Anatolian tree-ring studies are untrustworthy Douglas J. Keenan The Limehouse Cut, London E14 6N, United Kingdom; [email protected] 22 February 2006 The chronology of the Ancient Near East is poorly understood. Although many references give exact dates for events, such as the building of the Great Pyramid or the rise of certain kings in Babylon, in reality such dates are debated. Wood has the potential to resolve such debates. Many ancient buildings and other artefacts were constructed from wood, and in some circumstances, it is possible to precisely date this wood, by examining the pattern of its tree rings. Work on dating wood from the Ancient Near East has been done primarily in Anatolia (roughly, modern Turkey). This work has been conducted over many years and been published in respected journals; it has claimed to provide definitive dates for several important events in the early history of civilisation. Herein is reviewed some of this wood-dating research. The primary conclusion is that the research has invalidating flaws, which are obvious upon inspection. The underlying issue is that the system under which tree-ring research generally is conducted lacks transparency. 1. Introduction Most trees grow a tree ring each year. The thickness (and density, etc.) of tree rings varies from year to year, and is dependent upon the local climate, ecology, and other factors [Schweingruber, 1996]. Trees live for many years, and the tree rings grown over those years then form patterns, as shown in Figure 1. The figure displays cross-sections from three trees. Imagine that the A rings are from a living tree. Hence the outermost ring (next to the bark) was grown in the last year, the ring next to that was grown the year before, etc. Imagine too that the B rings are from a dead tree, which was found in a field. We do not know a priori the years in which this tree grew, but by matching the outer rings from B with the inner rings from A, we can determine this. Suppose the C rings are from a timber used in a building. The outer rings from C can be matched with the inner rings from B; thus we can determine when the C tree grew. The building must have been constructed after the C tree grew. Hence our tree-ring matching has given us information about the time of the building’s construction. Figure 1. Schematic example of tree-ring matching. An important goal in tree-ring studies is to build up overlapping tree-ring sequences, extending from the present to the distant past—Figure 1 illustrates. Usually, there will be several trees that grew rings for a particular year; an average ring-width for each year is then calculated. A series of such average ring widths that spans many years is called a “master dendrochronology” for the site at which the trees grew (from Greek, dendron = tree and chronos = time). Constructing a master dendrochronology for a site is essential for tree-ring dating of wooden artefacts from the site and surrounding area. The chronology of the Ancient Near East—oftentimes called the “cradle of civilisation”—is not well established. Although many references give exact dates for events, such as the building of the Great Pyramid or the rise of certain kings in Babylon, in reality such dates are debated [James, 1991; Cryer, 1995; Rohl, 1995; Bietak, 2003]. Tree-ring dating has the potential to resolve such debates. There is currently only one (substantial) master dendrochronology from anywhere in the Ancient Near East. Hence this master dendrochronology has great importance. This master is from Anatolia. “Anatolia” is a geographical term, roughly designating modern Turkey: see Figure 2. A master dendrochronology for Gordion (39.7 °N, 32.0 °E), in central Anatolia, was first developed in the 1970s. This master dendrochronology, however, does not extend continuously from the present to the past. (The situation is similar to what would happen if we had only the B and C rings in Figure 1. That is, we can match the B and C rings against each other, but this does not give us the date of any ring.) The master has been anchored in time—i.e. dated—largely via radiocarbon [Manning et al., 2001; Kromer et al., 2001] (originally, the master was dated via archaeo-history). In what follows, much of the work that has been done in Anatolian tree-ring matching is reviewed. The conclusions are disturbing, and have implications for tree- ring studies generally. 1 Figure 2. Map showing Anatolia. Anatolia is the large peninsula between the Black Sea and the Mediterranean Sea (constituting most of modern Turkey). In central Anatolia lies Gordion—where Alexander The Great famously cut the Gordion knot. Assiros (in Greece) and the two sites indicated by crosses are discussed in Section 7. The gateway is discussed in Section 4, and elsewhere. 