Quantifying uncertainty in isotope dendroclimatology

To maximise the potential of the tree-ring isotopic signal for palaeoclimate research it is essential to understand and characterise the natural variability between individual trees. This study explores the nature of inter-tree isotopic variability and evaluates the implications for developing robust palaeoclimate reconstructions. We confirm levels of natural inter-tree variability similar to those reported in previous studies, but demonstrate, using a large data set of isotopic measurements determined from individual rings of 100 trees, that to obtain a representative regional environmental signal and to reduce problems when combining records, higher levels of replication than those typically adopted in isotope dendroclimatology may need to be considered

Examination of stable carbon and oxygen isotopic variability in the cellulose and wholewood of Castanea sativa Mill., Fagus sylvatica L., Pinus sylvestris L. and Quercus robur L.

This paper presents results from a comparison of wholewood and cellulose carbon and oxygen isotope ratios for four UK tree species. These species occur within the historic buildings archive as both primary and supplementary construction materials and have been used to reconstruct the climate of the past. New advances in the application of stable isotopes have widened the scope of the isotope approach, but require the time-consuming purification of cellulose. Comparison of the oxygen and carbon isotope signals preserved in the wood and cellulose components confirms and builds upon previous research in this field and provides additional insight into the covariance of these two sample types between species, anV prispevku so predstavljeni rezultati primerjave analize stabilnih izotopov ogljika in kisika v lesu in celulozi drevesnih branik štirih najpogostejših drevesnih vrst v Veliki Britaniji: pravega kostanja, bukve, doba in rdečega bora. Les teh drevesnih vrst pogosto najdemo tudi v različnih lesenih konstrukcijah, kar nam, v kombinaciji z lesom iz živih dreves, omogoča rekonstrukcijo klime v čas pred instrumentalnimi meritvami. Razvoj detekcijskih tehnik za stabilne izotope je omogočil uporabo stabilnih izotopov tudi tam, kjer to tradicionalno ni bilo možno (npr. za datiranje starih stavb), še vedno pa je glavna ovira za širšo uporabo teh metod zahtevna in zamudna ekstrakcija celuloze iz posameznih lesnih branik. Primerjava stabilnih izotopov kisika in ogljika v lesu in (alfa)-celulozi je potrdila dosedanje vedenje in dodala nova spoznanja o primerljivosti razmerij stabilnih izotopov, analiziranih v lesu in celulozi, kar nam bi lahko omogočilo izločitev zamudne tehnike ekstrakcije celuloze in neposredno uporabo homogeniziranega lesa

Oxygen isotope dating of oak and elm timbers from the portcullis windlass, Byward Tower, Tower of London

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Estimating uncertainty in pooled stable isotope time-series from tree-rings

Stable carbon isotope time-series (δ13C) from tree-rings are capable of providing valuable palaeoclimatic information, but analysis of individual tree-rings is time consuming and expensive. Pooling material from several tree-rings prior to isotopic analysis reduces costs, but does not allow the magnitude of uncertainty in the mean δ13C chronology to be calculated unless the pool is broken and each tree-ring measured individually at regular intervals. Here we use a comparison of pooled and mean individual (the arithmetic mean of isotopic data from tree series measured individually) δ13C records between AD 1650 and 2007, comprising cores from 21 Scots pine (Pinus sylvestris L.) trees growing in the western Highlands of Scotland. The aim is to determine whether the true error structure of the time series is better captured by using the overall mean error estimate for the entire time series or by linear interpolation between the equally spaced measurements. We conclude that where autocorrelation exists within the error structure of a chronology, annual estimates of 95% confidence intervals, developed through linear interpolation at 5-year or 10-year intervals, are preferable to using the overall mean uncertainty. The method outlined increases the viability of pooled δ13C records for palaeoclimatic research by retaining error structure whilst reducing analytical time and costs. The method is applied here using tree-ring data, but could theoretically be applied to any well-replicated time-series

The Steiner tree problem in orientation metrics

Given a setΘofαi(i=1, 2, …, k) orientations (angles) in the plane, one can define a distance function which induces a metric in the plane, called the orientation metric [3]. In the special case where all the angles are equal, we call the metric a uniform orientation metric [2]. Specifically, if there areσorientations, forming anglesiπ/σ, 0⩽i⩽σ−1, with thex-axis, whereσ⩾2 is an integer, we call the metric aλσ-metric. Note that theλ2-metric is the well-known rectilinear metric and theλ∞corresponds to the Euclidean metric. In this paper, we will concentrate on theλ3-metric. In theλ2-metric, Hanan has shown that there exists a solution of the Steiner tree problem such that all Steiner points are on the intersections of grid lines formed by passing lines at directionsiπ/2,i=0, 1, through all demand points. But this is not true in theλ3-metric. In this paper, we mainly prove the following theorem: LetP,Q, andOi(i=1, 2, …, k) be the set ofndemand points, the set of Steiner points, and the set of theith generation intersection points, respectively. Then there exists a solutionGof the Steiner problemSnsuch that all Steiner points are in ∪ki=1 Oi, wherek⩽⌈ (n−2)/2⌉