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The history of the long-term variations in the astronomical elements used in paleoclimate research shows that, contrary to what might be thought, Milutin Milankovitch is not the father of the astronomical theory but he is definitely the father of paleoclimate modeling. He did not calculate these long-term variations himself but used them extensively for calculating the “secular march” of incoming solar radiation. He advanced our understanding of Quaternary climate variations by two important and original contributions fully described in his Canon of insolation. These are the definition and use of caloric seasons and the concept of the “mathematical climate”. How his mathematical model allowed him to give the caloric summer and winter insolation a climatological meaning is illustrated.

The relative role of external forcing and of intrinsic variability is a key question of climate variability in general and of our planet's paleoclimatic past in particular. Over the last 100 years since Milankovic's contributions, the importance of orbital forcing has been established for the period covering the last 2.6 Myr and the Quaternary glaciation cycles that took place during that time. A convincing case has also been made for the role of several internal mechanisms that are active on timescales both shorter and longer than the orbital ones. Such mechanisms clearly have a causal role in Dansgaard–Oeschger and Heinrich events, as well as in the mid-Pleistocene transition. We introduce herein a unified framework for the understanding of the orbital forcing's effects on the climate system's internal variability on timescales from thousands to millions of years. This framework relies on the fairly recent theory of non-autonomous and random dynamical systems, and it has so far been successfully applied in the climate sciences for problems like the El Niño–Southern Oscillation, the oceans' wind-driven circulation, and other problems on interannual to interdecadal timescales. Finally, we provide further examples of climate applications and present preliminary results of interest for the Quaternary glaciation cycles in general and the mid-Pleistocene transition in particular.

We use the benefits of the full-resolution methodology for time-series decomposition singular spectrum analysis to assess the quantitative impact of orbital and, for the first time, millennial-scale Sun-related climate responses from EPICA records. The quantitative impact of the three Sun-related cycles (unnamed ~9.7-kyr; proposed ‘Heinrich-Bond’ ~6.0-kyr; Hallstatt ~2.5-kyr), cumulatively explain ~4.0% (δD), 2.9% (CO2), and 6.6% (CH4) in variance, demonstrating for the first time the minor role of solar activity in the regional budget of Earth's climate forcing. A cycle of ~3.6 kyr, which is little known in literature, results in a mean variance of 0.6% only, does not seem to be Sun-related, although a gravitational origin cannot be ruled out. According to the recurrence analysis of Heinrich events (6.03 ± 1.4 kyr) and their correlation with EPICA stack ~6.0-kyr cycle, it is proposed that this band of solar activity be named the ‘Heinrich-Bond cycle’. On these basis, it is deemed that the ‘Heinrich-Bond’ solar cycle may act on the ice-sheet as an external instability factor both related to excess ice leading to calving process and IRD-layers (‘cold-related’ Heinrich events), and surface heating with meltwater streams (‘warm-related’ Heinrich events). The Hallstatt cycle is found in a number of solar proxies, geomagnetic secular variations, paleoclimatic oscillations, combination tones of Milankovitch forcings and resonant planetary beats, indicating an apparent ‘multi-forcing’ origin possibly related to planetary beat hypothesis. The orbital components consistently reflects the post-Mid-Pleistocene transition nature of the EPICA records in which the short eccentricity results in most of the variance (51.6%), followed by obliquity (19.0%) and precession (8.4%). Beyond the Milankovitch theory, evidence is emerging of a multiple-forcing cosmoclimatic system with stochastic interactions between external (gravitational resonances, orbitals, solar activity) and Earth's internal (geodynamics, atmosphere composition, feedback mechanisms) climate components, each having a strong difference in terms of the relative quantitative impact on Earth's climate.

The Earth has gone through multiple ice ages in the past million years. Understanding the ice age dynamics is crucial to paleoclimatic study, and is helpful for addressing future climate challenges. Though ice ages are paced by variations in Earth’s orbit geometry, how various climatic system components on the Earth respond to insolation forcing and interact with each other remains unclear. A prevailing view argues that the initial responses occur in the northern high latitudes (i.e. the northern high-latitude hypothesis, NHH). This opinion is challenged by recent reports, such as the lead of climate change in the Southern Hemisphere (SH) relative to that in the Northern Hemisphere (NH), the southern control on Atlantic meridional overturning circulations (AMOC), and the potential significance of Southern Hemisphere (SH). Alternatively, the tropical hypothesis (TH) argues for a leading role of the tropics. Both the NHH and the TH belong to a single-forcing mechanism, and have difficulty in interpreting phenomena, such as the saw-tooth pattern of the ice ages. Here we present a new proposal concerning the Earth’s ice age dynamics: the bimodal forcing hypothesis (BFH). The essential assumption of this hypothesis is that for glacial-interglacial cycles, the cooling (glaciation) starts from the northern high latitudes, whereas the warming (deglaciations) starts from the SH. Particularly, the BFH emphasizes the significance of SH oceans in accumulating and transferring heat for deglaciations. Thus, it is capable to reasonably explain the saw-tooth pattern. We compiled 100 paleotemperature records globally for validation. The BFH is consistent with most of these records, and provides a straightforward and comprehensible way to interpret ice age on Earth.