2. Matching tree rings No two trees will have exactly the same ring pattern, particularly when grown at different locations. Deciding where two ring patterns match (as illustrated in Figure 1) can be problematic, in practice. The approach to solving this problem in the pre- computer age was to rely on the skill of an experienced investigator. Nowadays, although investigator skill continues to be crucial, tree-ring matching also heavily relies on statistical methods. Generally, an investigator will try to confirm a statistical match by visually comparing the physical rings in wood samples. For Anatolian archaeological work, however, such visual confirmation is usually difficult or impossible, because the wood is often actually charcoal (i.e. burnt remains), and the species being compared are sometimes very different. Hence in Anatolian archaeological work, tree-ring matches are often made solely on the basis of ring-width measurements. For this reason, statistical matching is particularly important in Anatolian archaeological work. Ideally, a statistical method should give the (statistical) confidence level of a potential match. For example, comparison of two trees might conclude that we can be 99.7% confident that their rings match (such a match would then be accepted as valid). Unfortunately, no method of calculating confidence levels of tree-ring matches is known. The three commonly-used statistical methods will be briefly described next. The most commonly-used method for statistically matching tree rings relies on what are called “t-scores”. (The t-score is detailed in most introductory statistics texts; it is closely related to the coefficient of correlation.) In principle, a t-score is just a way of giving a confidence level assuming the following: 2 • the ring width in one year is independent of ring widths in other years, and • ring widths have the same normal (i.e. bell-shaped) probability distribution. The first assumption is well known to be false (because the environment in one growing season affects the tree not only in that growing season but also in the next). Experience with the t-score method indicates that it can nonetheless work well, provided that it is used in a manner appropriate for tree rings. Broadly speaking, a t-score above 3.5 is considered to indicate a tree-ring match. A t-score above 5.0 would be considered as implying a certain match by most tree-ring specialists. (These levels for t-scores are conventional; for critical discussion of how good those conventions are, see Section 5.) Another statistical method used in tree-ring matching relies on what I will call “g- scores”. (The g-score is commonly called “gleichläufigkeit” [Schweingruber, 1989] or “trend”.) The g-score is the proportion (or percentage) of years in which two trees’ ring widths increased or decreased together (i.e. increased or decreased from the prior year). This method thus ignores the size of the increase or decrease. Because it ignores so much information, the g-score method might be expected to be less reliable than the t- score method. Experience at Hohenheim, Germany, where g-scores were previously used, seems to support this: matches were thrice found to be in error, each time after strong assertions of reliability [Baillie, 1995: ch.2; Spurk et al., 1998]. Early trials in Ireland also indicated problems, and the method was abandoned there [Baillie, 1982: p.81–82,95]. Other testing found very high g-scores for matches known to be incorrect [Schweingruber, 1989: p.77]. In the pre-computer age, though, g-scores had one advantage: being easy to calculate. They are still sometimes used, perhaps out of habit. A third statistical method used in tree-ring matching is the “linear time series” method. Very briefly, this method is similar to the t-score method, except that the first assumption of t-scores (ring widths are independent of each other) is replaced by this: • the ring width in one year is linearly-dependent on ring widths of prior years. This assumption is much more realistic than the first t-score assumption, though still not fully accurate (because the growth mechanism of tree rings is more complicated).1 Among the three methods, then, the linear time series method is the best. That method, however, is not widely used in tree-ring studies. The reason for this is unclear (perhaps it is convention). The linear time series method was developed, in the 1970s, as a general tool for statistical analyses. Research papers applying it to tree rings appeared in the 1980s [Monserud, 1986; Yamaguchi, 1986; Biondi & Swetnam, 1987]. And the method is nowadays taught in first-year graduate courses at what is often considered to be the world’s leading institution for tree-ring studies, the