climate responses is discussed regarding new insights obtained by SSA time-series processing. A link among the atmospheric pCO₂, the sea surface temperature, and the δ¹⁸O long-term trend components is also provided to support the hypothesis of a dominant non-astronomical control on the Earth’s climate.

Methods/Experimental

This work contributes to the research issues by applying SSA to the global LR04 δ¹⁸O stack (Lisiecki and Raymo 2005b) and the tropical Ocean Drilling Program (ODP) Site 846 SST record (Herbert et al. 2010b) (referred to as HT846 in this study), both high-resolution time series covering ~ 5 million years to capture long-term climate dynamics. The global LR04 benthic stack was obtained from 57 oceanic series globally distributed over a wide latitudinal range, including the Atlantic, Pacific, and Indian Oceans (Lisiecki and Raymo 2005a). Benthic δ¹⁸O measures changes in global ice volume and deep water temperatures, which are controlled by high-latitude surface temperatures (Lisiecki and Raymo 2007). The ice volume component lags the deep water temperature signal, and the net phase of the δ¹⁸O record most likely is weighted towards the slow ice volume component (Lisiecki and Raymo 2005a; Herbert et al. 2010a; Berger et al. 2016). Because the LR04 stack incorporates information from so many sites, it has a high signal-to-noise ratio and more accurately reflects changes in global climate (Lisiecki and Raymo 2005a). The original resolution of the LR04 record ranges from 1 to 5 kyr within four time intervals with constant data spacing (Lisiecki and Raymo 2005a). The average resolution is 2.5 ± 1.4 kyr. The HT846 is an alkenone-based tropical SST record located in the Eastern Equatorial Pacific (EEP). The ODP Site 846 is considered not “typical” tropical SST signal because it cools more than the ODP 662 and 722 sites, probably as the result of upwelling changes in the EEP (Herbert et al. 2010a; Lisiecki 2010b); nevertheless, its high-resolution SST record extending ~ 5 Myr makes it suitable to capture both long-term dynamics and high-frequency cycles. The original data spacing of the HT846 record is uneven throughout the 5070 kyr of the time series (Herbert et al. 2010b), with an average value of 2.3 ± 1.2 kyr. SSA requires evenly spaced records. Therefore, both records were resampled at constant time intervals of 1.0 kyr. Further details on the methodology used in this study and a discussion of the quality and reliability of the time series can be found in Additional file 1. The valuable global ΔSST stack of Martinez-Boti et al. (2015) extends 3.4 Myr with a resolution lower than that of HT846 (which is one of the ten sites included in the stack). Thus, the ΔSST stack was used in this study as a comparison record to assess some common features between the tropical Site 846 and the global SST records. The LR04 stack is orbitally tuned to an ice model driven by June 21 insolation at 65° N from La93(1,1) orbital solutions (Laskar et al. 1993), with correction of the sedimentation rate (Lisiecki and Raymo 2005a). The HT846 record is synchronized using benthic foraminiferal δ¹⁸O measured in the same sediments at the study site and aligned to the LR04 stack (Herbert et al. 2010a). Unfortunately, high-resolution extended records of CO₂ proxies to study the long-term dynamics are not currently available. The valuable simulated time series of Van de Wal et al. (2011) and Stap et al. (2016) are not suitable for the purposes of the present study because the data are not δ¹⁸O independent. Nevertheless, the long-term links among climate proxies can also be studied with low-resolution records, provided that the data are temporally extended and in sufficient number and quality to ensure reliable equation fitting. In this study, the composite atmospheric boron-based pCO₂ proxy of the ODP Sites 668B-999A (Hönisch et al. 2009; Bartoli et al. 2011) and the atmospheric alkenone-based pCO₂ and SST proxies of the ODP Site 999A (Seki et al. 2010) were selected. Seki et al. (2010) proxies are rather poor in resolution but cover a long period of time. The high-resolution atmospheric CO₂ reconstructions of Martinez-Boti et al. (2015), based on multi-site boron-isotope records, were considered despite the short time series from 3.3 to 2.3 million years ago. The composite European Project for Ice Coring in Antarctica (EPICA) pCO₂ record (Luthi et al. 2008; Berger et al. 2016) and the δ¹³C-based pCO₂ proxy (Lisiecki 2010b) are also considered. In order to evaluate the trend relationships among δ¹⁸O, SST, and pCO₂ proxies, the high-resolution LR04 and HT846 SSA-component time series were downsampled at the approximate age of the low-resolution pCO₂ proxies from the ODP Sites 668B and 999A (Hönisch et al. 2009; Seki et al. 2010; Bartoli et al. 2011). By applying the advanced method for signal decomposition singular spectrum analysis (Vautard and Ghil 1989; Elsner and Tsonis 1996; Ghil et al. 2002; Hassani 2007), the 1.0-kyr resampled LR04 and HT846 records are partitioned in a new time series of its data components. The SSA is achieved by the computation of forward-backward covariance matrices with an order of 50 (embedding dimension) using the singular value decomposition (SVD) procedure. This method for time-series analysis can be used to isolate full-resolution independent signal components based on signal strength (variance). In contrast with Fourier analysis with fixed basis of sine and cosine functions, SSA uses an adaptive basis generated by the time series itself. As a result, the underlying model in SSA is more general and can extract amplitude-modulated wave components with higher resolution than Fourier analysis. Moreover, SSA can be effectively used as a non-parametric method for detection of structural changes in the time series, reflecting the main physical phenomena underlying the data (Vautard and Ghil 1989; Hassani 2007). In the present study, the SST and δ¹⁸O SSA-components capture important aspects of the nonlinear dynamic response of the climate system in a variance-oriented way. However, some high-variance δ¹⁸O and SST signal components can remain characterized by a still complex frequency spectrum with some bands dispersed in different components. A novel nested-SSA approach has been applied to these 50-order components to better separate the frequency bands and correctly estimate the variance fraction, by increasing the embedding dimension up to 300 and partitioning the component into subcomponents. More details on the SSA methodology and the complete SSA-components dataset are provided in Additional files 1 and 2. The SSA-components are then investigated by a Fourier frequency spectrum (FFS) with a data window to analyze the frequency power and to reduce spectral leakage in the Fourier spectra. The data tapering used in this study is the cs2-Hann window and the best exact N fast Fourier transform (FFT) algorithm. The peak detection uses peak-based critical limit significance levels. In this type of confidence limit, one seeks to disprove the null hypothesis where one postulates either a white noise signal or a red noise signal. The frequency peaks shown in this study are the most significant peaks above a 99.9% critical limit, unless otherwise indicated. For each peak, the time-integral squared amplitude (TISA) power is computed in relative percent. The summed power reported in the frequency analysis is merely the sum of the component powers, not the power of the composite signal that would result from the addition of the components. Because clear non-stationarity in some components complicates the Fourier representation, these signals are investigated by FFS for time intervals to capture dynamics over time. Finally, by using the La93 orbital solutions (Laskar et al. 1993) (see Additional file 1), the phase relationships to the related orbitally driven LR04-SST components were examined by cross-spectral analysis. The data were standardized on the entire Plio-Pleistocene record (mean = 0 and standard deviation = 1), and some time series were inverted in order to have the same paleoclimatic polarity (positive forcing or warming for positive standardized values). The software used in this research is AutoSignal™.

The chronostratigraphic reference charts used in this study are the ICS International Chronostratigraphic Chart (2017-02) for the Pliocene and Pleistocene and the ICS global chronostratigraphical correlation table for the last 2.7 million years (v. 2016a) for the Quaternary.

Results

Analysis of δ¹⁸O SSA-components

The SSA allowed the resampled LR04 signal to be decomposed into five δ¹⁸O time series, which cumulatively explain 99.5% of the original variance (LR04-filtered). The spectral framework of these δ¹⁸O components (abbreviated as comp.) is diversified, with fluctuations ranging from 1330-kyr to 11-kyr periodicity (Fig. 1, Table 1). The features of the δ¹⁸O components are described as follows.

Fig. 1

Time-series panel of the five δ¹⁸O components isolated from the LR04 signal by singular spectrum analysis, together with the LR04-filtered record (left) obtained by combining these data components (99.5% total variance). The x-axis scale (‰) is variable in relation to the variance fraction of the data components. Original LR04 δ¹⁸O data from Lisiecki and Raymo (2005b) resampled at 1 kyr. Time scale in kyr

Table 1 Main descriptive parameters and Fourier frequency results of the five δ¹⁸O components isolated from the LR04 signal by singular spectrum analysis. The spectral peaks of the trend component-1 are not significant (< 50% of critical significance level) and are shown only for the purpose of discussion. Original LR04 data from Lisiecki and Raymo (2005b) are resampled at 1 kyr

δ¹⁸O component-1

This component explains 81.5% of the total variance (eigenvalue 10.89) and constitutes the most significant fraction of the LR04 signal associated with a strong trend of isotopic enrichment (long-term LR04 component, LT-LR04). The FFS shows a broad spectrum of nonsignificant peaks (< 50% of critical significance level) with periods equal to ~ 1.33 Myr (TISA power 77.2%), 409 kyr (10.8%), 294 kyr (6.9%), and 195 kyr (5.1%), overlapping the general trend (Fig. 1, Table 1). To separate the oscillatory terms from component-1 and estimate the variance fractions, an SSA was performed by increasing the embedding dimension to 300. Three main subcomponents (abbreviated as subcomp.) were identified equal to a reconstruction R² of 0.999 (Table 2).

Table 2 Descriptive parameters and Fourier frequency results of the δ¹⁸O subcomponents isolated from the LR04 component-1 by singular spectrum analysis. The processing of the subcomponents was conducted to better separate and estimate the variance fraction of specific frequency bands from still complex data components. The italicized percentage values are the absolute variance of the subcomponents (referred to the total LR04 variance)

The component-1 subcomp-1 incorporates 96.2% of the component-1 variance (81.5%), equivalent to an absolute fraction of 78.4%. It exhibits the non-Milankovitch feature of a strong isotopic trend with mild oscillations and, together with component-1, allows the subdivision of the main drift into four subtrends (Fig. 2).

Fig. 2

Time-series panel of the δ¹⁸O component-1 and its subcomponents isolated by singular spectrum analysis. δ¹⁸O comp-1 exponential trend (‰) = 1.44194 + 2.92378 e^{(−t/6963.268)}. The vertical brown arrows show four subtrends of component-1 and their correlation to the NHG transitions known in the literature (MBO this study). To the right, the Fourier frequency spectrum of δ¹⁸O detrended comp-1 subcomp-3-11 (2.23% variance) for three time intervals are highlighted by red boxes. Note the increase in amplitude after the ONHG and MPT and the power increase of the ~ 93-kyr eccentricity cycle. x-axis scale variable (‰). The y-axis scale of the frequency spectrum increases upwards. Time scale in kyr

These subtrends are characterized by a mild curvilinear shape caused by a terminal acceleration of the isotopic enrichment, separated by a late warming step that temporarily interrupts the drift. The first subtrend in chronological order (subtrend-I) is in the range of 5.33–3.30 Myr (Zanclean-Early Piacenzian) and culminates with a major event of isotopic enrichment at approximately 3.30 Myr, related to the first Pliocene transition of climatic deterioration known as the onset of the Northern Hemisphere Glaciation (ONHG) (Shackleton and Opdyke 1977; Blanc et al. 1983; Lourens and Hilgen 1994; Lisiecki and Raymo 2007). This subtrend is interrupted by a rapid warming at approximately 3.2 Myr, when a new isotopic drift (subtrend-II) begins and culminates at approximately 2.5 Myr (Middle Piacenzian to Gelasian) in a second major climatic event known as the intensification of the Northern Hemisphere Glaciation (INHG) (Zagwijn 1974; Lisiecki and Raymo 2007; Seki et al. 2010). Because of its global significance, this episode of climatic deterioration at 2.5 Myr was recently used to ratify the new Plio-Pleistocene limit to the base of the Gelasian (GSSP 2.58 Myr) which is formally assigned to the Pleistocene (Gibbard and Head 2009). Subtrend-III begins with warming at approximately 2.35 Myr and reaches its peak at 1.54 Myr at the end of the Santernian (Middle Gelasian-Santernian). The most recent segment of isotopic enrichment (subtrend-IV) starts with the warming at 1.45 Myr (Early Emilian) and culminates with a noticeable acceleration at 0.65 Myr, close to the beginning of the Middle Pleistocene, correlating to Marine Isotope Stage (MIS) 16. The Mid-Pleistocene Transition (MPT)—recently dated to start at approximately 1.2 Myr (Head and Gibbard 2005; Clark et al. 2006; Head et al. 2008)—which marks the beginning of the classic “Pleistocene Ice Age”, falls within subtrend-IV but is not directly visible in this component. The end of the subtrend-IV marks the final stage of the MPT at about 0.7 Myr (Clark et al. 2006). After MIS-16, the cooling trend is broken by a wide swing of δ¹⁸O depletion that peaks at approximately 0.40–0.30 Myr (MIS-11 and MIS-9e), referred in this study as the Mid-Brunhes Oscillation (MBO), containing the Mid-Brunhes Event (MBE) at approximately 0.43 Myr (Berger and Yin 2012). This subtrend pattern shows four steps of gradual buildup of the NHG, followed by a relative stasis of temperature cooling and ice growth during the last 600 kyr (MBO).

