Astronomical Theory Research Articles

The Man in the Moone and the New Astronomy: Godwin, Gilbert, Kepler

My study discusses the sources of a text which has strong claims to being regarded as the first piece of science fiction in the English language. The Man in the Moone (1638) by Francis Godwin recounts an imaginary journey to the moon by its hero, Domingo Gonsales. It was written in the context of new astronomical theories, among which the most well known are those of Copernicus, Tycho Brahe and Galileo. Although some of his contemporaries (for example John Donne and William Drummond of Hawthornden) expressed disquiet about the unsettling implications of such theories, Godwin uses them as a central element in his story. Like Kepler, in his Somnium …de astronomia lunaris, Godwin utilises fiction in order to confirm aspects of new scientific theory — especially the diurnal rotation of the earth. But, as I show, his imaginary journey chiefly draws on the magnetic philosophy of this English contemporary, William Gilbert, especially the lunar theory proposed by Gilbert in his De magnete and further elaborated in his De mundo sublunaris.

Levi ben Gershom's Criticism of Ptolemy's Astronomy

Levi ben Gershom or Gersonides (1288-1344), one of the most original thinkers of the Middle Ages, devoted the first section of the fifth book of his Milhamot ha-Shem to an exposition of his astronomical system, which was based on his own observations and departed in many respects from prevailing views. Heir to a long tradition of criticism of Ptolemy, which he associated notably with al-Bitrūjī Book on the Configuration [of the World], but which reached him also through Maimonides' Guide and Averroes' Epitome of the Almagest, Gersonides tried to reconcile the physical and the mathematical descriptions of the heavenly motions and provide a true picture of the configuration of the world. The long chapters 43 and 44 of his Astronomy are devoted, respectively to the demonstration that neither Ptolemy's nor al-Bitrūjī's astronomical theories can be true. Critical editions of the Hebrew and Latin versions of chapter 43 are presented here, along with an annotated English translation.

Astronomical theory of climate change

The astronomical theory of paleoclimates aims to explain the climatic variations occurring with quasi-periodicities lying between tells and hundreds of thousands of years. Such variations are recorded in deep-sea sediments, in ice sheets and in continental archives. The origin of these quasi-cycles lies in the astronomically driven changes in the latitudinal and seasonal distributions of the energy that the Earth receives from the Sun. These changes are then amplified by the feedback mechanisms which characterize the natural behaviour of the climate system like those involving the albedo-, the water vapor-, and the vegetation- temperature relationships. Climate models of different complexities are used to explain the chain of processes which finally link the long-term variations of three astronomical parameters to the long-term climatic variations at nine scale of tells to hundreds of thousands of years. In particular, sensitivity analysis to the astronomically driven insolation changes and to the CO2 atmospheric concentrations have been performed with the 2-dimension climate model of Louvain-la-Neuve. It could be shown that ibis model simulates more or less correctly the entrance into glaciation around 2.75 Myr BP, the late Pliocene-early Pleistocene 41-kyr cycle, the emergence of the 100-kyr cycle around 850 kyr BP and the glacial-interglacial cycles of the last 600 kyr. During the Late Pliocene (in all ice-free - warm world) ice sheets can only develop during times of sufficiently low summer insolation. This occurs during large eccentricity times when climatic precession and obliquity combine to obtain such low values, leading to the 41-kyr period between 3 and 1 Myr BP. Oil the contrary in a glacial world, ice sheets persist most of the time except when insolation is very high in polar latitudes, requiring large eccentricity again, but leading this time to interglacial and finally to time 100-kyr period of the last 1 Myr. Using CO2 scenarios, it has been shown that stage II and stage I request it high CO2 to reach the interglacial level. Moreover. the insolation pattern at both stages and modeling results lead to conclude that stage II is a better analogue for our future climate than the Eem. Although the insolation changes alone act as a pacemaker for the glacial-interglacial cycles. CO2 changes help to better reproduce past climatic changes and. in particular. the air temperature and the southern extend of the Northern Hemisphere ice sheets. Insolation and CO2 scenarios for the next 130 kyr lead to all interglacial which will most probably last particularly lone (50 kyr). This conclusion is reinforced by the possible intensification of the greenhouse effect which might result from man's activities over the next centuries.

