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Estimating missing sapwood rings in three European gymnosperm species by the heartwood age rule
Abstract
Precise dating of the year of felling is one intended outcome of dendrochronology. However, occasionally some or all sapwood rings might be missing, either due to deterioration or because they were carved off, or for some other reason. Consequently, while heartwood is preserved, sapwood might be fully or partially missing. In such cases, the year of felling must be estimated by adding a suitable number of sapwood rings. A heartwood age rule (HAR) has been advocated for Scots pine and adapted to European larch and Cembra pine, implying a linear relationship between sapwood ring count and the square root of heartwood ring count, largely irrespective of position in the stem. The same rule applied to all observations of a species, irrespective of silviculture, location or fertility of the growth site. Scots pine had twice or thrice as many sapwood rings as Cembra pine, which had 10% more rings than larch. The magnitude of model residuals was proportional to estimated sapwood ring count. Relative residuals were roughly normally distributed. To be applicable in Bayesian modelling in dendrochronology analyses, detailed information on model errors has been provided.
... 95%) common confidence level. It should be noted that various techniques have been used to present the sapwood estimates, such as single arithmetic mean, arithmetic mean with standard deviation, skewed mean with standard deviation, range without an arithmetic mean, Bayesian statistical models, etc. (Hillam et al. , 2004Miles 1997Miles , 2006Gjerdrum 2013). ...
... Pinus is characterized by a higher number of sapwood rings in comparison to Quercus (Gjerdrum 2013). The number of sapwood rings of Pinus depends on the cambial age of the tree, i.e. the number of sapwood rings increases with the age of the tree (Yang et al. 1994;Park 2002;Miles 2006). ...
... A comparative study by the Norwegian Forest and Landscape Institute of the number of tree rings in the heartwood and sapwood suggests a certain coherence, named a heartwood age rule (hereafter in the text HAR), i.e. the square root of the cambial age minus the square root of heartwood rings equals a constant of ca. 3.0 (Gjerdrum 2003(Gjerdrum , 2013. However, because the total number of tree rings can be expressed as the sum of heartwood and sapwood rings, the HAR formula can be applied for estimating the number of Pinus sapwood rings, using the number of known heartwood rings (Gjerdrum 2013:229). ...
Pinus sylvestris L. is the predominant tree species used for wooden constructions in the Baltic area. Accordingly, the timber of Pinus is the most important object for investigation and dating carried out by dendrochronologists of the Baltic countries. However, the dating of historical Pinus is often challenging when the outer sapwood rings are missing in the wood samples. In Pinus, sapwood rings increase in number as the tree ages, and therefore calculating the approximate number of missing outer rings from a set range, a technique used for oak, is not possible. In Norway, a simple method for estimating the number of sapwood rings has been developed for some native species of conifers. The aim of this small-scale study was to assess the validity and the practical suitability of the Norwegian method for estimating the number of missing sapwood rings of mostly historical Pinus wood samples obtained in the southeastern part of the Baltic region. Our findings indicate that this method is not acceptable for estimating the number of missing sapwood rings for individual trees, but suggest that it may be applicable when dating tree-ring chronologies for a minimum of 20 trees, containing individuals up to 200 years old.
... The missing waney edge in the samples does not allow establishing a precise date of felling. When sapwood is partially missing, the year of felling could be estimated by adding an appropriate number of sapwood rings according to heartwood age rule (Gjerdrum 2013). When all sapwood rings are missing due to deterioration of wood or artificially removed because of weaker sapwood, the reconstruction of the date of felling is not possible. ...
... When all sapwood rings are missing due to deterioration of wood or artificially removed because of weaker sapwood, the reconstruction of the date of felling is not possible. According to Gjerdrum (2013) Scots pine is distinguished by high and variable number of sapwood rings. The average number of sapwood rings in Europe is 51±15 and depends on the cambial age of a tree (Gjerdrum 2013). ...
... According to Gjerdrum (2013) Scots pine is distinguished by high and variable number of sapwood rings. The average number of sapwood rings in Europe is 51±15 and depends on the cambial age of a tree (Gjerdrum 2013). However, it is not clear does this estimation is also valid for the Baltic countries. ...
Scots pine tree-ring chronology was compiled from the rostwerk constructions of Trakai Castle fore-work. The chronology involves dated 18 tree-ring-width series and runs for 220 years between 1192 and 1411. Constructed chronology shows high similarity with chronologies developed for Lithuania, Latvia and Poland. The investigated samples contain on average 33 sapwood rings with waney edge missing among all samples. The estimation of missing sapwood rings indicates the tentative date of felling in 1426. Abrupt growth depressions with missing rings are typical for the first half of the 13th century; two growth depressions lasted from 1219–1221 and 1237–1239 with the smallest measured ring width in 1238 (on average 0.27 mm). The 14th century is characterized by smaller variations in tree-ring pattern with major depression from 1356–1358.
