Comments on P.I. Kuniholm's "Dendrochronological investigations at Herculaneum and Pompeii"

by Lars-Åke Larsson and Torbjörn Axelson

At the Cornell university web site we recently found an article on dendrochronology and the excavations at Herculaneum and Pompeii (ref 1). The article is titled "Dendrochronological investigations at Herculaneum and Pompeii". It is written by prof Peter Ian Kuniholm and was originally published in a book in 2002 (ref 2). We found the article interesting especially as it contains a diagram from which we assumed that interesting dendro data could be retrieved and reanalyzed. Too many dendrochronological reports do not contain any data useful for verifying any of the reported results, but this one does really offer some opportunities to make some verifications.

Kuniholm describes how his laboratory after much work finally found that lots of wood found in Herculaneum was not of local origin but came from the Alpine area. The match between a mean value Herculaneum ring width curve and a South German oak curve is then characterized as "this extraordinarily good fit". To support these findings, two ring width curves are included as a graph showing the "Herculaneum Fir/Spruce and Pompeii Fir vs South German Oak".


The ring width curve from Kuniholm's article.

That "extraordinarily good fit" is then dressed in numbers as "the t-score between fir and oak is 4.44, the overlap is 362 years, the trend coefficient is 59.0 percent..."

Now, a T-value of 4.44 does not sound like a very good fit - normally we want to see a T-value well above 5 to consider it a fit, see ref 3. A simple calculation shows that a T-value of 4.44 with an overlap of 362 years corresponds to a correlation coefficient as low as 0.23! To accept such a low correlation value as a match we have to already be very confident that the curves we are matching are contemporary and correct!

Our curiosity was now awoken - let us take a very careful look at the curve diagram! It would also be interesting to match retrieved data from the diagram towards the Hollstein data (ref 4) and towards an available French Roman time curve.

Retrieving the data from the curves

The CooRecorder program has support to retrieve data from published curves (ref. 6), so it was not too difficult to extract the data behind the curves.

The extra ring at year AD 1

When comparing the retrieved South German Oak data towards the Hollstein data, we found that the retrieved curves contained an EXTRA ring before year AD 1. This is not a matter of the historically non-existent year zero, but an extra growth ring inserted into the sequence of grown ring widths. Also when we compared the data from the diagram towards a French mean value curve covering the time BC 124 to AD 164 it looked as if the French curve was missing a ring just before AD 1 As it looked improbable that both the Hollstein data and the French data were in error we decided to remove that extra ring and consider it a drawing mistake. Possibly this extra ring was inserted into the original data before plotting the diagram to make the calibration of the time scale correspond better to BC/AD years where year zero is non-existent.


Comparing the South German oak curve towards the Hollstein curve

After the extra ring was removed from the South German oak curve (SGERMOAK), the curve was compared to the Roman time curve of Hollstein (ref 4).

SGERMOAK_of_D:\ake\tree\Herculaneum\Herculaneum.rwl using No detrend
compared to the reference 
Hollstei_of_D:\ake\tree\Herculaneum\Herculaneum.rwl of length 676 using No detrend  Dated to 336
Minimum overlap used when finding best match: 40

Table sorted by Proportion of last two years growth (2,0,T (P2Yrs)/TTest 

--Rel Over  *P2Yrs------  BaPi-------  BesIE------  Skel-  GLK--  (year)              *Corr
-year  lap   CorrC TTest  CorrC TTest  CorrC TTest   Chi2    GLK                     StdDev
  236  399    0.53  12.6   0.49  11.3   0.47  10.7   51.2   0.71   (100) (as dated)  (0.14)
    7  399    0.23   4.7   0.15   2.9   0.13   2.6    0.0   0.58   (329)             (0.21)
 -352   47    0.44   3.3   0.42   3.1   0.44   3.2    0.4   0.71   (688)             (0.03)
    9  399    0.16   3.3   0.07   1.3   0.09   1.7    3.6   0.54   (327)             (0.19)

The high T-value of 12.6 indicates that the matching is very good. A block correlation analysis revealed - what could also be seen by visual inspection - that the curves matched well except for the oldest 60 years which match with a correlation coefficient of only 0.26. The younger sections (BC 240 - AD 100) of the curves had a correlation coefficient = 0.58

The South German Oak curve is identical to Bernd Becker's curve of 1981!