The frequency spectrum of comp-1 subcomp-1 still shows a nonsignificant residual peak at 1.33 Myr, very close to the ~ 1.2 Myr obliquity amplitude modulation cycle (Laskar et al. 2004, 2011; Boulila et al. 2011), tightly enveloped to the long-term trend, and to which the subtrend’s mild terminal oscillations may be related (Fig. 2, Table 2). The comp-1 subcomp-2 contains 0.8% only of the δ¹⁸O variance dominated by a 1.57-Myr periodicity (power 94.9%), which could be related to the 1.33 obliquity modulation cycle, and an ancillary term of 409 kyr. A wide spectrum of long-term cycles characterized the comp-1 subcomp-3-10, which explains 2.3% of the δ¹⁸O variance (294, 195, 163, 133, 107, and 95 kyr).

To estimate the variance fraction of the “pure” long-term trend, component-1 was detrended by subtracting an exponential fitting with least squares minimization (R² = 0.94) and the oscillatory signal was processed by a 300-order SSA (Fig. 2, Table 3). The LT-LR04 exponential fit contains 93.8% of the comp-1 variance, equivalent to an absolute contribution of 76.4%, whereas the detrended oscillatory terms explain an absolute 5.1% variance. The 2% variance difference between the comp-1 subcomp-1 (78.4%) and the comp-1 exponential fit (76.4%) may be attributed to the 1.33-Myr cycle still superimposed to the comp-1 subcomp-1. Considering the variance fraction of the comp-1 subcomp-2 (0.8%, Table 2), a ~ 2.8% contribution of the 1.57–1.33-Myr cycle may be estimated. Three subcomponents were isolated from the detrended comp-1 (Table 3). The detrended comp-1 subcomp-1 explains 2.25% of the δ¹⁸O variance and exhibits a spectrum dominated by a 3.75-Myr periodicity (power 95.8%) with an ancillary term of 855 kyr. Oddly, the cycle at about 1.57–1.33 Myr disappears in the detrended component-1, while a new 3.75-Myr cycle is ascribable to the 3.7-Myr g9-s9 terms of the Earth’s orbit secular frequency (Laskar et al. 2011). Prevailing 409-kyr (80.6%) and 294-kyr (19.4%) cycles characterized the detrended comp-1 subcomp-2, explaining only 0.61% of the δ¹⁸O variance. These periodicities may be related to the astronomically stable 405-kyr-long eccentricity cycle and to the 304-kyr Earth orbit secular frequency, respectively (Laskar et al. 2004, 2011; Boulila et al. 2011).

Table 3 Main descriptive parameters and Fourier frequency results of the δ¹⁸O subcomponents isolated from the detrended component-1 and component-2 by singular spectrum analysis. The processing of the subcomponents was conducted to better separate and estimate the variance fraction of specific frequency bands from still complex data components. The italicized percentage values are the absolute variance of the subcomponents (referred to the total LR04 variance)

The detrended comp-1 subcomp-3-11 explains 2.23% of the δ¹⁸O variance and shows a wide spectrum of frequency bands. A 294-kyr cycle (power 15.2%) may be related to the 304-kyr Earth orbit secular frequency. Oscillations of 163 kyr (17.2%) and 195 kyr (24.9%) may be linked to the long-period obliquity modulation cycles (~ 160–200 kyr) (Boulila et al. 2011). Finally, the short eccentricity cycles of 133 kyr (15.9%), 107 kyr (12.7%), and 95 kyr (14.1%) are also recognizable. The FFS of this subcomponent by time intervals (Fig. 2) shows two time horizons of amplitude shifting at about 3.32 Myr (ONHG) and 1.24–0.70 Myr (MPT) that delineate three intervals, in which occur a progressive increase in signal amplitude and a relative strengthening of the short eccentricity cycle (93 kyr) at the expense of the obliquity modulation cycles (195–205 kyr), revealing a transient nonlinear behavior of this small fraction of isotopic response.

δ¹⁸O component-2

Component-2 explains 7.3% of the total variance (eigenvalue 0.97) and exhibits four significant oscillatory components in the 41-kyr (power 40.1%) and 54-kyr (22.3%) obliquity bands and in the 95-kyr (20.9%) and 71-kyr (16.8%) short eccentricity bands (Fig. 3, Table 1).

Fig. 3

Time-series panel of δ¹⁸O component-2 and its subcomponents and Fourier frequency spectrum of comp-2 for three time intervals a, b and c, highlighted by red-labeled boxes. Note the evident increase in comp-2 amplitude after the ONHG and MPT, and the transition in periodicity from a obliquity to c eccentricity with a gradual upwards strengthening of the short eccentricity power. Interestingly, the amplitudes of the eccentricity in comp-2 subcomp-1-4, 9-15 are increasing, whereas the amplitude of the obliquity in comp-2 subcomp-5-8 is decreasing after the MPT. x-axis scale variable (‰). The y-axis scale of the frequency spectrum increases upwards. Time scale in kyr

Two shifting horizons of isotopic amplitude (3.32 and 1.24 Myr) are distinctly observed, correlating to the ONHG and MPT start, respectively, and defining three time intervals of increasing amplitude and a significant change in orbital periodicity. The oldest segment between 5.32 and 3.32 Myr (Zanclean-Early Piacenzian) exhibits the lowest amplitude and power and a relative prevalence of the obliquity cycle (41-kyr and 54-kyr). The eccentricity bands at 89 kyr and 102 kyr are particularly weak (Fig. 3a). From 3.32 to 1.24 Myr (Early Piacenzian-Emilian), a relative increase of the short eccentricity power (71-kyr and 91-kyr) over the obliquity cycle occurs (Fig. 3b). The most recent segment from 1.24 Myr exhibits a further increase in the average amplitude and an overwhelming power prevalence of the eccentricity 93-kyr cycle over the 41-kyr response, which maintains about the same power (Fig. 3c). To further isolate the two orbital terms from component-2, the SSA was performed by increasing the embedding dimension to 300, producing two subcomponents equal to a reconstruction R² of 0.998 (Fig. 3; Table 3). Subcomponent-1-4, 9-15 explains 75.3% of the component-2 variance, equivalent to an absolute variance fraction of 5.5%. It exhibits frequencies in the short eccentricity band (95-kyr, power 56.6%; 71-kyr, 43.4%). Subcomponent-5-8 explains 24.4% of the component-2 variance (1.8% absolute variance) in the obliquity frequency band (41-kyr, 67.5%, 54-kyr, 32.5%). Interestingly, the amplitude of this obliquity’s subcomponent is decreasing after the MPT (Fig. 3). The change in the nonlinear dynamic of the component-2 response (transition from obliquity to short eccentricity) is configured as a sort of “switching” of the orbital power and amplitude between the 41-kyr obliquity and the 93-kyr eccentricity cycles. From this perspective, due to the change in periodicity depending on the amplitude, component-2 may be the expression of a nonlinear phase-locking mechanism between obliquity and eccentricity astronomical forcing (Tziperman et al. 2006; Ruggieri et al. 2009). Notably, by modeling the Northern Hemisphere ice volume over the last 3 Myr, Berger et al. (1999) simulated similar power spectrum changes using a combination of insolation and linearly decreasing CO₂ concentration. Imbrie et al. (2011) simulated the same spectral behavior using the Pleistocene LR04 record with a new phase-space model of orbital forcings but with a state threshold function of the ice volume, showing that ice volume plays an important role in pacing the orbital response of the climate system. These simulated data, together with the observed features of the SSA comp-2 and detrended comp-1 subcomp-3-11 (Fig. 2), strengthen the evidence of a paleoclimatological transition where the ONHG marks the beginning of a weak and gradual sensibility of the climate system to a 93-kyr eccentricity forcing, supporting the hypothesis of an ice volume CO₂-induced control on eccentricity sensibility (Raymo 1998; Berger et al. 1999; Hansen et al. 2007; Lisiecki and Raymo 2007; Imbrie et al. 2011; Berger and Yin 2012).

δ¹⁸O component-3-4

This signal explains 8.1% of the δ¹⁸O variance (eigenvalue 1.08) with a 95.3% power at an obliquity-driven 41–39-kyr period (Table 1). Component-3-4 is characterized by a clear increase in the average 41-kyr amplitude and power towards the beginning of the MPT (Fig. 4a, b), followed by an amplitude stabilization and power reduction during the MPT and post-MPT (Fig. 4c). Nonstationary behavior is observed at the beginning of the MPT, where a change in the shape of the 41-kyr cycle that appears enveloped in a very weak 93-kyr signal can be noted (Fig. 4c), suggesting an apparent influence between the eccentricity and the obliquity cycles after the beginning of the MPT. The ONHG transition at 3.32 Myr does not seem to be associated with any particular features of component-3-4, except for a strong power increase in the 41-kyr cycle after the transition.

Fig. 4

Time-series panel of the δ¹⁸O component-3-4 (8.1% var.) and component-2 subcomp-5-8 (1.8% var.) related to obliquity. The Fourier frequency spectrum of component-3-4 in three time intervals is highlighted by red-labeled boxes. The spectrum is always dominated by obliquity 41-kyr power. Note a clear increase in the average 41-kyr amplitude and power towards the beginning of the MPT (box 4a and 4b), followed by an amplitude stabilization and power reduction (box 4c) and an amplitude reduction (comp-2 subcomp-5-8) during the MPT and post-MPT. The envelope of two to three obliquity cycles in a weak eccentricity 93-kyr framework after the beginning of the MPT is noteworthy (box 4c and magnified time series to the right). FFS scale power increases upwards from a to b and decreases from b to c. x-axis scale variable (‰). Time scale in kyr

δ¹⁸O component-5-7

This component explains 2.0% of the δ¹⁸O variance (eigenvalue 0.27) driven by precession-related bands at ~ 22 kyr (Table 1). This precession δ¹⁸O component also shows the nonlinear shape of the upwardly increasing isotopic amplitude (Fig. 1).

δ¹⁸O component-8-11

Component-8-11 exhibits 0.6% of the δ¹⁸O variance (eigenvalue 0.07) and contains a weight mean period at ~ 13 kyr (Table 1). Furthermore, the feature of increasing mean amplitude in this weak component is still observed (Fig. 1). From an interpretative viewpoint, component-8-11 is related to the “half-precessional” cycle of equatorial origin modulated at ~ 11 kyr (Berger et al. 2006). Hagelberg et al. (1994) found precession-related climate variability at periods from 10 to 12 kyr in three sites for the Late Pleistocene (ODP 846, ODP 663, and DSDP 609). They concluded that this variability may be derived from the high sensitivity of the tropics to summertime insolation in both hemispheres, triggering an amplified response of tropical precipitation and temperature that may be transmitted to high latitudes via Atlantic advective transport. The results of magnetic susceptibility and particle size analysis from the Northwestern Chinese Loess Plateau reveal well-defined half-precessional cycles during the last interglaciation, interpreted as a direct response to low-latitude forcing through its modulation of the East Asian summer monsoon (Sun and Huang 2006). However, despite this interesting evidence of the semi-precessional cycle of equatorial origin in the δ¹⁸O deep-temperature and ice-volume signal, its contribution to the total variance of the global δ¹⁸O record is less than 1%.

Analysis of the SST SSA-components

The resampled HT846 record was partitioned by SSA into five SST time series, which cumulatively explain 99.6% of the original variance (HT846-filtered) (Fig. 5, Table 4). The spectral frameworks of these SST components, ranging from 1266-kyr to 11-kyr periodicity, are very similar to that of the LR04 record. The features of the SST components are described and compared to the δ¹⁸O ones as follows.

Fig. 5

Time-series panel of the five SST components isolated from the ODP Site 846 record by singular spectrum analysis with the SST-filtered record (left) obtained by combining these data components (99.6% total variance). The x-axis scale (°C) is variable in relation to the component’s variance fraction. Original SST data from Herbert et al. (2010b) resampled at 1 kyr. Time scale in kyr

Table 4 Main descriptive parameters and Fourier frequency results of the five ODP Site 846 SST components isolated by singular spectrum analysis. Original SST data from Herbert et al. (2010b) resampled at 1 kyr

SST component-1

This component explains 87.8% of the original variance (eigenvalue 128.1) and contains the most significant fraction of the SST signal associated with a strong cooling trend (long-term HT846 component, LT-HT846). The FFS shows a broad spectrum of significant peaks with periods of ~ 1.27 Myr (TISA power 83.3%), 406 kyr (8.6%), 298 kyr (5.0%), and 193 kyr (3.1%), overlapping the general trend (Fig. 5, Table 4). A high-order SSA was performed to separate the oscillatory terms from the component-1 trend, from which three subcomponents were identified equal to a reconstruction R² of 0.999 (Table 5).

Table 5 Descriptive parameters and Fourier frequency results of the ODP Site 846 SST subcomponents isolated from the SST component-1 by singular spectrum analysis. The processing of the subcomponents was done to better separate and estimate the variance fraction of specific frequency bands from still complex data components. The italicized percentage values are the absolute variance of the subcomponents (referred to the total SST variance)

The component-1 subcomp-1 explains an absolute variance of 81.7% and exhibits a strong cooling trend with significant mild oscillations. The four LR04s’ subtrends are generally identifiable in the tropical SST long-term components, with some differences especially in subtrend-III due to a strong cooling event at ~ 2.1 Myr (Herbert et al. 2010a), which is less evident in the δ¹⁸O signal (Fig. 6). In addition, the MBO feature is less marked in the SST signal. These differences between deep-temperature/ice-volume and sea surface temperature signals could be due to temporal effects of upwelling in the EEP “cool” region (Lisiecki 2010b).