Key words: dating, Scots pine, tree-ring chronology, Trakai Castle, pointer years
... For oak (Quercus sp.), an estimate of missing tree rings in the sapwood can normally be given with high precision if all the heartwood is present (Baillie, 1982;Schweingruber, 1989). It is more difficult with conifers, but Gjerdrum (2002Gjerdrum ( , 2013 con-structed a formula to estimate missing sapwood if the number of rings in the heartwood is known. Most of the sapwood is present in the post-medieval chests in Table 1, and the outer dated tree ring is therefore probably close to the felling year. ...
... The medieval chests on the other hand are more problematical as sapwood is not detected. If only the sapwood is missing, the formula presented by Gjerdrum (2002Gjerdrum ( , 2013 gives an estimate of the felling years for the medieval chests from 1265 to 1380 (Table 1). It shows that all the chests are medieval and were felled during a hundred year period from approximately the mid-13th century. ...
... Although several tree rings are missing from the outer wood because the boards were planed, dating of the outer tree ring to the 1100s or 1200s clearly indicates that the chest in question is medieval and, according to the formula presented by Gjerdrum (2002Gjerdrum ( , 2013, indicates a date from the mid-13th century to approximately the mid-14th century. Since dendrochronology suggests that hardly any building activity took place during the first decades after the Black Death (Thun 2002: 170, 172), when the population was decimated, few or no new grain chests would be required. ...
... Many descriptive statistics and statistical models have been published to establish accurate estimates of the expected number of sapwood rings (Bleicher et al., 2020;Bräthen, 1982;Edvardsson et al., 2022;Gjerdrum, 2013;Haneca et al., 2009;Hillam et al., 1987;Hollstein, 1965Hollstein, , 1980Hughes et al., 1981;Jevšenak et al., 2019;Miles, 1997;Pilcher, 1987;Rybnicek et al., 2006;Shindo et al., 2024;Sohar et al., 2012;Wazny, 1990). These models are based on counts of sapwood rings from living and historical timbers and often rely on log-transformation of the original data, or use regression models including additional variables such as mean ring width, the cambial age of the tree or a combination of both. ...
... NSW is usually predicted directly by using the age (or NHW) or GSW variable for various deciduous and conifer tree species (e.g. Gjerdrum, 2013;Haneca et al., 2009;Hughes et al., 1981;Sohar et al., 2012;Yang and Hazenberg, 1991). We tested a different (indirect) approach of estimating NSW in which N_shareSW was first calculated with Model R (Table 4) and later multiplied by the number of heartwood rings (NHW) (Eq. ...
We analysed sapwood characteristics in 344 pedunculate oak (Quercus robur L.) samples from the south-western part of the Pannonian Basin. The samples came from 13 sites, located in Slovenia, Croatia and Serbia. The trees had an average of 13.3 sapwood rings, with a minimum of 5 and maximum of 32. Fifteen log-log linear regression models were employed to assess the statistical relationship between sapwood and heartwood variables. The number of sapwood rings (NSW), which is usually needed in dendroarchaeological dating, is significantly related to the number of heartwood rings (NHW), heartwood width (WHW) and heartwood growth rate (GHW). Older and more slowly growing trees had a higher average number of sapwood rings. Using NHW and WHW, we employed an additional multiple regression model and calculated coefficients for NSW predictions for real-world dendroarchaeological dating from the south-western part of the Pannonian Basin.
... The simple technique has been to add the average number of sapwood rings for the species altogether with estimated confidence interval calculated from the distribution of sapwood rings 28 . In case when all sapwood rings are missing and also the last heartwood ring is not preserved or determinable, the reconstruction of the date of felling is not possible. ...
We present the application of dendrochronological dating of the renovation and construction works of churches in the Kaunas and Vilnius regions of Lithuania. The model for the estimation of the missing rings of Scots pine was used in Lithuania for the first time. We have assessed 18 timber cross-sections from nine churches, which were used for the constructions from the second half of the 17th to 19th c. The oldest wood samples were dated from St. Michael’s Church in Vilnius (1668±4) and St. George, the Martyr, (Bernardine) Church in Kaunas (1693±3). The aim of this study was to compare the results of the investigation of timber samples from 9 churches with archival sources and literature data and to reveal the renovation history of the buildings. The study of written historical sources has revealed a lack of recorded building and reconstruction phases of the churches. This fact was later confirmed by the results of dendrochronological dating. The dating of the timber revealed undocumented reconstruction dates in Zapyškis church (1791±3), St. George, the Martyr, (Bernardine) Church in Kaunas (1711±4), St. Anne Church in Skaruliai (1693±3) and Vilnius Cathedral (1814±4).