University of Arizona Laboratory of Tree-Ring Research.2 The statistical methods that were originally used in Anatolian tree-ring studies were g-scores and/or t-scores. This presented a difficulty, however, because trees were sometimes found to match (against the master or another tree) at several places. That is, there were multiple matches with high g-scores and t-scores, and moreover, the match with the highest g-score was not always the match with the highest, or even second or third or fourth highest, t-score. There are feasible statistics-based approaches to this difficulty (e.g. use t-scores alone, but very conservatively). The approach that was adopted for Anatolia, however, was to rely largely on what is called a “D-score”. The D-score does not exist in statistics. It has been used solely with tree rings. D-scores do not have a mathematical derivation—unlike t-scores, g-scores, and times 1 For a review of other assumptions that are likely to be more accurate, see e.g. Tong [1990]. 2 Notes for the Laboratory’s course “GEOS 585A: Applied Time Series Analysis” are available at http://www.ltrr.arizona.edu/~dmeko/geos595e.html (accessed 2005-06-14). 3 series. In fact, D-scores were more or less just made D-scores up (in an unpublished 1987 thesis3), and using them to The D-score combines the g-score and t-score, via evaluate a tree-ring match the following formula. turns out to be little better gt − t/2 than rolling dice—for The problem here is that the above formula has no details, see the side box. apparent meaning. Consider, for instance, the obvious (There are other problems formula for the area of a rectangle: base × height. This with D-scores, not discussed formula is not just arbitrarily chosen; rather, it can be here, but plain to anyone derived and shown to have the meaning “area of familiar with mathematical rectangle”. Similarly, the formula for the area of a square statistics. In particular, D- whose sides have length l is l2, and again this formula is scores should correspond not arbitrary, but derived, and has meaning. with significance levels The same is not true for D-scores. The choice of (under some assumptions), gt − t/2 is an arbitrary one among numerous formulae that just as g-scores and t-scores could have been chosen to combine a t-score and g-score. For example, this formula might have been chosen instead. do. For similar comments on this, see Baillie [1995: gt2 p.20].) There is no reason given for choosing one formula over the Regardless of which other. Furthermore, if the second formula had been method is used for matching chosen, then the wood from the gateway discussed in tree rings, it is not always Section 4 would have been dated to 981 BC, rather than possible to match one tree 1140 BC. This illustrates that the choice of the date for the against another, even if the wood (among dates with high g-scores and t-scores) is trees grew at the same site. baseless—i.e. the date might almost just as well be chosen This is due to factors at random. affecting individual trees at the site—e.g. placement on a hill, local canopy effects, local animal influences, genetics, etc. A master dendrochronology, though, will smooth out variations in ring widths that are due to such factors. Therefore, in general, a tree can be matched more readily against a master dendrochronology than against another tree. (A master dendrochronology is almost always constructed from a single species of tree.) 3. Case: the shipwreck The master dendrochronology for Gordion was formally announced in a paper in 1996 [Kuniholm et al., 1996]. This paper also gave some dates for wood from archaeological sites—dates that were obtained by matching the wood against the master dendrochronology. The most important of those dates was perhaps for wood from a shipwreck, which was claimed to resolve some of the debate about dates. (The shipwreck was found off Uluburun, southern Turkey [Pulak, 1997].) In 1998, some details on the shipwreck wood were published [Wiener, 1998: p.314]. It turned out that there had not been a good quantitative match against the Gordion master (by t-, g-, or D- scores). The wood had been dated against the Gordion master solely on the basis of visual matching—a dubious practice. The visual match is 3 The D-score was first described in a 1987 thesis by B. Schmidt [Kuniholm & Newton, 1989: p.291; Kuniholm et al., 1992: n.3]. The author of the thesis has acknowledged that it has no mathematical derivation (B. Schmidt, private communication, November 2003). 