Abrupt climate changes constitute a relatively new field of research, which addresses variations occurring in a relatively short time interval of tens to a hundred years. Such time scales do not correspond to the tens or hundreds of thousands of years that the astronomical theory of climate addresses. The latter theory involves parameters that are external to the climate system and whose multi-periodic variations are reliably known and almost constant for a large extent of Earth history. Abrupt changes, conversely, appear to involve fast processes that are internal to the climate system; these processes varied considerably during the past 2.6 Myr, and yielded more irregular fluctuations. In this paper, we re-examine the main climate variations determined from the U1308 North Atlantic marine record, which yields a detailed calving history of the Northern Hemisphere ice sheets over the past 3.2 Myr. The magnitude and periodicity of the ice-rafted debris (IRD) events observed in the U1308 record allow one to determine the timing of several abrupt climate changes, the larger ones corresponding to the massive iceberg discharges labeled Heinrich events (HEs). In parallel, abrupt warmings, called Dansgaard-Oeschger (DO) events, have been identified in the Greenland records of the last glaciation cycle. Combining the HE and DO observations, we study a complex mechanism that may lead to the observed millennial-scale variability corresponding to the abrupt climate changes of last 0.9 Myr. This mechanism relies on amended Bond cycles, which group DO events and the associated Greenland stadials into a trend of increased cooling, with IRD events embedded into every stadial, the latest of these being an HE. These Bond cycles may have occurred during the last 0.9 Ma when Northern Hemisphere ice sheets reached their maximum extent and volume, thus becoming a major player in this time interval’s climate dynamics. Since the waxing and waning of ice sheets during the Quaternary period are orbitally paced, we conclude that the abrupt climate changes observed during the Mid and Upper Pleistocene are therewith indirectly linked to the astronomical theory of climate.

Recognition and interpretation of paleoclimate signals in sedimentary proxy datasets are time consuming and subjective. Acycle is a comprehensive and easy-to-use software package for time series analysis in paleoclimate research and education. It is designed to speed paleoclimate time series analysis, especially cyclostratigraphy, and to provide objective methods for estimating astrochronology. Acycle provides for detrending with multiple options to track and remove secular trends. A selection of power spectral analysis methodologies is offered for the detection of periodic signals. Many of the functions are specific to cyclostratigraphy and astrochronology that are not found in standard statistical packages. A specialized function is provided to assess the astronomical (Milankovitch) forcing of paleoclimate series and search for the most likely sedimentation rate by evaluating the correlation coefficient between power spectra of an astronomical solution and sedimentary proxy data. Sedimentary noise modeling (for past sea-level changes) is also provided in Acycle . As an example, Acycle is applied to a sedimentary proxy series from the cyclostratigraphy of the Paleocene-Eocene thermal maximum (PETM) in Core BH9/05 from the Paleogene Central Basin, Svalbard. Acycle detects significant astronomical forcing in the proxy series and relatively stable sedimentation rates during and after the PETM. Acycle runs in the MATLAB environment or as stand-alone software on Windows and Macintosh OS X, and is open-source software.

Previous modelling efforts have investigated climate responses to different Milankovitch forcing during Marine Isotope Stage (MIS) 13. During this time the climate has been highly variable at atmospheric CO2 concentrations of ~240 ppm. As yet, ice sheet-climate feedbacks were missing in previous studies. Therefore we use the state-of-the-art coupled climate-ice sheet model, AWI-ESM-1.2, to investigate the MIS-13 climate and corresponding Northern Hemisphere ice sheet (NHIS) evolution by performing simulations under three different astronomical configurations representing 495, 506 and 517 kyr BP. The simulated excess ice compared to present-day is mainly over the Cordillera, Arctic islands and Tibet. The global mean surface air temperature for the MIS-13 experiments have the same magnitude. At 506 kyr BP with boreal summer at perihelion, the Northern Hemisphere continents are warmer during summer than the other experiments, which could potentially inhibit the development of the ice sheets. The Cordilleran Ice Sheet is found to be especially sensitive to orbital (precession) forcing, at an intermediate CO2 level. This is probably due to its high elevation where the freezing point could be easily maintained. The other ice sheets over northeast America and Eurasia, however, are absent in our simulations. We propose that the alpine-based Cordilleran Ice Sheet is more sensitive and easier to build up than other NHISs in response to the astronomical controlled summer insolation. Dynamic surges are simulated for the Cordilleran Ice Sheet under fixed low orbital forcing. These surges due to internal ice sheet-climate feedbacks could potentially be the mechanism for the millennial scale H-like events.

