Milankovitch Theory and Climate

REVIEWS OF GEOPHYSICS, VOL. 26, NO. 4, PAGES624-657, NOVEMBER1988

MILANKOVITCH THEORY AND CLIMATE

A. Berger Institut d'Astronomieet de GeophysiqueG. Lema•tre, Universit• Catholique de Louvain Louvain-la-Neuve, Belgium

Abstract. Among the longest astrophysical and detailed seasonal cycle) is considered for the astronomical cycles that might influence climate different latitudes, their long-term deviations (and even amongall forcing mechanismsexternal to can be as large as 13%of the long-term average, the climatic system itself), only those involving and sometimes considerable changes between extreme variations in the elements of the Earth's orbit values can occur in less than 10,000 years. Mod- have been found to be significantly related to the els of different categories of complexity, from long-term climatic data deduced from the geologi- conceptual ones to three-dimensional atmospheric cal record. The aim of the astronomical theory of general circulation models and two-dimensional paleoclimates, a particular version of which being time-dependent models of the whole climate system, due to Milankovitch, is to study this relationship have now been astronomically forced in order to between insolation and climate at the global test the physical reality of the astronomical scale. It comprises four different parts: the theory. The output of most recent modeling ef- orbital elements, the insolation, the climate forts compares favorably with data of the past model, and the geological data. In the nineteenth 400,000 years. Accordingly, the model predictions century, Croll and Pilgrim stressed the importance for the next 100,000 years are used as a basis for of severe winters as a cause of ice ages. Later, forecasting how climate would evolve when forced mainly during the first half of the twentieth by orbital variations in the absence of anthropo- century, K•ppen, Spitaler, and Milankovitch re- genic disturbance. The long-term cooling trend garded mild winters and cool summers as favoring which began some 6,000 years ago will continue for glaciation. After K•ppen and Wegener related the the next 5,000 years; this first temperature mini- Milankovitch new radiation curve to Penck and mum will be followed by an amelioration at around Br•ckner's subdivision of the Quaternary, there 15 kyr A.P. (after present), by a cold interval was a long-lasting debate on whether or not SUCh centered at 23 kyr A.P., and by a major glaciation changes in the insolation can explain the Quatern- at around 60 kyr A.P. ary glacial-interglacial cycles. In the 1970s, with the improvements in dating, in acquiring, and 1. Introduction in interpreting the geological data, with the advent of computers, and with the development of The main purpose of this paper is to explain astronomical and climate models, the Milankovttch and to review the astronomical theory of paleocli- theory revived. Over the last 5 years it overcame mates that provides us with the opportunity to most of the geological, astronomical, and climato- better understand the dynamical behavior of the logical difficulties. The accuracy of the long- climate system. In the process I will also illu- term variations of the astronomical elements and strate this theory (Figure 1) to be both at a of the insolation values and the stability of crossing point of geology, astronomy, physics, their spectra have been analyzed by comparing chemistry, biology, and geophysics (all unions of seven different astronomical solutions and four the International Council of Scientific Unions) different time spans (0-0.8 million years before and related to processes of the solid Earth, the present (Myr B.P.), 0.8-1.6 Myr B.P., 1.6-2.4 Myr atmosphere, the hydrosphere, and the oceans (all B.P., and 2.4-3.2 Myr B.P.). For accuracy in the at the basis of the International Union of Geodesy time domain, improvements are necessary for per- and Geophysics (IUGG) associations). From this iods earlier than 2 Myr B.P. As for the stability point of view, it is a most fitting subject for of the frequencies, the fundamental periods global change studies [Malone and Roederer, 1984; (around 40, 23, and 19 kyr) do not deteriorate National Research Council, 1986]. It is also an with time over the last 5 Myr, but their relative example of an application of pure fundamental importance for each insolation and each astronomi- science that not only aims toward better under- cal parameter is a function of the period consid- standing, in this case of climate, but has appli- ered. Spectral analysis of paleoclimatic records cations that are directly relevant to the future has provided substantial evidence that, at least of our modern world. near the obliquity and precession frequencies, a This paper will be broadly subdivided into considerable fraction of the climatic variance is three parts: (1) climate changes at the astronom- driven in someway by insolation changesforced by ical frequencies, (2) Milankovitch theory as a changesin the Earth's orbit. Not only are the particular case of astronomical theories, and (3) fundamental astronomical and climatic frequencies revival of the astronomical theory since 1975, alike, but also the climatic series are phase- including modeling. locked and strongly coherent with orbital variations. Provided that monthly insolation (i.e., a 2. Paleoclimates and Quaternary Glacial-Interglacial Cycles

Copyright 1988 by the American Geophysical Union. If we first assume that a record of the atmospheric global mean temperature for the Earth's Paper number 8R0239. surface is available for the whole history of the 8755-1209/88/008R-0239505. O0 Earth, then its idealized variance spectrum (Fig-

624 Berger: Milankovitch Theory and Climate 625

ASTRONOMICAL THEORY

PALEOCLIMATES

A RELEVANT EXAMPLE FOR GLOBAL CHANGE

Solid Earth Atmosphere I•drolo•

Fig. 1. The astronomical theory of paleoclimates, an inter-union and IUGG inter-association problem. ure 2) would illustrate the large variability in ice ages (the glacial-interglacial stages of the time of this parameter. (Recently, Imbrie and Quaternary). They are also related to determinis- Shackleton [1986] have started collaborating on a tic astronomical variations in the orbital parame- project to evaluate such a distribution of climat- ters of the Earth [Milankovitch, 1941]: the cycle ic variance over a broad range of frequencies. at around 21,000 years to the axial precession; This project uses some of the records that have the period of about 41,000 yea•s to the change in been generated from Deep-Sea Drilling Project the obliquity of the ecliptic, or the axial tilt; sites as well as Pleistocene and Holocene records and the cycle at about 100,000 years to the eccen- and should provide fundamental insights into the tricity of the orbit of the Earth. Finally, the character of climatic change in Earth history.) peaks near 45 and 350 million years may be related As visualized by Mitchell [1976], the spectrum to glaciations due to orogenic and tectonic ef- shows a background level of variability, deriving fects and to the "drift" of the continents (plate from internal stochastic mechanisms and corres- tectonics). The astronomical theory thus focuses ponding to a low degree of predictability, which on one of the very well known deterministic forc- appears to increase in amplitude toward the longer ing mechanisms of the climate system, that of the time scales, superimposed on which is band-limited variations in the Earth's orbital parameters, and variability due to external forcing processes and on the characteristic frequencies of the climatic correspondingly to a much higher degree of pre- response [Berger et al., 1984]. dictability (narrow spikes and broader peaks). Our planet Earth was born some 4.5 billion The spikes are astronomically dictated; they are years ago. Many important events mark its evolu- strictly periodic components of climate variation, tion [Crowley, 1983]: suchas the diurnaland annual variations and 1. T•e earliest formof life datesback their harmonics, whereas the peaks represent var- 3.5 x 10 years ago. iations that are, accordingto Mitchell, either 2. T•e first appearanceof plants on land was quasi-periodic or aperiodic, but with a preferred 450 x 10v years ago. timeis associatedscale of withenergization. the synopticThe disturbancespeak at 3-7 daysmain- seams)3. Extensiveformed 300swampg x 10 years(at the ago.origin of coal ly at middlelatitudes. Theslightly raisedreg- 4. Openingof the Atlantic started 220x 106 ion of the spectrum at 100-400 years is associated ,years ago with the breakup of Pangaea. with variationson the time scale of, for example, 5. Dinosaursdisappeared 70 x 106years ago, the "Little Ice Age,"which began in theearly anda majorradiation of modernorders of mammals seventeenth century with rapid expansion of the occurred from 70 to 50 x 10 years B.P. At this mountain glaciers in Europe. The peak near 2500 time the evolution of the Rocky Mountains began. years is, perhaps,due to the coolingobserved 6. Alpine orogenesisstarted 40 x 106years after the so-calledpostglacial "Climatic Optimum" ago, and the Himalayanmountain building, 20 x 106 (also named the Atlantic interstade or hypsitherm- years later. al in the American literature) which predominated This long history has been studded with periods during the great ancient civilizations about 5000 when the climate has been markedly colder than at years ago and might be related to the characteris- others. These cold events, the so-called Ice tic time scale of the ocean [Pestiaux et al., Ages, have, on the geological time scale, been 1988]. The next three peaks are related to the relatively short lasting, covering only perhaps 5- 6P6 Berger: Milankovitch Theory and Climate

104 I I I I I I I I I I I

T SPECTRUM SURFACE Tectonic Annual revolution

Diurnal Orbital rotation variations

z 1o2

0 >.

0 >'

K IO

0.1 101o 10'9 108 10? 10•' 10$ 104 103 102 10 1 0.1 10-2 10-3 10-4 PERIOD IN YEARS

Fig. 2. Tentative spectrum of climatic variations. Estimate of relative variance of climate over all periods of variation. A background level of variability, deriving from internal stochastic mechanisms and corresponding to a low degree of predictability, appears to increase in amplitude toward the longer time scales and to be overlaid by band-limited variability, due to external forcing processes and corresponding to a high degree of predictability (adapted from Mitchell [1976]).

•o LAST MAJOR CLIMATIC CYCLE O- l "" '•'SENT • GLACIAL ICE SHEETS APPEAR IN N. HEMISPHERE

I00- • •AGE 5 ANTARCTIC ICE SHEET EXPANDS

200 - P[RMO- ANTARCTIC ICE SHEET FORMS; CARBONIFEROUS I MOUNTAIN GLACIERS OCCUR IN 300- BGLAClALAGE THE N. HEMISPHERE

400 - ORDOVICIAN s• I g•o • a5 600 1 CATE •SMALL GLACIERS ARE WIDESPREAD I PRECAM- 7• BRIAN IN ANTARCTICA I GLACIAC 8• j A• {S) o

900 WATERS AROUND ANTARCTICA COOL; SEA ICE FORMS I•a 40

50 •ANTARCTIC-AUSTRALIAN PASSAGE OPENS

55 CENOZOIC DECLINE BEGINS

Fig. 3. The last billion years of climate. Intervals when ice sheets occurred in polar regions are indicated on the left as glacial ages [Frakes, 1979]. An outline of significant events in the Cenozoic climate decline is given on the right (adapted from Imbrie and Imbrie [1979] and reproduced with permission from the authors and Enslow Publishers ). Berger: Milankovœtch Theory and Climate 62?

25 EOCENE JOL'GOCENEJMIOCENE J PL'OCENE QU. I I I I I I I I I I I I kyr B.P., averaged over the whole Earth, is estimated as roughly 4øC lower than today [CLIMAP o 20 Project Members, 1976, 1981; Manabe and Hahn, • - 1977; Webb et al., 1985]. But other changes af- fected also the sea surface temperatures, the sea level [Chappell and Shackleton, 1986], the intens- u• 10 _ = ity of the monsoons in the tropics [Kutzbach and Street-Perrott, 1985; Prell and Kutzbach, 1987], and the size of the ice sheets, particularly in middle and high latitudes of the northern hemisphere [Hughes et al., 1981]. As a matter of fact, this waxing and waning of the ice sheets occurred 60 50 40 30 20 10 0 1 in a more or less regular way: in Figure 5, one MILLIONS OF YEARS can recognize a sawtooth shape with a 100-kyr quasi-cycle over which shorter quasi-cycles of Fig. 4a. Estimate of the change in the averaged roughly 41 and 21 kyr are superimposed. It is surface temperature of central Europe over the these kinds of broad climatic features character- last 60 Myr as it was given by Woldstedt [1961] izing the last few million years (and probably (reprinted from Pollack [1982] with permission of other climatic variations of non-Ice Ages, like the author and the National Academy Press). It those which occurred during the Late Triassic must be pointed out that the Woldstedt time scale [Olsen, 1986]) which are explained by the astro- starts with the Quaternary. Moreover, the chrono- nomical theory of paleoclimates. This theory stratigraphy of the Eocene, Oligocene, Miocene, claims that the changesin the Earth's orbital and Pliocene, and Quaternaryhas been revised since. rotational parametershave been sufficiently large As shownin Figure 4b, they now begin at roughly during the Quaternary as to induce significant 55, 37.5, 22.5, 5, and 1.8 Myr B.P., respectively changes in the seasonal and latitudinal dœstribu- [Van Eysinga, 1983]. On the other hand, the long tions of the extraterrestrial insolation and so to interval of little variability of climate during force glacials and interglacials to recur in the the Tertiary given by Figure 4a reflects the temp- mannerdeduced from geological records. oral resolution and sampling frequency of the geological record, not the real climate history, whichis better depicted in Figure 4b. 3. AstronomicalTheory of Paleoclimates: A Historical Point of View

From the standpoint of climate dynamics the 10% of the Earth's time span. (These geological astronomical approach of glaciation theory is the "periods" (Ice Ages with capital letters) must be oldest explanation of the existence of glacial periods in the geological record of the Quaternary distinguished from the Pleistocene glaciations called Pleistocene ice ages (with lower case let- Ice Age and through the Milankovitch approach, ters) or glacials, which are "stages" at the geo- curremtly the most popular. As early as 1947 a logical time scale [Van Eysinga, 1983]. It is daily newspaper in the Netherlands published a difficult to define precisely an Ice Age. Accord- cartoon in which the present Earth climate was ing to Lamb [1977], it could be "a period when any suddenly entering a glacial stage following a change in the Earth's axis of rotation! islands or bigger landmasses which were then near the poles bore a cover of permanent ice." But it has also been characterized by "a very rapid decrease o[ temperature from low to high latitudes" 3O - • Japan - [Brooks, 1970]. Their occurrence is illustrated --.-- W Europe in Figure 3, in which one can recognize the last m • W North Americo 25 ..... NW U.S.A. /"• Pre-Cambrian Ice Ages, the late Ordovician Ice - ß...... S Englond .•'.f•t' '• ./- Age, the Permo-Carboniferous Ice Age, and our '.,.,./ Present Ice Age (within which we are enjoying the p respite of a marked interglacial stage), which was •, 20 .." preceded by the Antarctic ice sheet formation 25- ...... , 10 Myr B.P. [Kennett, 1977; Savin, 1977]. This • •5 last Ice Age, whichthe Earth entered2-3 x 106 - •.• • ,,'"! . .,'"'.... years ago, is usually called the Quaternary Ice Age. (However, there are many disputes about /,, ! ...... lo whether or not this geological period must be differentiated from the Tertiary [Campy and Cha- line, 1987]. It •s composed of the Pleistocene and the Holocene, which are usually preferred terminology for this period (see Appendix A).) In PI MioceneI I OligoceneI I EoceneI IPole(•cenelCret central Europe, for example, the mean temperature I0 20 :50 40 50 60 70 went down from 20 ø to 5øC (Figure 4). Million years This most recent Ice Age has been characterized by multiple switches of the global climate between Fig. 4b. Tertiary trends of mean annual tempera- glacial (with extensive ice sheets) and interglac- ture from paleobotanical data [Savin, 1977; ial stages. For example, although paleoclimate Frakes, 1979; Lloyd, 1984] (reprinted from Lloyd records are still incomplete, the mean air surface [1984] with permission from the author and Academ- temperature during the last glacial maximum, 20 ic Press and from S. M. Savin and Annual Reviews). 628 Berger: Milankovitch Theory and Climate

Core V28-238 (--tøN,160øE) 0 128 25t 347 440 592 ,,,750 x103 years

of PD8

-2.0%

-t.5%

- t.0%

-0-5%

DEPTH 0 200 400 600 800 t000 t200 t400 t600 IN CM Fig. 5. Oxygenisotope and paleomagneticrecord of the last 1.6 Myr in core V28-238 from the equatorial Pacific (~IøN 160øE) Isotope stages are shownin the upper part of the diagram. Isotopic values are from measurementson Globi•erinoides sacculifer (after Shackleton and Opdyke [1976, p. 453] with permission from the authors and the Geological Society of America).