Fig. 6

Time-series panel of the ODP Site 846 SST component-1 and its subcomponents isolated by singular spectrum analysis. SST comp-1 exponential trend (°C) = 33.58041–11.84075 e^{(−t/8830.503)}. The vertical brown arrows show four subtrends of component-1 and their correlation to the NHG transitions known in the literature (MBO this study). To the right, Fourier frequency spectrum of SST detrended comp-1 subcomp-3-11 (2.84% variance) for three time intervals are highlighted by red boxes. Note the increase in amplitude after the ONHG (but not after the MPT) and the power increase of the ~ 93-kyr eccentricity cycle. x-axis scale variable (°C). The y-axis scale of the frequency spectrum increases upwards. Time scale in kyr

The frequency spectrum of the SST comp-1 subcomp-1 still shows a significant peak of 1.27 Myr period (98.7% power), related to the ~ 1.2-Myr obliquity modulation cycle (Laskar et al. 2004, 2011; Boulila et al. 2011), to which the mild subtrend oscillations may be related (Table 5). The comp-1 subcomp-2 explains 3.0% of the HT846 variance dominated by a 1.50-Myr periodicity (94.1%), probably related to the same obliquity modulation cycle. A wide spectrum of long-term cycles characterized the comp-1 subcomp-3-10, explaining 3.1% of the original SST variance (399, 292, 213–193, 126, and 95 kyr).

To estimate the variance of the SST long-term trend, the component-1 was detrended by subtracting an exponential fitting with least squares minimization (R² = 0.87), and the oscillatory signal was processed by a high-order SSA (Fig. 6, Table 6). The LT-HT846 exponential fit explains 87.2% of the comp-1 variance, equivalent to an absolute contribution of 76.6%. The detrended oscillatory signal explains an absolute 11.2% variance. The 5.1% variance difference between the comp-1 subcomp-1 (81.7%) and the comp-1 exponential fit (76.6%) may be attributed to the 1.27-Myr cycle still superimposed on the comp-1 subcomp-1. Three subcomponents were isolated from the SST detrended comp-1 (reconstruction R² = 0.999). The detrended comp-1 subcomp-1 explains 5.56% of the SST original variance and exhibits a spectrum dominated by 1.37-Myr (power 51.9%) and 3.6-Myr (40.6%) cycles, with an ancillary term of 827 kyr. Again, the 3.7- to 3.6-Myr cycle appears in the LR04 and HT846 detrended comp-1 subcomp-1 only; however, in the HT846 record, the 1.37-Myr cycle does not disappear. Therefore, the 5.56% tropical SST variance (detrended comp-1 subcomp-1) related to the long-term cycles (1.37-Myr obliquity modulation cycle and 3.6-Myr Earth orbit secular frequency) is consistent with the 5.1% variance estimate by difference from comp-1 subcomp-1 (which includes the 1.27-Myr cycle only).

Table 6 Main descriptive parameters and Fourier frequency results of the ODP Site 846 SST subcomponents isolated from the detrended comp-1 and comp-2 by singular spectrum analysis. The processing of the subcomponents was made in order to better separate and estimate the variance fraction of specific frequency bands from still complex data components. The italicized percentage numbers are the absolute variance of the subcomponents (referred to the total SST variance)

Prevailing 405-kyr (70.3%) and 300-kyr (29.7%) cycles characterize the detrended comp-1 subcomp-2 explaining 2.81% of the SST variance. These frequencies may be related to the astronomically stable 405-kyr-long eccentricity cycle and to the 304-kyr Earth orbit secular frequency (Laskar et al. 2004, 2011; Boulila et al. 2011). The detrended comp-1 subcomp-3-11 explains 2.84% of the SST variance and shows a wide spectrum of frequency bands. A 295-kyr cycle (power 15.4%) can be attributed to the 304-kyr Earth orbit secular frequency. Oscillations of 193 kyr (45%) and 148 kyr (6.7%) may be linked to the long-period obliquity modulation cycles (~ 160–200 kyr) (Boulila et al. 2011). Finally, weak short eccentricity cycles of 136 kyr (9.2%), 126 kyr (14%), and 95 kyr (9.7%) are also recognizable. The FFS of this subcomponent by time intervals (Fig. 6) shows a relative strengthening of the short eccentricity cycle (93-kyr) at the expense of the obliquity modulation cycles (~ 195- to 158-kyr), whereas the increase in signal amplitude by time is not observable post-MPT.

SST component-2

This component explains 5.2% of the total variance (eigenvalue 7.56) and exhibits a basically 95- to 90-kyr short eccentricity periodicity (58.9%) with a 69-kyr term (41.1%) and a very weak but significant 41-kyr obliquity oscillation (Fig. 7; Table 4). Compared to the δ¹⁸O comp-2, the two shifting horizons of increasing amplitude (ONHG and MPT start) and the change in orbital periodicity from 41–54 to ~ 93 kyr by three time segments are less evident (Fig. 7a–c). The transition from obliquity to short eccentricity is less evident but still present as shown also by the subcomponent analysis (Table 6). Three subcomponents were isolated by a high-order SSA (R² = 0.999). Subcomponent-1-4 explains 3.65% of the original SST variance and shows a frequency spectrum in the short eccentricity band (95-kyr, power 43.2% and 69-kyr, 56.8%). Subcomponent-5-8, 11-15 explains 1.27% variance in a still complex transition spectrum from the obliquity (53-kyr, 60.2%) to eccentricity band (126-kyr, 39.8%). Finally, subcomp-9-10 explains only 0.27% of the SST variance in the obliquity frequency band (45-kyr, 62.2%; 41-kyr, 37.8%).

Fig. 7

Time-series panel of ODP Site 846 SST component-2 and its subcomponents and Fourier frequency spectrum of comp-2 for three time intervals a, b and c, highlighted by red-labeled boxes. The transition nature from a obliquity to c short eccentricity is less evident in this tropical SST site, but still present. The increasing amplitude of the short eccentricity is more clear in subcomp-1-4. The obliquity decrease after the MPT is still shown by subcomp-9-10. x-axis scale variable (°C). The y-axis scale of the frequency spectrum increases upwards. Time scale in kyr

SST component-3-4

This component explains 4.5% of the SST variance (eigenvalue 6.56) at the 87.7% obliquity-driven 41–40-kyr period (Table 4). The SST component-3-4 is still characterized by a less evident increase in the average amplitude by time approaching the beginning of the MPT (Fig. 8a, b), followed by a clear decrease in amplitude after the MPT start (Fig. 8c). A slight change in the shape of the 41-kyr cycle that appears enveloped in a very weak ~ 93-kyr signal can be observed after 1.2 Myr (Fig. 8c).

Fig. 8

Time-series panel of the ODP Site 846 SST obliquity’s component-3-4 (4.5% var.) and component-2 subcomp-9-10 (0.27% var.). Fourier frequency spectrum of comp-3-4 by three time intervals highlighted by red labeled boxes. The spectrum is always dominated by obliquity 41-kyr power. Note a clear increase in the average 41-kyr amplitude and power towards the beginning of the MPT (box 8a and 8b), followed by a clear decrease in amplitude after the beginning of the MPT (box 8c and comp-2 subcomp-9-10). The envelope of two to three obliquity cycles in a weak eccentricity ~ 93-kyr framework after the beginning of the MPT is less evident (box 8c and magnified time series to the right). FFS scale power increasing from a to b and was constant from b to c. x-axis scale variable (°C). Timescale in kyr

SST component-5-7

This component explains 1.6% of the SST variance (eigenvalue 2.24) driven by precession frequency bands at ~ 22 kyr (Table 4), similar to the precession δ¹⁸O component.

SST component-8-11

Component-8-11 explains a total 0.5% of the SST variance (eigenvalue 0.74) and shows a weight mean period at ~ 12 kyr (Table 4). An increasing mean amplitude in this weak component is still observed (Fig. 5). This component is similar to that of the δ¹⁸O identified in this study and can be related to the “half-precessional” cycle of equatorial origin modulated at ~ 11 kyr (Berger et al. 2006).

Summary of δ¹⁸O and SST forcing variance contribution

The SSA results allow the LR04 δ¹⁸O and ODP Site 846 SST forcing variance contribution to be estimated quantitatively in detail. A complex envelope of long-term orbital cycles accounts for a maximum of 5.1% of the δ¹⁸O variance (due to a small fraction of short eccentricity in detrend comp-1 subcomp-3-11; Table 3). Within the 2.23% variance of the δ¹⁸O detrend comp-1 subcomp-3-11, a ~ 0.95% short eccentricity contribution may be roughly estimated by using the TISA power of the short eccentricity terms (42.7% of 2.23% variance). This approach is justified because of the low variance of the detrend comp-1 subcomp-3-11, causing a negligible error. Therefore, δ¹⁸O long-period orbital modulation cycles (1.57–1.33 Myr and ~ 160–200 kyr obliquity amplitude modulation; 3.75 Myr and ~ 300 kyr Earth orbit secular frequencies) and the ~ 405-kyr-long eccentricity cycles tightly overlapped to the δ¹⁸O trend, influencing the Earth’s climate with an estimated variance of ~ 4.2%. Regarding the tropical SST, a similar complex envelope of long-term orbital cycles account for a maximum 11.2% of the HT846 variance (Table 6), and by subtracting the small variance of the short eccentricity term (32.9% of 2.84%, variance = 0.93%), a contribution of ~ 10.3% can be estimated.

Long-term cycles (1.5–1.0 Myr) were previously observed in the planktonic δ¹⁸O record of ODP Site 625B from the Gulf of Mexico and interpreted as a low-frequency component of the climate system, likely unrelated to orbital forcing (Joyce et al. 1990). Instead, according to Lourens and Hilgen (1994), the long-term 1.3-Myr period observed from some Mediterranean and equatorial Atlantic and Pacific sites resulted from a long-term obliquity modulation cycle. Through a correlation between Cenozoic icehouse sequences and astronomical cycles, Boulila et al. (2011) demonstrate a close correlation between ~ 1.2-Myr obliquity modulation cycles and third-order eustatic sequences, suggesting glacioeustasy as the major driving process of third-order sequences in an icehouse world. A complex envelope of Plio-Pleistocene long-term astronomical cycles and especially the 1.57–1.33-Myr obliquity amplitude modulation to which the mild NHG’s subtrend terminal oscillations may be related by transient interaction on the long-term trend are further geological evidences of the chaotic behavior of the Solar System (Laskar et al. 2004, 2011; Boulila et al. 2011; Westerhold et al. 2017), and the SSA results show that their influence on Earth’s climate, estimated for the first time in this study, have important differences in variance (global δ¹⁸O ~ 4.2%; tropical SST ~ 10.3%). Interestingly, the tight overlap of these long cycles could be the reflection of a close link between these weak orbital forcings and the much more effective forcing at the origin of the long-term trends through a temperature-ice volume-induced control on the long-cycle sensibility. The lack of the ~ 1.2-Myr eustatic cycles in the Mesozoic greenhouse world (ephemeral or no ice sheets) (Boulila et al. 2011) may support this hypothesis.

The short eccentricity does not manifest itself as a “pure” δ¹⁸O component; rather, it appears to move gradually to the Pleistocene climate signal as an interaction subcomponent only, with a long-term response (detrend comp-1 subcomp-3-11, ~ 0.95% variance) and the obliquity-eccentricity transitional component-2 (component-2 subcomp-1-4, 9-15, 5.5% variance). Therefore, the short eccentricity cycle contributes ~ 6.5% to the global Plio-Pleistocene δ¹⁸O signal. Similarly, the SST detrend comp-1 subcomp-3-11 explains ~ 0.93% of short eccentricity variance, and a 3.65% fraction is recorded in the SST comp-2 subcomp-1-4. A small fraction of short eccentricity terms are still recorded in the SST comp-2 subcomp-5-8, 11-15 for which a 0.5% variance can be estimated (39.8% of 1.27% variance), resulting in a SST short eccentricity total variance of ~ 5.1%. These values agree with the consideration that the amount of insolation perturbation at the eccentricity-driven ~ 100-kyr period is too small to directly cause climate change of an ice age amplitude (Imbrie et al. 1993; Berger et al. 1999, 2006; Lisiecki 2010a).

The 41-kyr obliquity cycle appears to transfer to the climate system both as a “pure” δ¹⁸O component, with signal strength of 8.1% (component-3-4), and as an interaction subcomponent like the obliquity-eccentricity transitional component-2 (comp-2 subcomp-5-8, 1.8% var.). Therefore, the total δ¹⁸O signal variance in the 41-kyr obliquity band is estimated to be 9.9%. The SST shows a similar behavior characterized by a “pure” component-3-4 (4.5% variance) plus transitional obliquity-eccentricity subcomponents (comp-2 subcomp-9-10, 0.27% var.; comp-2 subcomp-5-8, 11–15, ~ 0.76%), from which a total obliquity contribution of 5.5% may be estimated.