Proxy temperature data records featuring local time series, regional averages from areas all around the globe, as well as global averages, are analyzed using the Slow Feature Analysis (SFA) method. As explained in the paper, SFA is much more effective than the traditional Fourier analysis in identifying slow-varying (low-frequency) signals in data sets of a limited length. We find the existence of a striking gap from ~1000 to about ~20,000 years, which separates intrinsic climatic oscillations with periods ranging from ~60 years to ~1000 years, from the longer time-scale periodicities (20,000 year+) involving external forcing associated with Milankovitch cycles. The absence of natural oscillations with periods within the gap is consistent with cumulative evidence based on past data analyses, as well as with earlier theoretical and modeling studies.

Based upon research results over the past five decades, there has been a general acceptance that the ice ages were initiated by astronomical phenomenon. Specifically, marine, ice and terrestrial paleoclimate data have supported elements of the Milankovitch astronomical theory of the ice ages. However, there remain unresolved problems between the empirical findings and theory. The 100 thousand year problem has been the subject of extensive research since a 100 thousand year cycle that matches the Earth orbit eccentricity period dominates the frequencies found in paleoclimate records. Yet, eccentricity produces an insignificant variation in annual solar energy. Other problems include the Stage 11 problem, the missing interglacials problem, how glaciation is sustained over multiple tens of thousands of years and synchronous hemispheric glaciation. I shall show these problems are resolved by modification of the prevailing Milankovitch theory. In particular, two elements of the theory need modification. One is the limitation of eccentricity's role and the other assuming that glaciation results only from cool summer conditions. By applying the Solar Energy Invariance law to define e-seasons, how eccentricity provides conditions for glaciation is demonstrated. The results show eccentricity variations provide significant solar energy variations at the top of the earth's atmosphere to produce glaciation that is global. Global glaciation results in colder winter glaciation occurring in one hemisphere simultaneous with cool summer glaciation in the other hemisphere. Analysis with these modifications resolves each of the problems.

One hundred years ago the Serbian engineer, mathematician and geophysicist Milutin Milankovic published the seminal work Mathematical Theory of Thermal Phenomena Caused by Solar Radiation, which laid the foundation for mathematical modelling of climatic cycles. Milankovic succeeded in linking major climate change to three known astronomical parameters which controlled the amount of solar radiation on Earth during different seasons and at different latitudes, these are: Earth's orbit eccentricity around the Sun; the tilt or obliquity of Earth's axis of rotation; and the precession of the rotation axis or 'wobblelike' movement. The proposal of periodic fluctuations in Earth's climate (now known as Milankovic cycles) was rejected and ridiculed during the 1950s, but received acclaim in the seventies following publication of the outcomes of seminal multidisciplinary research by Hays, Imbrie and Shackleton.

How variations in Earth&rsquo, s orbit pace the glacial-interglacial cycles of the Quaternary are probably one of the greatest mysteries of modern climate science. These changes in the forcing are too small to explain the observed climate variations as simple linear responses. Consequently, to strictly apply the Milankovitch&rsquo, s theory, a mediator involving positive feedbacks must be found, endowing the climate response with a resonant feature. This mediation should help explain the Mid-Pleistocene Transition (MPT) by involving orbital variations as the only external forcing, contrary to the current theory that supposes the coevolution of climate, ice sheets, and carbon cycle over the past 3 million years. Supported by both observational and theoretical considerations, recent work shows that long-period Rossby waves winding around subtropical ocean gyres meet the requirements of the sought mediator. Propagating cyclonically around the subtropical gyres, the so-called Gyral Rossby waves (GRWs) owe their origin to the gradient &beta, of the Coriolis parameter relative to the mean radius of the gyres. The resulting modulated western boundary current, whose velocity is added to that of the steady anticyclonic wind-driven current, accelerates/decelerates according to the phase of GRWs. This amplifies the oscillation of the thermocline because of a positive feedback loop ensuing from the temperature gradient between the high and low latitudes of the gyres. Multi-frequency GRWs overlap, behaving as coupled oscillators with inertia resonantly forced by solar and orbital cycles in subharmonic modes. So, the efficiency of forcing increases considerably as the forcing period approaches a natural period of the GRWs. Taking advantage of (1) the alkenone paleothermometer in sediment cores sampled in the Tasman Sea floor, we show that, in the same way as during the MPT, but with periods 10 times longer, a transition occurred at the hinge of Pliocene-Pleistocene. Both transitions as well as the observed adjustment of the South Pacific gyre to the resonance conditions during the MPT are explained from orbital forcing alone&mdash, (2) data set of individual Globigerinoides ruber&delta, O&nbsp, 18 spanning the Holocene and the Last Glacial Maximum from sediment core in the eastern equatorial Pacific, we show how the El Ni&ntilde, o&ndash, Southern Oscillation (ENSO) activity is modulated according to subharmonic modes. Periods of warming induce a decrease in ENSO activity while periods of cooling induce an increase.