3.1. Pioneers of the Astronomical Theory can records of the Illinoian deposits, for example, glacial geology became strongly tied to as- In fact, it was only a few years after the tronomy [Meech, 1857]. Before 1864, JamesCroll addressdelivered by L. Agassizin 1837 [Agassiz, initiated a series of importantworks (they are 1838] at the openingof the Helvetic Natural Hist- quotedin Darwin's [1859] book) that wouldcon- ory Society at Neuchatel, "UponGlaciers, Moraines tinue to bear muchfruit into modermtimes. Three and Erratic Blocks," that Adh•mar[1842] published major astronomical factors were recognized in his (in Paris) his book explaining Agassiz's hypothe- model: axial tilt, orbital eccentricity, and sis on the existence of ice ages on the basis of precession. The importance of Croll is that he the knownprecession of the equinoxes (first dis- approachedthe glaciatton problem from the syner- cussedby J. Herschel in 1830), thereby implying gistic standpoint of the combinedeffects of all that there had likely been more than one (see tt•ree of the major astronomical factors on season- Table 1 and Imbrie and Imbrie [1979]). An astron- al insolation during perihelion and aphelion omer in Paris at that time Urbain Le Vernier, [Croll, [875]. A specific characteristic of his famedfor discovering the orbital anomaliesof modelessentially lies in its hypothesisthat the Uranus which led to the discovery of Neptune, critical season for the initiation of glacial immediatelycalculated the planetary orbital stages is northern hemispherewinter. He argued changesof the Earth overthe last 105years [Le that a decreasein the amountof sanlightreceived Verrier, 1855]. during tt•e winter favors the accamulationof snow Within the next decades, largely becauseof the and that any small initial increase in the size of discovery of the repetitive aspect of global glac- the area coveredby snowwould be amplified by the iation in the Vosges,in Wales, and in the Ameri- snowfieldsthemselves (positive feedback). After

TABLE 1. Milestones in Evolution of the Astronomical Theories of Pleistocene Ice Ages

Ast ronomy Climat ology Geology

Pre-Milankovitch Era (Nineteenth Century) 1855 Le Verrier and Pontecoolant 1830 Herschel 1837 Agassiz 1870 Stockwell 1842 Adh•mar 1840 Agassiz 1895 Harzer 1857 Meech 1863 Geckie 1864 Croll 1874 Geckie 1•75 Croll 1894 Da•a 1876 Murphy 1891 Ball 1901 Hildebrandt

Milankovitch Era (1900-1960) 1920 Milankovitch and Pilgrim 1920 Milankovitch 1909 Penck and Br•ckner 1941 Milankovitch and Miskovitch 1921 Spitaler 1930 Eberl 1950 Bro•wer and Van Woerkom 1924 Br•ckner 1955 Emiliani 1924 K•ppen and Wegener 1959 Zeuner 1930 Milankovitch 1937 Soergel 1938 Wundt 1940 Bacsak 1940 Milankovitch 1961 Jardetsky Berger: Milankovitch Theory and Climate 629

J F M A M J J A S 0 N D '1 I I I 1 8O 8O

6O 60

u.I 4O 4O CI 20 o 20

0 i- o••o \ •ø•,'t -- 20- '• -40• 200•oo •øø- 40- -60 o 60-

-80 80-

J F M A M J J A S 0 N D

-;a- MONTH

J F M A M J J A S 0 N D

6O - -I .,, 4O _ • 20 20 i- o _ • 0 i- • -20 -• -4o -6o • • •o 60- -8o -, , 80_ J F M A M J J A S 0 N D

-b- MONTH

Flg. 6. Present-day insolation as a function of latitude and day of the year in watts per square meter (a) at the top of the atmosphere and (b) absorbed at the surface [after Tricot and Berger, 1988]. having determined which astronomical factors con- As time went on, many geologists in Europe and trol the amount of sunlight received during the America became more and more dissatisfied with winter, he concluded that the precession of the Croll's theory, finding it at variance with new equinoxes must play a decisive role. He also evidence that the last ice age had ended not showed that changes in the shape of the orbit 80,000 (according to his view) but 10,000 years determine how effective the precessional wobble is ago. Moreover, theoretical arguments were advanc- in changing the intensity of the seasons. Croll's ed against the theory by meteorologists who calcu- first theory predicts that one hemisphere or the lated that the variations in solar heating des- other will experience an ice age whenever two cribed by Croll were too small to have any notice- conditions occur simultaneously: a markedly elon- able effect on climate (see appendix Table B! for gate orbit and a winter solstice that occurs far some key stages in the evolution of the astronomi- from the Sun. Later, Croll hypothesized that an cal theory). ice age would be more likely to occur during periods when the axis is closer to vertical, for then 3.2. Mœ1ankov[tch Era the polar regions receive a smaller amount of heat. Similar ideas about the astronomical œnflu- It was only during the first decades of the ence on climate changes have been addressed by twentieth century that Spitaler [1921] rejected Ball [1891], Ekholm [1901], and Hœ1debrandt Croll's theory that the conjunction of a long, [1901], who stressed the importance of the preces- cold winter and a short, hot summer provides the sion of the equinoxes, the obliquity of the ec- most favorable condœt[ons for glaciation. He liptic, and a small eccentricity, respectively. adopted the opposite view, first put forward by 630 Berger: Milankovitch Theory and Climate

600 550 550 •5• • $5• • ZS• tO0 I50 ;•a 50 0 •llennia

Fig. 7. The Milankovitcl• radiation curves for latitude 65øN over the past 600,000 years. Milankovitch identified certain low points on the curve with four European ice ages [Milankovttch, 194l]. The top figure is from Milankovitch's 1920 computation according to Stockwell and Pilgrim, and the bottom figure is from his 1941 computation according to Le Verrier and Miskovttch (see Table 1). Vertical axis gives the 65øN Milankovitch equivalent latitudes; time along the horizontal axis is in thousands of years before present.

Murphy [1876], that a long, cool summerand a provided the basis at the heart of his argument short, mild winter are tl•e most favorable. This that "under those astronomical conditions in which diminution of heat during ttle summerl•alf year was the heat budget around the summersolstice falls also recognized by Br•ckner, K•ppen, and Wegener below average, so will summermelt, with uncompen- [BrHckner et al., 1925] as the decisive factor in sated glacial advance being the result." glaciation. Milankovitch, however, was the first This theory requires that the summer in north- to complete a full astronomical theory of Pleisto- ern high latitt•des must be cold to prevent the cene ice ages, computing the orbital elements and winter snow from melting, in such a way as to the subsequent changes in the insolation and cli- allow a positive value in the annual budget of mate. snow and ice, and to initiate a positive feedback Miluttn Milankovitch was a Yugoslavian astron- cooling over the Earth through a further extension omer who was born in Dalj in 1879 and died in of the snow cover and subsequent increase of the Beograd in 1958. He was a contemporary of Alfred surface albedo. On the assumption of a perfectly Wegener (1880-1930), with whomhe becameacquaint- transparent atmosphereand of the northern high ed through Vladimir K•ppen (1846-1940), Wegener's latitudes being the most sensitive to insolation father-in-law [M. Milankovitch, 1950, 1952, 1957; changes, that hypothesis requires a minimum in the Schwarzbach, 1985; V. Milankovitch, My Father: northern hemisphere summer insolation at high Milutin Milankovttch, unpublished manuscript, latitudes. The essential product of the Milanko- 1988]. vitch theory is his curve (Figure 7) that shows Milankovitch's first book dates from 1920, but how the intensity of summer sunlight varied over his massive Special Publication of the Royal Serb- tile past 600,000 years, on which he identified ian Academyof Science was published in 1941 and certain low points with four European ice ages was translated into English only in 1969. Milan- reconstructed 15 years earlier by Albrecht Penck kovitch's main contribution was to explore the and Eduard Br•ckner [Penck and Br•ckner, 1909]. solar irradiance at different latitudes and seasons in great mathematical detail, producing tabu- 3.3. Milankovitch Debate lations and charts of classical and permanent importance, and to relate these in turn with plan- If we consider this curve, however, we are left etary heat balanceas determinedby the planetary in no doubt that Milankovitch's successwas only albedo and by reradiation in the infrared accord- an apparent one, becausethe Quaternaryhas had ing to Stefan's law. Oneof the mostinteresting manymore glacial periods than wasclaimed during results, shownin Figure 6a, was that although the first part of the twentieth century (see Fig- throughout most of the year insolation "at the top ure 5 and Morley and Hays [1981]). of the atmosphere"in equatorial regions under- If irrelevant but long-standing criticisms standably exceeds that of poleward areas, there (Appendix C) are left aside, the main factors are actually brief intervals near the summersol- influencing the dispute were (1) the accuracy of stice within each hemisphere when the reverse is the astronomical solution for the Earth's orbit true, particularly for southerly latitudes. This and rotation and of the related insolations (name- Berger: Milankovitch Theory and Climate 631 ly in polar latitudes), (2) the insolation changes in opposition to Fairbridge [1961], who has re- being too small for overcoming the resilience of ferred to the northern hemisphere middle latitudes the climatic system, and (3) the inaccurate geo- (40o-75 ø) as the latitudes sensitive to climatic logical time scale. change, since approximately 95% of the world's Until roughly 1970 the Milankovitch theory was mountain glaciers are located at this position. largely disputed because the discussions were Kukla, searching for the missing link in the ther- based on fragmentary geological sedime•tary rec- modynamic and meteorological balance of the atmos- ords and because the climate was considered too phere-hydrosphere-cryosphere system, used the resilient to react to "such small changes" in the insolation gradient curves [Kukla, 1972] and summer half-year caloric insolation. This last claimed [K•kla, 1975] to have pinpointed the rel- point was already documented by Simpson [1940], evant time and space coordinates in early autumn using a crude climate model. Moreover, he attrib- and in the continental interiors of North America uted the glacial-interglacial cycles to periodic and Eurasia. oscillations in the intensity of solar radiation, On the other hand, geologists searching for presumed to originate in the output of the Sun correlations between geological and astronomical itself [Simpson, 1934, 1957]. He suggested that times series have also used the most simple models an increase in solar radiation would first raise setting the equilibrium climatic state equal to a the surface temperature and increase evaporation linear combination of astro-insolation curves. everywhere, leading to heavy snowfalls on high Analysis of the idealized curve for surface water ground in high latitudes and consequently to glac- temperature of the Atlantic Ocean given by Emil- iation. Although this ingenious hypothesis does iani [1955] led Broecker [1966] to an astronom- •ot accord with the present observational evi- ical-climatic curve based upon an original combin- dence, it has led to the generation of many other ation of precession, tilt, and eccentricity. The insolation models with moderate success [Berger, overall effect of his weighting factors was to 1980a]. create a deep 18 kyr B.P. minimum, two important The first criteria to test the astronomical maxima at 120 and 80 kyr B.P., and a long period theory used a visual or statistical relationship of intermediate climate between 70 and 22 kyr between minima and maxima of geological and imso- B.P., where the 48 kyr B.P. pro•ninent warm peak lation curves [Brouwer, 1950; Jardetsky, 1961]. found in the Milankovitch curve is greatly de- The Milankovitch summer radiation curve for 65øN pressed. Assuming the half response time for the was used more frequently because of the more ex- continental glaciers to be 3000 years, his ice tensive nature of Pleistocene glaciation in the volume curve became consistent with observa- northern hemisphere. Among the active supporters tions. Following this idea, Broecker et al. of the Milankovitch theory were Soergel [19•7], [1968] used the 45øN insolation curve (where the who introduced a delay between the highest point precession effect is given more weight than is of the ice masses and the lowest point of radia- tilt effect) in such a way that the warm peak at tion; Blanc [19•7], who succeeded in discovering 50 kyr B.P. is largely removed and a new peak the connection between the climatic variations and appears at 106 kyr B.P. These results clearly the variations of sea level, in classifying them indicate that the last four sea level high stands, within the radiation curve, and thus in dating and therefore low ice volume (122, 103, 82, and 5 them astronomically; Wundt [1938], who recognized kyr B.P.), correspond closely in time to the last the importance of the albedo, of t•e continental_ four prominent warm peaks (127, 106, 82, and 11 configuration, and of the air and sea currents; kyr B.P.) in the modified curve of summer insola- yon Bacsak [1940], who paid more attention to the tion, not only in chronology but also in magni- interglacial periods; Emiliani and Geiss [1957], tude. This matching with the coral terraces of who proposed a theory of glaciation using insola- Barbados [Mesolella et al., 1969], of New Guinea tion changes to start (but not to end) glacial [Bloom et al., 1974], and of Hawaii [Ku et al., cycles; Zeuner [1959], who suggested that the 1974] was one of the first convincing arguments Scandinavian ice sheet had its origin at approxi- advanced in support of the orbital theory. How- mately that latitude; and Bernard [1962], who ever, on the basis of very accurate dating of core extended the application of the astronomical the- V12-122, Broecker and van Donk [1970] had to in- ory to the intertropical regions. crease by 25% the absolute time scale adopted by These qualitative coincidences of the principal Emiliani for deep-sea cores. They then proposed maxima and minima of both curves will, however, 45 ø , 55 ø, and 65øN summer insolation as a tool to remain somewhat illusory until the ambiguities explain the gradual glacial buildups over periods stemming from a priori assumptions about sensitive averaging 90,000 years and terminated by deglacia- latitudes and response mechanisms are resolved. tion completed in less than one-tenth this time As an attempt to solve this problem, the following (this close agreement between maxima of the North ideas have been proposed. Van den Heuvel [1966] Atlantic paleoclimatic curve and the 55øN insola- used the insolation at latitudes north of 70øN as tion curve since 225 kyr B.P. was also found later a guideline because there the dissymmetry between by Ruddiman and Mcintyre [1979] to suggest a caus- northern and southern hemispheres is largely at- al relationship). At the same time, Veeh and tenuated, owing to the fact that in Arctic and Chappell [1970] obtained, for the last 230,000 Antarctic regions the caloric insolation varia- years, a similar correlation between sea levels tions caused by changes of the obliquity are much derived from raised coral reefs of New Guinea and larger than those caused by changes in the pre- summer insolation at 45øN. Moreover, these sea cessional parameter. Following the same idea, level changes determined from dated coral reefs on Evans [1972] built an absolute time scale for the rising islands are synchronous with precessional whole Pleistocene from insolation received at both changes in solar radiation when orbital eccentric- 65øN and 65øS, making an allowance for latent ity is large, whereas oxygen isotope variations in heat, albedo, and a 4000-year time lag. This is deep-sea cores correspond in timing but not in 632 Berger: Milankovitch Theory and Climate

