Papers on the Milankovitch cycles and climate

This is a list of papers on the role of Milankovich cycles in Earth’s climate, especially in past climate changes. The list is not complete, and will most likely be updated in the future in order to make it more thorough and more representative.

UPDATE (February 20, 2016: Fixed some dead links. UPDATE (July 26, 2011): Tziperman et al. (2006), Rial & Anaclerio (2000) and Martinson et al. (1987) added. Thanks to Barry for pointing these out (see the comment section below).

Linear and non-linear response of late Neogene glacial cycles to obliquity forcing and implications for the Milankovitch theory – Lourens et al. (2009) “Constraints are given for the geometry and time lags of the prominent obliquity-paced glacial stages 100, 98 and 96, which mark a major phase in Northern Hemisphere (NH) glaciations during the late Pliocene (2.56–2.4 Ma ago). … Similar to late Pleistocene ice core and marine δ¹⁸O records, our late Pliocene δ¹⁸O record reveals significant power at 28 ky, which appear to be bound to the major glacial terminations. We argue that this beat most likely reflects the sum frequency of the 41 ky prime and its multiples of 82 and 123 ky, supporting the theory that the late Neogene glacial cycles are primarily determined by the linear and non-linear response mechanisms of the ice sheets to the obliquity forcing.”

Resolving Milankovitch: Consideration of signal and noise – Meyers et al. (2008) “In this study, we delineate sources of noise that distort the primary orbital signal in proxy climate records, and utilize this template in tandem with advanced spectral methods to quantify Milankovitch-forced/paced climate variability in a temperature proxy record from the Vostok ice core (Vimeux and others, 2002). Our analysis indicates that Vostok temperature variance is almost equally apportioned between three components: the precession and obliquity periods (28%), a periodic “100,000” year cycle (41%), and the background continuum (31%).” [Full text]

Consequences of pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to Milankovitch forcing – Tziperman et al. (2006) “The consequences of the hypothesis that Milankovitch forcing affects the phase (e.g., termination times) of the 100 kyr glacial cycles via a mechanism known as “nonlinear phase locking” are examined. Phase locking provides a mechanism by which Milankovitch forcing can act as the “pacemaker” of the glacial cycles. Nonlinear phase locking can determine the timing of the major deglaciations, nearly independently of the specific mechanism or model that is responsible for these cycles as long as this mechanism is suitably nonlinear. A consequence of this is that the fit of a certain model output to the observed ice volume record cannot be used as an indication that the glacial mechanism in this model is necessarily correct. Phase locking to obliquity and possibly precession variations is distinct from mechanisms relying on a linear or nonlinear amplification of the eccentricity forcing. Nonlinear phase locking may determine the phase of the glacial cycles even in the presence of noise in the climate system and can be effective at setting glacial termination times even when the precession and obliquity bands account only for a small portion of the total power of an ice volume record. Nonlinear phase locking can also result in the observed “quantization” of the glacial period into multiples of the obliquity or precession periods.” Tziperman, E., M. E. Raymo, P. Huybers, and C. Wunsch (2006), Paleoceanography, 21, PA4206, doi:10.1029/2005PA001241. [Full text]

In defense of Milankovitch – Roe (2006) “The Milankovitch hypothesis is widely held to be one of the cornerstones of climate science. Surprisingly, the hypothesis remains not clearly defined despite an extensive body of research on the link between global ice volume and insolation changes arising from variations in the Earth’s orbit. In this paper, a specific hypothesis is formulated.” [Full text]

