Modeling structure of Scots pine stems volume by grade categories using stochastic process

The study highlights methodological aspects of predicting stem volume of merchantable Scots pine trees by grade categories using distribution models of different quality zones along stems. The study is based on empirical data collected in the mature stand during clear-cut harvesting. In total it includes measurements of 245 tree stems for which sequence and lengths of different quality categories were evaluated. A semi-Markov model was applied to characterize a random process of height-relevant co-occurrence and length of merchantable wood, firewood, and residues. The model was determined by the following parameters: 1) input occurrence probabilities of specific grade category in the butt section of tree stems (initial state of the system); 2) distribution matrix of grade categories by lengths; 3) matrix with transition probabilities between grade classes on different stem heights. In this study, we considered the process in which the initial state of the system was associated with merchantable wood which was true for most pine stems. We used beta-function to model lengths of grade categories which parameters were fitted using relative stems height. We also used empirical data to calculate probabilities of transition between merchantable wood, firewood, and residuals along pine stems. The analysis indicates that the length distribution of merchantable wood and firewood depends on the relative height where the grade is observed, and total tree stem height. Thus, we identified four zones where the function of beta-distribution was used to model lengths of each grade category with customized parameters depending on the relative height of their location on tree stem. As a result, we developed a methodology that can be used to simulate datasets with tree stem characteristics, and further to predict the distribution of volume by grade categories depending on their diameters, heights, and merchantability. It is worth noting that our study is focused merely on merchantable pine stems, and one should expect another relationship for stems of different tree species as well as for merchantable pulpwood trees. Given the new standard for merchantable wood classification adopted in Ukraine, the developed methodology is suitable for updating existing tables of distribution of tree stem volumes by wood grade categories.