amplitude, reflecting changing isotopic composition of Pleistocene ice caps [Chappell, 1974]. Climatologists have also attacked the problem theoretically by adjusting the boundary conditions of energy balance models (EBM) and then observing the magnitude of the calculated response. If these early numerical experiments are viewed nar- rowly as a test of the astronomical theory, they are open to question because the model used contains untested parameterization of important physical processes. Indeed, in simple annual mean energy balance models [Budyko, 1969; Sellers, 1970] which suggested that the climatic response to orbital changes was too small to account for the succession of Pleistocene ice ages, the albedo feedback mechanisms in high latitudes, the oceanic circulation, the ocean-climate interactions, and the dynamics of the cryosphere were poorly simulated or even not simulated at all. As changes in the orbital parameters cause only small changes in the latitudinal distribution of the annual mean incident solar radiation and as Fig. 8. Elements of the Earth's orbit. The orbit seasonal changes could be many times as large, of the Earth, E, around the Sun, S, is represented orbital changes would perhaps lead to larger res- by the ellipse PyEA, P being the perihelion and A ponses in a seasonal model. From Adem's thermo- the aDhelion. Its eccentricity e is given by (a2 dynamic model, Shaw and Donn [1968] made such a - b2)l/2/a, a beingthe semimajoraxis andb the quantitative evaluation of the Milankovitch ef- semiminor axis. WW and SS are the winter and fect. Although their simulated temperature varia- summer solstice, respectively; y is the vernal tions seem to be controlled by the precession at equinox. WW, SS, and y are located where they are low latitudes and by the tilt at high latitudes, today. SQ is perpendicular to the ecliptic, and the mean decrease in high latitudes amounts to the obliquity s is the inclination of the equator only 1.4øC for the maximumsummer radiation defic- upon the ecliptic; i.e., s is equal to the angle iency at 25 kyr B.P. Similarly, using a statisti- between the~ Earth's axis of rotation SN and SQ. cal-dynamicalmodel, Saltzman and Vernekar[1971] Parameterm is the longitude of the perihelion havefound relatively small changesin surface relative to the movingvernal equinox,and is temperaturebetween 25 and 10 kyr B.P. For sucha equal to R + •. The annualgeneral precessionin summerradiation change of 7%,temperature change longitude,•, describesthe absolutemotion amountsto only 1.4øCat 85•N and 1.2•C at 65•N. of y along the Earth's orbit relative to the fixed stars. The longitude of the perihelion, R, is 3.4. Milankovitch Renaissance measured from the reference vernal equinox of A.D. 1950 and describes the absolute motion of the In the late 1960s, judicious use of radioactive perihelion relative~to the fixed stars. For any datingand other techniquesgradually clarified numericalvalue of m, 180• is subtractedfor a the details of the time scale [Broecker et al., practical purpose: observations are made from the 1968], better instrumental methods came on the Earth, and the Sun is considered as revolving scene for using oxygen isotope as ice age relics around the Earth [Berger, 1980b]. [Shackleton and Opdyke, 1973], ecological methods of core interpretation were perfected [Imbrie and Kipp, 1971], global climates in the past were single-valuedfunction of the solar constantSO; reconstructed [CLIMAP Project Members, 1976], and of the semimajor axis of the Earth's orbit, a atmospheric general circulation models [Smagorin- (related to the length of the year); of the orbit- sky, 1963] and climate models became available al eccentricity e and its obl•iquity •; of the [Alyea, 1972]. With these improvementsin dating longitude of the perihelion, m , measured from the and in interpretation of the geological data in moving vernal equinox; and of the rotational ang- terms of paleoclimates and with the advent of ular velocity of the Earth (related to the length computersand the developmentof astronomical and of the day and to the general circulation) (Figure climate models, it became necessary to investigate 8). Parameters e and • combine to form the cli- morecritically all four main steps of the astro- mate precessionalparameter e sin m. This param- nomicaltheory, namely, (1) computationof the eter plays an oppositerole in eachhemisphere and astronomicalelements, (2) computationof the is a measureof the difference in length between appropriate insolation parameters, (3) the devel- half-year astronomical seasons and of the differ- opment of suitable climate models, and (4) further ence between the Earth-Sun distance at both sol- analysis of geological data in the time and fre- stices. Obliquity affects mainly the seasonal quency domains in order to investigate the physi- contrast and the latitudinal gradient of insola- cal mechanisms and to calibrate and validate the tion. While • and e sin m only act to redistri- climate models. bute insolation among latitudes and seasons, the energy influx integrated over all latitudes and 4. Earth's Orbital Parameters over an entire year is found to depend only on e (a andS O being assumedconstant here). For any latitude on the Earth, the insolation Eccentricity defines the shape of the orbit available at the "top of the atmosphere" is a (presently 0.016), the obliquity measures the Berger: Milankovitch Theory and Climate 633

TABLE 2. Evolution in the Computation of Long-Term Variations of the Earth's Orbital Elements

Power as to the Disturbing Degree in Planetary Eccentricities and Inclinations

Masses Degree 1 Degree 3

Lagrange (1781) Anolik et al. (1969) Laplace (1798) Bretagnon 2 (1974) Pont•couland and Le Verrier (1834) Stockwell (1870) Harzer (1895) Milankovitch, Stockwell, and Pilgrim (1920) Milankovitch, Miskovitch, and Le Vettier (1941) Anolik 1 (1969) Bretagnon ! (1972-1974)

Brouwer and Van Woerkom (1950) Bretagnon 3 (1974) 2 Sharaf and Boudnikova (1969) Berger ! (1973-1977a) 2 Vernekar (1972) Berger 2 (1976) Berger 3 (1978a)

Numerals preceding entries indicate the degree of the expansion of obliquity and climatic precession with respect to the Earth eccentricity. Numerals after some names give the number of the solution. angle between the Earth's axis of rotation and the inclination i to the reference planeß A similar perpendicular to the ecliptic (its present value system of equations governs the Earth's rotation is 23ø27'), and the longitude of the perihelion is and precession laws. The most up-to-date solution a measure of the Earth-Sun distance at a particu- (Table 2) is now to the second order in the masses lar season (for example, at the present day, the and to the third degree to the planetary eccentri- Earth is about at the perihelion at the northern cities and inclinations. Critical analysis of hemisphere winter solstice). The perturbations of theories of the long-term variations of the ele- these orbital elements are due to the gravitation- ments of the Earth's orbit and their numerical al effects of the different planets on the Earth's comparisons lead to conviction that the most up- orbit. The differential equations of the to-date solution that I published in 1978 [Berger, planetary motions can be formulated as 1978a, b, c, d, e] is close to the ideal one and most probably provides valuable information back do 8 6 •R to 2 Myr B.P. (at least the accuracy of the fre- j,n k__•n= Z Z fi (o , ..., o ) quencies of my 1978 solution seems to be much dt j=! i=l ,n 1,n 6,n higher than was assumed by Berger [1984], accord- j•n ing to one recent computation made by Laskar

1 • n• 9 [1984, personal communication, 1987]. For exam- oi,n [h,k,p,q,a,l}in 1 • i • 6 ple, when the Milankovitch eccentricity is compared to the Bretagnon [1974] values used in my r s t solution for the last 1,000,000 years, large de- Rj,n = r,s,t,ur. A( aj ' an ,mj, mn) eje n (sini j /2) partures occur as early as 300 kyr B.P. (Figure 9). If the most important high-order terms are ß (sinin/2) u cos%j,n included, each of the classical astro-insolation parameters can be expressed as a quasi-periodic function of time: %j,n= bllj + b21n + b3=j + b4=n + b5•j + b6•n

e = e0 + r. Ei cos(l.t 1 + 8.)1 i The o represent the six orbital parameters: (h, k) combine the eccentricity and the longitude of the perihelion; (p, q) combine the inclination of sin m = Z Pi sin (eit + •i ) i the ecliptic and the longitude of the node; a is = •* + Z A. cos (f.t + •.) the semimajor axis, and I is the longitude of the 1 1 1 Earth; •, =, and • are the longitude of the plan- i et, the perihelion, and the node, respectively; r, Besides its simplicity and practicality for s, t, u, and the b are integers. R, the perturba- easy computation, this form allows us also to tion function, shows that the solutions will prog- obtain the main periods associated with the astro- tess in powers of small parameters: the ratio m nomical theory of climate as shown in Table 3. of the mass of the planets to that of the Sun, and The main periodicities of 100, 41, 23, and 19 kyr the eccentricity e of the planets' orbit and their and the 54-kyr periodicity are found in spectra of 634 Berger: Milankovitch Theory and Climate

0.0601 , , -- - ' ' periodicities at 308,000 and 25,700 years (Figure .,, '.,•' / / \ \ 10). That for 41 kyr has an origin which is a little more complicated, as is also the case for 100 kyr. 0.0 '" , . , If one analyses the parameters on which the 1000 950 900 850 800 750 main frequencies of precession and obliquity depend [Berger, 1976a], one finds that they are

0.060 ...... directly proportional to the dynamical flattening of the Earth, (C-A)/C, and related to the cube of 0.045 " ...... " " the inverse Earth-Moon mean distance. The latter 0.030 is roughly constant over our period of interest, as the Moon has moved away from the Earth by only 0.015 ' ' • Lx about 200 km (compared with a mean distance of 0.0 over 380,000 km) since 5 Myr B.P. As far as (C- 750 7•0 6•0 6•0 550 500 A)/Cis concerned,theproblem is more complicated, as Lt clearly changes with the accumulation of 0'060/ ...... / hugeice sheetsin polarregions. The problem is 0.045• ..... • by howmuch. A rapid circulation [Berger et al., -->-•, " '".. • 1987]of thiseffect at 20kyr B.P., a timewhen

0.00.0150.030{ ...... •x"'---x-'"• x ...... •••' '"'•••'""•troughlylatitudes,theAmerican 40 xshows an• 10 Eu•asiankm that ofin ice theice inabsence sheetsnorthern ofaccumulated apolar loading 500 450 400 350 300 250 depression of the Earth's crust, it affects the frequencies by 1% at the very maximum. The main 0.0601...... periodsof precessionand obliquity would thus be 0.045t,-"•..•• decreasedby130, 210, and 660 years respectively, 0.030•• - -'-..•...,....•.....• whichcurveswould of 1000lead yearsto a maximum shift inover the ainsolation full 100-kyr 0015•'•'••0'0 '"' •- glacialitLve tocycle. the isostatic These results,response however,of the lithos-aresens- 250 200 150 100 5• • phere, and the total effect seemsto be negligible over the whole Pleistocene period. Fig. 9. Long-termvariations of the eccentricity Computationsto reconstructthe astronomical of the Earth's orbit over the last 106years. The parametersover the last 5 Myr (only the last solid curve represents the Berger 3 solution [Ber- 250,000 and the next 100,000 years are shownin ger, 1978c], the dotted curve the Sharaf-Bud- Figure 11) showthat e varies between0.0 and nikova-Vernekar solution [Vernekar, 1972], and the 0.0607 with an average quasi-period of 95 kyr, and dashed curve the Milankovitch-Miskovitch-Le Ver- that e varies between 22ø and 24ø30' with a quasi- rier solution [Milankovitch, 1941] (see Table 2). period of 41 kyr. The revolution of the vernal point relative to the moving perihelion (which is related to climatic precession) has an average quasi-period of 21,700 years, whereas relative to geological records. These periods come from a set the fixed perihelion of reference, this quasi- of fundamental periods of the planetary system period is 25,700 years (the very well known astro- (the most important ones are related to Venus, to nomical precession of the equinoxes). Jupiter, and to the general precession in longi- The same conclusions hold for the insolation tude; see Table 4). The method used for solving parameters [Berger and Pestiaux, 1984]. The error the set of differential equations analytically due to the astronomical perturbations on their makes it possible to trace each period directly main frequencies remain well within less than 1% involved in the astronomical theory of paleocli- over the last 10 Myr. The fundamental periods do mates back to its source [Berger et al., 1987]. not deteriorate with time over the Quaternary, but The 23-kyr periodicity originates directly from their relative importance is a function of the

