The potential of generalized additive modelling for the prediction of radial growth of Norway spruce from Central Germany

Abstract

During the past decades managed forest ecosystems in Central Europe underwent vast changes, induced by extreme climate conditions and occasionally adverse forest management. Tree ring width patterns mirror these changes and thus have been widely examined as environmental archives and reliable empirical data sources in ‘tree growth modelling’. Dendrochronologists often suppose linear co-variation among the covariates, variable independence and homoscedasticity. Conventionally, these assumptions were achieved by eliminating biological age trends (detrending) and removing the autocorrelation from the time series (pre-whitening). Particularly detrending might be biased according to the scientific problem and sometimes inflexible age models. In this study, we tackle these issues and examine the suitability of a flexible Generalized Additive Model (GAM) on recently developed tree ring width time series of 30 Norway spruce stands (Picea abies [L.] H. Karst) from Central Germany.The model was established to simultaneously cope with the mentioned detrending issue, to unravel nonlinear climate-growth relationships and to predict mean ring width time series for spruce stands in the region. Particularly the latter was of primary interest, since recent forest planning relies on static yield tables that often underestimate the actual growth.The model reliably captured the empirical data, indicated by a small Generalized Cross Validation criterion (GCV = 0.045) and a deviance explained of 88.6 %. The flexible additive smoothers accounted for the social status of individual trees, captured low frequency variations of changing growth conditions adequately and displayed a rather flat biological age trend. The radial increment responded positively to summer season precipitation of the current and previous year. Positive temperature responses were found during the early vegetation period, whereas high summer season temperatures negatively affected the radial growth. The seasonal transition from spring to summer in June induced a shift in the climate response of the linear predictor, leading to a distinct negative effect of temperature and a no-role of precipitation on the linear predictor.Most important, utilizing the calibrated GAM for the purely climate-driven prediction of mean ring width time series from five independent spruce sites revealed proper coherencies. Herein, the mean ring width for sites located within the climatic-optimum for spruce growth were more exactly predicted than for sites with adverse spruce growth conditions. In addition, large mean ring widths were systematically underestimated, whereas small mean ring widths were precisely predicted. Overall, we strongly recommend GAMs as a powerful tool for the investigation of nonlinear climate-growth relationships and for the prediction of radial growth in managed forest ecosystems.