The Antarctic ice sheet and the triggering of deglaciations

A new physical mechanism involving the Antarctic ice-sheet extent is able to link climatic and CO 2 glacial–interglacial changes. It is furthermore able to explain many features of the glacial cycles, like the 100 kyr oscillations or the peculiarities of stage 11 (about 400 kyr BP). Indeed, from recent results, the glacial ocean bottom waters were possibly much more saline and consequently, may have an unsuspected large density. This glacial deep stratification could account for a significant part of the glacial–interglacial CO 2 difference. The formation of these waters around Antarctica involves brine rejection over the continental shelves and is directly linked to changes in sea ice formation and Antarctic ice-sheet extent. Using this new scenario, we formulate a conceptual model that reproduce the succession and the amplitude of glaciations over the last few million years. This new mechanism furthermore provides the clue to understanding the changes in the main climatic frequency from 23 to 41 ka about 3 Myr ago and from 41 to 100 ka about 1 Myr ago. The Antarctic ice-sheet influence on bottom water formation could provide the “missing piece” to complete the astronomical theory of Quaternary climates.

Fifty-thousand-year vegetation and climate history of Noel Kempff Mercado National Park, Bolivian Amazon

Pollen and charcoal records from two large, shallow lakes reveal that throughout most of the past 50,000 yr Noel Kempff Mercado National Park, in northeastern lowland Bolivia (southwestern Amazon Basin), was predominantly covered by savannas and seasonally dry semideciduous forests. Lowered atmospheric CO 2 concentrations, in combination with a longer dry season, caused expansion of dry forests and savannas during the last glacial period, especially at the last glacial maximum. These ecosystems persisted until the mid-Holocene, although they underwent significant species reassortment. Forest communities containing a mixture of evergreen and semideciduous species began to expand between 6000 and 3000 14C yr B.P. Humid evergreen rain forests expanded to cover most of the area within the past 2000 14C yr B.P., coincident with a reduction in fire frequencies. Comparisons between modern pollen spectra and vegetation reveal that the Moraceae-dominated rain forest pollen spectra likely have a regional source area at least 2–3 km beyond the lake shore, whereas the grass- and sedge-dominated savanna pollen spectra likely have a predominantly local source area. The Holocene vegetation changes are consistent with independent paleoprecipitation records from the Bolivian Altiplano and paleovegetation records from other parts of southwestern Amazonia. The progressive expansion in rain forests through the Holocene can be largely attributed to enhanced convective activity over Amazonia, due to greater seasonality of insolation in the Southern Hemisphere tropics driven by the precession cycle according to the Milankovitch Astronomical Theory.

Amplitude and phase of glacial cycles from a conceptual model

The astronomical theory of climate, in which the orbital variations of the Earth are taken to drive the climate changes, explains many features of the paleoclimatic records. Nevertheless, the precise link between insolation variations and climatic changes during the Quaternary remains mysterious in several aspects. In particular, the largest sea level changes of the past million years occurred when insolation variations were minimal, like during stage 11, and vice versa like during stage 7. Moreover, recent data from terminations II and III show surprising phase lead and lag between insolation and sea level variations. To explain these paradoxical amplitude and phase modulations, we suggest here that deglaciations started when a combination of insolation and ice volume was large enough. To illustrate this new idea, we present a simple conceptual model that simulates the sea level curve of the past million years with very realistic amplitude modulations, and with good phase modulations.