We also came to check the South German Oak curve to a curve published by Bernd Becker in 1981 (ref 8). We found the curves to be identical except for scaling and for an apparent misreading of Becker's ring width value for BC 287.

South German Oak curve (red/green) compared to Bernd Becker's curve of 1981 (black/blue).
Red numbers "0.98" at the bottom of the diagram indicate correlation coefficient values for 40 years long segments of the upper normalized curves.
The lower curves are ring width curves.

Comparing the Herculaneum mean value curve towards the South German oak curve

A correlation analysis run between the Herculaneum mean value curve (herculan) and the South German oak curve shows:

--Rel Over  *P2Yrs------  BaPi-------  BesIE------  Skel-  GLK--  (year)              *Corr
-year  lap   CorrC TTest  CorrC TTest  CorrC TTest   Chi2    GLK                     StdDev
   28  360    0.25   5.0   0.22   4.3   0.26   5.2    2.5   0.60    (72) (as dated)  (0.26)
   36  360    0.19   3.8   0.16   3.1   0.18   3.5    5.0   0.55    (64)             (0.18)
  215  184    0.23   3.2   0.22   3.1   0.26   3.6    5.3   0.59  (-115)             (0.10)

Relative position (index) 0 is then considered to correspond to the dating year of the South German oak curve, AD 100. Relative position 28 then corresponds to AD 72 as indicated above as the best match.

The above analysis shows that the correlation for the whole Herculaneum curve towards AD 72 of the South German oak curve is not too good with a correlation coefficient of only 0.25 - this is by no way "extraordinarily good"!

Though a blockwise correlation analysis with blocks of 50 years length shows something of great interest:

Block  -----Aimed------   -------Best
start  --------at  year   around that
    0     28 0.50    72      28 0.50
   25     53 0.52    47      53 0.52
   50     78 0.41    22      78 0.41
   75    103 0.58    -3     103 0.58
  100    128 0.58   -28     128 0.58
  125    153 0.40   -53     153 0.40
  150    178 0.25   -78     176 0.34*
  175    203 0.20  -103     203 0.20
  200    228 0.58  -128     228 0.58
  225    253-0.03  -153     252 0.20*
  250    278-0.05  -178     277 0.23*
  275    303 0.18  -203     302 0.19*
  300    328-0.01  -228     327 0.11*
Lowest block CorrC = -0.05 at index 250, year=-178
I.e. there is a very good match between the younger parts of the Herculaneum curve and the South German Oak curve!

A further analysis showed:

  • The segment 0-168 of the Herculaneum curve (BC 97 - AD 72) matches the South German Oak curve with the correlation coefficient = 0.51, T-value = 7.6

  • The segment 168-239 (BC 168 - BC 97), 72 years, matches with a correlation coefficient of 0.27.

  • The segment 239-359 (the rest) (BC 288 - BC 168), 120 years of the Herculaneum curve - the oldest segment - gives the correlation coefficient = 0.02 and there is no obvious missed or extra rings within it. I.e. the oldest 120 years of the Herculaneum curve does not match the South German oak curve!


Figure 189 - An unburned cross section

There are two pictures of cross cuts in the article, both with resolution high enough to allow for measurement of the ring widths (with an unknown scale factor). The first one with the caption: "Figure 189 An unburned cross section of spruce with tree rings from 291 B.C. to 129 B.C." The data we could measure from the picture was found to cover the time span BC 280 to BC 131 (We used the identity HPC2, see below). It had an excellent match towards the retrieved Herculaneum curve and has probably been used as a part of that curve when that curve was created. The correlation coefficient is 0.64 with an overlap of 149 years (T=10.1).

