# Verification of the Scots Pine (_Pinus sylvestris_ L.) Crown Length Model
## 2 Materials and Methods
### Biometric Measurements  
On the designated 20 plots, the diameter at breast height (\(DBH\)) was measured for 10,957 trees using a metal caliper Mantax Blue (Haglof, L\(\ddot{\text{a}}\)ngele, V\(\ddot{\text{a}}\)sternorrland, Sweden) with an accuracy of 1 mm. The measurements were carried out in two directions: N-S and W-E, and the arithmetic mean of both directions was assumed as the final \(DBH\). Based on the measurement of the diameter at breast height of all trees on each plot, 15 sample trees were selected, taking into account the dominant, codominant, intermediate, and suppressed trees. The selection was made using the English method developed by [PERSON] felling every \(k\)-th tree based on the formula [47]:  
\[k=\frac{N}{n} \tag{1}\]  
where \(N\)--total number of trees in a research area; \(n\)--assumed number of sample trees. The selected 300 sample trees (20 plots \(\times\) 15 sample trees = 300 trees) were cut down during the winter. After cutting, their length was determined with a metal tape measure with an accuracy of 0.01 m, which was adopted as the height of the tree (\(H\)), and crown length (\(CL_{emp}\)) was measured. The method of measuring the crown length based on the number of branches in the crown whorls was described in detail by [PERSON] and [PERSON] [14]. In the cases where the whorl was properly formed and had six branches, the crown was considered regular and its length was measured from the top of the tree to the base of the full whorl. In the cases where there had been a loss of branches in the whorl, the length of the crown was corrected. For example, if, in the lowest whorl, one branch (of the size corresponding to the other branches) was dead, the length of the crown was the distance from the treetop to the base of the \"in-complete\" whorl, minus one-sixth of the distance between this base and the base of the nearest whole whorl. Based on this assumption, it is assumed that the crown length would be reduced one-sixth of the annual growth of the stem. In other words, if there were two dead branches in the last incomplete whorl,  
Figure 1: Location of the experimental plots (number 1–20) in (**a**) the regional and (**b**) the European context. The maps were projected using the QGIS v 3.34.  
the measurement would be shortened by two-sixths of the annual growth (illustrated in graphic abstract). The data obtained from pine stands and felled sample trees used to verify the crown length model are presented in Table 1. Each plot was described using the following stand parameters: \(A\), age of the stand (years); \(N\), number of trees per ha; \(BA\), stand basal area (m\({}^{2}\) ha\({}^{-1}\)); \(H\), stand height (m); \(DBH\), diameter at breast height (cm). The diameter at breast height ranged from 9 to 32 cm. The measurements showed that 62% of the trees had \(DBH\) below 12 cm. Figure 2 shows the histogram of \(DBH\) distribution and a curve representing the density of the normal distribution (for mean, 12.3; SD, 3.2). \(DBH\) distribution was asymmetrical. The distribution contour indicated that the diameter at breast height was not normally distributed. To assess the normality of the \(DBH\) distribution, the Shapiro-Wilk, Kolmogorov-Smirnov, and Lilliefors tests were used. The calculated \(p\) values were lower than the critical \(p<0.05\). Rejection of the null hypothesis regarding the \(DBH\) distribution normality was clear.