TABLE3. Periods Associated with the Main Terms [Berger, 1977] in the Analytical Expansions of Precession, Obliquity, and Eccentricity

Precession Obliquity Eccentricity

Period Period Period No. Amplitude (years) No. Amplitude (years) No. Amplitude (years)

1 0.0186080 23,716 1 -2462.22 41,000 1 0.011029 412,885 2 0.0162752 22,428 2 -857.32 39,730 2 -0.008733 94,945 3 -0.0130066 18,976 3 -629.32 53,615 3 -0.007493 123,297 4 0.0098883 19,155 4 -414.28 40,521 4 0.006724 99,590 5 -311.76 28,910 5 0.005812 131,248 6 -0.004701 2,035,441 Berger: Milankovitch Theory and Climate 6]5

TABLE4. Fundamental Periods (in years) of Earth's Orbit and Rotation [Bretagnon, 1974; Berger, 1976a]

e sin • Argument sin i sin • Argument General Argument Precession

176,420 •'Venus 0 25,694 k 308,043 Jupiter 68,829 053 72,576 i:Mars 230,977 01 75,259 Earth 72,732 04 249,275 :Mercury 191,404 0 2 49,434 :Saturn 49,339 0 6 422,814 :Uranus 432,023 0 7 1,940,518 :Neptune 1,874,374 0 8

period considered: for example, the obliquity and 3. Can the insolation changes induce climatic the 19 kyr precession signals are largely depleted changes of magnitudes similar to those which have between 1.6 and 2.4 Myr B.P. (Figure 12). been recorded in geological data? If so, what The degree of confidence in the basic astronom- physical mechanisms are involved? ical solution makes it worth trying to answer the The answer to these questions is yes provided following three questions: that solar output and paleogeography were constant 1. Are the quasi-periodicities of the Earth's over the last 3 Myr and provided that astronomical orbital elements represented by significant cont- variations in the Earth's orbital parameters are ributions to variance as seen in climatic spectra? the ultimate modulaters of the climate. Other 2. Is there significant correlation and phase factors may be required to explain other, more coherency between insolation and geological curves? detailed climatic variations found in geological

(g5+ •) I ' [ I [308043 ] I I

I ! I 25694 ]

102535 [

76 929 308 043

Fig. 10. Branchdiagram for (a) the climatic precessione sin m, (b) obliquity, and (c) eccentricity [Berger et al., 1987]. This procedure, like a family tree, allows each period to be traced back to its source through linear combinationsof the frequencies listed in Table 4 for the • and 9 and in Table 1 of Berger [1976a] for the g and s; the k correspond to the astronomical precession of 25,694 years. 636 Berger: Milankovitch Theory and Climate

I i I I • I • •-• post: future ECCENTRICITY

& 1,1.1 E z

24.00

23.,50

22.00

22.50

I I I, I 250 200 150 IOO 50 O -50 -IOO

THOUSANDS OF YEARS AGO Fig. 11. Long-term variations of eccentricity, precession, and tilt from 250,000 years B.P. to 100,000 years A.P. [Berger, 1978c].

records and to shape them correctly, but the orb- data [Hays et al., 1976]. The 100-, 41-, 23-, and ital variations are assumed to be the dominant 19-kyr periods are indeed significantly superim- forcing functions. posed upon a general red noise spectrum (Figure 13). It is the geological observation of this 5. Spectra of Geological Records bipartition of the precessional peak, confirmed to be real in astronomical computations, which was In 1976, Hays, Imbrie, and Shackleton demon- one of the first most delicate and impressive of strated that the astronomical frequencies that I all tests for the Milankovitch theory. Since computed in a totally independent way [Berger, 1976, spectral analysis of climatic records of the 1977] were significantly present in paleoclimatic past 800,000 years or so has provided substantial

MID-MONTH INSOLATION

JUNE 60 N

SPECTRUM

19 MILANK BREI __•

BRE 2

SHARAF

BRE 3

3 BRE 4

19 BRE 5

Fig. 12. Spectral analysis of June insolation at 60øN for four different periods: 0- 800, 800-1600, 1600-2400, and 2400-3200 kyr B.P. The vertical axis is in relative unit and is proportional to the amount of variance explained by each frequency band (periods are given in thousands of years). Seven different astronomical solutions have been used as described by Berger [1984] and Berger and Pestiaux [1984]. Berger: Milankovitch Theory and Climate 63?

are used and the uncertainty in the geological •-I00,000 yrs time scale and in the spectral analysis is ac- counted for, Berger and Pestiaux [1987] have shown that the following peaks are significantly present in the astronomical bands: (1) 103,000 with a • y-45,000yrs standard deviation of 24,000, (2) 42,000 with a standard deviation of 8000, and (3) 23,000 with a standard deviation of 4000. In addition, Pestiaux et al. [1988] used cores with a high sedimentation rate and covering the last glacial-interglacial cycle to resolve the higher-frequency part of the spectrum. Besides the 19-kyr precessional peak, three other periods were indeed significantly detected: (1) 10,300 with a standard deviation of 2200, (2) 4700 with a standard deviation of 800, and (3) 2500 with a standard deviation of 500. These preferential frequency bands of climatic variability outside the direct orbital forcing band are still too broad to allow for a definite physical explanation. A tentative interpretation, though, may be given in terms of the climatic I I I I I I system's nonlinear response to variations in the I00 30 15 I0 7.5 6 insolation available at the top of the atmos- CYCLE LENGTH (THOUSANDS OF YEARS) phere. The first characteristic of the 10.3-, 4.7-, and 2.5-kyr near periodicities is, indeed, Fig. 13. Spectrum of climatic variation over the that they are roughly combinations tones of the past half-million years. This graph, showing the 41-, 23-, and 19-kyr peaks found in the insolation relative importance for different climatic cycles parameters. Moreover, Pestiaux et al. [1988] used in the isotopic record of two Indian Ocean cores, the Ghil-Le Treut-Ka[len nonlinear oscillator confirmed many predœctions of the Milankovitch climate model [Ghil and Le Treut, 1981; Le Treut theory. (Data are from Hays et al. [1976]. Re- and Ghil, 1983] to predict these shorter periods. printed from Imbrie and Imbrie [1979] with permis- The variance components centered near a 100-kyr sion from the authors and Enslow Publishers.) cycle, which dominates most climatic records, seems in phase with the eccentricity cycle, although the exceptional strength of this cycle evidence that, at least near the frequencies of needs a nonlinear amplification by the deep ocean variation in obliquity and precession, a consider- circulation, the carbon dioxide, the glacial ice able fraction of the climatic variance is driven sheets themselves, and related mechanisms such as in some way by insolation changes accompanying the ice albedo feedback, the elastic lithosphere, changes in the Earth's orbit [Imbrie and Imbrie, the viscous mantle, and ocean-ice interactions 1980; Berger, 1987]. If some long deep-sea cores

...... •'o VAR/f ETP VAR/f • ; : t COHERENCY 1,0 I00 41 23 •*• f \ - .-• ,• j",', I 0

• I I •,'•',."• •• ,' ,'' • • • BANDWIDTH Z

O Z ' I• • --- ' Z I '--.'

• 0,9 O ' oh) •o 0.8- ß [• •5•øsig''evel'• '•' •

0.5. O.3j 0.1; o.o,i o.o o.B o.b o. P I•. 50.0 35.3 25.0 20.0 16.7 14.3 12.5 II. I I0.0 Fig. 14. Cohereacy and variance spectra calculated from records of climatic and orbital variation spanning the past 780,000 years. Two signals have been processed: (1) ETP, a signal formed by •rmalizing and adding variations in eccentricity, obliquity, and precession and (2) •--0, the unsmoothed, stacked isotope record plotted on the SPEC•P time scale. (Top) Variance spectra for the two signals plotted on arbitrary log scales. (Bottom) Coherency spectrum plotted on a hyperbolic arctangent scale and provided with a 5% significance level. Frequencies are in cycles per thousand years. (Reprinted from Imbrie et al. [1984] with permission from the authors and D. Reidel.) 638 Berger: Milankovitch Theory and Climate

20.0 -- amplification mechanism can be found as in the double potential theory of Nicolis [1980, 1982] 95K and Benzi et al. [1982]. Imbrie et al. [1984] have made it clear that

160 the coherency of orbital and climatic variables in the 100,000-year band is enhanced significantly when the geologic record is tuned precisely to the obliquity and precession bands. Using the so-

z called orb[tally tuned S PECMAPtime scale (also • •2.0 54K developed by Martinson et al. [1987] for the last 300,000 years), they indeed found a coherency in

z :' ' the astronomical bands significant at better than the 99% level of confidence (Figure 14) (for an- bJ 19.0 other tdning procedure, see, for example, Herter-

•05-0 Ma ich and Sarnthein [1984]). • 0.7-02 Ma A fairly coherent phase relationship is also ...... 0.9 - 0.4 Ma reasonably well defined between insolation and ice ,,. ß. I.I -0.6 Ma volume, for example. Kominz and Pisias [1979] 4.0 werethe ft•st to showthat obliquityconsistently leads the 0 record by about 10,000 years, whereas precession seemed to be in phase witit the 23- kyr geological signal. However, the recent re- O0 I 0.000 0.020 0 040 0 060 0.080 0.100 sults obtained by S PECMAP show that these leads and lags are more complicated. Finally, Ruddiman FREQUENCY(cycle$/k yr) et al. [1986] succeeded in finding one of the Fig. 15. Area/variance composite of spectral secondary astronomical periods that I discovered analysis of winter sea surface temperature record in 1976, the 54-kyr period (Figure 15). from four record segments of deep-sea core K708- All these results lead me to conclude that, at 7/site 552A. (Reprinted from Ruddiman et al. least on the basis of statistical analysis, evi- [1986, p. 162] with permission from the authors dence has accttmulated that 60 m 10% of the isotop- and the Geological Society of America.) ic variance in the periodicity range 10-100 kyr per cycle over the last ! Myr ts a linear response to orbital forcinM [Imbrie et al., 1984]. (remember that the eccentricity variations alter However, the interpretation of the results is the total sunlight falling on the Earth by only not always as clear. The 100-kyr cycle, so domi- 0.2% at most). The 100-kyr climatic cycle can, nant a feature of the late Pleistocene record, indeed, be explained both by (1) a beat between does not exhibit a constant amplitude over the the two main precessional components (Wigley past 2-3 Myr as displayed on a three-dimensional [1976] demonstrated this point from nonlinear time evolutiot•ary spectrum of deep-sea core V28- climate theory), as is also the case for the 100- 2•9 (Figure16•. Clearly, this periodicitydisap- kyr eccentricity cycle in celestœal mechanics pears before 10 years ago, at a time when the ice (Thefrequency corresponding to the second_yeriod sheets were much less developed over the Earth, of the eccentricity in Table 3 (1/94945 y ) is reinforcing the idea that the major ice sheets may obtained from precession frequencies 3 and 1 have played a role themselves in modulating this (1/18976- 1/23716). Frequencies 1, 3, 4, 5, and 100-kyr cycle. SPbiCMAPhas also shown that the 6 come from the combinations 2-1, 3-2, 4-1, 4-2, phase lags in the climate response to orbital and 3-4, respectively [Berger et al., 1987].) or by forcing dependupon the nature of the climatic (2) the eccentricity signal directly, provided an parameters themselves and upon their geographical

2000 KYR

1670 KYR

ME POWER SPECTRALDENSITY 1370 KYR

1080 KYR

6• KYR

O I O O 1 50 2.O O 2 50 FREQLEr'IcYI N 10 c, P,3 KYR

Fig. 16. Evolutive maximum entropy spectral analysis of the whole record V28-239 [Pestiaux and Berger, 1984]. Berger: Milankovitch Theoryand Climate 639

- I00,000 I00,000 ly, midmonth high-latitude insolation in summer RCII-120 RCII-120 INDIAN OCEAN 44øS INDIAN OCEAN 44øS displays a stronger signal in the precession band T = 468K T=468K than in the obliquity band (Figure 18b) [Berger At and Pestiaux, 1984].

