Semi-empirical estimation of log taper using stem profile equations | Andrii Bilous, Viktor Myroniuk, Viktor Svynchuk, Oleksandr Soshenskyi, Oleksandr Lesnik, Yaroslav Kovbasa | Agricultural Journals

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.

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

The sustainable management of urban green areas requires clear and efficient protocols for measuring the biometric properties of tree vegetation. Specifically, operational in situ sampling solutions are essential to inventory forked (multi-stemmed) trees. This study aimed to assess the efficiency of two different sampling protocols for mean tree diameter at breast height (DBH) measurement of forked urban trees. The protocols were tested on a dataset of 76 forked trees, each having more than three stems and sampled in urban areas of Kyiv, Ukraine. First, we tested the efficiency of mean tree DBH estimations using measurements of randomly selected one, two, or three stems (random sampling, or RSM). Second, we examined different combinations of the thinnest, thickest, and average stems (identified visually) for each tree to estimate mean tree DBH (targeted sampling, or TSM). The distributions of mean tree DBH and root mean square errors (RMSE) were utilized to compare the utility of the two approaches. The TSM of three stems (the thinnest, thickest, and average) provided the highest accuracy of mean tree DBH estimation (RMSE% = 6.3% of the mean), compared to the RSM (RMSE% = 12.1%). The TSM of the four thickest stems demonstrated the overestimation of mean tree DBH for forked trees with five or more stems. Accurate mean tree DBH estimates can be derived with negligible systematic errors applying the RSM over a large number of measured trees. However, these estimates will not likely match the measurements from previous inventories due to random stem selection. We recommend using the TSM with measuring three specific stems as a balanced solution in terms of estimation accuracy, bias, and time costs.

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