Quantifying climatic influences on tree-ring width

Abstract. Before tree-ring series can be used to quantify climatic influences on growth, ontogenetic and microenvironmental effects must be removed. Existing statistical detrending methods struggle to eliminate bias, caused by the fact that older/larger trees are nearly always more abundantly sampled during the most recent decades – which happens also to have seen the strongest environmental changes. Here we develop a new approach to derive a productivity index (P*) from tree-ring series. The critical stem diameter, when an initial rapid increase in stem radial growth gives way to a gradual decrease, is estimated using a theoretical approximation; previous growth rings are removed from analysis. The subsequent dynamics of stem radial growth are assumed to be determined by: tree diameter and height; P* (gross primary production per unit leaf area, discounted by a "tax" due to the respiration and turnover of leaves and fine roots); and a quantity proportional to sapwood specific respiration (r1). The term r1 depends not only on the growth rate but also on tree height, because a given leaf area requires a greater volume of living sapwood to be maintained in taller trees. Height-diameter relationships were estimated from independent observations. P* values were then estimated from tree ring-width measurements on multiple trees, using a non-linear mixed-effects model in which the random effect of individual tree identity accounts for the impact of local environmental variability, due to soil or hydrological conditions, and canopy position (i.e. shading and competition). Year-by-year P* at a site should then represent the influence of year-by-year changes in environment, independently of the growth trend in individual trees. This approach was applied to tree-ring records from two genera (Picea and Pinus) at 492 sites across the Northern Hemisphere extratropics. Using a multiple linear mixed-effects regression with site as a random effect, it was found that estimated annual P* values for both genera show consistent, temporally stable positive responses of P* to total photosynthetically photon flux density during the growing season (PPFD₅) and soil moisture availability (indexed by an estimate of the ratio of actual to potential evapotranspiration). The partial effect of mean temperature during the growing season (mGGD₅) however was shown to follow a unimodal curve, being positive in climates with mGGD₅ < 9 to 11 ˚C, and negative in warmer climates.