The dissertation is aimed at investigation of the stem form of silver birch in forest stands of the Ukrainian Polissia, which provides a theoretical basis for estimating the wood volume and its distribution by timber sizes.
The database of the State Enterprise «Ukrderzhlisproekt» of the Forestry Fund of Ukraine as of 01.01.2011 was used to determine the characteristics of birch forests in the study region. The analysis of the forest fund showed that the forest cover within the study area reaches 27.7 %, and the largest area of birch forests is concentrated in the central part of the Ukrainian Polissia (Zhytomyr and Rivne regions). Pure birch forest stands in the Ukrainian Polissia make up 17.9 % of the total area of birch forests. Silver birch is a valuable forest tree species that forms mainly highly productive (Ia, I, rarely II site index by M. Orlov) and medium-stocked (with a relative stocking of 0.7) secondary birch stands, which are most common in fairly infertile and fertile wet site types. Middle-aged forest stands (31–40 years) dominate in the study area, and their accumulation in the future will exacerbate the problem of timber accounting during harvesting.
The study material consists of measurements of 369 birch sample trees collected on 26 temporary sample plots in birch stands of the Ukrainian Polissia. The temporal sample plots were established in birch stands of all ages, which are evenly distributed over the study area. The following parameters were measured on felled trees: stem length from the stump, stump height, diameter and bark thickness at the breast height (1.3 m above ground level of the standing tree) and at the midpoints of each 2-m section.
The distribution of the number of sample trees by diameter at breast height (8.2 cm–52.7 cm) and height (12.5 m–29.6 m) covered wide ranges. Each 4-cm diameter classes were represented by sample trees of different heights. The distribution of the collected data by height corresponded to the I-IV height classes of the volume tables. Generally, the study material represents typical birch stands in the study region.
The tree stem form of birch trees has been analyzed using taper equations. Statistical analysis indicated differences in the form of birch stems of different diameters, therefore we independently fitted four taper equations for the following groups of diameters: ≤20 cm; 20–28 cm; 32–40 cm; ≥40 cm.
The volume distribution of birch stems by timber size according to the current standards was predicted in the R software environment using a simulation algorithm that cross-cuts tree stems into timbers of different quality and sizes:
- prediction of stem taper outside and inside bark in order to determine the average diameter, volume of merchantable timber and firewood volume;
- modelling the merchantable length of the stems to predict the merchantable volume;
- sequential (from butt end to tree top) cutting stems into timber based on their priority (value);
- calculating the volume of logs and modelling the distribution of the timber volume of each diameter class as a function of tree diameter.
The developed taper model made it possible to determine the diameter of birch stems at any height with minor errors: the systematic error was ±0.03 cm; the relative error was 1.11 %; the root mean square error was 0.98 cm. The taper model was used in conjunction with models of stump height, bark thickness, and stem height to the merchantable limit of silver birch. Thus, we obtained a universal tool for determining the stem volume outside bark of a growing tree, the stem volume of a felled tree excluding the volume of the stump, the volume of merchantable timbers inside bark, the volume of firewood outside bark, and the volume of waste. A sectional Newton's volume formula was applied to calculate the volume using a relatively short section of 1/100 of the stem or timber length.
The study revealed a significant difference in the dimensional structure of merchantable volume obtained from trees of different merchantable categories. The proportion of merchantable timber of larger diameter classes was higher in «semi-merchantable» trees than in fully «merchantable» trees.
The systematic error of the mathematical models developed for different diameter classes of merchantable wood was insignificant. The highest relative errors were observed for the diameter classes of 20–29 cm and 30–39 cm obtained from «merchantable» trees (-6.5 % and 8.2 %, respectively) and for the diameter classes of 20–29 cm and 50–59 cm diameter classes obtained from «semi-merchantable» trees (6.8 % and 6.5 %, respectively). The absolute and the root mean square errors of the developed models increase with diameter classes. The lowest R-squared value was observed for timber with the diameter of 15–19 cm, but for all other diameter classes it was always significant at 5 % significance level.