Investigations of the timber from the St. Anne's Church in Skaruliai were carried out in 2018. Aim of the research was to revise the time of church building and to reconstruct the history of repair works. The results of dendrochronological dating were compared with the facts recorded in the archival documents. The oldest timber found in three beams of the ceiling was dated to 1572–1574. The beams were reused from the previous building. The dates question the traditionally established fact that Andriejus Skorulskis built the church in 1620–1622. Based on dendrochronological dates of timber constructions and historical sources, the construction time of the church can be defined to 1592–1606. The construction of the church might begin as earlier as in 1592, because an act was drawn up in Skaruliai on 29 June this year, by which the rights of collators of the church and parsonage were transferred to Andrius Miknevičius Skorulskis and his wife. Dating of beams indicates that construction works in the church took place in the 1600s. The visitation act of 1716 testifies the fact that a church already stood in 1606. Dating of the St. Anne's church in Skaruliai revealed at least five building renovation periods: 1670–1676, 1714–1716, 1731, 1756–1760 and after 1812.
Many timber finds lack some or all of the outer, sapwood rings formed in the years just before felling. In order to estimate felling date once the outermost remaining ring has been dated, it is necessary to estimate the number of sapwood rings originally present. Methods doing this for oak are reviewed in the light of an intensive study of living trees at one site and an extensive study of 175 samples from living trees in North Wales and northwest England. Some methods reported in the literature are found to be invalid. A method reported by Hollstein (1965) is most reliable, with modifications for known variations in sapwood number with position in the tree. At present the best available estimate is that a value of 30 sapwood rings be used (95% confidence limits: 19–50).
We studied heartwood and sapwood variation in western redcedar (Thuja plicata) at three sites, including a 95-year-old naturally regenerated, unmanaged stand, a 35-year-old planted spacing trial, and a 30-year-old naturally regenerated stand to which thinning and fertilization treatments had been applied. In the 95-year-old stand, we studied within-tree variation in heartwood and sapwood. In the thinning/fertilization trial and the planted spacing trial, we studied effects of cultural practices and growth rate on heartwood and sapwood. In the trees that we studied, sapwood width was generally fairly narrow, rarely exceeding 3.5cm. Heartwood formation in western redcedar appeared to begin at a relatively small stem diameter (7cm) and at a young age, probably 10–15 years. The amount and proportion of heartwood increased with distance downward from the top of the tree, with the implication that older trees will contain a greater proportion of heartwood than younger trees. For any given age, it appears that cultural treatments that favor rapid growth will result in stems with greater amounts of both sapwood and heartwood, and a greater proportion of heartwood.
This article offers a practical guide to goodness-of-fit tests using statistics based on the empirical distribution function (EDF). Five of the leading statistics are examined—those often labelled D, W , V, U , A —and three important situations: where the hypothesized distribution F(x) is completely specified and where F(x) represents the normal or exponential distribution with one or more parameters to be estimated from the data. EDF statistics are easily calculated, and the tests require only one line of significance points for each situation. They are also shown to be competitive in terms of power.
Knowledge about the transformation of sapwood into heartwood contributes to the understanding of the nature of pine trees and should be considered prior to the conversion of sawlogs to produce timber of prescribed properties and optimal revenue. In this study, heartwood formation was ascribed to the joint effect of ageing and growth rate. Observations of heart‐ and sapwood in 1656 trees and sawlogs of Scots pine ( Pinus sylvestris L.), sampled throughout Scandinavia, were analysed using mixed models. The most important finding was expressed in the pine heartwood age rule: heartwood age equals the square root of cambial age less three, to the second power. This global formula was valid irrespective of environmental factors and location within the tree, and described 93 per cent of the variance in the sample. Transition rate increases from 0.6 rings a−1 at 50 years to 0.8 rings a−1 at 200 years. The spatial amount of heartwood might be influenced by the silviculture through the annual ring width pattern. For samples missing sapwood, e.g. archaeological wood, the results might be combined with dendrochronology in specimen dating. When the diameter and the heartwood diameter of sawlogs were known, the mean annual ring width could be estimated with a standard deviation of 0.5 mm a−1. The simplicity, consistency and high correlation of the pine heartwood age rule confirms the importance of age as the main factor in heartwood formation.
An improved method of generating sapwood estimates for oak is developed. This suggests a revision of the 95% confidence range from 10–40 to 9–36 rings for trees from southern England. Current methods for estimating felling dates on timbers with incomplete sapwood do not generate true 95% confidence limits, and a Bayesian method for deriving such limits is presented. For timbers with no sapwood, the addition of 12 years to the date of the final ring is shown to give a 95% confidence limit on the terminus post quem for felling. The further application of these methods is illustrated by calculation of the common felling date for timbers from the Great Kitchen at Windsor Castle.
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