Earth’s orbital variations on timescales of 104–105 years, known as Milankovitch cycles, have played a critical role in pacing climate change and ecosystem dynamics, through glacial and/or monsoon dynamics. However, the climatic and biotic consequences of these cycles on much longer (~ 107 years) timescales remain unclear, due to a lack of long proxy records with precise age constraints. Here, we show ~ 10-Myr scale variations in early Mesozoic (250–180 Ma) records of lake-level, desert distribution, biogenic-silica burial flux, atmospheric CO2 levels (pCO2), and sea-surface-temperature (SST). Their phase relationships, coupled with carbon cycle modeling results, suggest that orbitally-paced summer monsoon dynamics modulates changes in terrestrial weatherability by ~ 20%, affecting changes in pCO2 of up to 500–1,000 ppmv and 3–7 °C SST. We also infer that these ~ 10-Myr scale climatic variations could have been causally linked to biotic turnover, size variations in dinosaur footprints, and tetrapod dispersal, potentially through spatio-temporal variations in resource availability and arid-hot climatic barriers at low-middle latitudes.

The periodic changes of atmospheric CO2 and temperature over the last 5 Myr reveal three features that challenge current climate research, namely: (i) the mid-Pleistocene transition of dominant 41-kyr cycles to dominant 100-kyr cycles, (ii) the absence of a strong precession signal of approximately 20 kyr, and (iii) the cooling through the middle and late Holocene. These features are not directly addressable by Earth’s orbital changes described by Milankovitch. Here we show that a closed photochemical system exposed to a constant illumination source can sustain oscillations. In this simple conceptual model, the oscillations are intrinsic to the system and occur even in the absence of periodic radiative forcing. With proper adaptations to the Earth system, this oscillator explains the main features of past climate dynamics. Our model places photosynthesis and the carbon cycle as key drivers of climate change. We use this model to predict the relaxation of a 1,000 PgC pulse of CO2. The removal of 50% of this CO2 will require one century, and will lead to a warmer and wetter future. However, more pronounced glaciation cycles emerge on the millennial timescale.

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.

It was recently found that the accepted picture of atmospheric variability was in error by a large factor. Rather than being dominated by a series of narrow scale-range quasi-oscillatory processes with an unimportant white noise “background”, it turned out that the variance was instead dominated by a few wide range scaling processes albeit occasionally interspersed with superposed quasi-oscillations. Although the classical model implied that successive million year global temperature averages would differ by mere micro Kelvins, the implausibility had not been noticed. In contrast, the new picture inverts the roles of background and foreground and involves four (possibly five) wide range scaling processes. As with any new paradigm, there are consequences; in this paper we focus on the implications for the spectra, intermittency and the extremes. Intermittency is an expression of the spatio-temporal sparseness of strong events whereas the extremes refer to the tails of their probability distributions and both affect the spectra. Although we give some results for the macro and mega climate regimes, we focus on weather, macroweather and climate: from dissipation to Milankovitch scales.

Geologic evidence suggests that the last glacial inception (115 kya) occurred within the mountains of Baffin Island. Global climate models (GCMs) have difficulty simulating this climate transition, likely because of their coarse horizontal resolution that smooths topography and necessitates the use of cumulus parameterizations. A regional configuration of the Weather Research and Forecasting (WRF) Model is used to simulate the small-scale topographic and cloud processes neglected by GCMs, and the sensitivity of the region to Milankovitch forcing, topography, and meteorology is tested. It is found that ice growth is possible with 115-kya insolation, realistic topography, and slightly colder-than-average meteorology, represented by specific years within the past three decades. The simulation with low GCM-like topography shows a negative surface mass balance, even with the relevant orbital parameter configuration, demonstrating the criticality of realistic topography. The downslope growth of the ice sheets is studied by looking at the sensitivity of the mass balance to initial snow cover prescribed beyond that of the present day. It is found that the snow-albedo feedback, via its effects on the mass balance, allows such larger snow cover to persist. Implications for GCM studies of glacial inception are discussed.