Orbital changes and climate – Ruddiman (2006) A review paper. “At the 41,000-period of orbital tilt, summer insolation forces a lagged response in northern ice sheets. This delayed ice signal is rapidly transferred to nearby northern oceans and landmasses by atmospheric dynamics. These ice-driven responses lead to late-phased changes in atmospheric CO₂ that provide positive feedback to the ice sheets and also project ‘late’ 41-K forcing across the tropics and the Southern Hemisphere. Responses in austral regions are also influenced by a fast response to summer insolation forcing at high southern latitudes.
At the 22,000-year precession period, northern summer insolation again forces a lagged ice-sheet response, but with muted transfers to proximal regions and no subsequent effect on atmospheric CO₂. Most 22,000-year greenhouse-gas responses have the ‘early’ phase of July insolation. July forcing of monsoonal and boreal wetlands explains the early CH₄ response. The slightly later 22-K CO₂ response originates in the southern hemisphere. The early 22-K CH₄ and CO₂ responses add to insolation forcing of the ice sheets.
The dominant 100,000-year response of ice sheets is not externally forced, nor does it result from internal resonance. Internal forcing appears to play at most a minor role. The origin of this signal lies mainly in internal feedbacks (CO₂ and ice albedo) that drive the gradual build-up of large ice sheets and then their rapid destruction. Ice melting during terminations is initiated by uniquely coincident forcing from insolation and greenhouse gases at the periods of tilt and precession.” [Full text]

Obliquity pacing of the late Pleistocene glacial terminations – Huybers & Wunsch (2005) “Here we present a statistical test of the orbital forcing hypothesis, focusing on the rapid deglaciation events known as terminations10, 11. According to our analysis, the null hypothesis that glacial terminations are independent of obliquity can be rejected at the 5% significance level, whereas the corresponding null hypotheses for eccentricity and precession cannot be rejected. The simplest inference consistent with the test results is that the ice sheets terminated every second or third obliquity cycle at times of high obliquity, similar to the original proposal by Milankovitch12. We also present simple stochastic and deterministic models that describe the timing of the late-Pleistocene glacial terminations purely in terms of obliquity forcing.”

Quantitative estimate of the Milankovitch-forced contribution to observed Quaternary climate change – Wunsch (2004) “A number of records commonly described as showing control of climate change by Milankovitch insolation forcing are re-examined. The fraction of the record variance attributable to orbital changes never exceeds 20%. In no case, including a tuned core, do these forcing bands explain the overall behavior of the records. At zero order, all records are consistent with stochastic models of varying complexity with a small superimposed Milankovitch response, mainly in the obliquity band. Evidence cited to support the hypothesis that the 100 Ka glacial/interglacial cycles are controlled by the quasi-periodic insolation forcing is likely indistinguishable from chance, given the small sample size and near-integer ratios of 100 Ka to the precessional periods. At the least, the stochastic background “noise” is likely to be of importance.” [Full text]

The 100,000-Year Ice-Age Cycle Identified and Found to Lag Temperature, Carbon Dioxide, and Orbital Eccentricity – Shackleton (2000) “Here, the ice volume component of this δ¹⁸O signal was extracted by using the record of δ¹⁸O in atmospheric oxygen trapped in Antarctic ice at Vostok, precisely orbitally tuned. … At the 100,000-year period, atmospheric carbon dioxide, Vostok air temperature, and deep-water temperature are in phase with orbital eccentricity, whereas ice volume lags these three variables. Hence, the 100,000-year cycle does not arise from ice sheet dynamics; instead, it is probably the response of the global carbon cycle that generates the eccentricity signal by causing changes in atmospheric carbon dioxide concentration.” [Full text]

Understanding nonlinear responses of the climate system to orbital forcing – Rial & Anaclerio (2000) “We have recently introduced the working hypothesis that frequency modulation (FM) of the orbital eccentricity forcing may be one important source of the nonlinearities observed in δ18O time series from deep-sea sediment cores (J.H. Rial (1999a) Pacemaking the lce Ages by frequency modulation of Earth’s orbital eccentricity. Science 285, 564–568). In this paper we shall discuss further evidence of frequency modulation found in data from the Vostok ice core. Analyses of the 430,000-year long, orbitally untuned, time series of CO2, deuterium, aerosol and methane, suggest frequency modulation of the 41 kyr (0.0244 kyr⁻¹) obliquity forcing by the 413 kyr-eccentricity signal and its harmonics. Conventional and higher-order spectral analyses show that two distinct spectral peaks at 29 kyr (0.034 kyr⁻¹) and 69 kyr (0.014 kyr⁻¹) and other, smaller peaks surrounding the 41 kyr obliquity peak are harmonically (nonlinearly) related and likely to be FM-generated sidebands of the obliquity signal. All peaks can be closely matched by the spectrum of an appropriately built theoretical FM signal. A preliminary model, based on the classic logistic growth delay differential equation, reproduces the longer period FM effect and the familiar multiply peaked spectra of the eccentricity band. Since the FM effect appears to be a common feature in climate response, finding out its cause may help understand climate dynamics and global climate change.” J. A. Rial and C. A. Anaclerio, Quaternary Science Reviews
Volume 19, Issues 17-18, December 2000, Pages 1709-1722, doi:10.1016/S0277-3791(00)00087-1. [Full text]

