A likelihood perspective on tree-ring standardization: eliminating modern sample bias

Abstract. It has recently been suggested that non-random sampling and differences in mortality between trees of different growth rates is responsible for a widespread, systematic bias in dendrochronological reconstructions of tree growth known as modern sample bias. This poses a serious challenge for climate reconstruction and the detection of long-term changes in growth. Explicit use of growth models based on regional curve standardization allow us to investigate the effects on growth due to age (the regional curve), year (the standardized chronology or forcing) and a new effect, the productivity of each tree. Including a term for the productivity of each tree accounts for the underlying cause of modern sample bias, allowing for more reliable reconstruction of low-frequency variability in tree growth. This class of models describes a new standardization technique, fixed effects standardization, that contains both classical regional curve standardization and flat detrending. Signal-free standardization accounts for unbalanced experimental design and fits the same growth model as classical least-squares or maximum likelihood regression techniques. As a result, we can use powerful and transparent tools such as R2 and Akaike's Information Criteria to assess the quality of tree ring standardization, allowing for objective decisions between competing techniques. Analyzing 1200 randomly selected published chronologies, we find that regional curve standardization is improved by adding an effect for individual tree productivity in 99% of cases, reflecting widespread differing-contemporaneous-growth rate bias. Furthermore, modern sample bias produced a significant negative bias in estimated tree growth by time in 70.5% of chronologies and a significant positive bias in 29.5% of chronologies. This effect is largely concentrated in the last 300 yr of growth data, posing serious questions about the homogeneity of modern and ancient chronologies using traditional standardization techniques.