Modern climatic data for the Pleistocene: Implications for a new concept of the orbital theory of paleoclimate

Based on analysis of paleoclimate data for the Pleistocene (and the Phanerozoic as a whole), this paper advances a new concept of the orbital (astronomical) theory of paleoclimate. The need for a new concept is shown to be necessitated by two circumstances. The first is the grave disagreement between the M. Milankovitch theory and empirical data. The second is the considerable drawbacks of this theory, which is currently viewed as being analogous to the astronomical theory of paleoclimate. In particular, the paper shows that the insolation curves calculated by Milankovitch for individual latitudes and caloric half-years (not to mention months or even days, as in the works of Milankovitch's followers) have no global paleoclimatic significance and cannot be used in paleoclimate reconstructions or modeling. Notions developed in the framework of the new concept provide a systematic basis on which to explain the singularities of climate changes coupled to orbital periodicities during the dierent geologic eras of the Phanerozoic. For example, proposed is a systematic approach to solving the issues of the 100-ka climatic periodicity of the Pleistocene, the mid-Pleistocene transition, and the lack of the 400-ka climatic periodicity within the last two million years.

Milutin Milanković (1879 - 1958) and his contribution to European astronomy

The contribution to European astronomy of Milutin Milankovic is analyzed. A crater on the far side of the Moon, a crater on Mars, and asteroid 1605 are named after this most distinguished Serbian astronomer. He explained the phenomenon of the ice ages by an astronomical theory. Milankovic elucidated also the history of the Earth’s climate as well as that of planet Mars, and in addition he was the author of the mathematical theory of climate and of the Earth’s polar motion. He did important contributions to celestial mechanics and the history of astronomy, and was a great popularizator of science. At the orthodox church council in 1923 in Istanbul, he submitted a proposal concerning the reform of the calendar, elaborated by him and by Maksim Trpkovic, providing for a more exact calendar than the Gregorian one. The calendar of Milankovic is now used by some orthodox churches, such as the Greek and Romanian ones.

From the astronomical theory of paleo-climates to global warming

The future of our climate is a primary concern not only at the human time scale but also at the geological time scale. At both time scales, modeling the climate system, estimating the climatic sensitivity from past climates or researching best analogs in the past are the most usual tools to predict what might be the future climate. Most of the time, paleoclimatologists feel that the last interglacial is a good candidate for our future warm climate. They study its stability and length that they compare to our pre¬ sent interglacial. Limitations to such procedures have been stressed. In particular, a special attention must be care to the forcings of past climates (both insolation and C02, in particu¬ lar) because they are important factors which shape the complex latitudinal distribution and seasonal cycle of the world climates. At least from the astronomical point of view the Eemian is not a good choice for the future of the Holocene. Better candidates would be around 400,000 YBP (isotopic stage 11) and even better around 2,000,000 YBP where interglacials lasted longer than during the middle Pleistocene. But first of all, it must be stressed that the orbital forcing for the present and next tens of thousands of years is almost unique, that the predicted C02 con- centration for the next centuries (and already the present ones) are unprecedented and finally that, according to our modeling results, the present Holocene interglacial will, most probably, last exceptionally long, with no counterpart over the last million years. Such a long duration is a very robust feature in our numerical experiments. It seems to be related to the pretty high value of CO 2 which lasts already since 10 kyr BP compensating for the declining astronomical forcing. In addition, our results show not only that the Holocene might last particularly long, but also that the sensitivity of our climate system to the green¬ house gas forcing might be exacerbated. As a consequence, there is a threshold in the greenhouse gas concentration of about 700 ppmv beyond which the Greenland ice sheet melts in about 5000 years and does not recover before a few tens of thousands of years. Such results reinforce the need of limiting the greenhouse gas emissions from human activities as soon as possible. In Bel¬ gium, in particular, one way of doing it efficiently is without any doubt by increasing the share of our electricity production from the nuclear sector. Scenarios for the next decades show clearly that this is unavoidable if Belgium is willing to meet its Kyoto target.

An outsider's review of the astronomical theory of the climate: is the eccentricity-driven insolation the main driver of the ice ages?