Late Quaternary Variations in Sea Surface Temperatures and their Relationship to Orbital Forcing Recorded in the Southern Ocean (Atlantic Sector) – Brathauer & Abelmann (1999) “Late Quaternary summer sea surface temperatures (SSTs) have been derived from radiolarian assemblages in the East Atlantic sector of the Southern Ocean. … In the subantarctic Atlantic Ocean, changes in SST and calcium carbonate content of the sediment precede variations in global ice volume in the range of the main Milankovitch frequencies.” [Full text]

The Timing of Major Climate Terminations – Raymo (1997) “A simple, untuned “constant sedimentation rate” timescale developed using three radiometric age constraints and eleven δ¹⁸O records longer than 0.8 Myr provides strong support for the validity of the SPECMAP timescale of the late Quaternary [Imbrie et al., 1984]. In particular, the present study independently confirms the link between major deglaciations (terminations) and increases in northern hemisphere summer radiation at high latitudes and shows that this correlation is not an artifact of orbital tuning. … Thus, the timing of the growth and decay of large 100-kyr ice sheets, as depicted in the deep sea δ¹⁸O record, is strongly (and semipredictably) influenced by eccentricity through its modulation of the orbital precession component of northern hemisphere summer insolation.” [Full text]

On the Structure and Origin of Major Glaciation Cycles 2. The 100,000-Year Cycle – Imbrie et al. (1993) “We present phase observations showing that the geographic progression of local responses over the 100,000-year cycle is similar to the progression in the other two cycles, implying that a similar set of internal climatic mechanisms operates in all three. But the phase sequence in the 100,000-year cycle requires a source of climatic inertia having a time constant (∼15,000 years) much larger than the other cycles (∼5,000 years). Our conceptual model identifies massive northern hemisphere ice sheets as this larger inertial source. When these ice sheets, forced by precession and obliquity, exceed a critical size, they cease responding as linear Milankovitch slaves and drive atmospheric and oceanic responses that mimic the externally forced responses.”

On the Structure and Origin of Major Glaciation Cycles 1. Linear Responses to Milankovitch Forcing – Imbrie et al. (1992) “We argue that the 23,000- and 41,000-year cycles of glaciation are continuous, linear responses to orbitally driven changes in the Arctic radiation budget; and we use the phase progression in each climatic cycle to identify the main pathways along which the initial, local responses to radiation are propagated by the atmosphere and ocean.”

Surface Water Response of the Equatorial Atlantic Ocean to Orbital Forcing – McIntyre et al. (1989) “The response of the mixed layer of the equatorial Atlantic to climate change, for times greater than 10 kyr, is predominantly forced by the precessional component of insolation. A zonal transect of three cores analyzed at 1-kyr intervals documents this response for 0-250 ka The western equatorial Atlantic is characterized by minimal variation in surface water character, indicating temporal stability of the mixed layer, except during intervals of maximum glaciation. In contrast, the eastern region shows marked temporal variations in estimated sea surface temperature and foraminiferal assemblages, with dominant periodicities centered on 23 kyr. At precessional periods, the eastern equatorial Atlantic responds in phase with southern hemisphere sea surface temperature and significantly leads northern hemisphere sea surface temperature and continental ice volume. These signals are the product of orbitally forced variations in (1) trade wind and monsoon-controlled divergence and (2) advection of heat from high southern latitudes.”