4 shown in Figure 3. The light line represents the Gordion master; it is high for years that had wide tree rings and low for years that had narrow rings. The heavy line represents the shipwreck wood. (For comparison, other figures showing visual matches are given in the next section.) It is clear that there is not a visual match. In other words, there was no match at all. The claim that the shipwreck wood had been dated was spurious. (The shipwreck wood comprises two pieces, which were matched against each other. The number of rings of their overlap, however, is only 23,4 which makes the match very unreliable—for reasons discussed in sections 4–5. Reliability is further lessened because one of the pieces was likely from the ship’s frame and the other was cargo [Pulak, 1997]—so there is no evidence that the two trees grew at the same location and time. Thus the claimed “match” is even worse than Figure 3 indicates.) Figure 3. The shipwreck wood matched against the Gordion master dendrochronology. (This figure is given by both Kuniholm [1997: fig.7] and Manning [1999: fig.63].) In 1999, a letter was sent to various e-mail lists, and also to the principal investigator in Anatolian tree-ring studies, pointing out some of the above (especially the statistical aspects) and concluding that there was no tree-ring match for the shipwreck wood [James, 1999]. Two years later, in the next major paper in Anatolian tree-ring studies, the tree-ring date for the shipwreck was acknowledged to be “not especially strong” [Manning et al., 2001: n.38]. The paper also claimed, though, that further work might allow the date to be “confirmed”; this claim does not seem realistic. (In 2003, more information on the shipwreck came to light: the originally-claimed visual match was merely better than any other match “at any point fifty years in either direction” [Wiener, 2003: p.244]. Apparently, the date for the shipwreck had been narrowed to ±50 years via archaeological considerations, before attempting a tree-ring 4 The earlier piece of wood ends 104 years before the later piece of wood [Kuniholm, 1997], and the later piece of wood has 127 rings (M.H. Wiener, private communication, April 2003). 5 match.5 Despite this, the claimed tree-ring match had been proclaimed by the investigators to be conclusive evidence that dates for events in the Ancient Near East could not possibly be in error by over a century (as some researchers have argued).) 4. Case: the gateway In order to ensure that a tree-ring match is reliable, it is typically necessary for the tree being matched to have at least 100 rings of overlap with the master dendrochronology (see further sections 5–6). Severe problems can arise when there are fewer. An example from Ireland will illustrate this (described by Baillie [1995: ch.3]). Several planks from a boat were securely dated against an Irish master. Attempts were also made to date one plank that had only 35 rings. As the investigator noted, “Normal practice at … most tree-ring laboratories … would have been to ignore this small piece … as intrinsically undatable”. As an exercise, however, an attempt was made. Figure 4 shows two positions where the 35-year ring pattern displayed visual agreement with an Irish master Figure 4. Examples of false matches. (top) and with a generalized master for the British Isles (bottom). As the investigator noted, these matches, especially the bottom one, are extremely good. The archaeological context, however, makes the date implied by the bottom match untenable, and the top match very unlikely. The investigator concluded as follows (emphases as in original) [Baillie, 1995: p.54–55]. The truth is that no one can put their hand on their heart and swear to a unique dating for such a short section of ring pattern. It doesn’t matter how good the match is. … anyone trying to tell you that they have dated such a short sample is kidding both themselves and you. He adds that there is nothing unique about this example. Pilcher [1990] says similarly: There are … examples in the literature of [tree-ring matching] on timbers of less than 50 years…. Most of these must be treated with considerable caution. … the dating is not true dendrochronology but is tree-ring-assisted dating or even tree-ring-assisted guesswork. Furthermore, Pilcher & Baillie [1987] tested sequences of rings from living (Irish oak) trees against a nearby master dendrochronology. For ring sequences of less than 5 For a discussion of problems in using archaeology to narrow the window of dates within which to search for a tree-ring match, see Baillie [1995: ch.3]. Some remarks related to this are also given in Section 7. 