We present a climate modeling approach to reproduce the rainfall patterns over Iran due to the climatic forcings during the past 6000 years. The selected periods are simulated using a spatially high-resolved atmosphere General Circulation Model (GCM). Our results show that the winter rainfall patterns over Iran have changed due to the changes in solar insolation with a wetter condition starting around 3 ka BP and reaching its maximum during the Medieval Climate Anomaly ca. 1 ka BP. The rainfall variability can be explained by the changes in atmospheric conditions as a result of changing incoming solar irradiance based on the Milankovitch theory. A shift in the Earth's energy budget leads to the modulation of the West Asian Subtropical Westerly Jet (WASWJ). The investigations support the hypothesis that during the Holocene a northward shift in the WASWJ contributes to the less cyclonic activities over Iran. This brings less moisture into the region during the winter.

Records from natural archives show that the strength of the East Asian summer monsoon (EASM) strongly depends on the orbital configuration of the Earth. However, the dominant orbital cycles driving EASM have been found to be spatially different. Speleothem stable oxygen isotopic records from southern China, which are believed to reflect large-scale changes in the Asian monsoon system, are dominated by climatic precession cycles. Further north, on the Chinese Loess Plateau (CLP), loess-and-paleosol sequences, which are argued to be controlled by monsoon intensity, are in pace with global ice volume changes dominated by obliquity, and after the mid-Pleistocene transition by 100-kyr cycles. To understand these critical discrepancies, here we apply a novel proxy based on the trace metal compositions of pedogenic carbonate in the eolian deposits on the CLP to reconstruct summer precipitation over the last 1.5 million years. Our reconstructions show that summer precipitation on the CLP is dominantly forced by obliquity not in pace with the ice-volume-imprinted loess-paleosol sequences before and after the mid-Pleistocene transition or with the precession-paced speleothem oxygen isotopic records. Coupled with climate model results, we suggest that the obliquity-driven variations of summer precipitation may originate from the gradient of boreal insolation that modulates the thermal contrast between the Asian continent and surrounding oceans.

The Plio-Pleistocene glacial cycles have dominated climate during the past ∼2.8 My, with alternating warm interglacial and cold glacial periods with ice caps covering large parts of North America and Europe. The early work of Milutin Milankovitch suggests that changes in summer insolation due to variations in the Earth’s orbit could be the main driver of these large cycles in ice volume. According to this theory, the long cycles regulating the tilt of the Earth’s axis, the precession of the equinoxes, and the eccentricity of the Earth’s orbit could have had a significant impact on the high-latitude insolation and climate through time. At times with relatively cool summers, snow and ice could have persisted through the melt season, and combined with a strong snow albedo feedback, would have led to full glacial conditions. With the discovery of long climate records from deep-sea sediment cores it has become clear that the glacial cycles of the Plio-Pleistocene do indeed exhibit periods with the same frequencies as the astronomical forcing of Milankovitch. However, the mechanisms linking this insolation forcing to the large and relatively rapid nonlinear changes in continental ice are still unclear.

Recent decades have registered the hottest temperature variation in instrumentally recorded data history. The registered temperature rise is particularly significant in the so-called hot spot or sentinel regions, characterized by higher temperature increases in respect to the planet average value and by more marked connected effects. In this framework, in the present work, following the climate stochastic resonance model, the effects, due to a temperature increase independently from a specific trend, connected to the 105 year Milankovitch cycle were tested. As a result, a breaking scenario induced by global warming is forecasted. More specifically, a wavelet analysis, innovatively performed with different sampling times, allowed us, besides to fully characterize the cycles periodicities, to quantitatively determine the stochastic resonance conditions by optimizing the noise level. Starting from these system resonance conditions, numerical simulations for increasing planet temperatures have been performed. The obtained results show that an increase of the Earth temperature boosts a transition towards a chaotic regime where the Milankovitch cycle effects disappear. These results put into evidence the so-called threshold effect, namely the fact that also a small temperature increase can give rise to great effects above a given threshold, furnish a perspective point of view of a possible future climate scenario, and provide an account of the ongoing registered intensity increase of extreme meteorological events.

We present here a simple and novel proposal for the modulation and rhythm of ice-ages and interglacials during the late Pleistocene. While the standard Milankovitch-precession theory fails to explain the long intervals between interglacials, these can be accounted for by a novel forcing and feedback system involving CO2, dust and albedo. During the glacial period, the high albedo of the northern ice sheets drives down global temperatures and CO2 concentrations, despite subsequent precessional forcing maxima. Over the following millennia more CO2 is sequestered in the oceans and atmospheric concentrations eventually reach a critical minima of about 200 ppm, which combined with arid conditions, causes a die-back of temperate and boreal forests and grasslands, especially at high altitude. The ensuing soil erosion generates dust storms, resulting in increased dust deposition and lower albedo on the northern ice sheets. As northern hemisphere insolation increases during the next Milankovitch cycle, the dust-laden ice-sheets absorb considerably more insolation and undergo rapid melting, which forces the climate into an interglacial period. The proposed mechanism is simple, robust, and comprehensive in its scope, and its key elements are well supported by empirical evidence.