The precession and semi-precession δ¹⁸O variance can be evaluated at about 2.0% and 0.6%, close to the SST contribution of 1.6% and 0.5%, respectively. In summary, the variance of the δ¹⁸O orbital components related to long-term, short eccentricity, obliquity, precession, and semi-precession cycles can be evaluated at approximately 4.2%, 6.5%, 9.9%, 2.0%, and 0.6%, respectively (total 23.2% variance), whereas the orbital SST components account for 10.3%, 5.1%, 5.5%, 1.6%, and 0.5%, respectively (total 23.0% variance). Within orbital forcings, the impact of the obliquity cycle appears to be the most consistent in the LR04 stack. In the tropical HT846 record, the most consistent orbital signal is related to the long-term cycles. These results agree with those of Kominz and Pisias (1979), which state that the fraction of the record variance related to orbital changes is less than 25%, and of Wunsch (2004), which states that this fraction never exceeds 20%. Interestingly, the cumulative influence on the Earth’s climate of orbital forcings estimated from the global δ¹⁸O stack is equal to that of the tropical SST single record, while the individual contribution of each astronomical term is quite different. This result could be attributed to the latitudinal gradients of orbital forcings (Berger 1978; Liu and Herbert 2004), while the constancy of the long-term variance might reflect a global latitude-independent nature of the paleoclimatic trend’s control factors. The fact that the δ¹⁸O and SST orbital components explain ~ 23% of the total variance clearly shows that astronomical forcing does not play a major role in guiding the response of the climate system in the Plio-Pleistocene, in agreement with Kominz and Pisias (1979), Raymo (1994), Wunsch (2004), and Mudelsee and Raymo (2005). However, ~ 76% of the Plio-Pleistocene climate variance is related to non-Milankovitch long-term controlling factors, drives approximately three fourths of the energy conveyed in paleoclimate records, and thus constitutes the main Earth’s climate system. This robust and stable trend signal needs to be explained.

Statistical analysis of the mean climate state through time

The SSA time series allow a quantitative analysis of the mean climate state through time. The Plio-Pleistocene δ¹⁸O and SST components and the solution of orbital forcings (Laskar et al. 1993) were standardized (mean = 0, standard deviation = 1) and binned at three arbitrary constant time intervals (532 kyr, 760 kyr, and 1064 kyr) to avoid data density distortion in descriptive statistics and significance tests of mean differences among groups (Table 7). Some data were inverted in order to have the same paleoclimatic polarity (Fig. 9).

Table 7 Significance tests of the mean differences among δ¹⁸O and SST components and the solution of orbital forcings (Laskar et al. 1993) binned at three arbitrary constant time intervals (532 kyr, 760 kyr, and 1064 kyr). Data standardized on the entire Plio-Pleistocene record (mean = 0, standard deviation = 1) and, where necessary, inverted to have the same paleoclimatic polarity (positive values for positive forcing and warming)

Fig. 9

Plots of the 95% confidence interval for the mean of a δ¹⁸O components and c SST components compared to orbital forcings (Laskar et al. 1993), binned at 532-kyr constant time intervals. Overlapped histograms of b Plio-Pleistocene δ¹⁸O and d SST orbital component-2-11 vs. trend component-1 subcomp-1. The averages of the astronomical components oscillate around the standardized mean with little statistically significance differences and a roughly normal distribution. Instead, the averages of the trend components differ very significantly, deviating markedly from the mean with a general multimodal distribution. Data standardized on the entire Plio-Pleistocene record (mean = 0, standard deviation = 1) and, where necessary, inverted to have the same paleoclimatic polarity (positive values for positive forcing and warming)

As observed in the comparison of the 95% confidence interval (CI) for the means (Fig. 9a, c) and in the significance tests of the mean differences in the analysis of variance (ANOVA) table (Table 7), the δ¹⁸O and SST trend components (comp-1, comp-1 subcomp-1, and comp-1 exponential fit) can very significantly change the signal mean for different time intervals. Instead, the δ¹⁸O and SST orbital components (comp-2-11) and the astronomical forcings modified the mean with little significance or no significance. These results are similar across all three binned time intervals showing that this feature is not a time frame artifact (Table 7). In more detail, the mean reaches a deviation from the standardized mean up to − 1.51–1.18 standard units through the time segments in the δ¹⁸O component-1, up to − 1.50–1.21 in the δ¹⁸O comp-1 subcomp-1, and in the range − 1.72–1.40 in the δ¹⁸O comp-1 exponential fit. The SST trend components exhibit similar results with deviations up to − 1.45–1.27, − 1.49–1.33, and − 1.67–1.50 for the comp-1, comp-1 subcomp-1, and comp-1 exponential fit, respectively. The δ¹⁸O and SST orbital signals reach maximum values of − 0.08–0.09 and − 0.09–0.04 standard deviations, respectively. Eccentricity reaches a maximum deviation from the standardized mean of − 0.30–0.28 units. Obliquity ranges from − 0.12 to 0.12 and precession from − 0.02 to 0.01. The insolation mean (65° N at June 21) oscillates in the range of − 0.08–0.06. The ANOVA analysis was also done to all single orbital components, obtaining similar results. The histograms of the Plio-Pleistocene δ¹⁸O and SST astronomical components-2-11, compared to that of the trend component-1 subcomp-1 (Fig. 9b, d), show a roughly normal distribution centered on the orbital response mean, while the trend component exhibits a multimodal distribution away from the standardized mean. This analysis suggests Plio-Pleistocene orbital forcing could be considered a random walk at zero-sum (the standardized mean): on long time scales, astronomical forcing oscillates around a basically time-invariant normally distributed mean of the Plio-Pleistocene climate system response. These results, consistent with those of the quantitative estimation of the variance, suggest that changes in the mean climate state during the Plio-Pleistocene were primarily caused by non-Milankovitch first-order controlling factors recorded in the global LR04 and tropical HT846 trend components (~ 76% variance). The orbital forcing acts at a hierarchically lower strength level (~ 23%), with cycles overlapping a primary trend forcing system.

Nonlinear response of δ¹⁸O and SST orbital vs. trend components

Figure 10 exhibits the exponential relationships between the orbital δ¹⁸O and SST components variance vs. the average δ¹⁸O-SST component-1 exponential fit trends by time segments binned at 532 kyr. This plot shows that the exponential increase in signal amplitude towards the Mid-Late Pleistocene is observed in all δ¹⁸O and SST orbital components, from semi-precession to the eccentricity band. The exponential growth of the orbital response variance is dependent on the long-term mean climate state (LT-MCS) at a given time (mean ice volume-bottom water temperature, average sea surface-atmospheric temperature), both at a global scale (LR04) and at a local tropical scale (ODP Site 846). The exponential R² ranges from 0.7 to 0.9 for the δ¹⁸O components and is slightly lower in the SST components (0.6 to 0.9). The minimum exponential fitting does not fall below an R² = 0.64 for SST component-2 subcomp-1-4 and R² = 0.72 for δ¹⁸O component-8-11. The exponential coefficient e^kx for the δ¹⁸O semi-precessional component is 1.05 (comp-8-11) and increases with the orbital period; it is 1.78 for the precessional component (comp-5-7), 1.88 for the obliquity component (comp-3-4), and 2.93 for the short eccentricity subcomponent (comp-2 subcomp-1-4; 9-15). The exponential coefficient is high (2.37) for the short eccentricity-obliquity modulation subcomponent (detrended comp-1 subcomp-3-11) (Fig. 10a). These data indicate an increase in δ¹⁸O exponential growth from semi-precession to ~ 100-kyr eccentricity response towards the Mid-Late Pleistocene. The amplitude flattening of the obliquity-driven δ¹⁸O component-3-4 during the MPT and post-MPT time shown in Fig. 4 is clearly evident in Fig. 10a also, a feature related to that observed by Lisiecki and Raymo (2007). Regarding the tropical SST, the absolute exponential coefficient e^kx for the semi-precessional component is 0.31 (comp-8-11). It is 0.37 for the precessional component (comp-5-7), 0.48 for the obliquity component (comp-3-4), and 0.67 for the short eccentricity subcomponent (comp-2 subcomp-1-4) (Fig. 10b). These results in tropical SST are similar to those of the global δ¹⁸O, although of lesser magnitude. The amplitude contraction of the obliquity-driven SST component-3-4 after the MPT start, shown in Fig. 8, is very evident even in Fig. 10b.

Fig. 10

Exponential relationships of the orbital variance of a δ¹⁸O components and b SST components vs. the average of component-1 exponential fit trends by time segments binned at 532 kyr. The right y-axis shows the variance of comp-2-11 (orbitals) with a different scale to not compress the left y-axis values

Figure 11 shows a quantitative analysis of the δ¹⁸O and SST response modulation relative to orbital forcing as a function of the LT-MCS. The standardized response sensitivity R_s is given by the following function

$$ {R}_{\mathrm{s}}=\left({\sigma^2}_{\mathrm{resp}}-{\sigma^2}_{\mathrm{forc}}\right)/{\upsigma^2}_{\mathrm{forc}}\times 100 $$

Fig. 11

Analysis of the order of magnitude in a δ¹⁸O and b SST response modulation relative to orbital forcing (standardized response sensitivity R_s, see text) as a function of the LT-MCS. The balance line (0%) indicates that the variance of response matches the variance in forcing, suggesting a self-sustained climate system, which is only paced by orbital cycles. Values much larger than zero would indicate a nonlinear reinforcement of the signal response. Negative R_s shows a response variance lower than orbital forcing, suggesting a damping mechanism for the climate system

where σ²_resp and σ²_forc are the variance of the standardized (0—mean; 1—standard deviation) orbital response component and forcing calculated by time segments binned at 532 kyr, respectively. For the purpose of this exercise, the eccentricity and obliquity response are approximated because small variances in these terms cannot be merged in a composite signal, or a small fraction of different frequency terms are included. Since the variance is small and the aim of this analysis is an order of magnitude estimate, the errors should be negligible. The δ¹⁸O short eccentricity response (~ 6.5% variance) was considered both as a single main subcomponent (comp-2 subcomp-1-4, 9-15; 5.5% variance) containing ~ 85% of the short eccentricity response and as the weighted mean by variance of the comp-2 subcomp-1-4, 9-15 (5.5% variance) and the detrend comp-1 subcomp-3-11 (2.23% variance), the latter containing also a small fraction of long-term cycles. The δ¹⁸O obliquity response (9.9% variance) was calculated as the weighted mean of the comp-3-4 (8.1%) and comp-2 subcomp-5-8 (1.8%). Similarly, the SST short eccentricity response (~ 5.1% variance) was approximated as a single comp-2 subcomp-1-4 (3.65% variance) explaining ~ 72% of the short eccentricity response and as weighted mean of the comp-2 subcomp-1-4 (3.65% variance) and the detrended comp-1 subcomp-3-11 (2.84% variance), the latter containing a small fraction of long-term cycles. The weighted mean of the SST comp-3-4 (4.5% variance) and comp-2 subcomp-9-10 (0.27% variance) was calculated as the SST obliquity response, covering ~ 87% of the total signal (4.77% of 5.5%). A self-sustained climate system, which is only paced by orbital cycles, would produce a response sensitivity near zero because the variance of the response would match the variance in forcing, whereas values much larger than zero would indicate a nonlinear reinforcement of the signal response. Negative R_s values show a response variance lower than orbital forcing, suggesting a damping mechanism for the climate system. Figure 11a exhibits a δ¹⁸O nonlinear eccentricity R_s up to 400% towards the Mid-Late Pleistocene similar to that of a precession response in shape but with a magnitude up to 200%. The two eccentricity curves are very similar, indicating a negligible error in the approximations. The δ¹⁸O obliquity R_s shows a nonlinear amplification up to 180% towards the end of the MPT, followed by strong variance depletion near to zero (balance line) post-MPT. This pattern of low δ¹⁸O obliquity variance is similar to that shown in Fig. 5b from Lisiecki and Raymo (2007). Remarkably, the asymptotic decay of the δ¹⁸O R_s towards the Early Pliocene becomes all negative up to − 100%, suggesting a damped orbital response during the time of minimum average ice volume and higher temperature. This R_s pattern is similar considering the SST (Fig. 11b), although more scattered and with a smaller positive magnitude which does not reach 200%. The SST obliquity R_s also shows strong variance depletion up to − 20% post-MPT as well as the new feature of asymptotic decay up to − 100% of all the SST R_s towards the Early Pliocene.

Link between the pCO₂ and the SST-δ¹⁸O long-term trend components

Figure 12 shows the Plio-Pleistocene cross plots among the δ¹⁸O, SST, and pCO₂ trend and orbital components. These plots offer an overall view of the long-term trend links among the proxies. Although it is possible to express the trend relationship as exponential regressions, it was decided to use a simpler linear fitting since the correlation coefficients are similar, in order to quantify the trend rates of change. The δ¹⁸O trend components exhibit a good linear interpolation vs. the boron-based pCO₂ trend of the Sites 668B-999A (Fig. 12a) and the alkenone-based pCO₂ trend of the Site 999A (Fig. 12b); differently, the δ¹⁸O orbital components are unrelated to the same pCO₂ long-term trends. Similar relationships are shown by the δ¹⁸O trend components and the alkenone-based SST trends of the Site 846 (Fig. 12c) and Site 999A (Fig. 12d). The tropical SST trend components of the Site 846 are linearly related to the boron-based atmospheric pCO₂ trend of the Sites 668B-999A (Fig. 12e) and the alkenone-based pCO₂ trend of the Site 999A (Fig. 12f); again, the SST orbital components are unrelated to the same pCO₂ long-term trends.