6 80 years, half of the sequences gave no statistical indication at all for the correct date. In other words, trees with less than 80 rings would, in general, not be reliably datable. The Anatolian investigators themselves say that at least 100 rings are typically needed to be certain of a match of a tree against the master dendrochronology. In eastern Anatolia is the archaeological site of Tılle Höyük (37.8 °N, 38.9 °E). This site contains the charcoalized remains of a gateway from the Bronze Age (see Figure 2). The gateway was constructed from many trees. Of those trees, 26 were matched against each other to form a master dendrochronology for the site [Kuniholm et al., 1993]. The gateway master does not extend from the present (it is only 218 years long), but was dated by other means (see below). Since the date for the gateway was announced, in 1993, it has been much cited by the investigators. In 2005, the investigators confirmed their confidence in it [Kuniholm et al., 2005]. Among the 26 trees in the gateway master, 6 had fewer than 40 rings recovered. Moreover, 21 of the trees had fewer than 60 rings recovered. Only two trees had more than 100 rings recovered, and their overlap (according to the investigators) comprised only 33 rings. The tree-ring matches used for the construction of the gateway master are thus seriously unreliable—so much so that the master could be said to not exist. Even if the gateway master had been well constructed, it would still then need to be dated (because it does not extend from the present). The date for the gateway master was obtained by matching it against the Gordion master, and the principal investigator claimed that the resulting match was “excellent” [Kuniholm, 1991]. The matching, though, was done primarily on the basis of D-scores [Kuniholm et al., 1993]. As discussed in Section 2, D-scores make a somewhat-arbitrary choice. Moreover, if t- scores had been used instead, the date would have been over 150 years later (the match claimed by the investigators had a t-score of 4.5, but there was another match that had a t-score of 5.1 [Kuniholm et al., 1993: p.189]). The match against the Gordion master was additionally asserted to have been “checked visually by sliding the graphs against each other” [Kuniholm et al., 1993: p.189]. The relevant graphs are shown in Figure 5. The gateway master [Kuniholm et al., 1993: fig.75] is on the top and the Gordion master [Kuniholm, 1993: insert] is in the middle. The alignment of the two graphs shows the investigators’ claimed match. The bottom graph is purely random; it is shown for comparison purposes. The visual match of the top and middle graphs seems to be far from convincing. Finally, the wood from Tılle Höyük might be undatable even in principle. In order to match trees against the Gordion master dendrochronology, there must be substantial correlation between the climate of the site where the trees grew and the climate of Gordion. Of the various aspects of climate that affect tree growth, (growing- season) precipitation is arguably the most important (with temperature and perhaps cloud cover also being highly consequential). Yet only about 12% of the variation in precipitation at Tılle Höyük is shared with the variation in precipitation at Gordion, at least in modern times.6 (Ancient times would seem unlikely to have been greatly different, although that cannot be ruled out.) This seems likely too small to be confident of a reliable match for Tılle Höyük (given the number of years for which rings are available). Thus, even if the gateway master had been reliably constructed, it might not have been datable against the Gordion master. More general aspects of comparing tree rings from different sites are considered in the next sections. 6 This is based on data for 1901–1998 [CRU, 2003]. Statistical analysis is by the author, for both annual and growing-season (considered here as April–September) precipitation. 7 Figure 5. The gateway master, the Gordion master, and a random graph. (The random graph was generated with a moving average process (of order 1) that had the same autocorrelation as the gateway data. High variation at the ends of the gateway graph might be due to the small sample sizes there.) 5. Testing t-scores This section presents some analyses for tree rings from modern trees. Modern trees can be analysed more readily that ancient trees, because much data for modern trees has been published in the International Tree-Ring Data Bank.7 By analysing modern trees, some of the potential problems with ancient trees will become clearer. As mentioned earlier, for Anatolian archaeological work, tree-ring matches are often made solely on the basis of ring-width measurements (not visually comparing whole wood). In this section, then, I consider the t-scores for the tree comparisons. One of the purposes of this section is to determine how high a t-score is needed in order to have a reliable tree-ring match. As discussed in Section 2, most tree-ring specialists will tend to consider a t-score greater than 3.5 as indicating a valid match, and a t-score above 5.0 