Generally, it is impossible to measure diameters and heights of all trees in a forest stand. Therefore, models of relationships between heights (h) and diameters (d) of trees are commonly used in practice for stem volume estimation. This study aimed at developing models of tree height-diameter (h-d) relationships as well as corresponding models of the tree stem volume for immature, mature and overmature stands of the main forest-forming species of Ukraine. This paper is a aggregation of long-term studies of the stem volume, which are based on the results of measuring about 10 thousand sample trees. Modelling of the tree height-diameter relationships was performed using relative height values. The methodology used in this study allowed generalising the measurements of sample trees collected in stands of various forest site types, productivity levels, and age categories. The average height of trees with a diameter of 24 cm was taken as the reference during modelling relative heights, while the diameter of 40 cm was chosen as the reference for overmature Scots pine stands. As a result, the parameters of a unified mathematical model of relative heights for immature, mature, and overmature stands of the main forest-forming tree species of Ukraine were established. Based on these models, height-diameter relationships in forest stands of different height classes were predicted. The authors demonstrated that the developed mathematical models substantially simplify the methodology of field work during timber surveys. The paper also presents models of the tree stem volume. These models predict the stem volume outside the bark based on diameters and heights of trees or using the developed models of h-d relationships. In this study, a unified system of mathematical models of stem volume by height classes were created for immature, mature, and overmature stands of the main forest-forming species of Ukraine. The results of the study are introduced to the National Forest Inventory of Ukraine for growing stock volume calculation at sample plot level using measurements of individual trees. The developed models can be used both by operation forestry (estimation of the timber volume during harvesting), and forest management (forecasting the future structure of forests and estimating the growing stock volume), as well as in the forest ecology

Stem taper equations are crucial for forest management allowing to reliably estimate merchantable wood volume. Their main benefit is the ability to predict stem diameters at a certain height of the stem. Ukraine has recently adopted European Union standards for round wood classification, which prompted the necessity to model stem taper and updates all reference data to conform with the new standards. This study is a systematic attempt to develop a set of taper equations for the most common forest tree species in the Polissia and Forest steppe of Ukraine. For this purpose, we used a data set of 1994 sample trees representing eight tree species collected on 238 sample plots. The Kozak A. (2004, My last words on taper equations. For. Chron.80, 507–515) model was chosen to fit the taper equations. To characterize the variability in stem shape among tree species, mixed-effect models were calibrated for this equation. In this model, random-effect parameters were selected based on their coefficients of variation through a bootstrapping process. This is a novel feature we suggest for the process of calibrating taper models. The Kozak A. (2004, My last words on taper equations. For. Chron.80, 507–515) equation showed a good performance in predicting diameters outside bark and estimating the total stem volume. Our mixed-effect modelling approach accurately characterizes the variation in stem form for different tree species based on adequately chosen random-effect parameters. The stem volumes derived from the developed taper models were compared with existing volume equations outputs (divergence up to 0.5 per cent). A deviation up to 5 per cent was found between the values of fitted and observed cylindrical form factors for the studied tree species. We expect that our taper equations will complement the future steps towards the development of reliable merchantable volume distribution models for the main tree species in the forests of flat land Ukraine, thus, contributing to transparency, reliability and sustainability of forest management and markets in Europe.

In January 2019 the forest industry in Ukraine adopted European standards for measuring and grading of round wood based on mid-point diameters, which caused major discrepancies from traditionally used estimates of timber volume using top diameters. To compare methods of merchantable wood volume estimation, we investigated the stem form inside bark for two dominant tree species in Ukraine, i.e. Scots pine (Pinus sylvestris L.) and common oak (Quercus robur L.). We used tree stem measurements to fit stem profile equations, whereas simulation was applied to derive log taper. We found that Newnham's (1992) variable-exponent taper equation performed well for predicting stem taper for both tree species. Then, we simulated the structure of harvested wood, so that it replicated annual distribution of logs by their length and diameters. As a result, the average log taper was estimated at 0.836 ÷ 0.855 cm·m^–1 and 1.180 ÷ 0.121 cm·m^–1 for pine and oak, respectively. The study also indicated that log taper varied along stems. The higher rates of diameter decrease were found for butt logs, for which the taper was 2.5–3.5 times higher than its average for the whole stem. The results of our study ensure the stacked round wood volume conversion between estimates obtained using top and mid-point diameters.

Height-diameter (h-d) relationships in forest stands are commonly used in various scientific and practical forestry applications. Accurate h-d models combined with tree stem volume equations are recognised to be effective in growing stock volume estimation. The purpose of the study was threefold: 1) development of a set of mathematical models of the h-d relationship in young and middle-aged forest stands for ten forest-forming species in Ukraine; 2) modelling stem volume in above mentioned forest stands; 3) comparison of established mathematical models with corresponding ones for premature, mature, and overmature forest stands. The study was based on permanent and temporal sample plots data (about 600) established in forest stands during 1950s-2020s within the most forested regions of Ukraine (Polissia, Forest-Steppe, Carpathians). In total, about 10,000 sample trees were measured on the sample plots to accurately estimate their stem volume outside bark. The h-d models demonstrated very similar relationships between stem heights and diameters for most of our species except for spruce and fir in mountain Carpathian forests where the steeper h-d curves were obtained. The study revealed that birch and hornbeam tree stems had the lowest volumes among surveyed species. The results also indicated that tree species tend to have higher volumes (up to 7% for coniferous, and up 10% for aspen and birch forests) in young and middle-aged forest sands than in older ones. For the other species, a statistically significant difference between stem volumes of trees of different ages was not observed. The developed mathematical models can complement the corresponding models for older groups of forest stands since they revealed an important aspect of relationships between the key tree stem parameters. These models are also applicable for a more precise stem volume estimation during thinning operations in the young and middle-aged forests in Ukraine