Modelling bark thickness for Scots pine (Pinus sylvestris L.) and common oak (Quercus robur L.) with recurrent neural networks

Variation of the bark depends on tree age, origin, geographic location, or site conditions like temperature and water availability. Most of these variables are characterized by very high variability but above of all are also affected by climate changes. This requires the construction of improved bark thickness models that take this complexity into account. We propose a new approach based on time series. We used a recurrent neural network (ANN) to build the bark thickness model and compare it with stem taper curves adjusted to predict double bark thickness. The data includes 750 felled trees from common oak and 144 Scots pine-trees representing dominant forest-forming tree species in Europe. The trees were selected across stands varied in terms of age and site conditions. Based on the data, we built recurrent ANN and calculated bark thickness along the stem. We tested different network structures with one- and two-time window delay and three learning algorithms-Bayesian Regularization, Levenberg-Marquardt, and Scaled Conjugate Gradient. The evaluation criteria of the models were: coefficient of determination, root mean square error, mean absolute error as well as graphical analysis of observed and estimated values. The results show that recurrent ANN is a universal approach that offers the most precise estimation of bark thickness at a particular stem height. The ANN recursive model had an advantage in estimating trees that were atypical for height, as well as upper and lower parts on the stem.