Although the astronomical theory of the climate (also known as the “Milankovitch” theory) explains a number of key features of the paleoclimate time series (especially frequency and phase distribution) in terms of orbital influence on the waxing and waning of ice sheets, it still faces several important unresolved challenges. In this review, we discuss five main challenges we believe the theory must resolve in order to survive: (1) The large amplitude of the ∼100 ky ice age cycles; (2) the switch from 41-ky- to 100-ky-long glaciations around 0.9 Ma BP; (3) the absence of significant spectral power at 413 ky over the past 1.2 Ma; (4) the variation in glacial cycle duration in the last 800 ky; and (5) the presence of non-orbital spectral peaks in the climate record. But in spite of these problems, we conclude that the Milankovitch theory may still be a viable one; at least in the original sense of Hays et al. [Science 194 (1976) 1121], that orbital changes somehow influenced the ice ages. Many investigators, ourselves included, appear to see the impact of orbital forcing in the data, clear evidence of astronomical forcing, as well as evidence which suggests that the climate system responds nonlinearly to all Milankovitch (orbital) frequencies.

Glacial cycles: Toward a new paradigm

The largest environmental changes in the recent geological history of the Earth are undoubtedly the successions of glacial and interglacial times. It has been clearly demonstrated that changes in the orbital parameters of our planet have a crucial role in these cycles. Nevertheless, several problems in classical astronomical theory of paleoclimate have indeed been identified: (1) The main cyclicity in the paleoclimatic record is close to 100,000 years, but there is no significant orbitally induced changes in the radiative forcing of the Earth in this frequency range (the “100‐kyr problem”); (2) the most prominent glacial‐interglacial transition occurs at a time of minimal orbital variations (the “stage 11 problem); and (3) at ∼0.8 Ma a change from a 41‐kyr dominant periodicity to a 100‐kyr periodicity occurred without major changes in orbital forcing or in the Earth's configuration (the “late Pleistocene transition problem”). Additionally, the traditional view states that the climate system changes slowly and continuously together with the slow evolution of the large continental ice sheets, whereas recent high‐resolution data from ice and marine sediment cores do not support such a gradual scenario. Most of the temperature rise at the last termination occurred over a few decades in the Northern Hemisphere, indicating a major and abrupt reorganization of the ocean‐atmosphere system. Similarly, huge iceberg discharges during glacial times, known as Heinrich events, clearly demonstrate that ice sheet changes may also be sometimes quite abrupt. In light of these recent paleoclimatic data the Earth climate system appears much more unstable and seems to jump abruptly between different quasi steady states. Using the concept of thresholds, this new paradigm can be easily integrated into classical astronomical theory and compared with recent observational evidence. If the ice sheet changes are, by definition, the central phenomenon of glacial‐interglacial cycles, other components of the climate system (atmospheric CO2 concentration, Southern Ocean productivity, or global deep‐ocean circulation) may play an even more fundamental role in these climatic cycles.

The 100 kyr cycle of deglaciation during the last 450 kyr: a new interpretation of oceanic and ice core data

Evolution of global ice volume over the last 2.5 Myr is examined using high resolution δ 18O records from deep sea cores in the Atlantic and Pacific oceans. Prior to 0.9 Myr BP, δ 18O variations occur almost exclusively at the 41 kyr frequency. An increase in δ 18O amplitudes is observed after 0.73 Myr BP accompanied by the 100, 41, 23 and 19 kyr frequencies. The deep sea δ 18O records and temperature records from Vostok ice cores show similar variations linked to the movement of planets as described by the astronomical theory. The 100 kyr frequency is equal to 124 kyr for the last two glaciations, and 83 kyr for the earlier two glaciations. The appearance of 23 and 19 kyr frequencies after 0.73 Myr indicates that the equatorial bulge of the Earth responsible for this forcing seems to be a recent geological phenomenon. The deglaciations over the 450 kyr BP would result from a change of orbital forcing and a weaker climate coupling of the hemispheres. The northern orbital forcing (41 and 23 kyr frequencies) would be replaced by the obliquity forcing (41 frequency). The succession of these two orbital forcings seems to be similar for the last four glaciations.

