[14] M. Milankovitch was the second scientist after J. Croll who contributed greatly to orbital theory development. Milankovitch theory differs in mathematically strict calculations of orbitally-caused variations of insolation at the upper atmosphere boundary for the last million years. He has accounted for the change in time of all the three orbital elements, whereas in the lifetime of Croll there were no reliable calculations concerning the change of obliquity.
[15] Milankovitch dealt with the zero values of average annual global insolation variations related to precession and Earth axis inclination problem alternatively than Croll did 50 years ago. Milankovitch considered only semi-annual insolation variations for certain latitudes. Besides, Milankovitch, contrary to Croll, according to Köppen advice, believed that glaciation is favoured by long cool summers rather than by long cold winters. To interpret the northern hemisphere glaciation he used the insolation diagram calculated for summer thermal half year at 65oN [Milankovitch, 1930]. Milankovitch regarded the deepest insolation diagram minima as northern hemisphere glaciations. Earth axis inclination variations and precession were nearly of the same contribution in that curve. Milankovitch as Croll 50 years ago ignored direct insolation changes related to eccentricity variations. Consequently, climatic cycles according to Milankovitch theory should mainly amount to 41 kyr due to Earth axis inclination and 19 kyr due to precession.
[16] Deep water oxygen-isotope data are known to have confirmed the Adhémar-Croll hypothesis on relation between climatic changes and orbitally-caused insolation variations. All the orbital periods have been shown to be reflected in paleoclimatic records. Furthermore, phase consistency between insolation effect and climatic response was found in the orbital frequency band. However, the same data showed significant contradictions between Milankovitch theory and empirical data [Bassinot et al., 1994; Berger, 1999; Elkibbi and Rial, 2001; Hays et al., 1976; Imbrie et al., 1993; Paillard, 2001, and others]. Major contradictions of Milankovitch theory are the following [Berger, 1999; Bol'shakov, 2001, 2003a, 2003c; Elkibbi and Rial, 2001; Hays et al., 1976; Imbrie et al., 1993; Paillard, 2001].
[17] (1) Climatic cyclicity of the Brunhes chron is primarily determined by the 100-kyr periodicity, assigned to eccentricity variations, whose direct influence has not been discussed in Milankovitch theory.
[18] (2) A number of glaciations and their time do significantly differ from similar glaciation parameters in the Milankovitch insolation diagram, plotted for summer insolation at 65oN.
[19] (3) According to empirical data, glacial events fall on eccentricity minima, whereas in Milankovitch theory they (the deepest minima on insolation diagram) mainly fall on the eccentricity maxima.
[20] (4) In his theory Milankovitch states that temperature variations are similar to his calculations of semi-annual insolation changes (the so-called linear mechanism of insolation variation amplification). Since insolation change for low and moderate latitudes is mostly precession-determined, summer and winter insolation change as well as summer and winter temperature are in opposite phases even at 55oN and 65oN. Thus by Milankovitch summer temperature falls, while winter temperature rises in the time of glaciations. Whereas during interglacials summer temperature rises, while winter temperature falls [Milankovitch, 1930, diagram 4]. However, as is well known nowadays, summer and winter temperatures changed in identical phases during Pleistocene glaciations and interglacials. [Kandiano and Bauch, 2003; Ruddiman and McIntyre, 1981].
[21] (5) Global climate changes are synchronous in both hemispheres (at least for last glaciation maximum and Holocene optimum). Whereas insolation curves that Milankovitch calculated for 65oN and 65oS latitudes are shifted for no less than 5 thousand years in determination of temporary insolation minima and maxima position corresponding with this climatic event.
[22] (6) About a million years ago the main climatic periodicity changed from 41 kyr to 100 kyr. That doesn't comply with the Milankovitch theory as variations of orbital elements didn't change significantly at that time.
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[24] In the end of year 2006 the paper titled "In defence of Milankovitch'' was published [Roe, 2006]. It would be better to call it "In defence of Milankovitch theory'', because Milankovitch died in 1958. In his article Roe points out: "...progress has been impeded by the lack of a well-formulated, specific, and generally-accepted hypothesis. The term "Milankovitch hypothesis'' is used in a variety of ways, ranging from the simple expectation that one ought to see orbital frequencies in time series of paleoclimate proxies, to the implication that all climate variability with time scales between 103 to 106 yr is fundamentally driven by orbital variations. Somewhere in the middle of this are the more vague statements found in some form in many textbooks, that orbital variations are the cause, or pacemarker, of the Pleistocene ice ages. Phrases like Milankovitch curves, Milankovitch insolation, Milankovitch frequencies, Milankovitch forcing, and Milankovitch cycles pervade the literature, adding to the somewhat nebulous picture''.