The Green River Formation (GRF) provides one of the premier paleoclimate archives of the Early Eocene Climatic Optimum (∼50 Ma), representing the apex of the early Cenozoic greenhouse climate. Rhythmic lake-level variability expressed in the GRF has inspired numerous hypotheses for the behavior of the Eocene hydrologic cycle, including its linkage to astronomical forcing, solar variability, and the El Nino Southern Oscillation (ENSO). However, the lack of sufficient proxy data to document atmospheric water-mass transport and the geographic pattern of evaporation/precipitation/runoff has made it difficult to discriminate between different models for astronomical forcing. Variable 87Sr/86Sr ratios of bedrock that encompass the GRF provide an opportunity to reconstruct the spatial expression of the Eocene hydrologic cycle and its linkage to lake level. Here Sr isotope data from the Wilkins Peak Member, a rhythmic succession that has been demonstrated to record Milankovitch forcing of lake levels, indicate that high lake levels reflect an increased proportion of runoff from less radiogenic rocks west of the basin, eliminating a number of the existing astronomical-forcing hypotheses. The 87Sr/86Sr variability is consistent with a change in mean ENSO state, which is predicted by climate models to be linked to orbital-insolation. Thus, the 87Sr/86Sr data reveal a coupling of high frequency (ENSO) and low frequency (astronomical) climate variability, and also predict the existence of sizable astronomically-forced alpine snowpack during the last greenhouse climate. More broadly, this study demonstrates the utility of 87Sr/86Sr as a powerful tool for reconstructing the deep-time hydrologic cycle.

Quaternary climate change recorded by Chinese loess closely parallels fluctuations in the benthic δ 18 O record. However, there are also some unique climate anomalies in and around the Asian inland Chinese Loess Plateau (CLP), where the climate was unusually humid during MIS 3 and 13, and extremely cold during MIS 22 and 38. Most explanations involve modifications to atmospheric circulation, but there is no single answer for such anomalies. Here, we compare relative geomagnetic paleointensity with benthic δ 18 O, and find that all anomalies occur when paleointensity negatively correlates with δ 18 O. The reason for this is not yet clear. Milankovitch theory fundamentally explains Quaternary climatic cycles by external forcing. Our results suggest that changes in the Earth's deep interior, especially geomagnetic field intensity, may play a significant role in some non-linear climate changes in mid-latitude long-term Quaternary climate change. We are currently pursuing the idea that fluctuations in global climatic background (δ 18 O record) and cosmic ray influx, which is controlled by the strength of the geomagnetic field, may from time to time act in concert to create regional anomalies such as those seen on the CLP.

Although monsoons are an important climatic factor in the Indo-Pacific region, the mechanism responsible for monsoon variations is not fully understood, particularly at the 10 5 year-scale, which includes the Milankovitch orbital cycles. Here, we provide a palynological result from the C9001C marine core drilled in the NW Pacific off the Shimokita Peninsula, eastern Japan. Based on the parallel δ 18 O record, the pollen record covers the past 130,000 years. During the interglacial periods (MIS1 and 5e), the C9001C core is dominated by cool temperate pollen of Fagus (beech) and Quercus subgenus Lepidobalanus (deciduous oak) that is similar to the present-day Shimokita vegetation. However, during the glacial periods (MIS2-4), the pollen spectra are dominated by subarctic elements of Betula (birch) and Picea (spruce), similar to the vegetation of Sakhalin and northern Hokkaido. These fossil pollen data are converted into quantitative climate variables by using the modern analog technique. Of the reconstructed paleoclimate variables, the mean annual temperature (Tann) correlates with the parallel δ 18 O record. By contrast, reconstructed precipitation in the summer (Psum) shows a similar pattern to the northern insolation variations particularly during MIS5, though the phase relation between the two curves requires further studies.

We test competing forms of the Milankovitch hypothesis by estimating the coefficients and diagnostic statistics for a cointegrated vector autoregressive model that includes 10 climate variables and four exogenous variables for solar insolation. The estimates are consistent with the physical mechanisms postulated to drive glacial cycles. They show that the climate variables are driven partly by solar insolation, determining the timing and magnitude of glaciations and terminations, and partly by internal feedback dynamics, pushing the climate variables away from equilibrium. We argue that the latter is consistent with a weak form of the Milankovitch hypothesis and that it should be restated as follows: internal climate dynamics impose perturbations on glacial cycles that are driven by solar insolation. Our results show that these perturbations are likely caused by slow adjustment between land ice volume and solar insolation. The estimated adjustment dynamics show that solar insolation affects an array of climate variables other than ice volume, each at a unique rate. This implies that previous efforts to test the strong form of the Milankovitch hypothesis by examining the relationship between solar insolation and a single climate variable are likely to suffer from omitted variable bias.

