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Wiggle Matching and the Milankovitch Hypotheses

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Wiggle Matching and the Milankovitch Hypotheses Class Notes: Wiggle Matching and the Milankovitch Hypotheses Carl Wunsch November 27, 2006 1Introduction The study of past climates encounters a number of severe problems not arising, or not as severe, in the study of the present climate state. The “big three” of these issues are: (1) the physical interpretation of sometimes extremely indirect climate proxies (e.g., are changes in [δ18O] really an accurate local thermometer?). (2) The accuracy of complex numerical models, that always contain a variety of errors when run over indefinitely long periods. (3) The problem of assigning dates to measurements that are commonly functions of depth and not time (the “age-model” problem). Here we look at the age-model problem and in particular, the inference that astronomical forcing controls much of climate change in general, and the Pleistocene ice ages in particular. Perhaps unexpectedly, this subject leads one into problems of human psychology and evolution. The human eye clearly evolved so as to be a powerful instrument for detecting weak patterns in noisy backgrounds. The rationale derives from a survival scenario: a human hunter in the jungle can in turn be stalked by a tiger. There are four main outcomes: (1) no tiger is present, and no tiger is seen; (2) no tiger is present, but a tiger is falsely perceived–leading to unnecessary termination of that day’s hunt. (3) A tiger is present and is correctly perceived, leading to successful escape; (4) A tiger is present but not detected, and the hunter is himself a meal. The reproductive cost of a false alarm (2–a false positive) is much less than a false negative (4– failure to detect). Thus people see patterns–everywhere. The most famous such patterns are the constellations to which the most ancient people assigned shapes and stories. A more modern example is in Fig. 1–showing on the “canali” (“lines” in Italian, not “canals”) as drawn by a sophisticated astronomer in the late 19th century. Also shown is a modern image from orbiting spacecraft. Many other such examples, where the eye picks out patterns that may or may not be real, exist in science. (Astronomers in particular have worried about this phenomeon; see the ref- erences in Wunsch, 2006). Statisticians have therefore developed objective tests to determine 1 Image courtesy of NASA. Figure 1: On the left is a view of Mars drawn in 1894 by Giovanni Virginio Schiaparelli and on the right is a recent Mars satellite compositve (from NASA website). whether some pattern (a “signal” is likely real or an accident of data or the eye’s ability to see patterns everywhere). A closely related problem is the great difficulty most people have in making correct inferences from statistical data (Kahneman, et al., 1982). Even experts are fooled.1 2 Wiggle Matching In the paleoclimate literature, the most common manifestation of the wish to see patterns lies in the practice known to its critics as “wiggle-matching”–the hypothesis that if two records show similar fluctuations, that they are identical, and one is permitted to infer that the fluctuations can be aligned within any absolute dating uncertainty. Some examples are shown in Figs. 2 - 5. In some of these cases, it is known that the record excursions are pure accidents, and there is no relationship between them. In the remaining cases, it is an hypothesis that the records should be aligned. Often the hypothesis cannot be proved or disproved, and one must prevent the assumption from becoming a published fact. It is actually easy to show that under certain circumstances two unrelated records will inevitably appear to have related oscillations. That circumstance arises when two records have similar frequency content. (See Appendix 1 for a brief discussion of frequency content and what is known as spectral estimation.) If two records have similar frequency content, they must have, 1 The class is asked to answer some simple questions. (A) A game (the game of Peter and Paul) is played by flipping a true coin. If the coin comes up heads, Peter pays Paul $1. If tails, Paul pays Peter $1. Sketch a “typical” curve of Peter’s winnings through time. (B) You are told that a couple has two children, of which one is a girl. What is the probability that the second child is a boy? For (A) see Feller (1957); for (B) Gauch (2003). 