Estimating tree age depending on tree height for Norway spruce, Scots pine, European beech, and sessile and common oak in Central Europe

Abstract The age of trees in forests, open land, or urban areas is important for biodiversity monitoring, sustainable management, or hazard assessment; but it is often unknown. The height of trees, on the other hand, is often known from remote sensing or can be measured easily and non-destructively. However, there is a sigmoidal relationship between tree age and height, whose inverse function can be used to estimate age from height. Here, we compiled measurements of tree height and age from pre-dominant and dominant trees on long-term experimental plots for the parameterization of a density- and site index-dependent height-age function, tree height = $${\text{f}}_{1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>f</mml:mtext> <mml:mn>1</mml:mn> </mml:msub> </mml:math> (tree age, site index, stand density). The study focused on Norway spruce ( Picea abies (L.) Karst.), Scots pine ( Pinus sylvestris L.), European beech ( Fagus sylvatica L.), and sessile and common oak ( Quercus robur L. and Quercus petraea (Matt.) Liebl.) in Central Europe. The extended Chapman-Richard function was used and its inverse function tree age = $${\text{f}}_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>f</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> (tree height, site index, SDI) enables age estimation from tree height. To quantify prediction uncertainty, a non-parametric bootstrap was applied to the inverted model, providing height-dependent 95% confidence intervals that account for both parameter variability and the non-linearity of the inversion. The accuracy of the age estimation was higher for low and medium height trees ( $$11-21\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>11</mml:mn> <mml:mo>-</mml:mo> <mml:mn>21</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> ) and decreased with tree height ( $$14-22\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>14</mml:mn> <mml:mo>-</mml:mo> <mml:mn>22</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> ), a pattern confirmed by the bootstrap-derived confidence intervals. We discussed the application possibilities and limitations of the functions for estimating tree age in the context of monitoring, inventory, evaluation or management of forests or urban trees.