• w 6. Astronomical Insolation (,• •"0 (~•ce volume) Estimated Z summer see -surf(3ce • .. //- ,••,ooo temperature o Another important advantage in considering monthly insolation instead of half-yearly values j 41,000 which were used by Milankovitch [1941], Bernard 23,000 [1962], Sharaf and Budnikova [1969], Vernekar 19,000 [1972], and Berger [1978f] is that fluctuations

k I I that are otherwise masked become easily recogniz- able. For example, 125,000 years ago (Figure 19), I / F during the Eemian Interglacial, all latitudes were I I00000 ATLANTIC41øN •- I/ ATLANTIC41eN overinsolated in July, particularly the northern I///-- ' T=246K ! II T=246K polar regions, where the positive anomaly amounted to up to 12%, the same being true at the last -,ooooo climatic optimum 10,000 years ago. This is espec- ,,- IHII Esttmated ially significant when a delay of some few thousand years, required for the ice sheets to start (•• $'eO(-icevolurne) IllI• summersea-surface to melt, is taken into account. • )' • temperatureBut the evolution of the detailed seasonal • 41,000 cycle that [ introduced in 1975 [Berger, 1976b] is even more significant, leading to the concept of the so-called insolation signature [Berger, 1979b]. The well-known stages associated with the Barbados [II (124 kyr B.P.) and •I (103 kyr B.P.) I•../..•-• 41,000 high stands of the sea [Broecker et al., 1968] clearly correspond (Figure 20) to an overinsola- tion that amounts to some 10% and are separated by an abortive glaciation at 115 kyr B.P. corresponding to isotopic stage 5d. The main glacial transition between stages 5 and 4, at 72 kyr B.P., is Fig. 17. Spectra of isotopic and sea surface underinsolated (Figure 21), and, more important, temperature variations measured at two different this drop in insolation was not compensated by any s•tes. Spectra in Figures 17a and 17b are taken significant increase during the whole main Wurm from Hays et al. [1976]. Spectra in •igures 17c glaciation phase. On the contrary, yet another and 17d are taken from Ruddiman and Mcintyre important decrease at 25 kyr B.P. augers the 18 [1981]. The isotopic spectra, which reflect var- kyr B.P. maximumextent of ice in the northern iations in global ice volume, are nearly identical hemisphere. Indeed, between 83 kyr and 18 kyr apart from differences due to different bandwLdths B.P. there was an overall solar energy deficiency (BW). But the temperature spectra are very dif- of 2.5 x 1025 cal north of 45øN, almost sufficient ferent: the southern hemisphere s•te responds to compensate for the latent heat liberated in the mainly at periods near 100,000 years, whereas the atmosphere during the formation of snow required North Atlantic at this latitude responds mainly at by the buildup of the huge 18 kyr B.P. ice sheets periods near 23,000 years. (Reprinted from Imbrie [Mason, 1976]. Finally, it was not before 15 kyr [1982] with permission from the author and Academ- B.P. that the summer insolation started to in- ic Press. ) crease sufficiently, leading to the 6 kyr B.P. Climate Optimum. •s an introduction to the modeling of the cli- location. For example, the sea surface tempera- mate response to these significant orbitally in- ture of the southern oceans seems to lead the duced insolation changes, these extra-terrestrial response of the northern hemisphereice sheets by insolation variations can be compared to those in roughly3000 years. the insolationincident and absorbed at the Theshape of the spectrumdepends also upon the Earth'ssurface [Ohmura et al., 1984]. In the location of the core andthe natureof the climat- radiative modelby Tricot andBerger [1988] the ic parameteranalyzed [Hays et al., 1976;Ruddiman atmosphere is divided into threelayers, with the andMcintyre, 198l; Imbrie, 1982]. For example, secondone filled up with an averagedcloud. The the 41-kyr cycle is not seen and the 23-kyr cycle interactions betweenmolecular absorption (by H20, is dominant in Atlantic sea surface temperatures C02, 03, andaerosols) and scattering (by air, of the last 250,000 years (Figure 17). This is aerosols, and clouds) are handled by the delta- not too surprising, as these spectra depend upon Eddington technique. Combining the reflection and the way the climate system reacts to the insola- transmission of each homogeneous layer, the down- tion forcing and upon the type of insolation to ward and upward fluxes are computed following the which it is sensitive. Indeed, contrary to the ascending method presented by Fouquart and Bonnel well-received Milankovitch idea that the high [1980]. Comparisons with other theoretical calcu- polarlatitudes must record the obliquitysignal lationsand observations show that this solar whereaslow latitudes recordonly the precessional radiative schemeis sufficiently accuratefor one(Figure 18a), the latitudinaldependence of reproducingcorrectly the present-dayatmospheric the insolation parametersis morecomplex: clear- conditions. As expected,the amplitudeof the 640 Berger: Milankovltch Theory and Climate

CALORIC SEASON

INSOLATION

spectrum

• , 90N

• J• , 60 N

I I , 3ON

i • 30s

90 S i i i i i i i'i A_Ai s Fig. 18a. Spectral analysis of caloric insolation for northern hemisphere caloric summer (NHCS) and northern hemisphere caloric winter (NHCW) for seven latitudes. The vertical scale is in relative units and is proportional to the amount of variance explained by each frequency band (periods are given in thousands of years) [Berger and Pestiaux, 1984]. long-term variations of the insolation "at the top latttudes is essentially due to atmospheric atten- of the atmosphere" calculated from this radiative uation that is larger in polar than in tropical model in which present-day parameters were assumed latitudes and to the high surface albedo of the is reduced by roughly a factor of 2, but the over- polar regions. Both of these factors are also all general pattern remains, except in high polar responsible for a specific behavior of the large- latitudes of the summer hemisphere, particularly scale latitudinal gradient of insolation (Figure the southern one (Figure 22). This change in high 23): the latitudinal gradient of extraterrestrial

MID-MONTH INSOLATION

Spectrum

90 N

60 N

23 4•j••s 30 N

j• /• I 60S

, i i i i i i i

Fig. 18b. Same as Figure 18a for four midmonth insolations: March, June, September, and December [Berger and Pestiaux, 1984]. Berger: Milankovitch Theory and Climate 641

- •o - - - - 30 - - o - - -30 - -4s - - _?$

ß ' I ' I ' I ' I ' I ' I ' I ' I ' I ' •00 180 180 170 1•0 1SO 140 1•0 1•0 I I 0 1O0 Fig. 19. Long-termvariations of the deviationsof solar radiation fromtheir A.D. 1950 values. These values are given for each latitude from the north pole to the south pole and for a period extendingfrom 200 kyr B.P. to 100 kyr B.P. The solid lines are for the positive deviations (insolation higher than it is today), and the dashedlines characterize the insolation below their actual values [Berger, 1978a, b, d] (units are calories per square centimeter per day). insolation is characterized by a periodicity of quencies as a clock for the geological record, 40,000 years, whereas for the absorbed insolation especially if one uses a combination of insolation (and also the insolation incident at the surface) parameters. it exhibits a higher frequency which corresponds to a period in the rangeof 21,000 years. In 7. PaleoclimateModeling fact, for the insolation reaching the surface, the large attenuation in polar latitudes is respons- Manyresearchers have tested the astronomical ible for insolation at 30ø driving the frequency theory with numerical climate models of different behavior of the gradient. These results meanthat complexities (involving the energy balance to the we must be careful when we use astronomical fre- general ctrculation). These models can be dist-

O JF MRM J JR$ONO O JF MR R$OND 0 JF MRM J JR$OND O JF MI:I R$OND

IOl 151 176 -- 177 IO2 127 -- - 12fl 15.1 I . - 179 IOl,. 151,. 179 . - 160 lOS 1'55 180 - 161 IO6 - 157 182 - - It:• IO• 158 18,.1 - 1513 I1•,. - 1• IO• - 160 185 IiO - 161 -- iii - 162 18• -- 18Z 112 - 163 -- i• 113 - -- I• Iit,. -- -- 190 115 - I• I•i -- 19• 116 - 1•2 -- 197 - -- 19• 118 1t.3 -- 169 IC• -- 119 -- I•) -- -- 111.6 IPl -- 121 -- 111.7 172 19• -- 1t.8 -- 198 - i t,.cj -- 199 12t. _ ISfl -- •0 i• 20O --

-- - BoPo

O JF 11RM J JRSOND O JF 11R!'I J JR 50ND O JF 11RIIJ JRSOND O JF ftR ftJ JP, SONO INSOLATIONSIGNATURE5 60 NORTH DEVIATION FROMMEAN

Fig. 20, Insolation signaturesfrom 200 kyr B.P. to 100 kyr B.P. Long-termvariation of the deviations from the meanstate of the midmonthdaily insolations for 60øN (annual cycle). The vertical scale is indicated in the upper left corner of the figure. Time is in thousandsof years, and the time step is 1000 years [Berger, 1979b]. 642 Berger: Milankovitch Theory and Climate

O Jl: MRM JJA$OND DJF MRM J JASON O O Jl: MRM J JRSDND O JI:MRM J JIq$ DND J I I I I I I I I I I I I I I I I I I I I I I I I

t I Vœf•TICAI.•[ =10LYIDAY 26 SI 76

27 52 77 77

28 53 78 78 29 5• 79 79

3O 55 8O 8o 3• 56 8!

82 57 82 82 33 58 83 83 9 •. 59 8• 8•

io 85 i! 36 • 6• 86 86 • 67 87 87 38 6:1 88 88 89 •0 65 9o 16 91 •2 67

•3 68 93 19 9• •5 7O 95 96 97 •8 73 98

•9 71,. 99 99

113o

DJFMI:IMJJASOND DJFI•AMJJASDND DJI:MRMJJR$ONO DJI:MRMJJRSDND INSOLATION 51CNATUEE5 60 NOI•TH DEVIATION F!•rll'l HEAtl

Fig. 21. Same as Figure 20 for 100 kyr B.P. to present time [Berger, 1979b].

ributed into four maintypes: (1) zero-dimension- get a responsequalitatively similar to the geo- al mathematical]nodeis, (2) seasonalclimate mod- logical record over the past 150,000years. When els not explicitly coupledto ice sheetmodels, their modelis forcedwith the orbital variations, (3) pure ice sheet modelsnot driven by climate the northernhemisphere snow limit shifts south- models,and (4) modelsof the atmosphere-ocean wardby a realistic 20ø duringan ice age (this is climate coupledto ice sheets. This modeling not the casein a calculationby Northand Coakley effort has led to recent progressin understanding [1979], wherethe ice line movesby only 3ø of the physicalmechanisms by whichthe climate sys- latitude equatorwardwhen forced at the 25 kyr tem respondsto the astronomically forced changes B.P. obliquity minimum). Schneiderand Thompson in the pattern of incoming solar radiation. Such [1979] also introduced a seasonal version of a mechanismsare related, in particular, to the ice zonally averagedenergy balance climate model. sheets, the lithosphere, the hydrological cycle, The seasonal and zonal variation of albedo and the the cloud properties, the albedo-temperature feed- zonal variation of thermal inertia are shownto back, the land-sea temperaturegradient, the CO2 interact with the astronomical insolation perturb- cycle, and the oceanic circulation. For example, ation, so that the simulation exhibits some of the employing crude parameterization within a simple features of the long-term climate record. How- climate model, Cess and Wronka [1979] concluded ever, although the computed record simulates well that zenith angle, bio-albedo, and latent heat the gross features of the glacial-interglacial feedbacks could, collectively, enhance by several transitions, the temperature amplitude of the 60øN factors the sensitivity of the Earth's simulated glacial maximum-to-climatic optimum is only about climate to change induced by orbital variabil- 0.8øK, whereas CLIMAPdata suggest it should be a ity. As the cryosphere is probably the only part factor severalfold greater, and the phase is sev- of the climatic system whose characteristic time eral thousand years too early. scales of response are of the same order as those of the orbital forcing, it is most likely that to 7.1. Ice Sheet Models and the 100-kyr Cycle prove the viability of the Milankovitch theory, the seasonal extent of ice cover and nonlinear This phase lag discrepancy, also found by Suar- feedbacksrelated to the polar'icecaps must also ez andHeld [1979], was expected from the equi- be includedproperly. In this respect, Suarezand librium modeland arises probablyfrom the fact Held [1979] have used a zonally symmetricmodel of that the deep ocean circulation is neglected and the global energy balance, incorporating the heat from the lack of simulating the growth and decay storage in an isothermal ocean 40 m deep, positive of ice sheets. As recalled by Imbrie and feedbacks due to the high albedo of snow and sea Imbrie [1980], there are indeed several indica- ice, and a seasonally varying insolation. They tions that one source of nonlinear behavior is the Berger: Milankovitch Theory and Climate 643

ZOO 100 180 170 160 160 140 130 120 II0 100 I m I m I m I I I m I m m ß m , I , I , I MID-MONTH INSOLATION JANUARY

eO- 4S- ,,is 30- 30 IS-

-;30 - -30 -4S -,is -CO - -6o -76 - -76 -OO -

'76 LU 8o CI 4s- 30 30

I-- 0 =

• -•o - -:30 • -•s - -,is .j -•o -

ß, . oo•o, _. , , • p, , : , , o •ooo I m I -_ q;, - ; t

- oo - eO- - 4S- 30

0 o

-30 -46 -

- .-90

YEARS BEFORE PRESENT Fig. 22. Long-term variations of the deviations from their present-day values of midmonth daily insolations for January. These values are given in watts per square meter and for a period extending from 200,000 to 100,000 years B.P. (Top) Insolation at the "top of the atmosphere." (Middle) Incident insolation at the surface. (Bottom) Ab- sorbed insolation at the surface. The solid lines are for the positive deviations, and the dashed lines characterize the insolation below their present-day values [Tricot and Berger, 1988]. tendency for ice sheets to shrink faster than they Using the caloric insolation anomalies, their grow, a time-dependent model being thus required model can produce continental ice sheets of the to understand these observed lags between orbital scale of those occurring in the late Cenozoic and forcing and the modeled climatic response. As a also with time lags consistent with the astronomi- pioneer, using a perfectly plastic ice sheet mod- cal data. While forcing is at periods near 19 el, Weertman [1976] has shown that a relatively kyr, 23 kyr, and 41 kyr, the model consistently small reduction of the 50øN summer half-year inso- predicts dominant long-period responses, most lation may trigger the buildup of the ice sheets, commonly at 100 kyr and/or 400 kyr, in addition to which are then allowed to grow through a strong significant responses at the forcing periods. The positive feedback. Incorporating Weertman's ice model output thus lends support to the hypothesis sheet into an energy balance climate model, Pol- that nonlinear response of the Earth system (asso- lard [1978] came to the same conclusion, although ciated with the growth and decay of the continent- the internal freedom of the model was in fact al ice sheets) to fluctuations of the orbital increased. The curve of his model's ice ages parameters is responsible for the long-period compares favorably with some aspects of the deep- climate fluctuations recorded in deep-sea cores. sea record, with a sea level air temperature dif- A more sophisticated three-dimensional time- ference between maximum and minimum ice sheet dependent ice sheet model based on present measur- extents reaching 9øC in the polar region's ed ice sheets has been used to study the effects summer. These simple models seem thus to simulate of the orbital radiation changes [Budd and Smith, correctly the phase and approximate amplitude of 1979, 1987]. A reasonable match with the inferred the 40-kyr and the 23-kyr cycles, but not the growth and retreat of the ice sheet from 120 kyr dominant 100 kyr sawtooth cycle at all. B.P. up to the present has been found possible, To contribute to the solution of the origin of but only with the inclusion of the effects of this 100-kyr cycle, Birchfield and Weertman [1978] albedo feedbacks and isostatic changes in the modified the Weertman continental ice sheet model bedrock elevation. It thus seems that the role of in such a way that larger ice sheets were obtained ice sheets in determining the long-period climate owing to a larger accumulation region with the response will possibly be clarified only with more inclusion of the rear half of the ice sheet. realistic parametric modeling of the cryosphere- 644 Berger: Milankovitch Theory and Climate