Fig. 12

Plio-Pleistocene cross plots between selected pCO₂ proxies and the δ¹⁸O (a, b) and SST (e, f) SSA-components. Plio-Pleistocene cross plots between selected SST proxies and the δ¹⁸O (c, d) SSA-components. A clear linear interpolation is shown between long-term trend components, whereas orbital components-2-11 are unrelated to the long-term trends. Proxy data: composite atmospheric boron-based pCO₂ proxy from ODP Sites 668B-999A (Hönisch et al. 2009; Bartoli et al. 2011), atmospheric alkenone-based pCO₂ and SST proxies from ODP Site 999A (Seki et al. 2010), alkenone-based SST proxy from ODP Site 846 (Herbert et al. 2010b), and LR04 δ¹⁸O stack (Lisiecki and Raymo 2005b)

However, in the plots with more data points, the amplitude increase of the orbital components is clearly visible as pCO₂ and SST decrease, corroborating the analysis of Figs. 10 and 11. These results show that the climate sensitivity to orbital forcing is lower when CO₂ and SST are higher (Early Pliocene) and that it increases non-linearly when CO₂ and SST are low (Mid-Late Pleistocene), in agreement to Martinez-Boti et al. (2015), a feature linked to the LT-MCS as shown in the present study. Despite that Site 846 is considered not “typical” tropical SST record, Fig. 13a shows a very close link between its trend component and that of the global ΔSST stack (Martinez-Boti et al. 2015) identified by SSA and driving 76.2% of the variance (ΔSST comp-1), noteworthy the same magnitude of the Site 846 SST and global δ¹⁸O trend components (76.6% and 76.4%, respectively). The inclusion of the Site 846 among the ten of the ΔSST stack should not significantly affect the global character of the signal. Moreover, Lisiecki (2010b) calculates 0.28 °C/Myr the upwelling cooling effect at Site 846 which roughly matches a 30% fraction of the total 1.0 °C/Myr trend (Herbert et al. 2010a), resulting about 70% of the Site 846 cooling trend to be due to non-regional effects, according to the results of the SSA.

Fig. 13

Late Pliocene-Pleistocene cross plot between trend components of global ΔSST stack and tropical SST at Site 846 (a). Cross plots between the ΔSST stack and b δ¹⁸O, c boron-based, and d alkenone-based pCO₂ SSA-components. Cross plots between the converted ΔSST stack (°C by means of the function in a) and e boron-based pCO₂ and f alkenone-based pCO₂ trends. The long-term trend components are clearly linked, whereas orbital components are unrelated to the long-term trends. Proxy data: composite atmospheric boron-based pCO₂ proxy from ODP Sites 668B-999A (Hönisch et al. 2009; Bartoli et al. 2011), atmospheric alkenone-based pCO₂ and SST proxies from ODP Site 999A (Seki et al. 2010), alkenone-based SST proxy from ODP Site 846 (Herbert et al. 2010b), LR04 δ¹⁸O stack (Lisiecki and Raymo 2005b), and global ΔSST stack (Martinez-Boti et al. 2015)

Figure 13 shows similar links of Fig. 12 among the global ΔSST long-term trend and the pCO₂ trends at Sites 668B and 999A (Fig. 13c) and 999A (Fig. 13d) and the global δ¹⁸O (Fig. 13b). Figure 13e, f exhibits the same relationships by converting the standardized ΔSST into SST (°C) using the function of Fig. 13a. The SST vs. boron-based CO₂ trend slopes correspond to a tropical rate of change of 25.6 μatm/°C (Fig. 12e), very close to the global converted ΔSST stack of 25.5 μatm/°C (Fig. 13e). At 25 °C and atmospheric pressure, these values are equivalent to a rate of change of 26.4 ppm/°C and 26.3 ppm/°C, respectively. Coherently, as shown in Fig. 14b, the two SST trends are subparallel in time, although the Site 846 is cool-shifted. Considering the alkenone-based CO₂ trend slopes, these rates of changes are of 42.6 ppm/°C (Fig. 12f) and 39.2 ppm/°C (Fig. 13f), respectively. Such variability in rate of changes (~ 26 ppm/°C vs. ~ 41 ppm/°C) could be due to differences in the CO₂ proxy estimation (boron-based vs. alkenone-based). These slope data offer an overall view of the Plio-Pleistocene long-term climate sensitivity, and the oscillations around the linear trend should indicate that it can change for discrete time intervals. On the other hand, the climate sensitivity to orbital forcing change by time in response to the initial conditions set by LT-MCS (Tachikawa et al. 2014; Martinez-Boti et al. 2015; Lo et al. 2017; this study).

Fig. 14

Comparison over time of the long-term trend components of δ¹⁸O and the a pCO₂ and b SST proxies. Composite atmospheric boron-based pCO₂ proxy from ODP Sites 668B-999A (Hönisch et al. 2009; Bartoli et al. 2011), atmospheric alkenone-based pCO₂ and SST proxies from ODP Site 999A (Seki et al. 2010), alkenone-based SST proxy from ODP Site 846 (Herbert et al. 2010b), EPICA pCO₂ record (Berger et al. 2016), δ¹³C-based pCO₂ proxy (Lisiecki 2010b), LR04 δ¹⁸O stack (Lisiecki and Raymo 2005b), boron-based pCO₂ proxy from ODP Site 999 and global ΔSST stack (Martinez-Boti et al. 2015). The horizontal lines are the Plio-Pleistocene average of pCO₂ alkenone (ODP Site 999A) and the standardized mean of the SST. All records are plotted on their own age scale

These results authorize to be considered of global in nature the non-Milankovitch trend links among pCO₂, SST, and δ¹⁸O. Considering that the main GHGs, such as carbon dioxide and methane, operate physically as the most effective positive (warming) climate forcings (Hansen et al. 2005; Hansen and Sato 2012; Van Der Meer et al. 2014), the hypothesis that the global long-term variation of atmospheric GHG concentration plays a relevant role in explaining the origin of the δ¹⁸O and SST trend components, driving ~ 76% of the Plio-Pleistocene signal variance, appears plausible.

Figure 14 shows the correlation over time between the δ¹⁸O enrichment trend components (LR04 comp-1 subcomp-1 and LR04 comp-1 exponential fit) and the CO₂ reduction trend of the ODP Sites 668B and 999A (Fig. 14a) and the SST cooling trends of the global ΔSST stack, ODP Sites 846 and 999A (Fig. 14b).

During the Zanclean, the pCO₂ alkenone ranged from 450 to 330 ppm, the highest values of the entire Plio-Pleistocene; the tropical SST was higher than the Plio-Pleistocene average; and the global δ¹⁸O was depleted more than the average (Fig. 14). Conversely, the mean orbital forcing was slightly negative (Fig. 9). These observations indicate Zanclean as a period of a higher than average positive climate state, supporting the hypothesis that the Zanclean warmer climate may have been driven by an important greenhouse effect due to higher atmospheric CO₂ (Bartoli et al. 2011). The lack of significant Northern Hemisphere ice growth and 100-kyr climate response prior to 3.3 Myr suggest that pCO₂ alkenone above 320–330 ppm is associated with warming sufficient to prevent significant Northern Hemisphere ice sheet growth even during cold orbital phases (Seki et al. 2010). The pCO₂ and SST show a significant reduction during the Zanclean (subtrend-I), supporting the hypothesis that the ONHG was triggered by the decreasing trend in atmospheric CO₂ (Pagani et al. 2010; Seki et al. 2010). Subtrend-II (Piacenzian) is also consistent with a reduction of pCO₂ alkenone and SST, suggesting an INHG triggered by a further decrease in atmospheric CO₂ according to Lunt et al. (2008), who stated that Greenland glaciation was primarily controlled by a decrease in atmospheric CO₂ during the Late Pliocene. Nevertheless, the Piacenzian remains a period of a δ¹⁸O-SST higher than average positive climate state, with slightly negative or neutral mean orbital forcing (Fig. 9). For this reason, the Piacenzian, excluding the ONHG event, is still characterized by an average warming fingerprint due to a residual greenhouse effect. According to this hypothesis, Lunt et al. (2012), using a modeling approach, showed that on a global scale, the largest contributor to mid-Piacenzian warmth (3.26–3.03 Myr) is high CO_2. Subtrend-III (Gelasian-Calabrian p.p.) does not appear to comply with the pCO₂ alkenone data, probably due to the low-resolution proxy in this range, while it is more consistent with the decreasing boron-based pCO₂ and the SST subtrends. For the first time during the Plio-Pleistocene, the long-term pCO₂and SST are below or close the mean and the δ¹⁸O is enriched more than the average (Figs. 14 and 9). The mean orbital forcing is neutral or slightly positive. The net result of these two unbalanced forcings may be a significant cooling effect and the start of an average “icehouse” world. Subtrend-IV (Calabrian-Middle Pleistocene p.p.) is consistent with a further reduction of pCO₂, reaching peak concentrations of 240–250 ppm (MIS-16), and with the continuation of the SST cooling trend. The long-term pCO₂, SST, and δ¹⁸O are consolidated below the mean, while the mean orbital forcing appears slightly positive, resulting in a lower than average negative climate state, strengthening the icehouse effect. No CO₂ variation corresponds to the MPT, although it falls at the beginning of subtrend-IV after a long time interval of surface/deep-water cooling and ice volume growth. Finally, the MBO (Mid-Late Pleistocene) marks a mild recovery of the long-term pCO₂ clearly visible in the EPICA trend comp-1 subcomp-3 and less distinctly in the CO₂ proxy records (see Additional file 1) (Lisiecki 2010b; Seki et al. 2010) and in the SST proxies (Fig. 14). The strong isotopic enrichment related to MIS-16 at the end of the subtrend-IV correlates well with the absolute CO₂ minimum in the EPICA comp-1 subcomp-3 at ~ 0.65 Myr. Considering that the δ¹⁸O response lags CO₂ (Shackleton 2000; this study), the correlation between the CO₂ maximum in the EPICA comp-1 subcomp-3 at ~ 0.4 Myr and the related but slightly delayed isotopic depletion in the δ¹⁸O comp-1 subcomp-1 is noteworthy (MBO). This observation supports the hypothesis that MIS-11, one of the most intense and prolonged interglacial oscillations of the Middle-Late Pleistocene, which is not proportional to eccentricity (Imbrie et al. 1993) or cool insolation-induced interglacials (Berger et al. 2012), may be an astronomical event boosted by GHG mid-term recovery, which reached the highest value at ~ 400 kyr (Luthi et al. 2008; Berger and Yin 2012; Berger et al. 2016). The origin of this GHG mid-term recovery could be partly due to the long-term orbital cycles that reach a maximum relative (warming) at ~ 300–200 kyr (Figs. 2 and 6); the 400-kyr eccentricity cycle really reaches a maximum at about 200 kyr (Laskar et al. 2011). However, the timing of these astronomical events does not seem consistent with the CO₂ maximum of EPICA at ~ 400 kyr. In addition, we cannot exclude a contribution of the circum-Pacific explosive activity (Jicha et al. 2009). The Late Pleistocene was a period of quiescence of the circum-Pacific explosive activity, which perhaps contributed to the mid-term CO₂ increment by a reduction in volcanic aerosols and the consequent minor algal ash-fertilization of the Pacific Ocean waters (Jicha et al. 2009).

Lagged patterns of δ¹⁸O and SST orbital components

The phase relationships between the standardized La93 orbital forcings and the orbitally driven LR04-SST components are shown in Table 8 for three time intervals. The results indicate that the δ¹⁸O and SST orbital components are all delayed on average compared to the related forcing of eccentricity, obliquity, and precession (with the small significant exception of the eccentricity in the pre-ONHG time due to very low SST signal coherency), although the patterns of coherency and phase lag are quite different across the time intervals.

Table 8 Cross-spectral analysis results among the orbital forcings (Laskar et al. 1993) and the orbitally driven δ¹⁸O and SST components for three time intervals. Data standardized (mean = 0, standard deviation = 1) and, where necessary, inverted to have the same paleoclimatic polarity (positive values for positive forcing and warming)

These cross-spectral results are in general agreement with Imbrie et al. (1993), Shackleton (2000), Lisiecki and Raymo (2005a), and Tziperman et al. (2006) and indicate that the climate system takes a certain amount of time to transfer the effect of orbital forcing to the global ice volume/deep water temperature and to the sea surface temperature. The coherency is generally lower in the tropical SST signal probably due to differences in the forcings controlled by high-latitude and low-latitude signals. The lagging of the δ¹⁸O signal is usually larger than that of the SST (Table 8) because the ice volume component lags the deep water temperature signal in the δ¹⁸O record (Lisiecki and Raymo 2005a; Herbert et al. 2010a). The coherency of the eccentricity signal increases from pre-ONHG time (incoherent) towards the Mid-Late Pleistocene, reflecting the progressive increase of eccentricity power both in global δ¹⁸O and local tropical SST signals. The delta-lag in eccentricity between δ¹⁸O and SST reaches its maximum during the Late Pleistocene (4.31–0.44 kyr), suggesting an increased contribution of the δ¹⁸O ice volume component over the water temperature signal. The δ¹⁸O and SST obliquity signals have the largest coherency and exhibit an average increasing trend in the lags towards the Mid-Late Pleistocene, starting from 4.10–3.46 kyr to 5.78–5.28 kyr and, finally, reaching values of 7.42–2.71 kyr (Table 8), in general agreement with Lisiecki and Raymo (2005a). The δ¹⁸O-SST delta-lag in obliquity is relatively small until the beginning of the MPT and becomes large after this transition, probably following global ice volume growth. The cross-spectral results relative to precession are more variable. The precession lag is basically constant (5.76–5.73 kyr) during pre-ONHG time, then it becomes quite “unstable” (3.57–7.85 kyr) between ONHG and MPT and reaches lags of 4.93–3.52 kyr post-MPT. The minimum δ¹⁸O phase lag relative to precession (3.57 kyr) during the ONHG-MPT time interval suggests the influence of a large global deep water temperature signal (Lisiecki and Raymo 2005a). During the same time interval, the precession’s SST lag reached its maximum (7.85 kyr) which could be due to the effect of a deep water upwelling in the EEP (ODP Site 846). Table 9 exhibits, for the last 5 Myr, the cross-spectral analysis results between SST and LR04 orbital components, showing a slight δ¹⁸O lagged response vs. SST, in agreement with Herbert et al. (2010a). The slightly earlier response of the δ¹⁸O eccentricity component (0.05 kyr) is due to the pre-ONHG weak and unstable eccentricity signal. After the ONHG, the eccentricity response is strengthened and becomes more stable resulting in a slight δ¹⁸O lag.