Comparing with the South German Oak curve

When we compared this curve towards the South German Oak curve, we had to force CDendro to show the implied match at BC 131 by limiting the search range:
WARNING: The search was LIMITED to the year interval -135 to -125

Table sorted by Proportion of last two years growth (2,0,T (P2Yrs)/TTest 

--Rel Over  *P2Yrs------  BaPi-------  BesIE------  Skel-  GLK--  (year)              *Corr
-year  lap   CorrC TTest  CorrC TTest  CorrC TTest   Chi2    GLK                     StdDev
  228  149    0.17   2.1   0.17   2.1   0.12   1.5    4.9   0.59  (-128)             (0.17)
  225  149    0.06   0.7   0.10   1.3   0.05   0.6    0.3   0.52  (-125)             (0.17)
  232  149    0.04   0.5   0.04   0.4   0.05   0.6    0.0   0.43  (-132)             (0.16)
  230  149    0.04   0.5  -0.02  -0.3   0.09   1.0    7.6   0.54  (-130) (as dated)  (0.22)
  229  149    0.01   0.2   0.08   1.0   0.10   1.2    0.5   0.48  (-129)             (0.12)
  233  149   -0.02  -0.3   0.01   0.2  -0.05  -0.6    0.3   0.50  (-133)             (0.15)
  231  149   -0.03  -0.4  -0.03  -0.4   0.02   0.2    0.0   0.51  (-131)             (0.17)

This means that this unburned cross section does not at all match the South German Oak curve at the implied position.

As the Herculaneum curve matches the South German Oak curve over the segment BC 168-131 (corrCoeff=0.57) we had expected to find some matching within that interval for the "unburned cross section", though its correlation coefficient for that segment is -0.06! - No match at all! We then have to consider whether the Herculaneum curve has possibly been built up from ring width curves without proper cross correlations!

Figure 190 – A charcoal cross section

Part of image pretended to show rings of BC 145 - AD 11 actually shows rings of BC 133 - BC 16

The article also contains a picture of a coaled cross section with the caption "FIGURE 190 A burned cross section of fir with tree rings from 145 B.C. to AD 11." The sample contains a lot of cracks, but it is possible to measure several sections and make a mean value ring width curve of them. In this way we were able to measure 117 rings, but when this ring width series (called HABC1A) was compared to the retrieved Herculaneum mean value ring width curve, we found that it matched at BC 133 to BC 16 (corresponding to index -15, see below) instead of BC 145 - AD 11. We guess that there has been a mix-up of images during the publication process.

HABC1A using No detrend compared to the reference
herculan using No detrend  Dated to 72
Minimum overlap used when finding best match: 50

Table sorted by Proportion of last two years growth (2,0,T) (P2Yrs)/TTest

--Rel Over  *P2Yrs------  BaPi-------  BesIE------  Skel-  Skel-  GLK--  (year)
--year  lap   CorrC TTest  CorrC TTest  CorrC TTest   Chi2  CorrC    GLK
   87  117    0.58   7.5   0.54   6.9   0.51   6.3    9.6   0.43   0.70   (-15) (as dated)
  133  117    0.36   4.2   0.35   4.0   0.29   3.3    2.7   0.22   0.57   (-61)
  163  117    0.31   3.5   0.26   2.9   0.21   2.3    9.2   0.30   0.62   (-91)
  187  117    0.28   3.1   0.21   2.3   0.20   2.2   13.0   0.19   0.59  (-115)
  117  117    0.26   2.9   0.24   2.7   0.20   2.2    0.3   0.18   0.50   (-45)

The retrieved data

For research purposes you may download the retrieved data stored within a .rwl file contained in a zipped file (ref 8). Please note, that we have removed that extra ring found before AD1 from the retrieved ring width files. Except for the curve data of the article, the .rwl file also contains a mean value curve from the Hollstein data of the Roman time (ref 4). This retrieved data from the curves is by no way exactly the same as that used by the author of the reviewed article. There are certainly at least some misinterpretations introduced by us when we retrieved the data from the curves. A measure of the actually small data degeneration during the retrieving process is that the retrieved data series match each other with a Baillie/Pilcher (B/P) T-value of 4.3 to be compared with the T-value = 4.44 reported by the author. Although when we are using the P2Yrs method (proportion of last two years growth, ref 5) we get a T-value of 5.0. The P2Yrs-method has a lower risk of erroneous matches than B/P at the same T-value. So with the retrieved data we actually found a stronger support for the match than that implied by the 4.44 value reported by the author. Another indication of the small data degeneration is how well the retrieved South German Oak curve of the diagram matches to that curve published by Bernd Becker (ref 7).