Extraterrestrialinsolation (Wm -2)

Solarradiation incident at the surface(Wm -2) z

Solarradiation absorbed at the surface(Wm -•)

-50 E•raterrestrialinsolation (Wm- •)•

Solarradiation incident at the surface(Wm -•)

Solarradiation absorbed at the surface(Wm-•)

MID-MONTH INSOLATION JULY

! ! , , i w ! • i • , i , , , i ! • i •o lOO o YEARS BEFORE PRESENT

Fig. 23. Long-term variations of July midmonth large-scale gradient of insolation over the last 200 kyr (in watts per square meters for the northern hemisphere (the three upper curves) and for the southern hemisphere (the three lower curves). The left scale gives the deviation from the present-day values of the gradient defined as the difference between 30 ø and 70 ø . For each hemisphere the upper curve gives the solar radiation at the "top of the atmosphere," the middle curve the radiation incident at the Earth's surface, and the lower curve the absorbed radiation at the Earth's surface [Tricot and Berger, 1988].

lithosphere. Noting the strong asymmetry of the the passive role of the southern hemisphere and 100-kry cycle, Oerlemans [1980] showed that a the lack of ocean-climate interactions, the domi- 50,000- to 100,000-year time scale, needed to nant 100-kyr signal and its asymmetry are well create a full-size ice sheet, is in accordance reproduced. with ice sheet/Earth's crust dynamics. In his A muchsimpler differential-type model was model, a continental northern hemisphere ice sheet proposed earlier by Calder [1974], who assumed yearis initiated insolationin atperiods 65øN.of Once minimum an icesummer sheet half- is mt•t ) belowa decline a certainin summer levelsunshine_•t (8 W m ) allows50øX (410 the W established, it keeps on growing even if insola- volume of glaciers and ice sheets to grow in sim- tion is above normal. Because of bedrock sinking, pie proportion to the deficit, while summer sun- ice sheets grow very slowly. If the ice sheet shine above that level melts ice with a different reaches a certain critical thickness, basal slid- proportionality. With a melting rate 5 times the ing occurs, and the mean height of the ice surface freezing rate, a realistic curve for the most decrease substantially. The consequent decrease recent glaciation (the last 78,000 years) has been in the mass balance causes the ice sheet to disap- obtained and applied over the past 860,000 pear within a few thousand years. The glacial years. According to the experiments performed by cycle starts again when two conditions are ful- Imbrie and Imbrie [1980], results for the past filled: summerinsolation should be well below 150,000 years are quite good, and the spectrum of normal, and the bedrock should have been raised this output contains significant power at cycles again. Such a reconstruction of the ice volume of 100 kyr and longer (not found in the orbital recordover the 1• t 600,000 years has given the input) , although the 41-kyr , 23-kyr , and 19-kyr best fit to the • 0 records when an internal time cycles are dominant. scale of 75,000 years is taken. Oerlemans and Imbrie and Imbrie [1980] have also developed a Bienfait [1980] have also pointed out the import- simplified glacial dynamics model especially de- ant role of the daily cycle in the process of signed for the explicit purpose of reproducing the melting. They have designed a simple energy bal- Pleistocene ice volume record from orbital forc- ance model of the ice/snow surface layer which ing. The rate of climatic change is made inverse- simulates this daily cycle and whose result is ly proportional to a time constant that assumes used to parameterize the mass balance of their one of two specified values, depending on whether dynamical model of a northern hemisphere ice the climate is warming or cooling. Such a model sheet. Forcing this model with the insolation tuned over the last 150,000 years is forced with variations in time and latitude provides a very orbital input corresponding to an irradiation reasonable simulation of the global ice volume curve for July at 65øN, with a mean time constant record of the last 700,000 years. Even if some of 17,000 years and a ratio of 4:1 between the objection can be made to such model, for example, time constants of glacial growth and melting. The Berger: Milankovitch Theory and Climate 645

...... Equilibrium bedrock I00120 , , i i I I , , I • • , ' ' ' •• • A .... Bedrocklagadded . [ I• ------Topographyadded g I ,til :o . Icecalving added_ I .' •:. .'.. ' ß ' .I:'" t' :'' ' 40 \ : : : ; - .'..' ...., i : _

o '0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Frequency(cycles per Kyear)

Fig. 24. Power spectral density of the ice volume simulated by four different models: no topography and the bedrock in isostatic equilibrium (dotted curve); with a bedrock lag added (chain-dotted curve); model run with piecewise-linear topography (dashed curve); model with a calving mechanism (solid curve) [Pollard, 1982]. model's simulation of the isotopic record of ice and isostatic rebound. He showedthat simple volumeover the past 150,000 years is reasonably modelswhich comprisethe interaction of two or good,but results for earlier timesare mixed,and moreof thesemechanisms are capable,in the ab- parametricadjustments do little or nothingto senceof any variations in solar radiation, of improvematters. This goal of themodeling effort self-sustainedoscillations in the range of 104 to simulate the climatic responseto orbital var- years (definitely below the major glaciation cycle iations over the past 500,000years also fails to peakof 100 kyr) and are only slightly blurred by producesufficient 100-kyrpower and produces too fluctuationson smallertime scales. Theseoscil- much19-kyr, 23-kyr, and413-kyr powers. More- lations havethe correct amplitudesand exhibit over, the modelloses its matchwith the record phasedifferences betweentemperature and ice around the time of the last 413-kyr eccentricity extent which correspondto the best currently minimum. This could be related to the fact that available paleoclimatological evidence. Concern- althoughthe characterof climatic recordis fair- ing the dominantperiodicity of 100kyr, Ghil ly constantover the past 600,000years, older proposestwo possible processes. One consists of Pleistocene records maybe quite different. If subharmonicresponse of a nonlinear climatic os- the nature of orbital variation is thought to have cillation of suitable amplitude to precessional remainedconstant over the past 2 Myr, Imbrie and periodicities in irradiation. The other consists Imbrte [1980] then concludethat to understandthe of the mutualamplification of internal random long climatic records,it maybe necessary(1) to perturbationsand of the small changesin irradia- developalmost intransitive models[Lorenz, 1968], tion causedby eccentricity in the Earth's or- (2) to build stochastic modelsto understandvar- bit. This last modelprovides groundsto solve iations unexplained by deterministic models [Has- the basic conflict between the apparent predict- selman, 1976], (3) to use models whose parameters ability shown by the phase coherence of the 100- vary with time, or (4) to produce in the climatic kyr climatic and eccentricity cycles [see Imbrie systeman intrinsic tendency to oscillate at 100 and Imbrie, 1980, Figure 10] and the very strong kyr or a resonance. Along this line, it must be sensitivity that the model needs in order to re- noted that the strong response of the Oerlemans produce the record accurately from eccentricity [1980] cryosphere on the 100-kyr time scale, as forcing. The resonance found between a determin- comparedto the 20-kyr and 40-kyr peaks, points istic small external forcing and a stochastic also to such a resonance which enables variations internal mechanism in a zero-dimensional climate in eccentricity to be supportedby the internal modelhas indeed allowed reproductionof the ob- dynamicsof the climate systemto create a strong served100-kyr cycle, a small changein the eccen- signal in global ice volume. tricity forcinginducing a large changein the On the other hand, a tendencyto obtain free probability of jumpingbetween two observable oscillations at periodsof the order of several climate states [Nicolis, 1980;Benzi et al., tens of thousandsof years in complexclimate 1982]. modelshas also been mentionedby Sergin [1979], As a consequence,recent ice sheet models show Kallenet al. [1979], andGhil [1981]. Indeed, that the 100-kyrcycle canbe simulatedwith [Ghil ofthe 10•-10m•in •hysical yearshave mechanisms been recognized activeon by time Ghilscales withoutand Le Treut, [Lindzen,1981; 1986] Saltzman internal et al., free 1984] oscillationsor [1981] to be global radiation balancechanges, related to resonanceswhen astronomically forced thermal inertia of the oceans, changesin the but is significantly reinforced whenisostatic hydrologiccycle, continentalice sheetdynamics, rebound[Hyde and Peltier, 1985]and iceberg calv- 646 Berger: Milankovitch Theory and Climate

ing are taken into account (Figure 24) [Pollard, 0 30 60 90 120 150 180 1982]. i I ßI I ! I I 7.2. General Circulation Models and Equilibrium Response 60 ,/' + + + + + + /" / -60 / '/ + + •+ + J Another suggestion that has generated considerable interest is that geography may help explain climate's sensitivity [North et al., 1983]. So, when orbital variations are used that favor in- creasingly cooler summers (as at the transition . : -o between 125,000 and 115,000 years B.P. and at the last glacial maximum 18,000 years B.P.), models with realistic distribution of continents and 30 •'" '", ? - 80 oceans generate the ice cap mostly over northern Canada and Scandinavia. The strongest orbital influences act at the most sensitive spots of the climatesystem. For example ' Royer et al' [1983] 60 0i 30I 60.I 90I 120I 150I 180•0 simulated a cooling of more than 2øC over northern America with an increase of precipitation over the Fig. 25. Schematic of simulated temperature, same area. Another suggestion for amplifying the pressure, wind, and precipitation differences, response of northern ice to orbital variations has 9000 years B.P. minus present, for June-July- come also from the possibility that North •tlantic August: higher temperatigre (pluses), intensified surface water remained warm well after insolation monsoon low (L), stronger low-level wind (double- in northern hemisphere high latitudes had favored shafted arrows), stronger upper-level wind (curved cooler summersand northern ice had even begun to arrow), increased precipitation (shading). (Re- grow. If so, at least at the precession frequen- printed from Kutzbach and Otto-Bliesner [1982] cies, insolation variations may combine both to with permission from the authors and the American increase the latitudinal gradients and to keep up Meteorological Society.) the supply of moisture in high latitudes, where it is retained as ice [Rudd[man and Mcintyre, 1984]. Glacial ice has generally received most of the attention, but evidenceexists that orbital varia- in tropical [Bernard, 1962; Rossignol-Strick, tions also influence the behavior of the North 1983; Short and Mengel, 1986] and equatorial clim- Atlantic deep ocean water and atmospheric features ate [Pokras and Mix, 1987]. such as the intensity of the westerly winds and of From a similar simulation of the climate at 9 the Indian monsoon. For example, changing the kyr B.P., Mitchell et al. [1987] found that in the orbital configuration to that of 9 kyr B.P., •en northern hemispherethe simulated warmingin high insolation seasonality was 14%higher than it is latitudes is greatest in autumnand winter because today, leads to an intensified southwest monsoon of changes in sea ice, the mid-latitudes are warm- (Figure 25) [Kutzbach, 1981]. This has been con- er throughout the year because of changes in firmed by the results obtained from Kutzbach's cloud, and the simulated surface temperature atmospheric general circulation experiments to change over land in summeris reduced in low lati- simulate the climates of January and July from 18 tudes and enhanced in mid-latitudes because of to 10 kyr B.P. at 3000-year intervals [Kutzbach changes in cloud and soil moisture. and Guetter, 198b]. In these integrations, ex- Adem[1988] completeda study of the last ternal forcing (the astronomical solar radiation) 20,000 years using a thermodynamicmodel of the and internal boundary conditions (land and sea northern hemisphere. From 18 to 12 kyr B.P. the ice, aerosoland CO 2 loadings)were taken into surfacealbedo feedback maintains the northern account. From 15 kyr B.P. onward this model simu- hemisphere cool with stronger seasonal variations, lates a strengthenedmonsoon circulation and in- the decreaseof the atmosphericCO 2 reinforcing creased precipitation in the northern hemisphere the anomalies. From 12 kyr B.P. to the present tropics, culminating in a maximumimpact at 9-6 time the computed monthly average northern hemis- kyr B.P. [Kutzbach and Street-Perrott, 1985]. phere surface temperature anomalies have the pat- Prell and Kutzbach [1987] have used the NCAR tern of insolation anomalies, except for a lag CommunityClimate Model [Washingtonand Parkinson, associated with the storage of heat in the oceans. 1986] to study the processes causing such changes in monsooncirculation for the past 150,000 7.3. Climate Modelsand Transient Response years. The simulated spatial patterns of climate variables and their zonal and regional averages In addition to the calculation of the Earth's revealed that under in'terglacial conditions, in- climate which is in equilibrium with a particular creased northern hemisphere solar radiation pro- insolation pattern and other boundary conditions duced a larger land-ocean pressure gradient, (the ice sheets, for example), the simulation of stronger winds, and greater precipitation over the transient response of a realistic climate southern Asia and North Africa. Under glacial system to orbital variations must allow a better conditions the simulated monsoonis weakenedin understanding of the physical mechanismsinvolved southern Asia, but precipitation is increased in in the relationship between the astronomical forc- the equatorial west Indian Oceanand equatorial ing and climate. I suggestedearlier [Berger, North Africa. Moreover, the monsoonis strongly 1979b] that the long-term astronomical variation tied to the precession parameter (their mmxima of the latitudinal distribution of the seasonal coincide), as is also the case for the variations pattern of insolation (Figures 20 and 21) is the Berger: Milankovitch Theory and Climate 64?