Table 9 Cross-spectral analysis results between orbitally driven δ¹⁸O and SST components for the last 5 Myr. Data standardized (mean = 0, standard deviation = 1) and, where necessary, inverted to have the same paleoclimatic polarity (positive values for positive forcing and warming)

Discussion

Origin of the δ¹⁸O and SST trend components

The LR04 trend component is related to the Plio-Pleistocene interval of the Cenozoic δ¹⁸O enrichment trend starting at the end of the Early Eocene Climatic Optimum (EECO, 53–51 Myr), documenting the progressive development of the Antarctic and Boreal ice sheets (Zachos et al. 2001). The gradual climate cooling during the Cenozoic is generally correlated to a CO₂ concentration decrease in the atmosphere (Raymo and Ruddiman 1992; Zachos et al. 2001; Royer 2006; Zachos et al. 2008; Van de Wal et al. 2011; Zhang et al. 2013; Van Der Meer et al. 2014). Recent studies on Pliocene and Pleistocene alkenone δ¹³C and boron-based pCO₂ proxies support this hypothesis (Seki et al. 2010; Pagani et al. 2010; Bartoli et al. 2011). Stap et al. (2014) find that the atmospheric temperature during the past 800 kyr has been controlled by a complex interaction of CO₂ and insolation, and both variables serve as thresholds for the NHG. Using CO₂ proxies and geochemical carbon cycle models, Royer (2006) shows that atmospheric CO₂ exhibits a pervasive and tight positive correlation with globally averaged surface temperatures, indicating that CO₂ played a strong role in driving the global climate for much of the Phanerozoic. The Cenozoic climatic record provides an important case study to understand the relationships between carbon cycling and climate (Zachos et al. 2001, 2008). In fact, much of the early Cenozoic was characterized by noticeably higher concentrations of GHGs and a much warmer mean global temperature. The most extreme event being between 53 and 51 Myr (EECO), when CO₂ concentration was on the order of 1000–1500 ppm, and the global temperatures reached a long-term Cenozoic maximum (Zachos et al. 2001, 2008; Beerling and Royer 2011). Zhang et al. (2013) estimate the new pCO₂ data for the Middle Miocene to be notably higher than published records with average pCO₂ concentrations in the range of 400–500 ppm, suggesting that CO₂ levels were highest during a period of global warmth associated with the Middle Miocene Climatic Optimum (MMCO, 17–14 Myr). Instead, during the mid-Pleistocene ice ages, CO₂ fell to 170–190 ppm, and the global temperature reached a long-term Cenozoic minimum (Beerling and Royer 2011; Berger et al. 2016). Considering a CO₂ variation from approximately 1000 ppm in the early Cenozoic to 170 ppm in the icy Pleistocene, the resulting negative climate forcing computed by Hansen and Sato (2012) for this CO₂ range exceeded 10 W/m², which is consistent with the observed strong Cenozoic cooling. These studies confirm the link among global temperature, the cryosphere, and atmospheric CO₂. The present study suggests a link between the atmospheric pCO₂ long-term variations and the SST-δ¹⁸O trend components and highlights the primary role of the long-term change of the atmospheric GHG concentration in explaining the origin of the high-variance, highly significant δ¹⁸O and SST trend components.

Factors controlling long-term atmospheric composition

Although it is generally accepted that the progressive Cenozoic cooling of the global climate resulted from a long-term decrease in atmospheric CO₂, details on how carbon cycle affects CO₂ and a clearer distinction of the involved time scales have not been fully resolved. Because of the relatively small size of the atmospheric reservoir, minimal imbalances between CO₂ sources and sinks cause rapid fluctuations in atmospheric CO₂ levels and global mean temperatures (Brady and Gislason 1997; Kent and Muttoni 2013). The results of the present study suggest ~ 76% of the Plio-Pleistocene climate variance could be driven by non-orbital carbon cycle. On time scales longer than one million years, atmospheric CO₂ levels are primarily controlled by the balance between the rate of volcanic and metamorphic sources from the Earth’s interior and the rate of sink through the chemical weathering of silicate minerals and through the burial of organic carbon (Walker and Hays 1981; Berner et al. 1983; Raymo and Ruddiman 1992; Brady and Gislason 1997; Schrag et al. 2002; Hansen and Sato 2012). Plate tectonics may affect the primary inputs of atmospheric CO₂ through mantle outgassing at seafloor spreading ridges, volcanoes, and the metamorphism of carbonate rocks along subduction zones (Van Der Meer et al. 2014). Long-term sinks for CO₂ are controlled by the burial of organic matter and by the weathering of silicate rocks to form carbonates (Raymo and Ruddiman 1992; Berner and Kothavala 2001; Schrag et al. 2002; Van Der Meer et al. 2014). The weathering of silicate rocks is a chemical process whereby CO₂ consumption is buffered by the temperature dependence on the weathering rate, preventing the so-called “ice catastrophe” when temperatures fall (Walker and Hays 1981). As the atmospheric CO₂ concentration rises, the temperature and precipitation increase. They thereby enhance chemical weathering and atmospheric CO₂ depletion, preventing “greenhouse” disasters on geological timescales. Chemical weathering is also affected by changes in continental land area and paleoaltitude distribution (Berner et al. 1983; Schrag et al. 2002). The alteration of surficial marine basalts at low temperatures (< 40 °C) is another potentially important sink for atmospheric CO₂ over geologic time (Brady and Gislason 1997). The numerical modeling of the carbon cycle by Berner et al. (1983) suggests that changes in volcanic outgassing over the last 100 million years were the primary cause of the transition between the greenhouse climates of the Cretaceous and the ice ages of the Plio-Pleistocene. Their results indicate that the CO₂ content in the atmosphere is highly sensitive to changes in the seafloor spreading rate and continental land area. A tropical concentration of continental area may lead to a more efficient burial of organic carbon through increased tropical river discharge and the chemical weathering of silicate rocks (Schrag et al. 2002). By affecting CO₂ volcanic degassing, metamorphic-magmatic decarbonation and changes in the continental land area available for chemical weathering, plate tectonics is considered the main long-term controlling factor of the global climate (Berner et al. 1983; Van Der Meer et al. 2014). However, it is a matter of debate as to which main mechanism can adjust the balance between the CO₂ source through geotectonic volcanic degassing and the CO₂ sink by the chemical weathering of silicate rocks. Some studies show conflicting results regarding the role of the seafloor spreading rate, which is believed to be the major control of CO₂ degassing (Berner et al. 1983; Raymo and Ruddiman 1992). In fact, according to Rowley (2002), the seafloor spreading rate remained relatively constant over the past 180 Myr, while Cogné and Humler (2006) indicate a general increasing trend in the last 50 Myr. These results are discordant with the observed cooling trend of the Cenozoic climate. Recently, a study of carbon-cycle evolution indicated that increasing physical erosion in response to widespread mountain building is the most prominent driver of carbon cycling over the past 100 Myr (Li and Elderfield 2013). Raymo and Ruddiman (1992) proposed that the uplift of the Tibetan plateau was an important driving force behind the Cenozoic long-term cooling by atmospheric CO₂ consumption due to the increase of the chemical weathering of silicate rocks. However, the Cenozoic long-term shift in Earth’s climatic state could be really related to regional transient differences in volcanic emissions by plate tectonic activity, which were particularly high during, e.g., the Late Paleocene and Early Eocene epochs (North Atlantic rifting and India-Asian northward migration) (Raymo and Ruddiman 1992; Zachos et al. 2001; Mosar et al. 2002; Zachos et al. 2008; Le Breton et al. 2012). From this viewpoint, a recent study on the Himalayan-Tibetan orogenic system shows a multiple collision model in which a continent-continent collision began around the Eocene/Oligocene boundary (34 Myr) (Aitchison et al. 2007), promoting the Early Oligocene glaciation (Zachos et al. 2001). Corroborating this hypothesis, the North Atlantic seafloor spreading rate (NASSR) exhibits a clear decreasing trend from high values in the Early Eocene (55–50 Myr) to a very low rate for most of the Oligocene (Mosar et al. 2002; Le Breton et al. 2012). On the other hand, recent studies seem to converge towards a significant 250–200-Myr period variation of the seafloor spreading rate (Becker et al. 2009; Coltice et al. 2013). Becker et al. (2009) proposed a spreading rate long-term slowdown since 140 Myr with minor cycles superimposed over time, such as a relative increase at ~ 50 Myr and a minimum at ~ 32 Myr. Even the timing of the global average spreading rate (GASR) calculated by Conrad and Lithgow-Bertelloni (2007) appears to support the hypothesis of a direct geotectonic “forcing” to the long-term composition of atmospheric GHGs. On a more detailed timescale, a study in the North Atlantic shows the consistency of the NASSR relative maximum at ~ 15 Myr and the MMCO (Merkouriev and DeMets 2014). The correlation of the NASSR minimum at approximately 1.2–1.0 Myr (the lowest value in the last 20 Myr) and the CO₂ proxy minimum at 0.9–0.7 Myr (Fig. 14a), which correlate to the strong LT-LR04 cooling at the end of subtrend-IV, seems plausible. Indeed, the contribution of the important negative forcing created by aerosols (Hansen et al. 2005) emitted into the atmosphere during phases of explosive volcanic paroxysm in the circum-Pacific (Jicha et al. 2009) must also be taken in account. In fact, hundreds of explosive eruptions occurred during an extremely vigorous period of circum-Pacific volcanism beginning in the Late Eocene, which likely led to the production of sulfur aerosols in the stratosphere and net cooling. The feedback mechanism related to the enormous supply of ash that fertilized the Pacific Ocean waters might have caused algal growth and CO₂ uptake and thereby contributed to Oligocene glaciation at approximately 34 Myr (Jicha et al. 2009). It is interesting to observe how the Plio-Pleistocene in the circum-Pacific was a period of intense explosive volcanic activity characterized by three activity peaks at approximately 4.8, 2.8, and 1.5 Myr (Jicha et al. 2009). We cannot exclude that these events contributed in part to the three most pronounced segments of δ¹⁸O enrichment highlighted in the LT-LR04 record (subtrend-I, subtrend-II, and subtrend-IV), culminating in the ONHG, INHG, and MIS-16 events, respectively. Moreover, the Late Pleistocene was a period of quiescence of the circum-Pacific explosive activity, which may have contributed to the mid-term CO₂ increment and δ¹⁸O impoverishment that occurred at approximately 400–300 kyr, a possible cause of the MBO. A further contribution to the global emission of CH₄ and CO₂ may also come from the thermogenic cracking of organic carbon-rich sediments in large igneous provinces (LIPs), which are associated with geotectonic spreading areas or subduction zones (Svensen et al. 2004). Finally, another climate-controlling factor is oceanic paleocirculation. The “Panama Hypothesis” states that the gradual closure of the Panama seaway, between 13 and 2.6 Myr led to a decreased mixing of the Atlantic and Pacific water masses and a strengthening of the Atlantic thermohaline circulation, increased temperatures and precipitation in Northern Hemisphere high latitudes, and culminated with the INHG during the Pliocene, at approximately 3.2–2.7 Myr (Bartoli et al. 2005; Lunt et al. 2008). However, Lunt et al. (2008), using a more sophisticated general circulation model (GCM), demonstrated that the ice volume difference between the “closed” and “open” seaway model configurations is small and concluded that it was not a major forcing mechanism. This view accommodates δ¹⁸O and SST components-8-11 of inter-tropical semi-precessional origin related to the oceanic heat transport towards high latitudes (Hagelberg et al. 1994; Berger et al. 2006), which contributes very little to the total variance of the paleoclimatic response (~ 0.6–0.5%). In summary, the geotectonic forcing appears a plausible hypothesis to explain the long-term changes in atmosphere composition (GHGs and volcanic aerosols) through direct (CO₂ outgassing and explosive volcanism) and indirect (orography and erosion, paleogeographic configuration, oceanic paleocirculation, and ocean fertilization) control by plate tectonics.

Nonlinear response and mean climate state

An interesting result of the present study shows that the nonlinear increase in signal amplitude from the Early Pliocene to the Late Pleistocene is observed in all δ¹⁸O and SST astronomical components and is exponentially linked to the LT-MCS (Figs. 10 and 11). These results reinforce the notion that the climate sensitivity of orbital forcings may be dependent on the mean climate state in agreement with Lisiecki and Raymo (2007) and Hansen et al. (2013), with possible threshold effects typical of nonlinear systems (Rial et al. 2004). Because the Plio-Pleistocene orbital forcings do not exhibit a similar increase in amplitude, it is believed that the process controlling the nonlinear behavior of the signal response originates inside the climate system. The net balance of positive and negative feedback mechanisms is the most likely process behind most of the nonlinearities in the climate (Berger and Loutre 1997; Archer et al. 2004; Rial et al. 2004; Lisiecki and Raymo 2007; Brovkin et al. 2007; Hansen et al. 2007; Hansen et al. 2011; Martinez-Boti et al. 2015).