will almost always be considered as being from a certainly-valid match. (The number of tree rings being compared is also relevant: 100 rings is generally considered to be enough for matching.) In the following, all t-scores were calculated after applying the transformation of Baillie & Pilcher [1973] to the (standardised) ring widths (the transformation is to replace ring width w by log(5w/(w +w +w+w +w )) ). This seems to be the i i i−2 i−1 i i+1 i+2 calculation that has been used for Anatolian tree-ring studies.8 (For comments related to this calculation, see Cook et al. [1990: sect.3.3]. I also tried some other calculations; the qualitative conclusions were similar to those reached herein.) As a first example, I examine trees rings from a site in south-western Turkey (36.7 °N, 29.9 °E, 1800 m above sea level).9 The master dendrochronology for the site 7 For details regarding the International Tree-Ring Data Bank (ITRDB), see http://www.ngdc.noaa.gov/paleo/treering.html and Grissino-Mayer & Fritts [1997]. 8 See the documentation for the Cornell tree-ring analysis program, available at http://corina.sourceforge.net/api/corina/cross/TScore.html (accessed 2005-06-14). 9 ITRDB file turk006.crn. 8 spans AD 1360–1988. The trees are junipers (the same species as the master dendrochronology for Gordion from ancient times). Consider the century-long portion spanning 1533–1632. If trees (from the site master) spanning 1533–1632 are compared with the site master at 1651–1750, the t-score is very high: 5.9. That is, if the trees rings from 1533–1632 had been found without any context, and if the master had only spanned, say, AD 1600–1988, then the tree rings would almost certainly have been claimed to date to 1651–1750. Indeed, the t-score of 5.9 is so high that almost all tree- ring specialists would accept the match; yet the date would be incorrect. Figure 6a shows the highest t-score of an incorrect match for each century-long portion of the master dendrochronology. For example, the figure shows that for the century-long portion beginning at 1533, there is an incorrect match with a t-score of 5.9. (The figure does not indicate the position of the incorrect match, merely what the t- score of the worst incorrect match is.) The figure demonstrates that a match with a t-score below 5.0 has a substantial chance of being erroneous (and a t-score of at least 6.0 seems to be necessary to have a truly secure match). If Anatolian tree-ring studies only accepted matches with t-scores well above 5.0, most of the presently-claimed matches would have to be rejected. For the second example, I examine trees rings from a site in north-western Turkey (40.0 °N, 30.1 °E, 1400 m above sea level),10 about 85 km north-west of Gordion. The master dendrochronology for the site spans AD 1306–1980. The trees are pines (which are coniferous, like junipers). Figure 6b is analogous to 6a, for trees at this site. As shown, the risk of an incorrect match is only slightly less than the risk for the junipers at the site in the first example. These two examples actually underestimate the problem, because each compares a century-long portion of the master against the master, rather than a single tree against the master. Comparison of a single tree against the master would naturally tend to be less reliable (as mentioned in Section 2). Additionally, the master dendrochronologies are less than a millennium long: the longer the master, the greater the chance of an incorrect match. (The two sites examined here have the longest masters among those Anatolian sites for which (i) there is data in the International Tree-Ring Data Bank and (ii) P.I. Kuniholm is a (co-)contributor.) In both the above examples, the trees being matched against the master were of the same species and grown at the same site as the master. This is what is done when constructing a master dendrochronology for a site. The examples used century-long portions of ring widths; a century was used because the Anatolian investigators have claimed that they can generally date a tree with 100 rings. That claim is contradicted by the above: a tree with 100 rings can be reliably dated only if its t-score (against the master) is well above 5.0. Moreover, even if the examples had used portions that were 250 years long, incorrect matches with t-scores of 5.0 would still have occurred (figures not shown). Plainly, then, the master dendrochronologies for ancient Anatolia are not reliable. (The master dendrochronologies of the modern sites probably are reliable, or nearly so, because many of the trees that were used to construct them were living; so the dates of those trees were known with certainty.) 10 ITRDB file turk001.crn. This site is in Eskişehir, and it is also discussed in Section 7. 9