-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 - 10.0 ...... ' ...... --

-o.oo5.00 0.00• 5.00 [• I • jilt 10.0 •,,, ,

20.0 - 0.50 •-

i 40.0 NH + SH , ' NH z 1.00 >-- 45.0 x o 50.0 ' • ' • ' • ' • ' • ...... -140 -120 -100 -80 -60 -40 -20 0 20 • 60 80 TIME (KYR) Fig. 26. Long-termvariations over the last glacial-inter•laci•al cycle (1) of the deviation from its present-dayvalue (assumedto be 30.5 x 10v kmZ) of the total continental ice volume over the Earth (full curve) simulated by Berger et al. [1988] and (2) of the oxygen isotopic ratio variations (dashed curve) given by Labeyrie eta!. [1987] and Duplessy et al. [1988]. The integration over the next 80,000 years has been carried out by H. Gall•e for the northern hemisphere ice sheets only, starting with the observed present-day conditions.

key factor driving the climate system, the complex viously thought [Sundquist and Broecker, 1985]. interactions between its different parts taking They could also have been linked in producing the turns with this orbital perturbation. A 2.5- higher temperatures of the Cretaceous, 100 Myr ago dimensional time-dependent physical climate model, [Be•,zer and Barron, 1984]. In the context of the taking into account the feedbacks between the antropogenicCO 2 impact on our future climate, atmosphere, the upper ocean, the sea ice, the ice this field undeniably merits more investigation. sheets, and the lithosphere, has confirmed this hypothesis [Berger et al., 1988]. The simulated 8. Conclusions long-term variations of the global ice volume over the past 125,000 years (Figure 26) agree remark- Recent new evidence seems to have laid to rest ably well with the sea level curves of Chappell the argumeats that orbital variations might cause and Shackleton [1986] and Labeyrie et al. only minor climate fluctuations but not the major [1987]: significantly, the norther,• hemisphere climatic changes manifested in the ice ages, the ice sheets were growing owing to snowfalls, the largest and most abrupt climatic changes known water vapor pumped from the oceans being carried during the past 2 Myr. Among the competing theo- out by the atmospheric general circulation. ries to explain the coming and going of the Quat- All the mechanisms for generating northern ice ernary ice ages and other similar climatic vari- sheets in response to orbital forcing share, ap- tions of the past, only the astronomical theory parently, a common problem, namely, the synchron- (of which the Milankovitch theory is a particular eity of glaciations in both hemispheres. A pos- version) has been supported so far by substantial sible inter-hemispheric link might be the ocean physical evidence. circulation [Duplessy and Shackleton, 1985; Du- This evidence shows that, both in the frequency plessy et al., 1987] or the worldwide effect of and in the time domains, orbital influences are changes in atmospheric carbon dioxide conceqtra- felt by the climate system and implies that the tions [Manabe and Broccoli, 1985]. Recent re- astronomical theory might provide a clock with constructions of these past CO2 variations have which to date old Quaternary sediments with a been possible because of the analysis of oceanic precision several times greater than is now poss- data [Shackleton et al., 1983] and ice data (Fig- ible. On the other hand, there is evidence that ure 27) [Barnola et al., 1987; Lorius et al., the orbital variations-climate link (namely, at 1985; Jouzel et al., 1987; Neftel et al., 1982], periods shorter than 100,000 years) has been a and evidence shows that orbital changes lead the viable mechanism during the past few hundred mil- changesin CO2, which in turn lead those in ice lion years, also at times when major ice masses volume by an average of 2500 years [Pisias and were probably absent [Herbert and Fisher, 198•]. Shackleton, 1984]. In such a case the variations If we accept the astronomical theory as a funda- in atmospheric CO2 could be, in someindirect way, mental principle, a time will comewhen geology part of the forcing of ice ages [Genthon et al., will provide astronomers with estimates of period- 1987] or, better, modulate the response of the icities in the range of tens of thousands to hun- climate system to orbital forcing [Berger et al., dreds of thousand years, allowing us to test theo- 1988]. Climate and the carbon cycle appear thus ries of the planetary system and its stability to have been more tightly linked than was pre- over the whole of Earth's history. 6q8 Berger: Milankovitch Theory and Climate

280

-½30 o o

-2.S ßg -60 -5.0 • -•70 -•80 -7.5 -•90

-•0.0 -500

Age•kyr ee• 0 •0 80 120 160 •tg. 27. tn pa•s pet mt[•on by volumeversus age tn the Voscok•ecotd (uppe• curve) [•atno[a e• a[., [987]. A•mosphet[c :empe•a:ute change derived g•om :he •so:optc ptog[[e (•o•e• curve) [Jou•e• e• a•., [987]. (Rep:tnced f•om Batno[a e• a[. [[987] •h permission fEom •he authors and HacHt•Lan •ga•tnes.)

Along the lines of these reconstructions of the ate cold peak around 5 kyr A.P., a major cooling climatic rhythmsrecorded in pre-Quaternarystrata about 23 kyr A.P., and full ice age conditions 60 [Fisher, 1986], we have computedthe effect of the kyr A.P. varying Earth-Moon distance on the main astronomical periods over the last 2 billion years (Table 9. Implications for the Future 5). The nonlœnearœty of the relationship between this Earth-Moon distance and the "constant" of the This kind (see Appemdix D for a summary) of astronomical precession is responsible for a fast- simulation is now of real practical interest; the er decreaseof the9obliquœtyperiod, in sucha way timescale is compatiblewith the decay of radio- that before 2 x 10 years B.P. the precession active elements trapped in nuclear wastes produced periods are as long as the obliquity period. in atomic energy power plants, and for the safety Finally, significant advances made in climate of our future generations, there is a need to theory combined with advances in paleoclimatology study in depth the stability of the sites of nu- indicate that there is now a unique opportunity to clear waste disposal. In the light of all these use the geological record as a criterion against results the relevance of the Milankovitch theory which to judge the performance of physically mot- for modernclimate research lies in climate model ivated models of climate and so to identify mech- validation and sensitivity analysis and in a bet- anisms by which different parts of the climate ter understanding of the seasonal cycle and other system respond to changes in radiative boundary climatic cycles. Because of its contribution to conditions. The importance of this opportunity is an accurate knowledge of our low-frequency climat- that both the temporal and the spatial pattern of i c background (and even the high-frequency part as these changes can be specified exactly. Except shown by Borisenkov et al. [1985]) and to an im- for the daily and annual cycles we know no other proved theory of climate, it provides useful in- place in the climatic spectrum for which this sights for further applications such as the study exactitude is possible. Consequently, the astronomical theory is the only one that can be used to TABLE 5. Direct Impact of the Varying Earth-Moon predict precisely the duration of natural quasi- Distamce on the Astronomical Periods periodic changes in climate. Using a simple model astronomically forced, researchers have shown that Period, Years the dynamic behavior of the climate over the last 400,000 years reproduced fairly well [Imbrie and Epoch, Imbrie, 1980; Berger, 1980a; Berger et al., 1988]. Extrapolation thus begins slowly but sure- 109 Years 19,000 23,000 41,000 ly to be allowed (Figures 26 and 28) [Berger, B. P. Be come s Be comes Be come s 1980b], at least for a period over which we can assume that there is sufficient predictability 0.5 17,500 20,800 34,0'00' [Nicolis and Nicolis, 1986]: assuming no humam 1 16,600 19,500 29,900 interference at the astronomical scale, orbital 2 !4,700 16,800 21,200 forcing predicts that the general cooling that 2.5 13,400 14,750 14,800 began 6 kyr B.P. will continue with a first tooder- Berger: Milankovitch Theory and Climate 649

_330 ,,. ß,. - 99 -6 • øfs, -2

. 60 -342 -270 -21

-4.2 ' i I I i i -400 -500 -200 -I00 0 I00 (x I000 yr) Fig. 28. Long-term climatic variations over the past 400,000 years and prediction for the next 60,000 years assuming no human interference at the astronomical time scale (pluses are data from Hays et al. [1976]; the solid curve is a simulation from a re- gressive model using the insolations as a forcing and allowing for a 3000-year memory of the climate system [Berger, 1980b]). of man's impact on climate and climate forecasting history, the Pleistocene-Holocene epochs have been at the annual to decadal time scales. Mitchell studied more intensively than the rest of the pal- [1977] claimed that the warming effect of carbon eoclimatic record because of relatively easy ac- dioxide [Bolin et al., 1986] may interact with the cess to a wide variety of geological exposures, astronomical prediction by interposing a superin- and amenability of the data to more rigorous, terglacial, with global mean temperatures in the quantitative analysis. next few centuries reaching levels several degrees A fundamental tool for the palcoclimatic inter- higher than those experienced at any time in the pretation of geological records involves a tech- last million years (remember that this is happen- nique that has been an invaluable aid in examining ing close to a climatic optimum). Provided the the climatic history of the last million years: climatic systemdoes not jumpinto a newvery warm the 180/160stable isotopeanalysis [Duples•sx, equilibriumstate, the next ice agewould have to 1978]. Themost commonly used fossils for l•O wait until this CO2 warmœnghas run its course, analyses are foraminifera, single-celled amoeba- more than a thousand years from now. like organismswith CaCO3 shells. There are both The astronomical theory has allowed us to im- planktonic (surface and near surface) and benth•c prove and to test advanced techniques of data (bottom dwelling) varieties. The fundamental analysis and models which can be transferred to geologicalproblem associated with 180 interpreta- evaluate climatic variations and variability at tionsinv?•ves the realizationby Emiliani [1955] our human time scale. Consequently, it is not that the O content of seawater can also be af- merely of academic interest but really lies at the fected by the formation of ice sheets. roots of any program which aims to better under- On the other hand, palcomagnetic studies and stand the climate system and its behavior. isotope techniques have provided the key to age interpretation of Quaternary stages. For example, Appendix A: Pleistocene-Holocene Climates Shackleton and Opdyke [1973] were the first to determine that the last major reversal, the The inferred planetary evolution d•rœng the Brunhes-Matuyamaboundary, occurred within 180 last 4.5 x 109 years exhibits both long-term stage 19. Following thœs work, correlations were trends and fluctuating components [Berger, 1979a, later extended to the entire Pleistocene [Shackle- 1981; Wtgley, 1981; Crowley, 1983]. The long-term ton and Opdyke, 1976]. climatic trends have been influenced by changes in Northern hemisphere glaciation was apparently solar luminosity, in atmospheric composition, and initiated several million years after Antarctic in palcogeography.Glacial-interglacial stages glaciati•n. Thepresent best estimate is about observedwithin the last Ice Age (the high-ire- •.0 x 10• years ago, a time whenAtlantic deep quency part of the spectrum at the geological time water production may have increased and closely scale [Bradley, 1985]) are due to orbitally induc- spaced, large-scale glacial-interglacial oscilla- ed forcing and to feedback œnteractions within the tions were initiated. However, analyses of North atmosphere-hydrosphere-cryosphere-lithosphere- Atlantic and North Pacific records indicate some biosphere system and are superimposedon a global pronounced temperature decreases that extend back coolingof terrestrial,most probably plate tec- to at least10 x 106years B.P., while the Arcgic tonics, origin [Barron et al., 1984]. Ocean has been ice covered for the last 5 x 10 Although comprising less than 0.1% of Earth years. TABLE BI. Some Key Stages in the Evolution of the Astronomical Theory of Paleoclimates

,. Year Investigator Description Pre-Milankovitch Pioneers 1842 Adh•mar variation in the direction of the earth's axis 1875 Croll minimum in winter insolation, precession effect, e maximum, ice cap albedo feedback smaller amount of insolation in polar regions, obliquity minimum 1891 Ball precession of the equinoxes 1901 Ekholm obliquity 1901 Hildebrandt small eccentricity

Milankovitch Era: Cool Summerat High Northern Latitudes 1876 Murphy 1921 Spitaler 1925 BrHckner, K•ppen, Wegener 1920 Milankovitch 1930 Milankovitch 65øN equivalent latitude, caloric northern hemisphere summer 1941 Milankovitch 1937 Soergel lag between insolation and extend of ice masses 1937 Blanc sea level 1938 Wundt albedo, continental configuration, air and sea currents 1940 von Bacsak interglacials 1950 Brouwer 1957 Emiliani and Geiss insolation only starts glaciation 1959 Zeuner application to Scandinavian ice sheet 1961 Jardetsky

Milankovitch Debate: Caloric Seasons at Different Latitudes 1961 Fairbridge 40ø-75 ø caloric summer: continental area 1961 Wundt summer irradiation high latitudes in northern and southern hemispheres 1962 Bernard pluvials and interpluvials in Africa 1966 van den Heuvel • • 70øN, obliquity, symmetry between northern and southern hemispheres 1966 Broecker combination of precession, tilt, eccentricity; 6000 year lag 1968 Kukla winter half-year irradiation at 55øN 1968 Broecker et al. 45øN caloric summer insolation 1969 Mesolella et al. application to Barbados: coral terraces, sea level

1972 Vernekar computation for all latitudes in northern and southern hemispheres, 19691979 SharafVulis andand MoninBudnikova t of summer and winter caloric insolation 1970 Broecker and van Donk 45ø-55ø-65øN caloric summer insolation 1970 Veeh and Chappell 45øN, application to New Guinea

Milankovitch Debate: Spectrum of Geological Data 1929 Bradley 21 kyr: varves of the Tertiary Green River epoch 1964 van Houten 21 kyr: nonmarine Triassic strata 1966 van den Heuvel obiquity and half precession (precession following Hays et al. from Emiliani's curves) 1967 Kemp and Eger precession (obliquity following Hays et al. [1976]; Caribbean cores P6304-8/9 1967 Bond and Stocklmayer 21 kyr; upper Paleozoic strata in Rhodesia 1967 Mann 109 kyr, 30.8 kyr, 24.25 kyr; Missourian rocks 1969 Dansgaard et al. 13 kyr; Camp Century ice cover

Milankovitch Debate: Physical Models 1968 Shaw and Donn Aden's model, AT = 1.4øC (25 kyr B.P. high latitudes) 1969 Budyko energy balance model; A glacial boundary ~1 ø latitude 1970 Sellers energy balance model; AT ~0.1øC(minimum obliquity, high latitudes) 1971 Saltzman and Vernekar statistical-dynamical model, AT = 1.4øC (25 kyr B.P., 85øN)

Milankovitch Renaissance: Caloric Seasons 1972 Kukla season-to-season difference in winter insolation for 25ø-75øN 1972 Evans 65øN and 65øS; time lag 4 kyr computation for all latitudes N-S, summer and winter 19781973 Berger } caloric equator 1974 Bloom et al. application to New Gunea, coral terraces 1974 Ku et al. application to Hawaii, coral terraces 1974 Chappell precession and large eccentricity, application to coral reefs 1974 Calder different thresholds growth and decay of ice sheets, 50øN summer insolation 1976 Mason insolation deficit for • • 45øN 1976 Johnson and McClure hemisphere average and 70øN summer irradiation TABLE B1. (continued) 651