The most important positive feedback mechanisms that are able to amplify the climate response to primary forcing are the CO₂ exchange between the ocean and the atmosphere, the water vapor feedback, the methane release from permafrost peat bogs and from hydrates, all mechanisms related to greenhouse gases, and the surface albedo feedback. Hansen et al. (2007) revealed a remarkable correspondence between the Vostok Antarctic temperature and GHG climate forcing, confirming that the temperature causes gas changes over several hundred years and suggesting that increasing warming temperature causes a net release of GHGs from oceans, soils, and the biosphere. In the EPICA ice cores, atmospheric greenhouse gases have strongly covaried with Antarctic temperature and δ¹⁸O benthic throughout eight glacial cycles over the last 800 thousand years (Jouzel et al. 2007; Luthi et al. 2008; Loulergue et al. 2008; Berger et al. 2016). Even Schneider et al. (2013) at EPICA Dome C, during the glacial inception at the end of MIS-5e, confirm a 5-kyr lag in the CO₂ decline with respect to temperatures. They explain this lag by terrestrial carbon release and carbonate compensation. Brovkin et al. (2007), by simulating the effects of changes in atmospheric and oceanic circulations in response to glacial changes in radiative forcing, find that the net effect of five feedback mechanisms related to oceanic circulation and marine biogeochemistry is able to explain a 65 ppmv drop in glacial atmospheric CO₂, compared to 80–90 ppmv recorded in the ice cores (approximately 70–80% of the total drop). Cooler oceanic water can absorb more CO₂ than warmer water. As the ocean warms, it releases CO₂ to the atmosphere, providing an amplifying climate feedback that causes further warming. If the atmosphere is warmed, the saturation vapor pressure increases, and the amount of water vapor in the atmosphere will tend to increase, leading to further warming, because water vapor is an important greenhouse gas. Liptak and Strong (2016), in a modeling study of the Arctic Sea, confirm the existence of a positive thermodynamically driven sea ice-atmosphere feedback up to 35%. A recent study shows that permafrost is a very large carbon pool stored as peat and methane in circumpolar areas (Tarnocai et al. 2009). Lawrence et al. (2008) suggest that a rapid melting of Arctic Sea ice may start a feedback loop that rapidly melts Arctic permafrost, triggering further warming feedback by the release of methane and carbon dioxide. Methane hydrates are a form of water ice saturated by a large amount of methane within its crystal structure. Extremely large deposits of methane hydrates have been found within marine sediments along continental margins of the Earth (Dickens 2003). The release of this trapped methane has the potential to cause a significant increase in temperature as a feedback mechanism triggered by bottom water warming. This hypothesis has been proposed as a possible explanation of early Cenozoic hyperthermals, such as the Paleocene-Eocene Thermal Maximum (PETM) at approximately 55 Myr, a transient warming that shows characteristics of an extreme event of short-term positive feedback (Dickens 2003; Zachos et al. 2008). If the planet becomes warmer, the ice sheet area tends to decrease, exposing a darker surface of land and open water that absorbs more sunlight, causing additional heating. Instead, during times of global cooling, additional ice increases the reflectivity, which reduces the absorption of solar radiation and results in more cooling (albedo effect). According to Hansen et al. (2013) and Hansen (2013), the net effect of fast positive feedback is to amplify the global temperature response by a factor of two to three, and this reinforcement is state dependent. Even Menviel et al. (2008) state that the atmospheric CO₂ response is a delicately balanced sum of the terrestrial and marine inventory changes, emphasizing the importance of the initial climate state on the CO₂ response to large-scale ocean circulation changes. However, exponential growth cannot continue indefinitely because some negative feedback processes act as balancing mechanisms. The new findings of Early Pliocene asymptotic decays of R_s (Fig. 11) could represent the evidence of a damping effect of carbon cycle by negative feedback processes. The continental weathering is a chemical process of atmospheric CO₂ consumption that requires tens of thousands of years to act (Walker and Hays 1981; Schrag et al. 2002; Hansen 2013). Instead, the iceberg cooling effect is a fast negative feedback that comes into play as iceberg discharge reaches a rate that cools the regional ocean surface (Hansen and Sato 2012). The interaction between vegetation and climate is another interesting component in climate system dynamics, but the question of the overall role of the biogeophysical and biogeochemical feedbacks is not yet solved because both feedbacks can be positive or negative (Claussen 2009). Nevertheless, shifts in vegetation patterns have presumably provided a negative feedback in the climate system due to their influence on carbon cycle and great areal changes. During glacial inception, forests were reduced in their areal extent leading to an increase in atmospheric CO₂ concentration, while during deglaciation, atmospheric CO₂ concentration should have decreased due to the buildup of forests (Claussen 2009). Palynological studies attest to major changes in vegetation ecosystems both at glacial and interglacial time scales (Ning et al. 1993; Elenga et al. 2000; Bertini 2010). During a glacial climate, tropical rainforests reduce in their extent to tropical seasonal forests in tropical lowlands and to xerophytic taxa in tropical highlands (Elenga et al. 2000). Boreal forests regress equatorward with a compression and fragmentation of the forest zones, while cold steppe vegetation expands (Ning et al. 1993; Bertini 2010). However, after the Zanclean and towards the Late Pleistocene, a progressive impoverishment of the subtropical forest ecosystem occurs with an increase in herbaceous taxa following the long-term cooling and drying climate trend (Ning et al. 1993; Bertini 2010). Another negative feedback mechanism is the increase in precipitation rate in a greenhouse climate that may intensify weathering rates as fresh water is flushed more rapidly through soil and sedimentary rocks (Schrag et al. 2002). Removal of CO₂ is accomplished through burial of organic carbon, and increasing river discharge may lead to a more efficient burial of organic carbon (Schrag et al. 2002). The oceanic carbon pump by primary productivity can act as possible damping mechanism, but the complex feedback between climate and ocean require a better understanding. In fact, on orbital time scale, export production by barite accumulation rates was generally higher during cold periods (Ma et al. 2015). This interpretation could imply a positive feedback on carbon cycle that reinforces the cooler orbital response, but it is difficult to predict the net changes in CO₂ efflux (Ma et al. 2015). On the other hand, based on the long-term trends, export production was on average higher during the warmer Late Pliocene than the colder Pleistocene (Ma et al. 2015). On the contrary, the depositional conditions of the Plio-Pleistocene Mediterranean sapropels exhibit warm and wet precession-related changes of phytoplankton productivity by river runoff increasing and bottom water anoxia (Emeis 1998; Gallego-Torres et al. 2007; Moller et al. 2012), suggesting a negative feedback on carbon cycle (Schrag et al. 2002) and a possible damping effect on warming climate response.

On a geological time scale, almost all these mechanisms are sufficiently “fast” (less than 100 kyr) and can act over an orbital short-term hemicycle like precession or “semi-precession.” Being geologically fast processes, the feedback response should have in theory a similar frequency modulation as the primary astronomical forcing, although the processes should exhibit a slight delay compared to the latter and to the initial temperature change induced by insolation components (Berger and Loutre 1997; Ruggieri et al. 2009; Hansen et al. 2011). The δ¹⁸O and SST lags shown in the present study support this hypothesis. Moreover, the amplitude of the feedback response should be linked to the orbital hemicycle duration and to the scale effect of the surfaces/volumes involved in the processes (Schrag et al. 2002; Menviel et al. 2008; Hansen et al. 2013), a possible explanation of the nonlinear features shown in Figs. 10 and 11. Therefore, the net cumulative effect of positive and negative fast feedback mechanisms, added to the initial temperature change, could lead to the exponential response of each astronomically driven response as a function of the LT-MCS at a given time (initial condition), the duration of the orbitally paced feedback processes, and the synergy of scale-dependent processes. The different growth rates of the nonlinear orbital responses (Fig. 10) and the asymmetry in R_s (Fig. 11) suggest a high-efficiency paced system depending on whether feedbacks amplify (R_s > 0) or suppress (R_s < 0) response changes in the orbital forcings with a state-dependent magnitude related to the duration time of the feedback processes. Interestingly, the results of the present study indicate an amplified orbital response during times of a global icehouse state (Mid-Late Pleistocene, with the remarkable exception of obliquity), which can reach a magnitude of three to five times global δ¹⁸O or two to three times tropical SST forcing, and a maximum of two times the damped response for all signals during the time of a global greenhouse state (Early Pliocene). In this study, it is proposed that orbital response be considered basically as composite feedback responses paced by orbital and damped or amplified in a range of − 100 to + 400% the forcing, as function of the LT-MCS at a given time (initial conditions), the hemicycle duration, and the synergy of the feedback processes. Therefore, the sensitivity of the climate system to orbital forcings could depend on the long-term climate factors in terms of average atmospheric GHG composition, the average concentration of volcanic aerosols, the global mean temperature, the cryosphere average volume, and, presumably, the global forest cover and ocean primary productivity, factors affecting high-efficiency feedback mechanisms related to carbon cycle and ice-albedo. This interpretation may explain the energy excess “paradox” of the astronomically paced signals compared to the small energy of the orbital forcing, especially concerning the eccentricity bands (Imbrie et al. 1993; Wunsch 2004; Berger et al. 2005; Berger et al. 2012). The progressive increase in the strength of the 95-kyr δ¹⁸O response from the Zanclean (very weak) to the Mid-Late Pleistocene may be interpreted as the effect of increased sensitivity to eccentricity due to the growing trend of the global ice volume following the cooling trend. In this time interval, the LT-LR04 component undergoes an average enrichment from 2.99‰ (Zanclean) to 4.18‰ (Middle Pleistocene-Holocene) due to long-term changes in atmosphere composition, and the climate system may become sensitive to the weak eccentricity insolation by overcoming the critical condition of global mean temperature and average ice volume, a hypothesis already formulated by Raymo (1998) and many others (Berger et al. 1999; Raymo et al. 2006; Berger and Yin 2012). The models of Imbrie et al. (2011) and Abe-Ouchi et al. (2013) also support this hypothesis. Their studies show that ice volume plays a very important role in pacing the orbital response of the climate system. Considering orbital signals basically as feedback responses paced by orbitals may explain why the ~ 100-kyr eccentricity-driven response is so strong post-MPT, when the obliquity “ice killing,” which prevents a long-life ice sheet, was strongly mitigated by damping effect (Fig. 11). Also, the hysteresis loop of the North American ice sheet may have contributed to lead a long-life ice sheet. After the inception of the ice sheet, its mass balance remains mostly positive through several precession cycles, whose amplitudes decrease towards an eccentricity minimum (Abe-Ouchi et al. 2013). The larger the ice sheet grows and extends towards lower latitudes, the smaller is the insolation required to make the mass balance negative. A long-life ice sheet sensitive to eccentricity during a time of a global icy state may have activated a synergistic response of positive feedback processes modulated on ~ 100-kyr eccentricity response times. The negligible response of δ¹⁸O in the eccentricity band during the Zanclean could be due to the higher mean temperature and the lower mean global ice volume, which would fail to move permanently to the climate signal due to obliquity “ice killing,” a powerful forcing during this period. Considering the asymptotic decay of the δ¹⁸O and SST R_s up to a maximum of − 100% towards the Early Pliocene (Fig. 11), a working hypothesis could be a damping effect due to the action of negative feedbacks during the time of higher global average temperature, such as, for instance, a higher global forest coverage, a greatest ocean primary productivity, and a more efficient burial of organic carbon. Zanclean was a period of global greenhouse state, characterized by high atmospheric GHGs and mean global temperature (Bertini 2010; Seki et al. 2010; Bartoli et al. 2011). During Zanclean, northern and central Italy were covered by vegetation dominated by hygrophilous and thermophilous forest taxa typical of a humid subtropical to warm-temperate climate. Precipitation was sufficiently high for the persistence of a “broad-leaved evergreen/warm temperate mixed forest” up to 3.5 Myr (Bertini 2010). Therefore, a wide forest cover, along with a possible high ocean primary productivity and organic carbon burial, could increase the quantitative role of the CO₂-related negative feedbacks (Emeis 1998; Schrag et al. 2002; Gallego-Torres et al. 2007; Claussen 2009; Moller et al. 2012; Ma et al. 2015) causing a damping effect of the orbitally paced responses. In the Mid-Late Pleistocene, an icy state leads to a significant reduction in global forest cover, making these processes quantitatively less important but emphasizing the vegetation-snow albedo feedback in synergy with the sea-ice albedo feedback which tends to amplify Northern Hemisphere and global mean temperature changes (Claussen 2009).