The global climate cyclicity transferred from an Early Pleistocene mode dominated by the obliquity periodicity to a new Middle Pleistocene state dominated by the eccentricity periodicity in the absence of any significant changes in orbital forcing, known as the Early–Middle Pleistocene transition (EMPT), is an unresolved issue of Milankovitch orbital theory. Here we contribute new insights into the orbital characteristic and dynamics of the Asian summer monsoon precipitation changes across the EMPT. Spectral analyses of precipitation over the past 1.6 Myr reconstructed from a new loess magnetic susceptibility (χ) stack suggest that the EMPT of the summer monsoon precipitation characterized by a shift from obliquity to eccentricity rhythm occurred over a ~640 kyr long-term period from ~1.24 to 0.6 Ma rather than quasi-instantaneously on a much shorter duration. The eccentricity cyclicity initiated as early as 1.24 Ma, subsequently intensified and became the dominated pacing from 1.1 Ma, while obliquity weakened at ~1.1 Ma and significantly weakened at ~0.7 Ma. These EMPT characteristics of the summer monsoon precipitation reflect complex impacts from global climate systems and regional climate changes in the Northern and Southern Hemispheres, and in both low- and high-latitude regions.

A mechanism is proposed in which climate, carbon cycle and icesheets interact with each other to produce a feedback that can lead to quasi-100 ky glacial-interglacial cycles. A central process is the burial and preservation of organic carbon by icesheets which contributes to the observed glacial-interglacial CO2 change (the glacial burial hypothesis, Zeng, 2003). Allowing carbon cycle to interact with physical climate, here I further hypothesize that deglaciation can be triggered by the ejection of glacial burial carbon when a major icesheet grows to sufficiently large size after a prolonged glaciation so that subglacial transport becomes significant. Glacial inception may be initiated by CO2 drawdown due to a relaxation from a high but transient interglacial CO2 value as the land-originated CO2 invades into deep ocean via thermohaline circulation and CaCO3 compensation. Also important for glacial inception may be the CO2 uptake by vegetation and soil regrowth in the previously ice-covered regions. When tested in a fully coupled Earth system model with comprehensive carbon cycle components and semi-empirical physical climate components, it produced under certain parameter regimes self-sustaining glacial-interglacial cycles with durations of 93 ky, CO2 changes of 90 ppmv, temperature changes of 6°C. Since the 100 ky cycles can not be easily explained by the Milankovitch astronomical forcing alone, this carbon-climate-icesheet mechanism provides a strong feedback that could interact with external forcings to produce the major observed Quaternary climatic variations. It is speculated that some glacial terminations may be triggered by this internal feedback while others by orbital forcing. Some observable consequences are highlighted that may support or falsify the theory.

Changes in Earth’s orbit set the pace of glacial cycles, but the role of spatial variability in the insolation forcing of global ice volume remains unknown. Here, we leverage the intrinsic dynamical information in empirical records to show that ice volume responded to summer energy at high northern latitudes, as predicted by Milankovitch theory. However, the external forcing of ice volume encompasses insolation signals with a wide range of orbital frequency content, and cannot be fully accounted for by a unique time series. Southern mid-latitude insolation forcing coincides with the position of the subtropical front and the westerlies, which have been implicated in Quaternary climate changes. Dominant forcing modes at northern mid-latitudes are anti-phased with the canonical Milankovitch forcing, consistent with ice volume sensitivity to latitudinal insolation gradients.

The notion that small changes can have large consequences in the climate or ecosystems has become popular as the concept of tipping points. Typically, tipping points are thought to arise from a loss of stability of an equilibrium when external conditions are slowly varied. However, this appealingly simple view puts us on the wrong foot for understanding a range of abrupt transitions in the climate or ecosystems because complex environmental systems are never in equilibrium. In particular, they are forced by diurnal variations, the seasons, Milankovitch cycles and internal climate oscillations. Here we show how abrupt and sometimes even irreversible change may be evoked by even small shifts in the amplitude or time scale of such environmental oscillations. By using model simulations and reconciling evidence from previous studies we illustrate how these phenomena can be relevant for ecosystems and elements of the climate system including terrestrial ecosystems, Arctic sea ice and monsoons. Although the systems we address are very different and span a broad range of time scales, the phenomena can be understood in a common framework that can help clarify and unify the interpretation of abrupt shifts in the Earth system.

