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.

中文翻译：

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广义加性建模预测德国中部挪威云杉径向生长的潜力

摘要 在过去的几十年中，由于极端气候条件和偶尔不利的森林管理，中欧管理的森林生态系统发生了巨大的变化。年轮宽度模式反映了这些变化，因此作为“树木生长模型”中的环境档案和可靠的经验数据来源被广泛研究。树木年代学家通常假设协变量之间存在线性协变、变量独立性和同方差性。传统上，这些假设是通过消除生物年龄趋势（去趋势）和从时间序列中去除自相关（预白化）来实现的。根据科学问题和有时不灵活的年龄模型，特别是去趋势可能会有偏差。在这项研究中，我们解决了这些问题，并在最近开发的 30 个来自德国中部的挪威云杉林分 (Picea abies [L.] H. Karst) 的年轮宽度时间序列上研究了灵活的广义加性模型 (GAM) 的适用性。该模型的建立是为了同时处理上述去趋势问题，解开非线性气候增长关系，并预测该地区云杉林分的平均年轮宽度时间序列。特别是后者是主要兴趣，因为最近的森林规划依赖于经常低估实际增长的静态产量表。该模型可靠地捕获了经验数据，由一个小的广义交叉验证标准 (GCV = 0.045) 和 88.6% 的偏差解释表明。灵活的加法平滑器解释了个体树木的社会地位，充分捕捉到不断变化的生长条件的低频变化，并显示出相当平坦的生物学年龄趋势。径向增量对当年和上年的夏季降水有积极的响应。在早期植被时期发现了积极的温度响应，而夏季高温对径向生长产生了负面影响。6 月份从春季到夏季的季节性转变导致线性预测器的气候响应发生变化，导致温度的明显负面影响和降水对线性预测器的无作用。最重要的是，利用校准的 GAM 对来自五个独立云杉站点的平均环宽时间序列进行纯粹的气候驱动预测，揭示了适当的一致性。在此处，位于云杉生长最佳气候范围内的站点的平均年轮宽度比具有不利云杉生长条件的站点的预测更准确。此外，系统地低估了大的平均环宽度，而精确地预测了小的平均环宽度。总的来说，我们强烈推荐 GAM 作为研究非线性气候增长关系和预测管理森林生态系统径向增长的有力工具。