Reply to Saliba

Professor Saliba takes exception to views expressed in my Review Essay (“Conaguring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy,” Perspectives on Science 1998, vol. 6, no. 3, pp. 288–330). His criticisms and reservations mainly relate to questions about the character and the value of what I have called the hay’a project in Islamic astronomy, how and when this project was launched, and about contrasts with other projects and approaches in the same discipline, especially concerning the important question of the relations between physics and mathematics as viewed by the practitioners of the discipline. The following brief comments, kindly solicited by the editors of Perspectives on Science, are meant to sharpen some of our more serious differences, and, hopefully, to remove some misunderstandings. First, with regard to the term hay’a, Saliba makes too much of the term itself as an indication of when a new, and speciacally Islamic, project came into existence. Hay’a is a common Arabic word which means shape, agure or form; and, whether or not it originally rendered a Greek term, it could equally apply to the Aristotelian form (we now say “conaguration”) of the universe as a structure of homocentric spheres, and to the Ptolemaic system of eccentric spheres and epicycles. As Saliba knows, the term appears in the title of one manuscript of the Arabic version of Ptolemy’s Planetary Hypotheses, and could be applied to something as simple as the agure (hay’a) of the earth. That the term came to refer to the science of astronomy in general is therefore not surprising: it emphasized a tendency, prevalent among a large number of Islamic astronomers, to view astronomical theory as primarily concerned to represent the heavens in terms of nested solid spheres obeying some physically accepted principles of motion. Thus an early use of the word hay’a does not by itself imply the motivations and

Evidences of precession and obliquity orbital forcing in oxygen-18 isotope composition of Montalbano Jonico Section (Basilicata, southern Italy)

Quantitative signal processing methods have been applied to a δ 180 profile for a land-based stratigraphic section, extending from the upper part of lower Pleistocene to the lower part of middle Pleistocene. The section is well exposed with a continuous succession of muds and muddy silts, about 400 m thick, located in the southernmost part of Bradano Trough, near Montalbano Jonico in Basilicata (south Italy). The sampled part of the section is about 240 m thick, in which a foram benthic species ( Cassidulina carinata) is continuously available for oxygen isotope ratio measurements. The aim of the data treatment is to discover how much of the Earth's orbital periodic movements, precession and obliquity, which represent the dominant periodicities in paleoclimatic variations from the base of the Pleistocene until 0.735 Myr BP, are responsible for the oscillations observed in the oxygen-18 record of the Montalbano Jonico section. A time framework of the section was constructed on the basis of calcareous nannofossil biostratigraphic analyses, preliminary magnetostratigraphic results and oxygen isotope correlation with the record from DSDP s607 (isotope data collected in the NOAA World Data Center). The resulting time-scale extends from 1.15 to 0.74 Myr. Power spectrum analysis was performed on the isotope data to illuminate the most important periodicity components of the Montalbano Jonico record. The periodic components of 41,000 and 21,000 yr are present in this record; the former associated with periodic changes in the tilt of Earth's axis and the latter with periodic changes with the precession of the equinoxes, as predicted by the astronomical theory of ice ages. They are, however, not the most important components of the power spectrum, in which a lower frequency component contains most of the variance. This low-frequency component is centered at a period around 208,000 yr. This periodicity seems not to be attributable to any known astronomical or paleoclimatic phenomenon. An attempt was made to verify if this periodicity was due to the composite effect of precession and obliquity signals together at different frequencies from their forcing frequencies. In order to investigate this effect, isotope data have been parameterized in terms of a sum of simple functions of precession and obliquity signals with unknown coefficients. The coefficients are estimated from the time series with the assumption that the best coefficients are those which minimize the ‘noise’ i.e. the difference between the data function and the precession and obliquity functions. Cross-spectra analyses were also performed on the data and the precession signal and on the data and the obliquity signal. The power spectrum of the residual ‘noise’ functions and the cross-spectra demonstrate that precession and obliquity signals are not in phase with the data at their forcing frequencies and so damp. The precession and obliquity signals were then shifted towards lower frequencies at equally spaced lags, the resultant ‘noise’ power spectra were plotted for every combination of lags of precession and obliquity. The results of this data processing demonstrate that it is possible to have a combination of precession and obliquity cyclicities that could be responsible for the signal with 208 kyr periodicity.