Discussion

The main message of prof Kuniholm's article was a report that his institute had identified wood in Herculaneum and partly Pompeii which originated from the Alpine region. He characterized the curve matching between his Herculaneum mean value curve and a South German oak curve as an "extraordinarily good fit" but reports the very low T-value of 4.44 at an overlap of 362 years. An analysis reveals that he could instead have reported a T-value as high as 8.3 with an overlap of 250 years (P2Yrs) or at least 7.7 with the Baillie/Pilcher method, often used by the Cornell institute. This seems to be a really good match especially if we also consider that it is a match between two so different species as oak and fir.

We may only speculate on why the oldest tail of the Herculaneum curve does not match the South German Oak curve. The quality of the South German Oak curve can be validated by comparison with the Hollstein Roman time curve. The matchings seem to be sufficient. The match between the measurements from figure 190 and the oldest tail of the Herculaneum curve is very good, so there are little reason to expect that any severe errors were introduced when we retrieved the data from the published curve. Only the very oldest few years may be disputed.

The spruce and fir samples were separated into two groups: the spruce (Picea abies) samples are all found in the older part of the curve and the fir (Abies alba) samples in the younger part. This means that it is the fir-part of the curve which matches the German curve and the spruce part which does not. May for instance different altitudes of the spruces and the firs make the firs but not the spruces datable towards the oak chronology? If so, the Picea-part of the curve hopefully could be dated towards the Abies-part of the chronology, but unfortunately no data which can prove the quality of this bridging between the data is available nor is any discussion about the problem of the non existent match between the spruce-part of the chronology and the oak-chronology included in the article. So unfortunately there is no evidence that the old tail of the chronology is correctly dated.

Anyhow the reported overall T-value of 4.44, which is about the same as we got (4.3), indicates that the error is probably not to be found within our data retrieval. The lack of published original measurements makes it impossible to evaluate what has gone wrong!

We still hope that it will become more common to publish original measurement data so that crossdating jobs can be validated by anybody interested! We think that dendrochronology performed without publishing all data is no science! Keeping data used for an analysis secret after the analysis has been published is not up to the scientific standards of natural science!

In this case some data was made available (though not in the most convenient format), but unfortunately not enough to verify the correctness of the older part of the Herculaneum curve. We hope that prof. Kuniholm and the Cornell institute will eventually publish a follow up article in which enough data is included to verify also the older part of the curve.

December 17 2009.

References

ref 1: P.I. Kuniholm, Dendrochronological Investigations at Herculaneum and Pompeii in book The natural History of Pompeii pp. 235-239 (See ref 2 below.)
http://dendro.cornell.edu/articles/kuniholm2002 (This link works in May 2015. An older link "www.arts.cornell.edu/dendro/HercPompCaptured.pdf" is broken.)
ref 2: W. F. Jashemski and F. G. Meyer, eds., The Natural History of Pompeii, Cambridge University Press (2002), pp. 235-239.
ref 3: T Axelson & L-Å Larsson, What is a good T-test value?
ref 4: L-Å Larsson, The German oak chronology - an analysis of some publically available data, http://www.cybis.se/forfun/dendro/hollstein
ref 5: CybisWiki, P2Yrs: http://www.cybis.se/wiki/index.php?title=P2Yrs
ref 6: Methodology: Catching the ring width data underlying a plotted curve, http://www.cybis.se/forfun/dendro
ref 7: Becker, B.: (1981) FÄLLUNGSDATEN RÖMISCHER BAUHÖLZER anhand einer 2350jährigen Süddeutschen Eichen-Jahrringchronologie, Fundberichte aus Baden Württemberg No.6, 369-386.
ref 8: Herculaneum and Hollstein data