Age dating and the orbital theory of the ice ages: Development of a high-resolution 0 to 300,000-year chronostratigraphy – Martinson et al. (1987) “Using the concept of “orbital tuning”, a continuous, high-resolution deep-sea chronostratigraphy has been developed spanning the last 300,000 yr. The chronology is developed using a stacked oxygen-isotope stratigraphy and four different orbital tuning approaches, each of which is based upon a different assumption concerning the response of the orbital signal recorded in the data. Each approach yields a separate chronology. The error measured by the standard deviation about the average of these four results (which represents the “best” chronology) has an average magnitude of only 2500 yr. This small value indicates that the chronology produced is insensitive to the specific orbital tuning technique used. Excellent convergence between chronologies developed using each of five different paleoclimatological indicators (from a single core) is also obtained. The resultant chronology is also insensitive to the specific indicator used. The error associated with each tuning approach is estimated independently and propagated through to the average result. The resulting error estimate is independent of that associated with the degree of convergence and has an average magnitude of 3500 yr, in excellent agreement with the 2500-yr estimate. Transfer of the final chronology to the stacked record leads to an estimated error of ±1500 yr. Thus the final chronology has an average error of ±5000 yr.” Douglas G. Martinson, Nicklas G. Pisias, James D. Hays, John Imbrie, Theodore C. Moore, Jr. and Nicholas J. Shackleton, Quaternary Research
Volume 27, Issue 1, January 1987, Pages 1-29, doi:10.1016/0033-5894(87)90046-9. [Full text]

The orbital theory of Pleistocene climate : support from a revised chronology of the marine δ¹⁸ O record – Imbrie et al. (1984) “Observations of δ¹⁸O in five deep-sea cores provide a basis for developing a geological time scale for the past 780000 years and for evaluating the orbital theory of Pleistocene ice ages. The statistical evidence of a close relationship between the time-varying amplitudes of orbital forcing and the time-varying amplitudes of the isotopic response implies that orbital variations are the main external cause of the succession of late Pleistocene ice ages.”

Modeling the Climatic Response to Orbital Variations – Imbrie & Imbrie (1980) “According to the astronomical theory of climate, variations in the earth’s orbit are the fundamental cause of the succession of Pleistocene ice ages. This article summarizes how the theory has evolved since the pioneer studies of James Croll and Milutin Milankovitch, reviews recent evidence that supports the theory, and argues that a major opportunity is at hand to investigate the physical mechanisms by which the climate system responds to orbital forcing. After a survey of the kinds of models that have been applied to this problem, a strategy is suggested for building simple, physically motivated models, and a time-dependent model is developed that simulates the history of planetary glaciation for the past 500,000 years. Ignoring anthropogenic and other possible sources of variation acting at frequencies higher than one cycle per 19,000 years, this model predicts that the long-term cooling trend which began some 6000 years ago will continue for the next 23,000 years.” [Full text]

Variations in the Earth’s Orbit: Pacemaker of the Ice Ages – Hays et al. (1976) “Three indices of global climate have been monitored in the record of the past 450,000 years in Southern Hemisphere ocean-floor sediments. … The 42,000-year climatic component has the same period as variations in the obliquity of the earth’s axis and retains a constant phase relationship with it. … The 23,000-year portion of the variance displays the same periods (about 23,000 and 19,000 years) as the quasi-periodic precession index. … The dominant, 100,000-year climatic component has an average period close to, and is in phase with, orbital eccentricity. … It is concluded that changes in the earth’s orbital geometry are the fundamental cause of the succession of Quaternary ice ages.” [Full text]

Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem – Milankovic (1941) Ruddiman (2006) says: “The starting point for understanding orbital forcing of climate (and specifically the ice ages) is Milankovitch (1941), who hypothesized that summer insolation changes at the periods of orbital tilt and precession drive northern hemisphere ice volume. He proposed summer ablation as the physical mechanism that connects this forcing and response, and he noted that the slow ice response should lag approximately 5K behind the summer insolation signal.”

On the excentricity of the Earth’s orbit, and its physical relations to the glacial epoch – Croll (1867)