2 Image removed due to copyright restrictions. Citation: See Figure 2.1.4. Brooks, and C.E.P. "Variations in the Levels of the Central African Lakes Victoria and Albert." Geophys Mem London 2 (1923): 337-344. Image courtesy of AMS. Figure 2: Left panel is taken from Wunsch (1999) and shows two statistically independent records that show strong visual resemblance over finite time spans because they have similar frequency content. An objective test of similarity would reject the hypothesis that these records are related. Middle panel shows a plot of sunspot number and the Dow Jones Industrial average through time (author unknown). They do seem to track impressively well. Right hand panel, top, is from Brooks (1923) and shows the apparent correlation between Central African lake levels and sunspot numbers. Lower panel shows that the oscillations on the 11-year sunspot cycle had disappeared by the 1920s, and the entire character was different toward the end of the record. Figure 3: (Re-drawn from Hendy et al., 2002) showing the apparent correspondence between the δ18O record in Santa Barbara Basin and that in the GISP2 record. That an equivalent degree of high frequency variability exists in both records is evident; whether the oscillations actually correspond as the dashed lines indicate, is much less obvious. 3 Figure 4: Identification of supposedly corresponding events in the Hulu Cave record and in Greenland ice core (re-drawn from Alley, 2005). Notice, e.g., that the large excursions in the Hulu cave record near -45KY and -30KY have no counterpart in the Greenland record. Figure 5: Maximum monthly temperature records for Oxford, England taken from completely different time spans. But as the physics of temperature change there has probably remained fixed, the two records have similar frequency content. Note how easy it would be to align the various maxima and minima if there should be any uncertainty in the record timing (there isn’t any here). 4 on average, the same number of positive and negative excursions about the mean in any interval (see for example, Vanmarcke, 1983). Thus it is almost inevitable that one can draw lines between corresponding maxima and minima in any finite record interval. But demonstrating that the maxima and minima represent the same event requires much stronger evidence. (A bit more discussion is given in Wunsch, 2006). 3 The Milankovitch Hypotheses Another part of human psychology that has been much studied is the understandable wish that the world should be predictable. That is, when some event occurs, one should be able to rationalize why it occurred, and preferably be able to explain the chain of reasoning. Some events are, however, very difficult to discuss in causal terms: e.g., why a hurricane occurred in a particlar location on a particular day; why a field of ocean surface waves led to a breaker at a particular time and place. In principle, one might explain the latter as having been caused by a superposition of waves coming from several directions that just added up to become unstable at that moment and place. In practice, such events are much more easily understood in statistical terms, because the chain of events could never have been predicted in detail. The wish for causality pervades the discussion of paleoclimate, and it may well be true that much of what is inferred about the past depends upon a readily rationalizable chain of events. Again, the main issue is less that one can demonstrate that past climate is primarily stochastic in nature, and more that one should not rush to claim causality just because of its psychological appeal. That leads us to the hypothesis that major climate shifts arise from small shifts in the Earth’s orientation relative to the sun–as predictable a process as exists in nature. There are several Milankovitch hypotheses and not all authors are careful in defining which they are referring to: "It is widely accepted that climate variability on time scales of 103 to 105 years is driven primarily by orbital, or so-called Milankovitch, forcing." (McDermott et al., Science, 2001). "...it is now quite clear that orbital forcing played a key role in pacing glaciations during the Quaternary...." (Bradley, R. S., Paleoclimatology, Academic Press, 1999, p. 281) "The orbital theory of climate is the prevailing theory of glacial-interglacial climate change over tens of thousands to hundreds of thousands of years." (Cronin, T. M., Principles of Paleoclimatology, Columbia Un. Press, 1999, p. 131) 5 "...we confirm that moisture source temperature signal recorded in Vostok deuterium excess over the last 150ka fully reflects the obliquity time-varying relative contribu- tion of low and high latitudes to Vostok precipitation." (F. Vimeux et al., Earth and Plan. Sci. Letts., 203, 2002, p. 829) "...a strong case has been made that on the time scale of tens of thousands of years, the Earth’s climate is being paced by the so-called Milankovitch cycles..." (W. Broecker, Earth Sci. Revs., 51, 137-154, 2000). Note that there have been some strongly dissenting views, including Winograd et al. (1992); Roe and Allen (1999); Wunsch (2004), but they have been largely ignored or rationalized away. 3.1 A Bit About Earth Orbit To understand these inferences, we need to briefly review the orbital motion of the Earth about the sun.
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