Astronomical calibration of loess–paleosol deposits at Luochuan, central Chinese Loess Plateau

The 140 m loess–paleosol profile at Luochuan in the central Chinese Loess Plateau was sampled at 5-cm intervals in loess units and at 3 cm in paleosol units, in order to obtain a high resolution climatic record covering the past 2.5 million years. All samples were measured for magnetic susceptibility, which is regarded as a good proxy index of the East Asian summer monsoon strength. On the basis of the astronomical theory of Pleistocene climatic change, an age model of the Luochuan loess–paleosol sequence was developed by tuning the magnetic susceptibility record to time-series of insolation changes. The results show that the ages of the boundaries between the Malan and Lishi, and Lishi and Wucheng loess formations are 71 and 1320 kyr BP, respectively. The onset of loess accumulation is at 2470 kyr BP. Our age model was tested by comparing the orbitally derived ages with absolute age determinations of magnetic reversals, and cross-spectrum analyzing with solar radiation variations for summer at 65°N. These indicate that the calibration provides a reliable time scale for the Luochuan loess–paleosol deposit.

Sedimentary cycles and volcanic ash beds in the Lower Pliocene lacustrine succession of Ptolemais (NW Greece): discrepancy between 40Ar/ 39Ar and astronomical ages

A high-resolution cyclostratigraphy for the rhythmically bedded lignite–marl sequences of the Lower Pliocene Ptolemais Formation is combined with 40Ar/ 39Ar dating results of intercalated volcanic ash beds. Detailed field reconnaissance in three open-pit lignite mines reveals three end-member sediment types: lignites, composed primarily of organic material; grey marls, a mixture of carbonate and organic material; and beige marls, almost exclusively composed of carbonate. These lithologies are arranged in two basic types of sedimentary cycles: lignite–grey marl and lignite–beige marl cycles. A cyclostratigraphic composite section comprising 56 lignite–marl cycles is constructed which combines the consistent cycle patterns from three parallel sections. The concordant positions of 20 volcanic ash beds in these sections confirm the cyclostratigraphic correlations and indicate that the lignite–marl cycles result from regional, basin-wide forcing rather than lateral facies migrations. 40Ar/ 39Ar ages on sanidine and biotite separates from nine volcanic ash beds were obtained by multiple total fusion and incremental-heating experiments. The 40Ar/ 39Ar ages range between 5.00±0.05 and 4.04±0.04 Ma and are, in general, consistent with the stratigraphic order. A least-square linear regression using the measured 40Ar/ 39Ar ages gives an average duration of 21.8±0.8 kyr per lignite–marl cycle. Evidently, the lignite–marl cycles in the Ptolemais Formation are linked to the precessional variation in the Earth's orbit through its influence on Mediterranean climate. For the first time, 40Ar/ 39Ar dating results, totally independent from any other dating and or tuning technique, confirm the astronomical theory of climate change. The 40Ar/ 39Ar ages of the volcanic ash beds show a constant ∼200 kyr (∼4.5%) age discrepancy with the astronomical ages of the same ash beds. This inconsistency remains difficult to explain. The discrepancy is unlikely to have resulted from erroneous astronomical ages, through incorrectness in the astronomical tuning, inaccuracies of the magnetostratigraphic data or the orbital time-series used, and/or errors in the APTS. The 40Ar/ 39Ar dating results neither give clear indications for a possible source of error. From the excellent data set it is evident that neither loss of radiogenic 40Ar, nor an underestimation of the contribution of Ca- and K-derived Ar isotopes could have caused the discrepancy. Moreover, the discrepancy is also beyond the errors in the systematic variables, like the decay constants of 40K or the ages for the neutron-fluence monitors.