Year Investigator Description

1976 Ruddiman and Mcintyre 55øN-summer i•solatio n 1979 Ruddiman and Mcintyre 65øN low caloric summer insolation 1979 Kukla and Berger astronomic climate index, interglacials 1979 Kominz and Pisias 50øN 1980 Ruddiman and Mcintyre 70øN summer insolation-oceanic moisture, precession 1980 Dansgaard 65øN summerinsolation and north-south gradient thresholds

Milankovitch Renaissance: Monthly Insolation 1975 Kukla fall insolation 1978 Berger monthly insolation pattern 1979 Berger et al. insolation-climate index

Milankovitch Renaissance: Spectrum of Proxy Data 1973 Chappell 100 kyr, 60 kyr, 45 kyr, precession (obliquity following Hays et al. [1976]; coral reefs, Caribbean and Atlantic deep-sea cores 1975 Briskin and Berggren 413 kyr, V16-205 tropical North Atlantic core 1976 Ruddiman and Mcintyre 85 kyr, K708-7 from NE Atlantic Ocean 1976 Hays et al. 105 kyr, 41 kyr, 23 kyr, 19 kyr; RClI-120, E49-18 deep-sea cores in southern Indian Ocean 1977 Kukla 100 kyr; soil record from central Europe (up to 2 Myr B.P.) 1978 Shackleton 400 kyr; Atlantic Deep Sea Drilling Project Tertiary sites 1979 Kominz et al. 400 kyr, 104 kyr, 93.2 kyr, 58.5 kyr, 52.2 kyr, 41 kyr, 30 kyr, 23 kyr, 19 kyr; western equatorial Pacific core V28-238 1979 Briskin and Harrell other astronomical cycles; deep-sea cores V16-205, V28-239, RCll- 120/E49-18

Milankovitch Renaissance: Spectrum of Astronomical Data 1977 Berger 413 kyr, 95 kyr, 123 kyr, 100 kyr, 50 kyr, 41 kyr, 53 kyr, 30 kyr, 23.7 kyr, 22.4 kyr, 18.98 kyr, 19.16 kyr, 16 kyr, 56 kyr

Milankov[tch Renaissance: Climatological Models 1973 Chin and Yevjevitch almost periodic stochasting forcing; explained variance: 41% 1976 Hays et al. linear model; explained variance: 80%; RCII-120/E49-18 1976 Weertman ice sheet model; obliquity-precession cycle 1977 Berger energy balance model; AT small but cooling extends to 60øN 1978 Petersen and Larsen autoregressive integrated moving average model; Cart[bean, Atlantic, and Pacific deep-sea cores 1978 Rooth et al. terrestrial relaxation oscillation of 100,000-year cycle and obliquity and precession curves 1978 Keer explained variance from astronomical forcing: 10% 1978 Pollard Weertmanimproved model; obliquity-precession cycles 1978 Birchfield and Weertman Weertman improved model, all astronomical peaks 1979 Coakley energy balance model; AT small 1979 North and Coakley energy balance model; oceanic mixed larger, seasonal change;A ice line: 3 ø latitude 1979 Cess and Wronka amplification expected from zenith angle, bio-albedo, latent heat feedbacks 1979 Suarez and Held energy balance model (ocean), albedo feedback, seasonal; A ice line: 20 ø latitude 1979 Schneider and Thompson energy balance model (seasonal); A (glacial-interglacial, 60øN) = 0.8øC 1979 Berger et al. almost nonlinear autoregressive insolation models; insolation June 85øN, December 65øN, March 25øN, September 15øS, June 55øS, Oecember 75øS; climate memory: 3000-year lag; all astronomical peaks; RCll-120/E49-18, R2 = 50-87% 1979 Kominzand Pisias stochasticforcing, R2 = 26%from V28-238 1979 Kukla and Berger astronomic climate index; 100-43-23-19-7 kyr periods 1979 Kallen et al. several tens of thousands of years free oscillations 1980 Ghil several tens of thousands of years free oscillations 1980 Imbrie and Imbrie differential models, different time scales for growth and decay of ice sheets, 65øN July insolation, all astronomical peaks; deep-sea cores RCll-120, V28-238 1980 Oerlemans ice sheet/Earth crust dynamics; 100 kyr; Carribean core V12-122 1980 Oerlemans and Bienfait Oerlemans plus daily cycle snow/ice melting; 100-kyr 1980 Benzi et al. stochastic resonance amplifies the 100-kyr eccentricity cycle

Milankovitch Big Bang 1980 Berger for references, see this paper and, for example, the work by Berger et al. [1984], Bradley [1985], Hecht [1985], Imbrie [1982], Kutzbach [1985], and National Research Council [1982] 65P Berger: Milankovitch Theory and Climate

Appendix C: A Discussion of Past (and Now iments [e.g., Herbert and Fisher, 1986], the time Irrelevant) Criticisms of the Milankovitch Theory scale of Cretaceous climate or of earlier Ice Ages (as in the case of the infra-equatorial glaciation Opponents have, in the past, made the following of the Mesozoic era in the Sahara, South Africa, criticisms of the Milankovitch approach: and Australia) is more related to geographical 1. The theory goes awry by its prediction of variables and plate tectonics than to orbital contrapuntal or alternating insolation effects parameter variations [Barron and Washington, 1984; relative to the two hemispheres. Alternating Barron et al., 1984]. hemispheric glaciation cycles are indeed not observed, and nor are they predicted by climate Appendix D: Relevance of the Astronomical Theory models which are astronomically forced. However, to the Modern World as the high-latitude caloric insolation is mainly dependent on obliquity, whereas that of low lati- The astronomical theory has the following ad- tudes is essentially dependent on precession, and vantages: as the obliquity effect is the same in both hemis- 1. It provides an absolute clock with which to pheres, whereas the precession effect is the oppo- date Quaternary sediments with a precision several site, the nature of the Milankovitch model itself times greater than is now possible. implies an asymmetry between hemispheres which is 2. It provides data to astronomers to test the minimal (almost nonexistent) for all latitudes stability of the planetary system for pre-Quatern- higher than 70 ø (the Milankovitch critical lati- ary times. tudes). On the other hand, the model also implies 3. It provides the boundary conditions neces- compensation of negative summer deviations by sary for a better understanding of the climatic positive winter deviations. Under such condi- system and the interactions between atmosphere, tions, not only would the summer temperatures in hydrosphere, cryosphere, biosphere, and lithos- northern high latitudes be such as to tend to help phere, which, at the astronomical time scale, all prevent snow and ice from melting, but also the play a role. implied milder winters would tend to allow a sub- 4. It allows a better understanding of the stantial evaporation in the intertropical zone and seasonal cycle and allows us to test the perform- more abundant snowfalls in temperate and polar ance of the climate models over a broad spectrum latitudes, this humidity being transported there of climatic regimes. by an intensified general circulation due to the 5. It allows a better understanding of the CO2 maximum in the latitudinal insolation gradient cycle, its sensitivity to climate changes, and its [Berger, 1976b]. interactions with the climate subsystems. Moreover, Suarez and Held [1979] demonstrated 6. It predicts natural climatic variability at with a simple energy balance that although varia- the geological time scale for the next 100,000 tions in the Earth's orbital parameters mmy be years, a period compatible with the decay of ra- responsible for the large fluctuations in the dioactive elements trapped in nuclear wastes pro- extent of norther• hemisphere ice sheets during duced in atomic power stations (climate stability the Pleistocene, it is necessary to look for mech- of the sites of nuclear waste disposal). anisms other than the interhemispheric exchange of 7. It allows a better understanding of the heat in the atmosphere in order to explain the low sens[tivity of our present-day interglacial clim- temperatures of the souther• hemisphere during ate and of the possible superinterglacial that glacials. It was proposed that among the poten- could be generated by human activities within the tial mechanisms for this cooling of the southern next 50 years or less. hemisphere are the cross-equatorial heat transport 8. It enables us to compute accurately the by the ocean circulation [Manabe and Broccoli, insolation changes at the decadal time scale due 1985] and/or the fluctuations in the conceatration to change in orbital elements, in relation to the of carbon dioxide [Broecker, 1982] as deduced from satell[te measurements of the solar constant and ice cores from the Antarctic [Barnola et el., its variations. 1987] and Greenland [Neftel et el., 1982] ice 9. It allows a better understanding of the sheets or in the loading of aerosols in the atmos- planetary system and the climatic variations of phere. the planets [Ward, 1974; Ward et el., 1979]. 2. The theory fails to account for the fact 10. It allows us to transfer theoretical know- that all the Quaternary events have their maximum ledge (spectral analysis, numerical schemes, etc.) impact in the northern hemisphere. Within the and technologies (deep-sea drilling, satellites, framework of the astronomical theory by which supercomputers, etc.) to society at large. orbital parameter changes are seen as the essential modulators of the long-term climatic behavior Acknowledgments. Improvements in the astronom- (in that they place the climate system in a state ical theory have been possible only through inter- which is more or less sensitive to other factors), national collaboration initiated, in particular, there is absolutely no reason that this astronomi- by the CLœMAP(Climate: Long-Range Investigation, cal theory must account for all the climatic Mapping and Prediction) and SPECMAP(Mapping Var- changesduring the Quaternary. In particular, the lagoonsin OceanSpectra Over a FrequencyRange abruptPleistocene climate changes [Berger, 1982] 10 • to 10-B Cyclesper Year) groupsin the United will most probably find their origin within the States a•d by the Commission of the European Com- complex interactions and feedback mechanisms bet- munities. Many thanks to all colleagues for their ween the components of the climate system itself. helpful discussions. The members of the Institut 3. The theory is not needed to explain other d'Astronomie et de G&ophysiqueGeorges Lema•tre major glaciations. It is evidently a question of have significantly contributed to some recent time scales. Although astronomical signatures are results presented here. Works by J. Guiot, P. beginning to be found in many pre-Quaternary sed- Pestiaux, J.P. van Ypersele, C. Tricot, H. Gal- Berger: Milankovitch Theory and Climate 6õ3 l•e, P. Gaspar, T. Fichefet, I. Marslat, I. van nomical solution of Berger, 1978), Contrib. 36, der Meersch, F. Goffin, M. F. Loutre, and V. De- Inst. d'Astron. et de G•ophys.G. Lema•t're, ' hant are gratefully acknowledged. I am indebted Univ. Catholique, Louvain-la-Neuve, Belgium, to H. Cattle (Meteorological Office, Bracknell, 1978d. England) and to unknown referees for their most Berger, A., Numerical values of caloric insolation helpful comments during the finalization of this from 1,000,000 YBP to 100,000 YAP (astronomical review paper. N. Materne-Depoorter typed the solution of Berger, 1978), Contrib. 3.7, Inst. numerous revisions of the manuscript. Thanks to d'Astron. et de G•ophys.G. Lema•tre, Univ. the Belgian National Foundation for Scientific Catholique, Louvain-la-Neuve, Belgium, 1978e. Research, the Minist•re de •a •ommunau•e Fran- Be•, A., Long-term variations of caloric inso- caise, the International Climate Commission of lation resulting from the Earth's orbital ele- IUGG-IAMAP, the iNQUA International Commission of ments, Quato Res., 9_• 139-167, 1978f. Paleoclimate, and the Organizing Committee of the Berger, A., Spectrum of climatic variations and XIX IUGG General Assembly of Vancouver for their their causal mechanisms, Geoph•s. Surv., 3, financial help. 351-402, 1979a. Berger, A., insolation signatures of Quaternary References climatic changes, Nuovo Ciment0, 2C(1), 63-87, 1979b. Adem, J., Possible causes and numerical simulation Berger, A., A critical review of modeling the of the northern hemispheric climate during the astronomical theory of paleoclimates. and the last deglaciation, Atmosfera , 1, 17-38, 1988. future of our climate, in Sun and Climate , pp. adh•mar,J. a., Revolutiondes Mer• D•lu•.esP•r- 325-356, Centre National d'Etu'des Spatiales, iodiques., publication priv•e, Paris, 1842. Toulouse, France, 1980a. Agassiz, L., Upon glaciers, moraines, and erratic Berger, A., Milankovttch astronomical theory of blocks; address delivered at the opening of the paleoclimates, a modern review, Vistas. Astron. , Helvetic History Society at Neuchatel, 24 July • 103-122, 1980b. 1837 by its president, New Philos. J. Edin- Berger, A. (Ed.), Climatic Variations and Vari- burgh, 24___,864-883, 1838. ability: Facts and Theories, D. Reidel, Hing- Alyea, F. N., Numerical simulation of an ice-age ham, Mass., 1981. paleoclimate, Atmos. Sci.. PaP. 193, 120 pp., Berger, A., Accuracy and frequency stability of Colo. state univ., Fort Collins, 1972. the Earth's orbital elements during the Quater- Ball, R., The C.auseof an Ice-Age, London, 1891. nary, in Milankovitch and Climate, edited by A. Barnola, J. M., Y. S. Korotkevitch, D. Raynaud, Berger et al., pp. 3-40, D. Reidel, Hingham, and C. Lorius, Vostok ice Core: A 160,000 year Mass., 1984. record of atmosphericCO2, Nature., 3.29(6138), Berger, A., Pleistocene climatic variability at 408-414, 1987. astronomical frequencies, in Global Change, Barron, E. J., and W. M. Washington, The role of edited by H. Faure and N. Rutter, International geographic variables in explaining paleoclim- Quaternary Association, Ottawa, Ont., 1987. ates: Results from cretaceous climate model Berger, A., and Pestiaux, P., Accuracy and stabil- sensitivity studies, J. Geoph•s. Res., 89__, ity of the Quaternary terrestrial insolation, 1267-1279, 1984. in Milankov•.tch and Climate., edited by A. Berg- Barron, E. J., S. L. Thompson, and W. W. Hay, er et al., pp. 83'112, D. Reidel, Hingham, Continental distribution as a forcing factor Mass., 1984. for global-scale temperature, Nature, 310, 574- Berger, A., and P. Pestiaux, Astronomical fre- 575, 1984. quencies in paleoclimatic data, in The Climat9 Benzi, R., G. Parisi, A. Sutera, and A. Vulpiani, of Chinaand Global Climate. ', edited by Ye Duz- Stochastic resonance in climatic change, Tel- hen'g•Fu congbin, ChaoJiping, M. 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