Mid-Late Pleistocene obliquity damped responses

To attempt the interpretation of these nonlinear features (Figs. 10 and 11), some possible mechanisms are discussed in this section as working hypotheses for future studies. The global δ¹⁸O and tropical SST sharply decline to near-zero in obliquity R_s during the Mid-Late Pleistocene suggesting an attenuation mechanism of the obliquity driving force and, consequently, a reduction of the feedback amplification processes linked to the mean icy state. Understanding this phenomenon is important because the post-MPT obliquity forcing attenuation could have contributed to the strengthening of the eccentricity response, favoring a long-life ice growth. Lisiecki and Raymo (2007) state that the change in δ¹⁸O glacial dynamics at ~ 1.4 Myr is associated with an abrupt decline in 41-kyr power and a decrease in modulation sensitivity to obliquity. Interestingly, the shape of the δ¹⁸O and SST components-3-4 after the MPT (Figs. 4c and 8c), characterized by the envelope of two to three low-amplitude obliquity cycles in a weak ~ 90–93-kyr framework, suggests a connection between eccentricity and obliquity, similar to that proposed by Huybers (2007) of obliquity-cycle skipping. The obliquity-pacing results indicate that the 100-kyr variability could result from the skipping of one or two obliquity beats, corresponding to 80-kyr or 120-kyr glacial cycles that, on average, give 100-kyr periodicity, resulting from long-term changes in the climate system, such as ice sheet growth (Huybers 2007). Why does obliquity-cycle skipping occur? Climate friction is a dissipative feedback between obliquity variations and climate which may cause a secular drift of the spin axis (Laskar et al. 2004). In response to obliquity forcing, glacial and interglacial conditions drive the redistribution of the ice/water mass and the isostatic adjustment to the surface loading, affecting the dynamical ellipticity of the Earth (obliquity–oblateness feedback) (Rubincam 1993, 1995; Levrard and Laskar 2003; Laskar et al. 2004). Delayed responses in both climatic and viscous relaxation processes may introduce a secular term in the obliquity evolution (Rubincam 1995). Because both the Earth’s ice load history and viscoelastic structure are not strongly constrained, it is difficult to produce accurate predictions of the coupled response of the entire system (Laskar et al. 2004). Therefore, simplifying assumptions have to be made to estimate the magnitude and the direction of the secular drift (increase or decrease in the obliquity). Specifically, the sign of the secular obliquity change is particularly sensitive to the obliquity-lag estimates and changes of oblateness (Williams et al. 1998; Levrard and Laskar 2003). Levrard and Laskar (2003) showed that climate friction impact is positive and likely negligible over the last 3 Myr, based on the model assumptions that the ice sheet response time-lag could not be longer than the obliquity period and explicitly assumed it to be 8 kyr. However, the secular change of obliquity becomes negative for low obliquity lag response (< 4.2 kyr) and high positive change of oblateness (Levrard and Laskar 2003). Response lags are difficult to estimate. According to Lisiecki and Raymo (2005a), the δ¹⁸O lag in obliquity reaches values of ~ 6.8 kyr in the Pleistocene. The results of the present study indicate a δ¹⁸O obliquity lag of 7.4 kyr post-MPT (Table 8), close to the value used by Levrard and Laskar (2003). In contrast, the obliquity lag estimation of Hilgen et al. (1993) provides a lower value of 5.6 kyr with respect to the Late Pleistocene if the phase relation with precession is kept constant. Considering the margin of error of these estimates, it is currently not possible to establish whether the obliquity lags may be lower post-MPT to justify the observed obliquity damping effect. Furthermore, other simplified assumptions in the dissipative equations model, together with age model bias, could affect the final results. A recent study by Adhikari and Ivins (2016) using space geodetic and satellite gravimetric present-day data has shown that global-scale continent-ocean mass transport changes (terrestrial water storage and global cryosphere) explain nearly the entire amplitude (83 ± 23%) and mean directional shift (within 5.9° ± 7.6°) of the observed polar motion on a very short present-day time scale. The study of Adhikari and Ivins (2016) suggests a high sensitivity of the poles to the mass transport changes and to the isostatic rebound. In conclusion, new studies are needed to clarify the effective role of climate friction or to identify other mechanisms that might be responsible for this unusual transition in obliquity response.

Tropical SST coupled with benthic δ¹⁸O cycles

Despite the differences in signal-to-noise ratio and oceanographic context between the LR04 δ¹⁸O and the ODP Site 846 SST records (global benthic stack and upwelling tropical single record), the SSA results show the tropical SST tightly coupled with benthic δ¹⁸O over the past five million years, both at long and orbital time scales, in agreement with the original work of Herbert et al. (2010a). Some differences certainly exist (e.g., a strong cooling event at ~ 2.1 kyr or MBO warming less marked in the SST signal; the tropical trend cooling slightly negative shifted compared to global ΔSST, nonetheless subparallel in time) (Fig. 14b), but they may be explained in terms of temporal and regional upwelling effects at the ODP Site 846. These similarities suggest common causes for both the δ¹⁸O long-term trend and cycles and their expression in the tropical SST. The most likely candidate for some orbitally paced cycles lies in high-latitude oceanographic processes tied to the global carbon cycle (Liu and Herbert 2004; Herbert et al. 2010a). These processes drive the oceanic circulation through changes in deep water properties, affecting vertical density stability and upwelling in the tropical oceans. Changes in the atmospheric GHG composition controlled by insolation processes in the high latitudes may also act to imprint obliquity on the tropical Pacific where the local direct effect of obliquity is weak (Liu and Herbert 2004; Medina-Elizalde and Lea 2005; Masson-Delmotte et al. 2006). The δ¹⁸O-SST delta-lag in obliquity became large after the beginning of the MPT, suggesting a signal of global ice volume growth (Table 8). Such observations, together with the high coherence between SST and δ¹⁸O obliquity responses (Table 9) may suggest remote connections from high latitudes towards the tropics. These interpretations could explain why the tropical SST obliquity component contains a small variance in comparison to that of δ¹⁸O (5.5% vs. 9.9%). The smaller coherency between tropical SST and δ¹⁸O precession components (Table 9) might indicate that the response in the EEP was caused by low-latitude precession forcing and regional effects and was less coupled to the high-latitude ice volume (Liu and Herbert 2004). Tachikawa et al. (2014) found residual SST variability characterized by a 23-kyr periodicity in the western Pacific warm pool (WPWP) region. They concluded a wind-driven northward surface current advection towards the WPWP to be responsible for the regional SST precessional periodicity, attributed to meridional shifts of the Intertropical Convergence Zone. Even the “half-precession” cycle of equatorial origin (Berger et al. 2006), isolated in this study by SSA from both tropical SST and global δ¹⁸O records, may be transmitted to high latitudes via advective transport (Hagelberg et al. 1994). The last interglacial half-precession cycle from the Northwestern Chinese Loess Plateau, interpreted as a direct response to low-latitude forcing through its modulation on the East Asian summer monsoon (Sun and Huang 2006), supports this interpretation. The coherency increase of the short eccentricity’s δ¹⁸O and SST signals and the maximum delta-lag in eccentricity between δ¹⁸O and SST (4.31 vs. 0.44 kyr) towards the Late Pleistocene (Table 8) may reflect the progressive rise of eccentricity power and an increased contribution of the high-latitude δ¹⁸O ice volume component over the water temperature signal. Berger et al. (2006) show the presence of significant 100-kyr and 11-kyr cycles in the amplitude of the seasonal cycle in the intertropical regions, but the amplitude decreases rapidly when moving away from the equator. The small differences in variance between the short eccentricity’s SST and δ¹⁸O components (5.1% vs. 6.5%) might depend on these considerations. Conversely, the big difference in variance of the closely enveloped long-term cycles (Earth’s orbit secular frequencies, obliquity modulation cycles, and long eccentricity cycles) between SST (10.3%) and δ¹⁸O (4.2%) components could suggest a greater sensitivity of the tropics to these long-term cycles. The tropical oceans should be shielded from feedback processes that produce large temperature sensitivity in the high latitudes, such as ice-albedo feedbacks, sea ice-atmosphere feedback, and permafrost feedback (Lawrence et al. 2008; Tarnocai et al. 2009; Herbert et al. 2010a; Liptak and Strong 2016). With the exception of obliquity, the marked difference in eccentricity and precession R_s in the Late Pleistocene between δ¹⁸O (200–400%) and SST (100–170%) (Fig. 11) may be due to a lower synergy of the positive feedback mechanisms in tropical regions. In summary, both remote connections from high-latitude and direct low-latitude orbital forcings could couple Plio-Pleistocene global δ¹⁸O and tropical SST orbital cycles through oceanic and atmospheric circulations. Finally, the remarkable constancy (~ 76%) of the Plio-Pleistocene trend variance among global δ¹⁸O, local tropical SST (Site 846), and global SST (ΔSST stack) might reflect the latitude-independent nature of the long-term factors controlling the atmosphere composition and global mean temperature.

Conclusions

The main conclusions of this study can be summarized as follows:

• 1) A detailed evaluation is provided of the variance paced by long-period orbital modulation, short eccentricity, obliquity, precession, and half-precession cycles, estimated for the δ¹⁸O at approximately 4.2%, 6.5%, 9.9%, 2.0%, and 0.6%, respectively, and for the tropical SST at about 10.3%, 5.1%, 5.5%, 1.6%, and 0.5%, respectively, both resulting in total orbital contributions of ~ 23.0%. On long time scales, the Plio-Pleistocene astronomical forcing could be considered a random walk at zero-sum in which the orbital responses oscillate around a basically time-invariant quasi-normal distributed mean, supporting the hypothesis that orbital forcings did not have a major role in guiding the Plio-Pleistocene climate system response.

• 2) The exponential growth of the orbital variance towards the Late Pleistocene is function of the LT-MCS at a given time and regards all δ¹⁸O and SST components with an increasing rate related to the orbital period, from half-precession to eccentricity. The asymmetry of the R_s suggests an amplified orbital response during times of a global icehouse state (Mid-Late Pleistocene, with the exception of obliquity), which can reach a magnitude of + 200 to + 400% global δ¹⁸O forcing, or + 100 to + 170% the tropical SST forcing, and a minimum up to − 100% the damped response for all signals during time of a global greenhouse state (Early Pliocene).

• 3) It is proposed that orbital responses be considered as composite feedback lagged responses paced by orbitals and damped or amplified in a range of − 100 to + 400% the forcing, depending on the initial conditions set by LT-MCS, the hemicycle duration, and the synergy of the feedback processes related to carbon cycles and albedo effects. This interpretation may explain the energy excess “paradox” of the astronomically paced signals compared to the small energy of the orbital forcing, especially concerning the eccentricity bands.

• 4) The asymptotic decay of the δ¹⁸O and SST R_s up to − 100% towards the Early Pliocene could be due to a damping effect of negative feedbacks during a time of higher mean global temperature. Zanclean was a period of global greenhouse state, and a wide forest cover along with a possible high ocean primary productivity and a more efficient burial of organic carbon could have increased the quantitative role of the CO₂-related negative feedbacks, causing a damping effect of the orbitally paced responses.

• 5) The global δ¹⁸O and tropical SST anomalous sharply decline to near-zero in obliquity R_s during the Late Pleistocene suggesting an attenuation mechanism of the obliquity driving force and a reduction of the related feedback amplification processes. The post-MPT obliquity damping may have contributed to the strengthening of the eccentricity response by mitigating the obliquity “ice killing,” favoring a 100-kyr long-life hysteresis ice growth volume. A long-life ice sheet sensitive to eccentricity during the time of a global icy state may have activated a synergistic response of positive feedback processes modulated on short eccentricity response times. In the Mid-Late Pleistocene, an icy state leads to a significant reduction in global forest cover making its negative feedbacks quantitatively less important but emphasizing the positive feedback processes, such as the vegetation-snow albedo in synergy with the sea-ice albedo and permafrost feedbacks. However, the origin of the post-MPT obliquity attenuation mechanism is an open question.

• 6) The tropical SST orbital cycles are tightly coupled with the global benthic δ¹⁸O cycles over the past five million years, suggesting both Plio-Pleistocene oceanic and atmospheric remote connections from high-latitude and direct low-latitude orbital forcings.

• 7) The tropical SST, the global SST, and the global δ¹⁸O trend components, each explaining ~ 76% of the Plio-Pleistocene climate variance, could be related to the long-term pCO₂ proxies, suggesting non-orbital latitude-independent control factors. These trend components significantly change the climate mean using arbitrary time intervals, suggesting the Plio-Pleistocene mean climate state was changed primarily by long-term carbon cycle controlling the Earth’s atmospheric composition. The geotectonic forcing appears to be a plausible hypothesis to explain the long-term changes in atmospheric composition (GHGs and volcanic aerosols) through direct (CO₂ outgassing and explosive volcanism) and indirect (orography and erosion, paleogeography, oceanic paleocirculation, and ocean fertilization) control by plate tectonics.

• 8) The NHG gradually developed in four phases (subtrends) of progressive lowering of the average temperatures and ice volume growth, triggered by long-term changes in the atmospheric composition. Nevertheless, transient interaction effects with very long-term orbital cycles, expression of the chaotic behavior of the solar system, may have contributed to setting these transitions. After MIS-16, the cooling trend was broken by a wide swing of δ¹⁸O depletion and SST recovery, a relative stasis of ice growth and temperature cooling during the last 600 kyr (MBO), which could be related to mid-term GHG recovery.

The idea of the geotectonic forcing is the most attractive hypothesis by a long time, and the recent improvements in the seafloor spreading rate evaluation lead in the right direction. However, further studies are needed to better estimate high-resolution seafloor spreading rate and to assess the role of the volcanic CO₂ degassing and the explosive volcanic aerosols in the budget of the carbon cycle. Even much higher resolution CO₂ proxies, covering a long time period, are necessary to better address carbon cycle. Nevertheless, the relevance of the primary long-term climate system, controlling the Earth’s atmospheric composition and modifying the average global climate, must be underlined. Finally, singular spectrum analysis provides a valuable tool in cyclostratigraphy with the remarkable advantage of separating full-resolution time series by variance strength.