Why the Ice Ages Don't Keep Time

The ice ages and other recent climate change should come and go with clocklike regularity, or so the astronomical theory that links these changes to variations in Earth9s orbit and spin axis implies. But the ice ages don9t quite keep time, raising doubts about how much the astronomical theory can explain. Now, on page 564, a geophysicist explains why the timing of the ice ages seems to be off by invoking an interaction between orbital forcings that resembles the way FM radio signals are generated. And on page 568, researchers present a new record of the start of the ice ages 2.75 million years ago that ties them to an intensification of one orbital cycle.

Processes of buildup and retreat of the Greenland Ice Sheet

Sensitivity experiments were conducted to study the influence of several physical processes on the evolution of the Greenland ice sheet over the last 250,000 years. The experiments were carried out by means of a three‐dimensional thermodynamical model. The mass balance is modeled by a surface energy balance model. This means that variations in orbital parameters following from the astronomical (Milankovitch) theory can be incorporated in the ablation calculations. It is shown that with regard to the Greenland ice sheet, variations in shortwave radiation are only of minor importance for the changes in volume over time. Calculations of the various components of the energy balance under glacial and interglacial conditions show that the changes in absorbed shortwave radiation resulting from changes in orbital parameters are considerably smaller than the variations in the sensible heat flux caused by temperature variations. Thermodynamics are only of importance for the volume changes of the ice sheet if the climate, is on average, stable over a long period. In between 110 kyr B.P. and 20 kyr B.P. the ice volume increased slowly due to the cooling of the ice, which resulted in a higher effective viscosity and thus a thicker ice sheet. The long response time of the thermodynamics means that the thermodynamics cannot play a crucial role during transition from a glacial to a deglacial period which occur typically within several thousands of years. The mass balance height feedback has an important function in the buildup of the ice sheet after a warm period like the Eemian. Without isostatic bedrock compensation the ablation will remain very high in some marginal parts, yielding a considerably smaller ice sheet volume for the last glacial period.

The timing of Pleistocene glaciations from a simple multiple-state climate model

The Earth's climate over the past million years has been characterized by a succession of cold and warm periods, known as glacial–interglacial cycles, with periodicities corresponding to those of the Earth's main orbital parameters; precession (23 kyr), obliquity (41 kyr) and eccentricity (100 kyr). The astronomical theory of climate, in which the orbital variations are taken to drive the climate changes, has been very successful in explaining many features of the palaeoclimate records1. Nevertheless, the timing of the main glacial and interglacial periods remains puzzling in many respects2,3,4,5. In particular, the main glacial–interglacial switches occur approximately every 100 kyr, but the changes in insolation forcing are very small in this frequency band. Similarly, an especially warm interglacial episode, about 400,000 years ago7, occurred at a time when insolation variations were minimal. Here I propose that multiple equilibria in the climate system can provide a resolution of these problems within the framework of astronomical theory. I present two simple models that successfully simulate each glacial–interglacial cycle over the late Pleistocene epoch at the correct time and with approximately the correct amplitude. Moreover, in a simulation over the past 2 million years, the onset of the observed prominent ∼100-kyr cycles around 0.8 to 1 million years ago is correctly reproduced.

Charles Lyell and climatic change: speculation and certainty

Abstract In the first edition of the Principles of Geology , Charles Lyell announced his theory of the geographical determination of climate and speculated on possible climatic changes during the geological and historical past. In light of the subsequent discovery of ice ages, the proliferation of theories of climatic change, and the great climate debates of his time. Lyell’s theory remained remarkably stable. This paper examines Lyell’s appropriation, modification and rejection of the views of his contemporaries. It provides perspectives on elite and popular ideas of climate and climatic change from the late eighteenth century to 1875, examines Lyell’s position on climatic change in geological and historical times, and explores in some detail the mutual influences of Lyell and James Croll, the proponent of an astronomical theory of ice ages.