Until now, cause of the Mid-Pleistocene Transition (MPT), when the dominant periodicity of climate cycles changed from 41,000 to 100,000 years in the absence of significant change in orbital forcing, are still an open question in Paleoclimatology. Here we show how a Bayesian data analysis and nonlinear dynamical reconstruction methods can help to reveal the main mechanisms underlying the Pleistocene variability. Our Bayesian data-driven model from benthic d18O records (LR04 stack) accounts the main factors which may potentially impact climate of the Pleistocene: internal climate dynamics, gradual trends, variations of insolation, and millennial variability. In contrast to some theories, we uncover that under long-term trends in climate, the strong glacial cycles have appeared due to internal nonlinear oscillations induced by millennial noise. We find that while the orbital Milankovitch forcing does not matter for the MPT onset, the obliquity oscillation phase-locks the climate cycles through the meridional gradient of insolation. The research was supported by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».

This paper applies time series modeling methods to paleoclimate series for temperature, ice volume, and atmospheric concentrations of CO2 and CH4. These series, inferred from Antarctic ice and ocean cores, are well known to move together in the transitions between glacial and interglacial periods, but the dynamic relationship between the series is open to question. A further unresolved issue is the role of Milankovitch theory, in which the glacial/interglacial cycles are correlated with orbital variations. We perform tests for Granger causality in the context of a vector autoregression model. Previous work with climate series has assumed nonstationarity and adopted a cointegration approach, but in a range of tests, we find no evidence of integrated behavior. We use conventional autoregressive methodology while allowing for conditional heteroscedasticity in the residuals, associated with the transitional periods. Copyright © 2015 John Wiley & Sons, Ltd.

International audience; Changes in Late Quaternary oceanic primary productivity in the western tropical Pacific were reconstructed using coccolith counts from the improved SYRACO system in piston core MD01-2386 retrieved from the Halmahera Sea near northwest New Guinea. The calculated primary productivity exhibits cycles on obliquity and precession timescales over the last 192 ka. There are marked differences between primary productivity records from the western tropical Pacific and the South China Sea (SCS), with the former being dominated by precession, and the latter showing all three Milankovitch cycles (eccentricity, obliquity and precession). Empirical Orthogonal Function (EOF) analyses reveal two significant EOF modes in the western tropical Pacific and SCS records. EOF-1 accounts for 38% of the total variance and exhibits obvious precessional cycles corresponding to Northern Hemisphere summer insolation, while EOF-2 accounts for 22% of the total variance and exhibits strong 41-kyr periodicity, suggesting different biological responses to hydroclimate changes in the two regions. A more complex hydroclimate regime influenced by the East Asian monsoon and the large contrast in regional topography and circulation during glacial cycles are considered to be the primary drivers of the stronger temporal variability in productivity in the SCS compared to the relatively stable western tropical Pacific. (C) 2015 Elsevier Ltd. All rights reserved.

Understanding what drove Northern Hemisphere ice sheet melt during the last deglaciation (21–7 ka) can help constrain how sensitive contemporary ice sheets are to greenhouse gas (GHGs) changes. The roles of orbital forcing and GHGs in the deglaciation have previously been modelled, but not yet quantified. Here, for the first time we calculate the relative effect of these forcings on the North American deglaciation by driving a dynamical ice sheet model (GLIMMER-CISM) with a set of un-accelerated transient deglacial simulations with a full primitive equation based ocean atmosphere general circulation model (FAMOUS). We find that by 9 ka, orbital forcing has caused 50% of the deglaciation, GHG 30% and the interaction between the two 20%. Orbital forcing starts affecting the ice volume at 19 ka, 2,000 years before CO2 starts increasing in our experiments, a delay which partly controls their relative effect.

Astronomically calibrated cyclostratigraphy relies on correct matching of observed sedimentary cycles to predicted astronomical drivers such as eccentricity, obliquity, and climate precession. However, the periods of these astronomical cycles, in the past, are not perfectly known because: (i) they drift through time; (ii) they overlap; and (iii) they are affected by the poorly constrained recession history of the Moon. This paper estimates the resulting uncertainties in ancient Milankovitch cycle periods and shows that they lead to: (i) problems with using Milankovitch cycles for accurate measurement of durations (potential errors are around 25% by the start of the Phanerozoic); (ii) problems with correctly identifying the Milankovitch cycles responsible for observed period ratios (e.g., the ratio for long-eccentricity/short-eccentricity overlaps, within error, with the ratio for short-eccentricity/precession); and (iii) problems with verifying that observed cycles are Milankovitch driven at all (the probability of a random period ratio matching a predicted Milankovitch ratio, within error, is 20–70% in the Phanerozoic). Milankovitch-derived ages and durations should therefore be treated with caution unless supported by additional information such as radiometric constraints.