[25] One can mainly agree with the above statement. In fact, the right wording of Milankovitch theory is for some reason a knotty problem. For example, in the introduction to the International conference "Milankovitch and climate'' (1984) collected papers, signed by its well-known editors A. Berger, J. Imbrie, J. Hays, G. Kukla, B. Saltzman, Milankovitch theory is defined as follows: "The essence of the Milankovitch theory is that the major fluctuations in global climate associated with the ice-age cycle are caused by variations in the pattern of incoming solar radiation - variations that are, in turn, caused by slow changes in the geometry of the earth's orbit that occur in response to predictable changes in the gravitational field experienced by the Earth''. Another example is the beginning of Clemens and Tiedemann [1997] paper: "Milankovitch theory - that climate is controlled by variations in the Earth's orbital parameters - has gained wide acceptance...''. However, these definitions describe not a particular Milankovitch theory, but a more general orbital hypothesis that J. Adhémar, J. Croll and other scientists used as a basis for the development of paleoclimate orbital theory different versions long before Milankovitch. Nevertheless, it is just this incorrect Milankovitch theory interpretation that is generally accepted.
[26] In my opinion the right interpretation of Milankovitch theory could be the following. "Milankovitch theory is one of the versions of a more general orbital paleoclimate theory; the essence of the latter concerns the relationship between the global climatic variations and those of insolation caused by changes in the Earth's orbital parameters. According to Milankovitch theory, climate changes in northern hemisphere are similar to insolation variations of summer thermal half year at 65oN he calculated. In particular, the deepest minima correspond to glaciations''. In support of the wording given it is noteworthy to remind that it was the agreement between insolation diagram glaciations and those of A. Penk and E. Bruckner's Alpine stratigraphical scale that provided the grounds for the general acceptance of Milankovitch theory during the first half of the 20th century.
[27] Unfortunately, Roe, instead of original wording of Milankovitch theory, suggests a new wording, i.e., strictly speaking, a different theory [Roe, 2006]: "In this paper, a specific formulation of the Milankovitch hypothesis is suggested and defended: orbitally-induced variations in summertime insolation in the northern high latitudes are in antiphase with the time rate of change of ice sheet volume''. Hence it may be concluded that this publication [Roe, 2006] is another admission of Milankovitch theory drawbacks. It is worth noting that the new wording doesn't solve any of Milankovitch theory above mentioned problems, but only makes the correlation between theory and empirical data more difficult.
[28] However, I believe that the more correct line of attack on the Milankovitch theory problems is the critical analysis of its main statements and the revealing of its main advantages and drawbacks in the course the further investigation. Such analysis was made in the following publications [Bol'shakov, 2001, 2003a, 2003c]. As a result, apart from its certain value due to mathematically accurate calculations of insolation variations, the following major drawbacks of Milankovitch theory have been defined.
[29] (a) To determine the variations of individual orbital elements paleoclimatic value with strictly calculated quantitative insolation oscillations, Milankovitch hasn't accounted for the qualitative variations of the oscillations. In other words, eccentricity variations cause changes of Earth-oriented total average annual heat flow. However, variations of the obliquity and precession as mentioned above do scarcely change any annual insolation of the entire Earth, causing only energy latitudinal and seasonal redistribution respectively. These significant qualitative differences of insolation change associated with different orbital elements, were neglected in Milankovitch theory. For this reason alone the quantitative parameters Milankovitch calculated to determine insolation changes can't be regarded as the global climatic effect of corresponding orbital elements real measure.
[30] (b) The method of quantitative estimation of insolation at the upper atmospheric boundary variations paleoclimatic value can't be considered as accurate. This method is based on the calculations for individual thermal half years and geographic latitudes. After all one can not believe that for half year the insolation affects the global climate and for another half year doesn't. As well as one can not assume that the insolation of one latitude determines the global climate changes in single interrelated climate system of the Earth possessing great inertia. Another reason for this method to be rejected is that the mentioned above semi-annual precession insolation variations, as well as those associated with obliquity insolation variations of high and low latitudes change in antiphase.
[31] Therefore if we calculate insolation changes that are continuous in time, i.e. annual and in space, i.e. for all the Earth latitudes, the contribution of variations related to Earth axis inclination angle and precession would be zero. Apparently, in this situation it is beyond reason to establish a theory that associates global climatic oscillations only with insolation changes caused by obliquity and precession variations, because these changes are virtually zero. Probably that was the reason for Milankovitch to use semi-annual insolation changes at certain latitudes for paleoclimatic interpretations. Nevertheless, as discussed earlier, the account of insolation changes continuous in time and space is required for the correct derivation of the theory.
[32] (c) One more trouble is much less detailed and mathematically strict (as compared to insolation variations calculation) estimation of various Earth feedbacks, which he considered not that important when compared with Croll who did it 50 years earlier. Milankovitch was not fully aware of the feedbacks' real importance and controlling role in climate changes. Milankovitch considered the quantitative variations of semi-annual insolation he calculated to be the basic factor of paleoclimatic changes.
[33] Thus M. Milankovitch affected paleoclimate orbital theory in two different ways. On the one hand, mathematically strict calculation of orbitally-determined insolation variations should be regarded as a progress in theory development. On the other hand, he attributed a disadvantage to the theory development providing a global paleoclimatic significance to discrete (semi-annual and at one latitude) insolation variations. Moreover, considering insolation variations to be the primary and direct factor defining the presence of glacial cycles, Milankovitch brought the orbital theory development back into pre-Croll time: J. Croll has already made a conclusion that glaciations can't directly result from variations of orbital elements (and from caused by these variations insolation changes, see above).
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